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Doctoral Thesis

Modeling of steam consumption in chemical batch plants

Author(s): Pereira, Cecilia Mónica

Publication Date: 2013

Permanent Link: https://doi.org/10.3929/ethz-a-010060560

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DISS. ETH NO. 21480

Modeling of Steam Consumption

in Chemical Batch Plants

Cecilia Pereira

DISS. ETH NO. 21480

Modeling of Steam Consumption

in Chemical Batch Plants

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZURICH

(Dr. sc. ETH Zurich)

presented by

Cecilia Mónica Pereira

M Sc UZH, Universität Zürich

born on September 15th, 1979

citizen of Uruguay and Italy

accepted on the recommendation of

Prof. Dr. Konrad Hungerbühler, examiner

Prof. Dr. Rudiyanto Gunawan, co-examiner

2013

ACKNOWLEDGEMENTS I

Acknowledgements

During the time of my PhD thesis at the Safety and Environmental

Technology Group at the ETH Zürich, I have received generous

support and encouragement of many people. Konrad

Hungerbühler offered me the opportunity to carry out my work in

his group, where I have greatly benefited from his experience at

the interface of academia and industry. Very special thanks to

Konrad. Advice and guidance given by Stavros

Papadokonstantakis have contributed enormously to my work,

motivating and supporting me to explore new ideas and

challenges. I deeply appreciate suggestions and feedback offered

by Stefanie Hellweg, who participated in all progress meetings

and Zieldialogs during my thesis.

Without the collaboration of my industry partners, this dissertation

would not have been possible. They have provided me with the

main data source for my project, contributing with their expertise

and hospitality during the data collection campaigns. I would also

like to express my gratitude to the Bundesamt für Energie (BFE)

and Bundesamt für Umwelt (BAFU) for their financial support.

I appreciate the relevant work carried out by Ines Hauner during

her master thesis under my supervision. Claude Rerat, during

years my office mate, has contributed with his expertise in energy

consumption modeling to my work, and has significantly helped

me with my programming skills. I would also like to thank Jürgen

Sutter and Peter Mumenthaler for their technical support. Many

other current and former members of the Safety and

Environmental Technology Group have supported and shared

II ACKNOWLEDGEMENTS

interesting discussions with me. Special thanks go to Prisca Rohr,

Isabelle Lendvai, Martin Scheringer, Matthew MacLeod, Asif

Qureshi, Andreas Buser, Andrej Szijjarto, Andrea Bumann,

Sebastien Cap, Elisabet Capón and Annelle Gutiérrez.

Finally, I owe my deepest gratitude to my parents. They have

always supported me unconditionally in all aspects of life. Gracias

mamá, gracias papá!

SUMMARY III

Summary

The minimization of energy consumption in the chemical industry

is one of the key principles of green chemistry. This has led to the

development of evaluation tools, which include energy use as a

metric, not only in academia but also in the industry. The use of

these evaluation tools requires process specific data of energy

consumption, which is usually scarce particularly in multiproduct

and multipurpose batch plants. In this thesis we developed

shortcut models of steam consumption, which typically represents

the highest energy utility consumption.

First, we introduced a new methodology for modeling the steam

consumption in chemical batch plants based on standard process

documentation, rules of thumb, expert opinion, and

thermodynamic principles. Additionally, we proposed uncertainty

intervals for the model outputs based on fuzzy set theory. Three

case studies using production data from multiproduct and

multipurpose batch plants of three different chemical companies

were carried out for parameterization and validation of the

proposed methodology. While in the first two cases, the validation

against reference values considered the steam consumption in

several equipments or vessels involved in reaction and work-up

processes (kilograms of steam per equipment), in the third case

study the steam consumption was modeled and validated for

entire synthesis paths (kilograms of steam per product). The

validation results showed that the documentation based models

provide acceptable estimations of steam consumption in chemical

batch plants, and that the uncertainty intervals are in agreement

with the batch-to-batch variability of the steam consumption.

IV SUMMARY

Secondly, statistical models, namely probability density functions

(PDF) and classification trees were fitted to real production data.

These models take the form of generic intervals defined as

interquartile ranges derived from the PDF parameters, and as

classes derived from the classification trees. The use of the

models is possible at different levels of process design, the

minimal required information being the reaction type. The PDF

models were assessed with diverse metrics for the goodness-of-

fit and the classification trees by means of cross-validation. The

prediction performance of both types of models was further

evaluated in two case studies. The validation results show that

the statistical models proposed in this work provide satisfactory

interval estimations of steam consumption.

Depending on the application target one model might be more

convenient than the other, meaning that a compromise between

modeling time and accuracy has to be done. While the

documentation based approach is a more detailed procedure

which delivers a deterministic estimated value with an uncertainty

range, the statistical models resulting in generic intervals are

much faster to use. Even though the PDF models allow

reasonable predictions of steam consumption, their most

interesting applications are for benchmarking and uncertainty

analysis. Additionally, the transparency of the classification trees

facilitated the analysis of the effect of their predictor variables –

reaction type and operational parameters – upon the steam

consumption, resulting in a set of dominating classification rules.

Consequently, besides the predictive capabilities of the statistical

models, they serve as descriptive and explanatory tools. Both

modeling approaches to steam consumption proposed in this

SUMMARY V

thesis are of high importance in early phases of process design,

in the field of Life Cycle Assessment (LCA) and for

benchmarking.

VI ZUSAMMENFASSUNG

Zusammenfassung

Die Minimierung des Energieverbrauchs in der chemischen

Industrie ist eines der Hauptprinzipien der Grünen Chemie. Dies

hat in der Forschung sowie in der Industrie zur Entwicklung von

Bewertungsmethoden, die Energieverbrauch als Metrik

berücksichtigen, geführt. Die Anwendung dieser Methoden

benötigt spezifische Daten von Energieverbrauch, die

normalerweise nicht verfügbar sind, besonders in Mehrprodukt

und Mehrzweck Batch Betriebe. In dieser Doktorarbeit wurden

shortcut Modelle von Dampfverbrauch, den der grösste

Energieverbrauch darstellt entwickelt.

Zuerst wurde eine neue Methode, basierend auf

Betriebsvorschriften, Heuristiken, Expertisen und

thermodynamischen Prinzipien, zur Modellierung des

Dampfverbrauches in chemischen Batch-Anlagen entwickelt.

Zusätzlich wurden Unsicherheitsintervalle basierend auf die

Theorie der unscharfen Mengen (Fuzzy Set Theory) entwickelt.

Drei Fallstudien mit Produktionsdaten von Mehrprodukt- und

Mehrzweck-Batch-Anlagen von drei verschiedenen chemischen

Unternehmen, wurden zur Parametrisierung und Validierung der

neuen Methodologie durchgeführt. In den ersten zwei Fällen

wurde der Dampfverbrauch von mehreren Apparaten, die für die

Reaktionsstufe (Reaktor) und die Trennungsverfahren gebraucht

werden (Kilogramm Dampf pro Apparat), modelliert und gegen

Referenzwerte validiert. In der dritten Fallstudie wurde der

Dampfverbrauch für gesamte Synthesewegen (Kilogramm Dampf

pro Apparat) modelliert und validiert. Die Ergebnisse der

Validierung haben gezeigt, dass diese neuen Modelle vernünftige

ZUSAMMENFASSUNG VII

Abschätzungen des Energieverbrauches in chemischen Batch-

Anlagen liefern, und dass die Unsicherheitsintervalle mit der

Variabilität des Dampfverbrauches zwischen verschiedenen

Batches übereinstimmen.

Im zweiten Schritt wurden statistische Modelle –

Wahrscheinlichkeitsdichtefunktionen und Entscheidungsbäume –

an echte Produktionsdaten angepasst. Diese Modelle können als

Interquartil-Intervalle und als Klassen, abgeleitet jeweils aus den

Wahrscheinlichkeitsdichtefunktionen, und aus den

Entscheidungsbäumen, dargestellt werden. Die Anwendung

dieser Modelle ist auf verschiedenen Stufen der

Prozessauslegung möglich, wobei die minimale nötige Input-

Information der Reaktionstyp ist. Die

Wahrscheinlichkeitsdichtefunktions-Modelle wurden anhand von

verschiedenen Anpassungsgüte-Kriterien bewertet, die

Entscheidungsbäume anhand von Kreuzvalidierungsverfahren.

Die Voraussagekraft beider Modelle wurde zudem in zwei

Fallstudie bewertet. Die Validierungsresultate weisen darauf hin,

dass die statistischen Modelle, die in dieser Doktorarbeit

entwickelt wurden, ausreichende Intervallabschätzungen des

Dampfverbrauches liefern.

Abhängig vom Anwendungszweck ist einer der beiden

Modellierungsansätze geeigneter als der andere. Dies bedeutet,

dass ein Kompromiss bezüglich Modellierungszeit und

Genauigkeit betrachtet werden muss. Während der auf

Betriebsvorschriften basierende Ansatz eine detailliertere

Methode ist, die einen deterministischen Wert mit einem

Unsicherheitsintervall liefert, kann man die statistischen Modelle

VIII ZUSAMMENFASSUNG

viel schneller anwenden. Obwohl die

Wahrscheinlichkeitsdichtefunktions-Modelle vernünftige

Abschätzungen des Dampfverbrauches erlauben, ist ihre

interessanteste Anwendung das Benchmarking und die

Unsicherheitsanalyse. Die Transparenz der Entscheidungsbäume

erlaubt zusätzlich die Analyse des Effekts der Prädiktorvariablen

– Reaktionstyp und Betriebsparameter – auf den

Dampfverbrauch. Dies führt zu einem Set von

Klassifizierungsregeln. Während die statistische Modelle zur

Voraussagen des Dampfverbrauches genutzt werden können,

beide Modellierungsarten können für deskriptive und erläuternde

Zwecke angewendet werden.

Die zwei Modellierungsansätze, die in dieser Arbeit

vorgeschlagen wurden, sind von hoher Bedeutung in früheren

Phasen der Prozessauslegung, sowie für Life Cycle Assessment

und Benchmarking.

RESUMEN IX

Resumen

La reducción del consumo de energía en la industria química es

uno de los principios claves de la química verde. Esto ha

propiciado el desarrollo de herramientas de evaluación, que

incluyen consumo de energía como métrica, no solo en el ámbito

académico sino también en la industria. El uso de estas

herramientas de evaluación requiere datos específicos de

consumo de energía, los cuales son usualmente escasos,

especialmente en plantas de producción por lotes multi-producto

y multi-propósito. En esta tesis desarrollamos modelos

abreviados ‘shortcut’ de consumo de vapor, el cual representa

generalmente la fuente de energía de mayor consumo.

Primero, introdujimos una metodología para el modelado del

consumo de energía en plantas químicas por lotes basada en

documentación estándar de procesos, reglas de oro, opinión de

expertos y principios termodinámicos. Además, propusimos

intervalos de incertidumbre basados en la teoría de conjuntos

difusos para los resultados de los modelos. Para la

parametrización y la validación de la metodología propuesta se

realizaron tres estudios de caso, en los cuales se utilizaron datos

de producción de plantas multi-producto y multi-propósito.

Mientras que en los dos primeros casos se consideró el vapor

consumido en diferentes reactores o tanques durante la reacción

y los procesos de separación (kilogramos de vapor por reactor),

en el tercer estudio de caso el vapor consumido fue modelado y

validado para rutas completas de síntesis (kilogramos de vapor

por producto). La validación de los resultados demostró que los

modelos basados en documentación proporcionan estimaciones

X RESUMEN

satisfactorias de consumo de vapor en plantas química por lotes,

y que los intervalos de incertidumbre corresponden a la

variabilidad en el consumo de energía entre lotes.

En segundo lugar, modelos estadísticos, concretamente

funciones de densidad de probabilidad (FDP) y arboles de

clasificación fueron ajustados a datos de producción reales.

Estos modelos toman la forma de intervalos genéricos definidos

como rangos intercuartílicos derivados de los parámetros de las

funciones de densidad de probabilidad, y de clases derivadas de

los arboles de clasificación. El uso de estos modelos es posible a

diferentes niveles del diseño de procesos, siendo el tipo de

reacción la información mínima requerida. Los modelos FDP

fueron evaluados con diversas métricas de ajuste de bondad, y

los arboles de clasificación por medio de validación cruzada. El

rendimiento de predicción de los dos tipos de modelos fue

además evaluado en dos estudios de caso. Los resultados de la

validación demuestran que los modelos estadísticos propuestos

en este trabajo proporcionan resultados satisfactorios de

estimaciones de intervalos de consumo de vapor.

Dependiendo de cuál sea el objetivo de la aplicación, un modelo

puede ser más conveniente que el otro, lo que significa que se

debe llegar a un compromiso entre tiempo requerido para el

modelado y exactitud. Mientras que el enfoque basado en

documentación representa un procedimiento más detallado, que

proporciona valores determinísticos con intervalos de

incertidumbre, los modelos estadísticos resultan en intervalos

genéricos que son mucho más rápidos de aplicar. A pesar de

que los modelos FDP permiten predicciones razonables de

RESUMEN XI

consumo de vapor, su aplicación más interesante reside en el

benchmarking y en el análisis de incertidumbre. Además, la

transparencia proporcionada por los arboles de clasificación

facilita el análisis del efecto de sus variables de predicción – tipo

de reacción y parámetros operacionales – sobre el consumo de

vapor, resultando en un conjunto de reglas de clasificación

dominantes. Por lo tanto, además de las capacidades predictivas

de los modelos estadísticos, estos sirven como herramientas

descriptivas y explicativas. Los dos enfoques de modelo de

consumo de vapor propuestos en esta tesis son de importancia

significativa en etapas tempranas del diseño de procesos, en el

área de análisis de ciclo de vida y en benchmarking.

XII CONTENT

Table of Contents

1 Introduction ...................................................................... 1

1.1 Energy Consumption in the Chemical Industry ........... 1

1.2 State of the Art ............................................................ 4

1.3 Goal of the Thesis ....................................................... 7

1.4 Structure of the Thesis ................................................ 9

2 Documentation based Models of Steam Consumption10

2.1 Bottom-up Modeling .................................................. 10

2.2 Standard Operating Procedures (SOPs) ................... 10

2.3 Model Development .................................................. 12

2.3.1 Application Example ........................................ 20

2.4 Model Uncertainty ..................................................... 28

2.4.1 Fuzzy Intervals ................................................ 29

2.4.2 Application Example ........................................ 30

3 Statistical Models .......................................................... 34

3.1 System Boundaries ................................................... 34

3.2 Training and Validation Datasets .............................. 35

3.3 Stages of Process Design ......................................... 37

CONTENT XIII

3.4 Selection and Classification of Chemical Reactions .. 38

3.5 Classification Models ................................................ 39

3.5.1 Selection of Predictor Variables and

Discretization of Target Attribute ...................... 41

3.5.2 Model Selection and Evaluation ....................... 46

3.5.3 Selection of Important Rules ............................ 48

3.6 Probability Density Function Models ......................... 50

4 Results Documentation based Approach .................... 52

4.1 Case Study I ............................................................. 53

4.1.1 Dataset ............................................................ 53

4.1.2 Theoretical Energy Consumption ..................... 54

4.1.3 Energy Losses ................................................. 55

4.1.4 Sensitivity and Uncertainty Analysis ................ 56

4.1.5 Total Energy Consumption .............................. 60

4.2 Case Study II ............................................................ 62

4.2.1 Dataset ............................................................ 62

4.2.2 Total Energy Consumption .............................. 63

4.2.3 Top-down Energy Modeling ............................. 65

XIV CONTENT

4.3 Case Study III ........................................................... 69

5 Results Classification Trees ......................................... 71

5.1 Model Selection and Evaluation ................................ 71

5.2 Selection of Important Rules ..................................... 78

6 Results Probability Density Function Models ............. 85

6.1 Model Development .................................................. 85

6.2 Model Evaluation per Reaction Type ........................ 89

6.3 Further Parameterization of the Models .................... 91

7 Application of the Statistical Models ............................ 93

7.1 Case Study I ............................................................. 93

7.2 Case Study II ............................................................ 95

8 Conclusions and Outlook ........................................... 107

8.1 Practical Relevance and Applications ..................... 107

8.2 Outlook ................................................................... 111

8.2.1 Extension of the Modeling Approaches to other

Process Parameters ...................................... 111

8.2.2 Optimization Problem for Selection of

Classification Trees ....................................... 112

Nomenclature ........................................................................ 113

CONTENT XV

Appendix ............................................................................... 117

A Supporting Information to Chapter 2 ....................... 117

B Supporting Information to Chapter 3 ....................... 121

C Supporting Information to Chapter 4 ....................... 145

D Supporting Information to Chapter 5 ....................... 160

E Supporting Information to Chapter 6 ....................... 169

F Supporting Information to Chapter 7 ....................... 177

Bibliography .......................................................................... 182

INTRODUCTION 1

1 Introduction

1.1 Energy Consumption in the Chemical Industry

The environmental dimension of sustainable development is

significantly affected by energy consumption and management

(Patterson, 1996). In this context the chemical industry has been

identified as one of the major consumers of energy in

manufacturing compared to other industrial sectors (Steinmeyer,

2000, Vandecasteele et al., 2007). In addition recent

environmental assessment studies of the production of common

chemicals in developed countries have shown that energy related

impacts are often over 50% of the total environmental impact

(Wernet et al., 2011). Therefore improving of energy efficiency in

chemical production has been recognized as a key target for the

chemical sector and for environmental regulations (Jenck et al.,

2004). Moreover, minimization of energy use is an approach

towards changing the nature of a chemical product or process for

reducing the risk to the environment and human health (Paul T.

Anastas and Warner, 1998).

Improvement of energy efficiency of chemical production

processes can be achieved in different ways such as process

control and optimization for selecting the best operating

conditions (Le Lann et al., 1999), efficient heat transfer

(VaklievaBancheva et al., 1996, Phillips et al., 1997,

Oppenheimer and Sorensen, 1997), pinch analysis (Smith, 1995,

Shenoy, 1995, Linnhoff, 1993), use of catalysts for lowering the

reaction activation energy (Paul T. Anastas and Warner, 1998),

2 MODELING OF STEAM CONSUMPTION IN CHEMICAL BATCH PLANTS

designing processes that minimize the requirement of separation

and purification steps, and recycling of waste (Capello et al.,

2008). Considering this, different design alternatives can be

compared as part of multi-objective decision-making frameworks

(Cano-Ruiz and McRae, 1998, Sugiyama et al., 2008b, Sugiyama

et al., 2008a). This is especially interesting at early phases of

process design, when modifications and improvements are less

costly and time-consuming to implement than in later stages.

For comparing the environmental impacts of the different

alternatives, methodologies such as Life Cycle Assessment

(LCA) (Burgess and Brennan, 2001) can be used. LCA is a

method for assessing the environmental impact of products and

processes over the entire product life cycle, thus it can be used in

process design for comparison and selection of options (G. E.

Kniel et al., 1996, Bauer and Maciel, 2004, Hellweg et al., 2004).

One of the Life Cycle Impact Assessment (LCIA) indicators is the

Cumulative Energy Demand (CED), which accounts for the total

amount of primary energy potential used during the production

life cycle. Recent studies have shown that the CED correlates

well with other LCIA indicators, serving as an estimation of

general environmental impact (Huijbregts et al., 2006, Wernet et

al., 2009). Other evaluation methodologies developed by the

industry such as the eco-efficiency analysis by BASF (Peter

Saling et al., 2002) and the green technology guide by

GlaxoSmithKline (Concepción Jiménez-González et al., 2001,

Concepción Jiménez-González et al., 2002) also consider energy

use as an impact indicator.

INTRODUCTION 3

Previous to the setting of energy goals, and besides the different

approaches for energy efficiency improvement and evaluation of

environmental impacts, an understanding of the energy use and

comparison against standards of similar processes

(benchmarking) are required. However, process energy

consumption data is usually scarce. This is mainly due to the low

cost of energy consumption in batch plants, namely 5-10% of the

total costs (VaklievaBancheva et al., 1996), compared to the

significant contribution of the raw materials costs. Thus, efforts for

achieving high energy efficiency in batch plants are usually

limited (Bieler et al., 2003). Additionally, energy flow

measurements can be more complicated (i.e., requiring mass

flow, temperature and pressure measurements of the energy

utilities) and therefore costly compared to the material flows of

reagents.

Most of the energy used in chemical production processes is in

the form of thermal energy (heating and cooling) or mechanical

energy (pumping, compression) (Steinmeyer, 2000). While the

most common energy utilities used for cooling during reaction and

separation processes are water and brine, the main energy utility

used for heating is steam. Electricity is the energy utility used to

generate mechanical energy. Among all these different energy

utilities used in the chemical industry, steam is the most prevalent

one, with the highest potential for improvement of energy

efficiency (Bieler, 2004).


1.2 State of the Art

While continuous production processes have been extensively

investigated for energy optimization by means of pinch analysis

and process integration (Linnhoff, 1993), the documentation of

energy flows in multiproduct and multipurpose batch plants, has

been traditionally neglected due to additional complexities caused

by the dynamic nature of the processes and to minor contribution

of energy to the plant economics. Consequently energy data es-

pecially for steam consumption, which is the energy utility with the

highest consumption and saving potentials, has to be modeled or

estimated by empirical know-how in many cases.

In order to fill this gap, different methodologies have been

proposed: energy estimations based on rigorous process

simulation (Concepción Jiménez-Gonzalez et al., 2000), in-house

technical knowledge (Rolf Bretz and Frankhauser, 1996), a top-

down approach which correlates the total energy utility

consumption with the total amount of chemicals produced in one

production building (Bieler et al., 2003), and a bottom-up

approach based on energy balances and estimation of thermal

losses of single unit operations, which can be further aggregated

for different levels of analysis (Bieler et al., 2004). In these last

two studies, it has been demonstrated that the top-down

approach is more suitable for dedicated monoproduct batch

plants, while the bottom-up methodology is also suitable for

multipurpose batch plants with high varying production

processes, being a more comprehensive but also more time-

consuming approach. Extended versions of the bottom-up

approach based on higher resolution data for dynamic modeling

INTRODUCTION 5

of energy consumption have claimed an average modeling error

of 10% at unit operation level and less than 30% at production

building level (Szïjjarto et al., 2008). This level of accuracy has

been shown to be adequate for allocation and monitoring of

energy consumption, highlighting energy saving potential in

multipurpose batch production buildings (Andrej Szïjjarto et al.,

2008, Rerat et al., 2013). However, since the high resolution

bottom-up approach requires extensive dynamic process data

from the control system as model input, it is not suitable for fast

screening purposes, unless it is embedded in the automated

plant monitoring systems. When this is not the case and energy

consumption has to be allocated to many different products in

different production buildings, or when a high resolution is not

required (e.g., estimating inventories for life cycle assessment), a

fast screening methodology based on standard process

documentation and rules of thumb can be a valuable tool.

Although the bottom-up models of Bieler (Bieler et al., 2004) can

serve as the basis for a methodology of this kind, a procedure for

systematic data extraction and filling of data gaps present in

standard process documentation has not been proposed yet.

In this work we propose a standard process documentation

based approach for modeling the steam consumption of single

unit operations in chemical batch plants, starting from previously

developed bottom-up models (Bieler et al., 2004) enhanced by

thermodynamic principles and rules of thumb for filling data gaps.

This new approach allows a systematic identification of the

different unit operations described in standard process

documentation by means of specific keywords, provides default


values and options for filling data gaps, and proposes uncertainty

intervals for the energy consumption models.

In spite of the simplicity of these documentation based models,

they are not of general applicability, since they still require de-

tailed process information as input, which is usually available in

later design stages and can be partially confidential. Therefore, a

second modeling approach is needed in cases when standard

operation procedures (SOP) are not available, namely in early

phases of process design, or when very fast estimations have to

be performed for screening purposes, a typical case for environ-

mental assessments. In addition to the documentation based ap-

proach, in this thesis we propose models of steam consumption

based on statistical analysis of production data available via a

consortium of industrial partners representing leading companies

in fine chemical and pharmaceutical production.

There are several examples of the use of statistical analysis in

the fields of Life Cycle Assessment (LCA) and process design,

such as modeling of relationships between design and inventory

parameters (Mueller and Besant, 1999, Mueller et al., 2004),

evaluation of distribution functions of emission factors (Cooper et

al., 2008), scenario analysis of process and material alternatives

by means of decision trees (Cooper et al., 2008), stochastic LCA

inventory modeling (Canter et al., 2002), characterization of rela-

tionships between technologies and pollutants by means of hier-

archal cluster analysis and principal component analysis (Cosmi

et al., 2004), development of greenness metric of synthetic pro-

cesses for active pharmaceutical ingredients using hierarchal

cluster analysis and principal component analysis (Curzons et al.,

INTRODUCTION 7

2007), enhancing the quality of Life Cycle Inventories (LCI) by

means of data reconciliation applying analysis of covariance (Hau

et al., 2007), and uncertainty analysis using stochastic models (B.

Maurice et al., 2000, Sugiyama et al., 2005).

1.3 Goal of the Thesis

The goal of this work is to provide shortcut models of steam con-

sumption of production processes in chemical batch plants, which

allow fast predictions for screening purposes. These models are

of two different types, one based on production documentation,

which results in a deterministic value with an uncertainty interval,

and a second type based on statistical analysis of production da-

ta, resulting in probability density functions and classification

trees, which can take the form of generic intervals.

The standard process documentation based approach estimates

the steam consumption of single unit operations in chemical

batch plants, starting from previously developed bottom-up mod-

els (Bieler et al., 2004) enhanced by thermodynamic principles

and rules of thumb for filling data gaps. This new approach allows

a systematic identification of the different unit operations de-

scribed in standard process documentation by means of specific

keywords, provides default values and options for filling data

gaps, and proposes uncertainty intervals for the energy consump-

tion models. Furthermore, this new approach is validated in two

case studies, demonstrating the general applicability of the bot-

tom-up approach for modeling the energy consumption in batch

production plants. Besides representing a prediction tool in itself,


the documentation based approach is used to generate the da-

taset for the building of the statistical models.

The probability density function (PDF) models describe the varia-

bility of the gate-to-gate steam consumption for the production of

one kilogram of product for a particular reaction type. Fitting of

distributions to data consists of finding the type of distribution and

the value of the parameters that give the highest probability of

generating the sample data. In our case the fitting was accom-

plished by means of the well known maximum likelihood method

(MLE) (Myung, 2003), and the goodness of the fit was evaluated

using standard statistical tests and the Akaike Information criteria

(Akaike, 1974). The generic interval models derived here corre-

spond to the interquartile ranges of the fitted distributions. The

interquartile range, which is the difference between the lower and

upper quartiles, namely the 25th and 75th percentiles of a PDF,

concentrates on the middle portion of the distribution. Thus, inter-

quartile ranges are judged to be useful as predictive models.

Classification trees can serve not only as predictive models, but

also as descriptive models to distinguish between objects from

different classes, and explain which features determine that ob-

ject to belong to a particular class in the same way as logistic re-

gression. In this work the models based on classification trees

assign categories – in the form of pre-defined intervals– to the

gate-to-gate steam consumption for the production of one kilo-

gram of product, given a particular set of attributes. Besides the

reaction type, which is in principle the only parameter considered

in the PDF models, the set of attributes of the classification trees

may also include information about process characteristics and

INTRODUCTION 9

operation parameters, depending on the stage of process design.

1.4 Structure of the Thesis

In Chapter 2 the documentation based approach is introduced,

including model development, uncertainty analysis and

application examples. Chapter 3 presents the selection and

evaluation procedure of the two types of statistical models

developed in this work, namely the classification trees and

probability density functions. In Chapter 4 the three case studies

for the validation of the documentation based approach are

presented. Chapter 5 presents the results of the cross-validation

of the classification trees for model selection and evaluation, as

well as the selection of important rules. Chapter 6 includes the

results of the probability density function models per reaction type

and discusses the further parameterization of these models. In

Chapter 7, the performance of the classification trees and

probability density function models is evaluated in a first case

study. Additionally, the probability density function models are

applied to a second case study, where the steam consumption of

different industrial synthesis routes for the production of a

pharmaceutical intermediate is estimated and a ranking of the

different alternatives is provided. Chapter 8 presents the

conclusions and outlooks of this thesis.


2 Documentation based Models of Steam Consumption

2.1 Bottom-up Modeling

The documentation based models relies on a bottom-up ap-

proach, defined as the summation of the energy consumption of

the single parts of a system (Werbos, 1990). In this context the

bottom-up modeling of steam consumption starts with the identifi-

cation of the relevant unit operations (UOs), described in the

standard operating procedure (SOP) as it is shown in Figure

2.2.1. Here, by unit operation, it is meant individual process steps

such as heating, evaporation or maintaining a constant tempera-

ture. Secondly, steam measurements are collected, if they are

available. In the worst case scenario, where neither measure-

ments nor process documentation are available, as it is often the

case in early phases of process design, empirical or statistical

models based on similar processes or process simulations can be

used. Once the measurements or estimated values for the single

unit operations are collected, they can be summed up to the de-

sired level of analysis (e.g. all unit operations comprised in a ves-

sel, during the reaction step or work-up processes, during a

whole production path, etc.).

2.2 Standard Operating Procedures (SOPs)

The data for the model development was acquired from two dif-

ferent chemical companies in Switzerland in the form of standard

operation procedures (SOPs). SOPs are written instructions that

DOCUMENTATION BASED MODELS 11

document the way the unit operations are performed in the pro-

duction plants. Often, these standard procedures follow the DIN

norm, at least in many batch plants in Europe. Normally, the first

chapter of an SOP consists of a short description, which includes

the reaction synthesis path, the working principle, the mass flow

diagram, some characteristics of the raw materials (e.g., molecu-

lar weight and purity), and other process related information (e.g.,

product yield, capacity of the plant and product use).

Figure 2.2.1. Documentation based approach (shaded box) for modeling steam consumption of unit operations in batch plants facilitating bottom-up modeling of steam consumption in multipurpose production buildings.

The second chapter generally includes process safety related

information, while the third chapter describes in a more detailed

way the performance of each unit operation and the


corresponding production parameters, (e.g., temperatures,

operation times, etc.). Furthermore, an SOP normally includes

equipment characteristics, (e.g., equipment volume and

construction material), quality and environmental requirements.

On the other hand, although SOPs are rich in process related

information, they are not complete for constructing energy

balances, due to a traditional lack of interest of “low volume, high

value” chemical batch production in energy costs, focusing mainly

on the more cost related material flows. Moreover, SOPs are

relatively static documents, in the sense that they do not provide

any information about batch-to-batch variability. As a result of

these two factors, performing an energy balance over the whole

production boundary using SOPs as the main data source would

be a highly time consuming task without a systematic

methodology for extracting the energy relevant information in

SOPs, filling the inevitable data gaps and providing realistic

estimations about the accuracy of the calculations. In the

following, we propose such a methodology focusing on steam

consumption. However, an extension to other energy utilities,

such as cooling water and brine, should be straightforward. In the

rest of the text, the terms steam and energy consumption are

used interchangeably.

2.3 Model Development

The first step of the process documentation based approach is to

define a set of keywords for the processes which require steam

consumption. These keywords are “charge”, “heat”, “evaporation”,


“reflux”, “hold” and “reaction”. The description of the underlying

phenomena behind these keywords and the basic equations for

the single unit operations are presented in Table 2.3.1. In most

cases, the equations are based on simple first principles from

thermodynamics and heat transfer, except for reflux conditions,

where an empirical constant is used to describe the time-

dependent steam consumption. This is due to the absence of

information for the reflux ratio, which is the typical case in SOP

documentation. The energy losses are also characterized by an

empirical loss coefficient, which represents the heat transfer due

to radiation and free convection from the equipment surface

(Bieler et al., 2004). The input data include reaction mass,

process temperatures and physicochemical properties of the

material present in the unit operation, as well as some equipment

characteristics.

As can be seen in Table 2.3.1, the total energy consumption of

one unit operation consists of two terms, the theoretical energy

consumption and a time-dependent energy loss term. For all

parameters involved in these equations, data sources and

assumptions for default values are provided. For instance, a

substance or mixture charged into a vessel is assumed to be at

room temperature (20°C), unless something else is mentioned in

the SOP. In the case of missing data for heat capacities, a

substance is classified into three different categories, acid/base,

organic or water, and corresponding values are assigned.

Similarly, for enthalpy of vaporization data gaps, a substance is

classified according to its boiling point into low, middle and high

boiling point substance, and corresponding values are assigned.

Regarding the mass and total surface of the equipment, standard


values coming from DIN norms are assigned, based on the

nominal volume and material of the vessel. Enthalpies of reaction

are normally found in risk analysis documentation, rather than in

the SOP, and are based on final mass of the process step. The

proposed default values should be used as a mean for filling data

gaps in cases when the required information is not found in the

SOP. In the case of properties like heat capacity and enthalpy of

vaporization, more accurate values can be found in the literature,

at least for common substances and solvents, or can be

calculated by property estimation methods. In this way, the

accuracy of the model predictions can be improved with respect

to the estimations using default values. However, the proposed

default values should serve as a good basis for fast screening

calculations. Finally, 5-bar steam is used for temperatures below

145°C, and 15-bar steam for temperatures up to 190°C, the

steam consumption being calculated on the basis of its

condensation enthalpy.


Table 2.3.1. Modeling of individual unit operations according to the process documentation based approach.

UO key-word

Description Formula Para-meter

Assumption/ Substance/ Equipment specification

Source/ Default value

Unit

Charge Heating of the new mass filled into the vessel to the same temperature (above 20°C) as the rest of the reac-tion mixture inside the vessel.

)( 2 iiitheo TTcpmE −⋅⋅= 2.3.1 mi SOP kg

cpi acid/base 1.5 kJ/(kg K)

( ) tTTAKE amloss ⋅−⋅⋅= 2 2.3.2 organic 2.2 kJ/(kg K)

water 4 kJ/(kg K)

−

−⋅

⋅

⋅−=

is

s

TT

TT

AU

cpmt 2ln

2.3.3 T2 SOP °C

Ti 20 °C

K Empirical (Bieler et al., 2004)

1.98 kJ/(min m

2 K)

A DIN-Norm m2

Tam 20 °C

Ts T2 <145→ 5-bar steam

159 °C

T2 >145→ 15-bar steam

201 °C

U STNR and 600 W/


cp >3.5 (m2 K)

otherwise 250 W/ (m

2 K)

Heat Heating of the total mass inside the vessel to a final temperature above 20°C.

( ))( 12

12

TTcpm

TTcpmE

eqeq

theo

−⋅⋅+

−⋅⋅=

2.3.4

∑=

n

i

imm 2.3.5 mi as in Charge

m

cpm

cp

n

i

ii∑ ⋅

=

)(

2.3.6 cpi as in Charge

tTTT

AKE amloss ⋅

−

+⋅⋅=

212

2.3.7 T2 as in Charge

T1 20 °C

−

−⋅

⋅

⋅−=

1

2lnTT

TT

AU

cpmt

s

s 2.3.8 meq STNR DIN-Norm

STNR kg

STEM DIN-Norm Stem

kg

cpeq STNR 0.5 kJ/(kg K)


STEM 0.7 kJ/(kg K)

K as in Charge

A as in Charge

Tam as in Charge

Ts as in Charge

U as in Charge

Evapo-ration

Simple evapora-tion. It is always assumed if no re-flux conditions are mentioned.

iitheo HvmE ∆⋅= 2.3.9 mi as in Charge

iHv∆ Tboil low 350 kJ/kg

( ) damdloss tTTAKE ⋅−⋅⋅= 2.3.10 Tboil middle 900 kJ/kg

Tboil high 2250 kJ/kg

K as in Charge

A as in Charge

Td SOP °C

Tam as in Charge

td SOP/expert knowledge

min

Reflux Distillation under reflux conditions, with C being a constant fitted to

diitheo tCHvmE ⋅+∆⋅= 2.3.11 mi as in Charge

iHv∆ as in Evapora-tion

( ) damdloss tTTAKE ⋅−⋅⋅= 2.3.12 C empirical 5508 kJ/min


measurement data of steam consump-tion of recovery of butanol under strong reflux condi-tions.

td SOP/expert knowledge

K as in Charge

A as in Charge

Td as in Charge SOP °C

Tam as in Charge

Hold Keep the process temperature con-stant.

( ) hamhloss tTTAKE ⋅−⋅⋅= 2.3.13 K as in Charge

A as in Charge

Th SOP °C

Tam as in Charge

th SOP min

Reaction Energy produced or consumed due to exothermic or endothermic chem-ical reactions.

rtheo HmE ∆⋅= 2.3.14 m as in Charge RAD kg

rH∆ RAD kJ/kg


Table 2.3.2. Definition of the symbols used in Table 2.3.1.

Symbol Description Unit A Surface area m

2

C Reflux constant kJ/min cp Heat capacity of the mixture kJ/(kg K) cpi Heat capacity of the substance kJ/(kg K) cpeq Heat capacity of the equipment kJ/(kg K) Etheo Theoretical energy consumption kJ Eloss Energy losses kJ K Loss coefficient kJ/(min K) m Mass of total reaction mixture kg meq Mass of the equipment kg mi Mass of substance-i kg T1 Initial temperature of reaction mixture °C T2 Final temperature of reaction mixture °C Tam Ambient temperature °C Tboil Boiling point °C Td Distillation temperature °C Th Process temperature kept constant °C Ti Temperature substance-i °C Ts Saturation temperature of steam °C t Heating time min td Distillation time min th Holding time min U Heat transfer coefficient W/(m

2 K)

rH∆ Enthalpy of reaction kJ/kg

iHv∆ Enthalpy of vaporization kJ/kg


2.3.1 Application Example

To illustrate this data extraction and modeling procedure, the

steam consumption for the batch production of 3200 kg of a raw

and wet product C is calculated, that is not including purification

and drying steps. Figure 2.3.1 shows a simplified example of the

SOP for the production of C. It is important to notice that while

some values can be directly extracted from the recipe section of

the SOP, other values have to be inferred from the mass flow

diagram of the SOP. The first unit operation is the preparation of

a reactant solution and heating for further filtration. After the first

filtration, the reaction step takes place in vessel 2, and

subsequently crystallization and washing steps are performed in

vessel 3. The suspension is filtered and the mother liquor is

transferred to vessel 4 for recovery of acetone. The description of

the reaction, crystallization and washing steps are not included in

this example since they are not relevant from a steam

consumption point of view. However, these processes are

depicted in the mass flow diagram.

In Table 2.3.3, the procedure for modeling the steam

consumption according to the methodology introduced above is

depicted in detail. The calculation steps, the production data and

their sources are presented, and a reference is made to the

equations of Table 2.3.1. Table 2.3.3 is divided into three

subsections, the first one corresponding to the modeling of the

heating of the reactant solution in vessel 1, the second part to the

modeling of the solvent recovery in vessel 4, and the last section

to the bottom-up modeling of the total steam consumption for the


production of C. The bottom-up model in this case is the sum of

the total steam consumption in vessel 1 and vessel 4 resulting in

9000 kg of 5-bar steam for the production of 3200 kg of product

C.


Figure 2.3.1. Example of a standard operation procedure (SOP).


Table 2.3.3. Calculation of steam consumption for the production of 3200 kg of raw and wet product C (equal batch size)

according to the SOP presented in Figure 2.3.1.

Procedure Data Source Calculation Equation number Table 2.3.1

I. Modeling of energy consumption of the heating unit operation in vessel 1

Calculate the total mass in vessel 1

mwater=4000 kg SOP

kg 10100

450016004000

=

++=m

2.3.5 mA=1600 kg SOP

macetone=4500 kg SOP

Calculate the heat capacity of the mixture

cpwater=4 kJ/(kg K) Default

kJ/kgK 9.2

10100

2.245002.2160044000

=

⋅+⋅+⋅=cp

2.3.6 cporganic=2.2 kJ/(kg K) (A and acetone are organic)

Default

Calculate the theoretical energy consumption for heating of the reaction mixture and equipment

T1=20°C (initial temperature) Default

kJ 844750)2045(5.09000

)2045(9.210100

=−⋅⋅

+−⋅⋅=theoE

2.3.4 T2=45°C (final temperature) SOP


mass mequipment=9000 kg (STNR and NV=25 m

3)

Default

cpequipment=0.5 kJ/(kg K) (STNR)

Default

Calculate the heating time for calculation of energy losses

U=250 W/(m2 K) =15 kJ/(min

m2K) (STNR and cp<3.5)

Default

min 2.920159

45159ln

4215

9.210100

=

−

−⋅

⋅

⋅−=t

2.3.8 Ts=159°C for T2<145°C

Default

A=42 m2 (STNR and NV=25

m3)

DIN norm

Calculate the energy loss-es during heating of the reaction mixture and equipment mass

K=1.98 kJ/(min m2 K) empiri-

cal (Bieler et al., 2004)

kJ 24865

2.92

20454298.1

=

⋅

+⋅⋅=lossE

2.3.7

Calculate the total energy consumption during the heating unit operation

losstheototal EEE +=

kJ 869615

24865844750

=

+=totalE


II. Modeling of energy consumption of solvent recovery in vessel 4 II.1. Modeling of heating unit operation

Calculate the heat capacity of the mixture

mML=36000 kg (mother liq-uor)

SOP*

kJ/kgK 8.3

36000

2.24500431500

=

⋅+⋅=cp

2.3.6 macetone-water=4500 kg (distil-

late) SOP*

mwater=31500 kg (residue) SOP*

Calculate the theoretical energy consumption for heating of the reaction mixture and equipment mass

T1=20°C (initial temperature) Default

kJ 11294400

)2098(5.016000

)2098(8.336000

=

−⋅⋅+

−⋅⋅=theoE

2.3.4

T2=98°C (final temperature) SOP

mequipment=16000 kg (for STNR and NV=40 m

3) Default

cpequipment=0.5 kJ/(kg K) (STNR) Default

Calculate the heating time for calculation of energy losses

U= 600 W/(m2 K)=36 kJ/(min

m2 K) (STNR and cp>3.5)

Default

min 4720159

98159ln

6636

8.336000

=

−

−⋅

⋅

⋅−=t

2.3.8 Ts= 159°C for T2<145°C

Default


A= 66 m2 (for STNR and

NV=40 m3)

DIN norm

Calculate the energy loss-es during heating of the reaction mixture and equipment mass according to Table 2.3.1


cal (Bieler et al., 2004)

kJ 239536

47202

20986698.1

=

⋅

−

+⋅=lossE

2.3.7

Calculate the total energy consumption during the heating unit operation

losstheototal EEE += kJ 11533936

23953611294400

=

+=totalE

II.2. Modeling of the distillation unit operation

Calculate the theoretical energy consumption for the distillation of the mix-ture acetone-water

macetone-water=4500 kg (distil-late)

SOP*

kJ 5702400

30055089004500

=

⋅+⋅=theoE

2.3.9 ∆Hv-acetone=900 kJ/kg (solvent with middle boiling tempera-ture)

Default

Reflux conditions are men-tioned in the SOP, therefore reflux is considered.

SOP

Calculate the energy loss-es during distillation

t=300 min (average distilla-tion time of the mixture ace-tone – water in the corre-sponding production plant)

Expert knowledge

kJ 3057912

300)2098(6698.1

=

⋅−⋅⋅=lossE 2.3.10



cal(Bieler et al., 2004)

A= 66 m2(for STNR and

NV=40 m3)

DIN norm

Td=98°C SOP

Calculate the total energy consumption during the distillation unit operation

losstheototal EEE += kJ 8760312

30579125702400

=

+=totalE

II.3. Sum of the heating and the distillation unit operations

Sum the total energy val-ues for the heating and the evaporation unit opera-tions

kJ 20294248

876031211533936

=

+=totalE Bottom-up

III. Modeling of the total steam consumption for the production of product C

Sum the total energy con-sumption in vessels 1 and 4

kJ 21163862

20294248869615

=

+=totalE Bottom-up

Convert the total energy consumption in kJ to kilo-grams of 5-bar steam

Hs=2350 kJ/kg (condensa-tion enthalpy of steam (Bieler, 2004))

Default kg 00092350

21163862==Steam


2.4 Model Uncertainty

The uncertainty in the proposed documentation based bottom-up

modeling approach has two different sources: the use of standard

process documentation, and the use of default values, model

simplifications and assumptions. Although the standard process

documentation approximates production averages, it does not

always reflect the reality, since it does not provide any information

about the batch-to-batch variability. The reasons for this batch-to-

batch variability may vary, including variation of scheduling

patterns prolonging holding times, malfunction of controllers,

intended variation of process parameters to meet flexible,

dynamic production needs or even variation of ambient

conditions. On the other hand, examples of modeling

uncertainties are all the default values used for production

parameters, in order to deal with SOP data gaps, or the simplified

form of some models, as for instance the distillation models and

the energy loss terms.

Besides the use of simple intervals (Jean-Luc Chevalier, 1996),

or the traditional techniques based on probability theory, such as

analytical uncertainty propagation methods (Hong et al., 2010,

MacLeod et al., 2002), or Monte Carlo analysis (Morgan. and

Henrion., 1990), other methodologies based on fuzzy set and

possibility theory have been successfully applied to treat

uncertainty (Ferrero and Salicone, 2003, Mauris et al., 2001).

Compared to simple intervals, fuzzy intervals provide more

detailed information about the uncertainty distribution that is an

indication of central tendency and skewness or asymmetry, and


not only upper and lower bounds. On the other hand, they require

more data and are computational more expensive than simple

intervals. Comparing the approaches based on probability theory

and those based on fuzzy/possibility theory, the last ones are

mathematically less robust but can be generated more readily

from small datasets and perform better when the data and model

imprecision are due to ambiguity rather than randomness, being

more compatible with heuristic information (Tan. et al., 2002). In

this work the different uncertainty sources described above are

assessed together in one term by means of simple and fuzzy

intervals (see Section A.1 in the appendix for a formal definition

of fuzzy intervals). This means that no propagation of the

individual uncertainty terms is performed, but rather a top-down

modeling of the total uncertainty. Both interval approaches were

chosen considering the data availability, the nature of the

uncertainty types, and the information obtained from the

uncertainty distribution.

2.4.1 Fuzzy Intervals

The fuzzy intervals proposed in this work represent absolute

values of relative errors showing the absolute deviations of the

documentation based energy models from reference data. As it is

shown in Figure 2.4.1, from the validation procedure the relative

errors between observed (reference) data and model results are

calculated, and subsequently the 2.5th, 25th, 75th and 97.5th

percentiles for this set of relative errors can be defined. These

percentiles further define the support and core values of the

trapezoidal membership functions (i.e., giving a, b, c and d the


2.5th, 25th, 75th and 97.5th percentile values, respectively) building

in this way our first fuzzy interval of relative errors. Parallel to this

step, a sensitivity analysis was performed in order to identify the

most influential parameters for error reduction between observed

and modeled values. After identification and correction of the

influential parameter data, the relative errors and the subsequent

percentiles are recalculated. Therefore, two different fuzzy

intervals are proposed, a broader one corresponding to the case

of less precise process parameter information, and a narrower

one corresponding to the availability of more precise data.

2.4.2 Application Example

Continuing with the example presented before (Section 2.3) and

the obtained result of total steam consumption (9000 kg of steam)

we can report the obtained value for the uncertainty range based

on the fuzzy intervals. To illustrate this, Table 2.4.1 presents the

resulting intervals corresponding to one fuzzy interval defined as

(5, 15, 40, 60). The interval between 5% and 60 % includes all

possible values which the relative errors can take in this example.

All values outside of this range are considered as not plausible.

Additionally, 15% and 40% are more plausible than 5% and 60%,

since they belong to the core of the fuzzy interval, see Figure

2.4.2. According to the values of Table 2.4.1 and considering only

the core, one would conclude as more plausible a lower bound

between 5400 and 7650 kg of steam and an upper bound

between 10350and 12600 kg of steam for the process steam

consumption.


Figure 2.4.1. General procedure to generate uncertainty fuzzy intervals for

estimating relative errors within modeling of steam consumption in chemical

batch plants.


Figure 2.4.2. Uncertainty estimation of the documentation based approach in

the form of a fuzzy interval for relative errors. The values a=5 and d=60

correspond to the support, and the b=15 and c=40 values to the core of the

fuzzy interval.


Table 2.4.1. Application of trapezoidal fuzzy intervals (a, d: support and b, c: core of the fuzzy interval) to express uncertain-ty for the total steam consumption calculated in the example of Section 2.3.1. The shading part refers to the more plausible values according to the core of the fuzzy intervals. In the case of more precise process data, the interval estimation for steam consumption is narrower.

Fuzzy interval (a,b,c,d)

Relative error %

Relative error* [kg steam/ batch]

Lower bound [kg steam/ batch]

Upper bound [kg steam/ batch]

Fuzzy interval for less precise data

a 5 450 8550 9450 b 15 1350 7650 10350 c 40 3600 5400 12600 d 60 5400 3600 14400

Fuzzy interval for more precise data

a 1 90 8910 9090 b 5 450 8550 9450 c 20 1800 7200 10800 d 50 4500 4500 13500

* In this batch 9000 kg of steam were consumed.


3 Statistical Models

Assuming that energy utility consumption is mostly dependent on

the synthesis reaction type and on operation parameters of the

production processes rather than on specific reactants and prod-

ucts, it is possible to build generic models for steam consumption.

The models of steam consumption proposed here are based on

classic statistical modeling, where probability density functions

(PDF) are fitted to data, and on classification trees, represented

by a set of logical rules, which facilitate human interpretability. In

both cases the models can take the form of generic intervals.

3.1 System Boundaries

A reaction synthesis route includes the chemical synthesis and

work-up unit operations for the separation and recovery of the

product. In the reaction step the substrates are partially converted

to products and by-products. This reaction step can be followed

by work-up processes such as distillation, crystallization, extrac-

tion, etc. or by a next reaction step if this is an intermediate prod-

uct and recovery is not needed. Thus, as it is depicted inside the

area defined by the black pointed line in Figure 3.2.1, a synthesis

route can include one-to-n reaction steps, each of them followed

by zero-to-m work-up recovery processes. The models developed

in this work predict the steam consumption within the boundaries

defined by the grey boxes. Each steam model corresponds to a

single reaction plus the work-up processes which immediately

follow that reaction step, if there are any. From now on we will

STATISTICAL MODELS 35

refer to this system simply as reaction. The empirical yield ranges

corresponding to the analyzed reaction classes in this work are

given in Table B.1.1.2 in the appendix.

Special purification steps and drying of the product are not ad-

dressed within the system, because this would have to include a

dependence of energy consumption on the sequence of the reac-

tion step within the synthesis path. Thus, the steam models are

independent of whether the corresponding reaction is performed

as the last step of a synthesis route or not. Production of raw ma-

terials and auxiliaries, solvent recovery and waste treatment are

also not considered in the reaction models. Models and tools for

this scope are generally available (e.g., ecoinvent (Frischknecht

et al., 2005), finechem (Wernet et al., 2009), ecosolvent (Capello

et al., 2007)). Considering this, for a comprehensive cradle-to-

gate life cycle analysis, a synthesis path can be modeled as a

sequence of distinct reaction-steps by combining the individual

reaction models and filling in data for the processes not included

in the system boundaries of this work.

3.2 Training and Validation Datasets

The data acquisition for the model development was performed in

collaboration with nine industry partners in Switzerland, Germany,

France and United States, covering different sectors from basic

chemicals to pesticides and pharmaceutical products.

Since the data provided by most companies was in the form of

standard operation procedures (SOPs) and not as measured val-

ues, the training data (250 points) for the building of the statistical


models were estimated by means of the documentation based

approach previously introduced in Section 2. The values are giv-

en in kilograms of 5-bar steam per kilogram of product, according

to the system boundary defined above.

An additional industrial dataset was available from some of the

industrial partners for testing and comparing the performance of

the classification trees and the PDF models against new samples

that have not been used for model development. This case study

dataset consists of 17 modeled data of steam consumption, not

all of which, however, correspond to the documentation based

modeling approach.


Figure 3.2.1. System boundaries for the steam models. The outer black dashed

line represents a full synthesis route where raw materials and auxiliaries (Aux)

are entering the system and a product and waste (WST) are leaving the system.

The synthesis route can comprise one to n reaction steps. The system boundary

corresponding to one reaction is given by the grey boxes, including the reaction

synthesis and work-up processes, if they take place. The steam consumption

models are defined for each reaction system.

3.3 Stages of Process Design

Whereas at the earliest stage of process design, which we call

S1, only information regarding the reaction type is available, at a

second level of process design namely S2, the type of work-up

processes are also known. Later on, at the third (S3) and fourth

(S4) stages of process design, operational parameters such as


time and temperatures as well as mass flows are respectively in-

cluded. The latest stage of design – considered in this work –

called S5, assumes that the steam consumption of the energy

intensive distillation processes is known. For the classification

trees, which include several variables of nominal, binary and con-

tinuous type, the number and type of predictor variables differ ac-

cording to the stage of process design.

3.4 Selection and Classification of Chemical Reactions

The reaction types considered in this work cover very common

and frequent performed reactions in the chemical industry.

However, the selection of the reaction types is restricted to the

collected data, thus it does not represent a comprehensive study

of all existing reactions in production sites.

The selected reaction classes shown in Figure B.1.1.1 in the

appendix were derived heuristically following the standard form of

reaction classification in text books, which considers the formal

structural change, namely the bonds changed in a reaction.

Whenever possible, aggregation of similar reaction classes into

one group was performed in order to increase the number of data

points within a class. Similarity refers in this case to the type of

molecules involved in the reaction. For instance, in Alkylation and

Arylation reactions, alkyl and aryl groups, which are both

hydrocarbons, are introduced into a molecule. Thus Alkylations

and Arylations are included in the same reaction group. The

same is true for the different sub-classes of the

Alkylation/Arylation group, namely the C-,N-,O- and S-


Alkylations/Arylations. In Acylation reactions an acylating group is

introduced into a molecule. Whereas N- and O-Acylations were

aggregated in most cases, N-Acylation reactions with cyanuric

chloride as reactant were considered separately as an individual

reaction class due to its special process characteristics. In

addition to the expert knowledge, a univariate analysis of

variance (ANOVA) (Field, 2009) was performed in order to test

whether or not the mean steam consumption of these similar

reactions were significantly different among them (see Appendix,

Section B.1.2). ANOVA is a statistical technique used to

determine on the basis of one dependent measure, steam

consumption in this case, whether samples are from populations

– reaction groups – with equal means. Whereas for alkylation

reactions no significant difference was revealed and thus they

were grouped together, for acylation reactions a significant

difference was observed between acylations using cyanur

chloride as reactant and acylations using other reactants than

cyanur chloride. Therefore two different acylation categories are

considered.

3.5 Classification Models

Classification trees represent rules underlying data with

hierarchical, sequential structures. These rules partition the data

in every node of the tree based on a particular predictor variable

value (Figure 3.5.1). At every node, the resulting split optimizes

the classification for the respective tree depth. The tree is

typically grown to its full size achieving maximum classification

performance for the training data (e.g., using the CART algorithm


(L. Breiman et al., 1984)) and then pruned back in a cross

validation procedure to avoid overfitting (Section 3.4.2.). To

classify an unknown instance, this is routed down the tree

according to the values of the attributes tested in successive

nodes, and when a leaf is reached the instance is classified

according to the class assigned to the leaf.

As it was mentioned before, classification trees can include

several predictor variables of nominal, binary and continuous

type. In this work, the number and type of predictor variables

differ according to the stage of process design.

Figure 3.5.1. Example of a general classification tree. C(t): subset of classes

accessible from node t, F(t): predictor variables subset used at node t, decision

rule used at node t.


3.5.1 Selection of Predictor Variables and Discretization of Target Attribute

In theory irrelevant predictor variables are not selected by the tree

algorithm, however it has been observed that distracting variables

can deteriorate the classification performance and the interpreta-

bility of the tree (I. Witten, 2005). To test this effect, classification

trees were compared using two different training datasets (da-

taset-1 and dataset-2) with the same instances but different num-

ber of predictor variables. Dataset-1 comprises only a subset of

predictors from the most inclusive dataset-2, selected based on

empirical knowledge about their influence on steam consumption

(see Table 3.5.1).


Table 3.5.1. Definition of the predictor variables in the training datasets 1 and 2.

Stage Predictor Type Dataset-1 Dataset-2 Description

S1 reaction type categorical x x Reaction type defined according to Figure B.1.1.1

mechanism categorical x x Reaction mechanism defined according to Table

B.1.1.1 Total 2 2

S2 mechanical binary x indicates presence or absence of mechanical processes (yes/ no). Mechanical processes include filtration, centrifugation and washing work-up processes

miscellaneous binary x indicates presence or absence of miscellaneous processes (yes/ no). Miscellaneous, are work-up processes which cannot be classified in any of the already mentioned categories (e.g. dilution of the reaction mixture and stirring at high temperature)

crystallization binary x indicates presence or absence of crystallization

processes (yes/ no)

distillation binary x x indicates presence or absence of distillation processes during the reaction work-up. It refers to simple evaporation or distillation under reflux conditions (yes/ no)

acid base reaction

binary x indicates presence or absence of acid-base reactions (yes/ no). Acid-base processes correspond to neutralization and precipitation work-up processes (e.g. previous to mechanical separation processes)

evaporation binary x indicates presence or absence of evaporation


processes (yes/ no). Evaporation refers to simple evaporation occurring during the reaction synthesis or any work-up step

reflux binary x x indicates presence or absence of reflux conditions

during the reaction synthesis or during the reaction work-up (yes/ no)

last reaction binary x indicates if the considered reaction is the last one of the

synthesis route (yes/no) Total* 4 10

S3 Tmean continous x Average operation temperature in °C

Tmax continous x x Maximal operation temperature in °C

time continous x x Sum over time in hours required for heating of the reaction mixture, solvent evaporation, keeping the temperature constant above the atmospheric temperature under reflux conditions or not, during the reaction synthesis and work-up processes within the defined boundary system

Total* 6 13

S4 PMI continous x x Process Mass Intensity1

PMIs continous x Solvent Mass Intensity2

PMIw continous x Water Mass Intensity3

RME continous x Reaction Mass Efficiency4

Total* 7 17

S5 Steamdist continous x x Steam consumption during distillation processes Total* 8 18


* The total number of predictor variables per design stage is cumulative, meaning that at a certain stage i the variables appearing at the previous stages are also present at stage i.

(1)product

total

m

mPMI = , (2)

product

solvents

m

mPMI = , (3)

product

waterw

m

mPMI = ,

(4)reagents

product

m

mRME =

where mtotal is the total input mass of raw materials, mproduct the mass of product,

msolvent the total input mass of solvent, mwater the total input mass of water,

mreagents the total input mass of reagents.

Regarding the discretization of the steam consumption, the

number and the width of the intervals (classes) had to be

specified. For this purpose a histogram of the steam data (Figure

3.5.2) pointed towards a compromise between homogenous

intervals and sufficient sample size in every interval. Again two

scenarios were tested, considering three (Table 3.5.2) and five

classes (Table 3.5.3) to evaluate the influence of the number of

output classes in the classification performance of the trees.


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Steam consumption [kg/kg product]

Fre

quency

Figure 3.5.2. Histogram of the steam consumption values included in the

training dataset.

Table 3.5.2. Discretized intervals of steam consumption (target attribute)

considering three output classes. The values are given in kilograms of steam

consumption per kilogram of product.

Class label Interval Number of data points

High 3-16 61 Middle 1-3 51 Low 0-1 122

Table 3.5.3. Discretized intervals of steam consumption (target attribute)

considering five output classes. The values are given in kilograms of steam

consumption per kilogram of product.

Class label Interval Number of data points

High 5-16 28 Middle-high 3-5 33 Middle 1.5-3 35 Middle-low 0.5-1.5 48 Low 0-0.5 90


3.5.2 Model Selection and Evaluation

Similarly to a stepwise regression, in which the estimated R2 in-

creases with each additional variable, more splits in a classifica-

tion tree result in a lower misclassification error considering the

training dataset. However, as it is the case in stepwise regres-

sion, where after a certain point the introduction of more variables

causes decrease deterioration of the generalizability performance

of the model (i.e., the model starts to capture the noise included

in the data), too large classification trees can have a poorer per-

formance than trees with the right size. This phenomenon is

known as overfitting

The tree is typically grown to its full size achieving maximum

classification performance for the training data (e.g., using the

CART algorithm (L. Breiman et al., 1984)) and then pruned back

in a cross validation procedure to avoid overfitting. Tree pruning

means the trimming of the fully grown tree from the later to the

earlier nodes. The optimal level of model complexity is achieved

when the generalization performance is maximal. In order to de-

tect overfitting and assess the generalization capability of the

models, stratified tenfold cross validations were carried out. In

this case cross validation was performed by randomly dividing the

data into ten equal partitions. Each tenth is held out in turn for

testing and the remaining nine-tenths are used for training. Thus

the training procedure is performed ten times on different da-

tasets and every time the cross-validation defines the degree that

the tree must be pruned. From the average performance during


the ten-fold cross validation the pruning degree of the tree and

the modeling accuracy and generalization metrics are inferred.

Then to propose a final classification tree, this pruning degree is

imposed in a tree trained with all the available data. This is a

standard procedure when the data for training and testing is lim-

ited (I. Witten, 2005).

The classification performance of every output class of the tree

can be evaluated based on the counts of instances correctly and

incorrectly predicted by the model, summarized in a confusion

matrix. The confusion matrix is a contingency table, showing the

distribution of the data in the predicted classes (columns) with

respect to the actual classes (rows). Based on the confusion ma-

trix three different performance metrics, namely sensitivity, speci-

ficity and accuracy, can be calculated. These metrics can be ex-

pressed as follows:

FNFPTNTP

TNTPAccuracy

+++

+= 3.5.1

FNTP

TPySensitivit

+= 3.5.2

FPTN

TNySpecificit

+= 3.5.3

where TP (true positives) accounts for the number of instances

belonging to one class and predicted within that class, FN (false

negatives) is the number of instances belonging to one class but

not predicted within that class, FP (false positives) is the number

of instances predicted to be in one class but not belonging to that

class, and TN (true negatives) is the number of instances not be-


longing to one class and not being predicted into that class. While

high sensitivity for a certain output class implies a very general

model for this class, namely a lot of data points fitting into few

rules, low sensitivity denotes a very specific model with many

rules containing small portions of data. In order to visualize this

trade off, plots of sensitivity against (1-specificity), also called re-

ceiver operating characteristic (ROC) plots, are used (Perkins

and Schisterman, 2006, Youden, 1950). While sensitivity is the

true positives rate, (1-specificity) represents the false positive

rate. Perfect classification is depicted by the point on the left top

corner, namely the (0,1) point. Whereas high sensitive and specif-

ic models will appear on the left side of the diagonal line close to

the (0,1) point, a model which does not predict better than a ran-

dom guess will be on the right side of the line. Two different

quantitative metrics exist to quantify the optimal model perfor-

mance using ROC plots: the distance between the model point

and the (0,1) point, and the distance to the random line, also

called Youden index (Perkins and Schisterman, 2006, Youden,

1950).

The same metrics can be defined for the overall performance of

the classification tree, the difference being that they can be sum-

marized to the true positives rate of all the classes.

3.5.3 Selection of Important Rules

Besides the tree performance for every output class and overall,

classification trees produce logical rules, in which the nodes of

the tree correspond to a question about a predictor variable and


each branch represents an answer. Extraction of important logical

rules is therefore an important step towards model interpretability

and transparency. The importance of these rules can be consid-

ered in relation to the importance of certain predictor variables, in

the sense that an important rule should also contain important

predictors. The predictor importance indicates how strongly at-

tributes are correlated to the class, meaning the contribution of

the predictor in predicting the output class. This importance can

be quantified considering the risk reduction from parent to chil-

dren nodes due to splitting on every predictor variable (see for-

mulas in Appendix, Section B.2).

The selection of important predictors also serves the purpose of

parameterization of the PDF models, the second type of models

developed in this work.


3.6 Probability Density Function Models

The PDF models describe the variability of the gate-to-gate steam

consumption for the production of one kilogram of product for a

particular reaction type. These models are probability density

functions fitted to different datasets of steam consumption, each

of them defined by one reaction type.

The fitting was accomplished by means of the maximum likeli-

hood method (MLE) (Myung, 2003), which finds the type of distri-

bution and the value of the parameters that give the highest

probability of generating the sample data (see Appendix, Section

B.3) . The goodness of the fit was evaluated using standard sta-

tistical tests such as Chi-Square, Kolmogorov-Smirnoff, Ander-

son-Darling and the Akaike Information criteria (Akaike, 1974)

(see Appendix, Section B.3).

Generic interval based predictive models can also be derived

from the interquartile ranges of the fitted distributions. The inter-

quartile range is the difference between the lower and upper

quartiles, namely the 25th and 75th percentiles of a PDF, concen-

trates on the middle portion of the distribution (Figure 3.6.1).

Considering that the reaction type constitutes the main predictor

variable for the PDF models, parameterization of these models

means that for a specific reaction type the dataset is split to sub-

sets according to process parameters, such as temperature, time,

etc. An example would be the partition of the dataset for the con-

densation reaction into two datasets, a first one for condensations

where distillation processes take place and a second one where


distillation processes do not take place. In this context the rules

extracted from the classification trees are used to define the rele-

vant parameters for splitting the datasets of each reaction type.

The need for further parameterization arises when the model in-

tervals of the initial PDF models are very broad or when the

goodness of fit indicates a poor fitting of the data.

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

Steam consumption [kg/ kg product]

Fre

quency

25th percentile 75th percentile

interquartile range

Figure 3.6.1. Histogram of steam consumption data with superimposed fitted

exponential probability density function.


4 Results Documentation based Approach

The documentation based methodology for energy modeling

described above was validated in three different case studies

against reference data from three different chemical companies in

Switzerland. The system boundary for the first case study

comprises all unit operations performed in one vessel during the

production of a specific product. Besides a vessel-product

boundary, the second case study also considers the full synthesis

route for the production of a specific product (outer black dashed

in Figure 3.2.1) and the entire production building (i.e., including

the whole series of chemical products). The system boundary for

the third case study corresponds to a single reaction step as

defined in Section 3.1 (grey boxes in Figure 3.2.1).

In addition to the model validation, the results from the first case

study were used to determine the fuzzy uncertainty intervals

introduced in Section 2.5. The cores of these fuzzy intervals were

then used for the model predictions of the second case study. For

simplicity reasons we focus only on the core, in a way analogous

to simple intervals. Even though the full fuzzy interval is not

applied in our case studies, we present the comprehensive

approach in order to enable further uncertainty calculations which

are out of the scope of this thesis, but which could be of interest

for further calculations applying fuzzy logic algebra. For example,

this would be the case when an estimate of the energy cost in

one production site is required, where the energy consumption

model results and the cost of steam are both represented by

fuzzy intervals.

RESULTS DOCUMENTATION BASED APPROACH 53

4.1 Case Study I

4.1.1 Dataset

Dataset-1 comes from a multipurpose batch production building in

Switzerland, where around 50 products including specialty

chemicals and intermediates are produced per year. The

production building has 38 equipments operated in batch mode

with typical nominal volumes between 6.3 to 40 m3. Besides the

equipments operated in batch mode, there are also unit

operations in continuous mode, which were not considered in this

work. This is due to the fact that unlike for batch processes, for

continuous operations there are usually measurements of steam

consumption. Therefore, the documentation based energy

modeling is particularly interesting for batch processes.

Dataset-1 comprises values of 5-bar steam consumption for 18

steam consumption relevant equipment-product pairs produced in

several batches in the production building. This allows an

estimation of the batch-to-batch variability of the steam

consumption for each equipment-product pair. For this reason,

the median and the 2.5th and 97.5th percentiles of steam

consumption for each equipment-product pair were calculated.

These steam data come from an Energy Monitoring Tool (EMT)

installed in the plant, which is a model-based tool that uses

mainly existing data acquisition systems for monitoring the

production to calculate both theoretical energy consumption (5-

bar steam consumption) and associated losses. The calculation is

performed for every production step at high resolution (i.e., on

minute basis) and the results can be aggregated at different


levels. In this work, an aggregation per batch and individual

equipment-product pair has been selected, consisting of a set of

batch process steps for a specific product produced in that

equipment. It should be noted that at the equipment-product level

the average of the absolute relative error values of the EMT is 10

%. In this work, for simplicity it is assumed that the EMT values

are error free, hence the intrinsic uncertainty of the EMT is not

considered in the validation procedure of the documentation

based approach.

4.1.2 Theoretical Energy Consumption

As can be seen from the scatter-plot in Figure 4.1.1, most values

fall near the diagonal indicating a good agreement between

predicted and observed values. In addition, most of the model

predictions fall within the batch-to-batch variability ranges. This is

visually depicted by the reference intervals crossing the diagonal

line. There are, however, some data points that deviate

considerably from the reference data ranges. For example, in the

case of points 10 and 16, the inaccuracy of the model predictions

is due to the modeling of reflux conditions, which depends only

on operation time and an empirical constant (constant C in 2.3.11

of Table 2.3.1) and not on accurate data of reflux ratios of the

distillation processes carried out in these equipments. In these

cases either a more detailed model should be used, or

alternatively, a parameterization of constant C for diverse

distillation operation modes would be required for more accurate

results using the documentation based approach. Regarding

point 4, the overestimation is a consequence of the inaccuracy of


the standard physicochemical properties used in the model.

Replacing these standard property values with accurate

substance specific data, if available, would provide the necessary

additional accuracy. A detailed analysis for all equipment-product

pairs of Figure 4.1.1 is presented in Table C.3.1 in the appendix.

2000 4000 6000 8000 10000 12000 14000

2000

4000

6000

8000

10000

12000

14000

Model predictions [kg steam/batch]

Ob

se

rve

d m

ed

ian

& b

atc

h−

to−

ba

tch

va

ria

bili

ty

[kg

ste

am

/ba

tch

]

4

10

16

Figure 4.1.1. Model predictions (documentation based approach) against

reference values (model based plant monitoring system) for the theoretical

energy consumption per equipment-product pair in the first case study (dataset-

1). The batch-to-batch variability corresponds to the 2.5 and 97.5 percentiles of

the observed energy consumption over several batches.

4.1.3 Energy Losses

Compared to the theoretical energy consumption, the predicted

values of energy losses present a higher deviation from the

reference, as can be seen in Figure 4.1.2. Among the different

sources of deviation, it is worth to mention inaccuracies regarding


the heat exchange area of the equipment, the temperature

control of the reaction mixture and the standard values used for

the loss coefficient (K in equation 2.3.10 of Table 2.3.1) for unit

operations at low temperature. A detailed analysis for all

equipment-product pairs of Figure 4.1.2 is presented in Table

C.3.1 in the appendix. Despite the aforementioned deviations, the

energy loss model performs satisfactorily in most of the cases,

especially for the unit operations with higher energy losses, which

can be considered as the most relevant for identification of the

energy saving potential.

4.1.4 Sensitivity and Uncertainty Analysis

The relative errors from the validation of the theoretical energy

consumption and energy losses in the first case study were used

to derive generic model uncertainty intervals based on the fuzzy

set theory. For this purpose, a sensitivity analysis was performed

in order to detect the most influential parameters on the model

results. For the theoretical energy consumption, the factor with

the highest effect on the energy model results was found to be

the existence of reflux conditions. For the energy losses, the

duration of a unit operation was identified as the most influential

parameter on model predictions. A detailed discussion of the

sensitivity analysis procedure is provided in the appendix (Section

C.1). In order to capture the influence of the reflux ratio and the

duration of a unit operation on the model uncertainty, different

fuzzy intervals were proposed depending on the available

process information. The more detailed the information is, the

narrower the fuzzy interval will be. The resulting uncertainty


intervals are depicted in Figure 4.1.3, in the form of relative errors

for the models of theoretical energy consumption, energy losses

and total energy consumption. The uncertainty intervals for the

total energy consumption models shown in Figure 4.1.3 are

derived through propagation of the respective values for the

theoretical energy consumption and energy losses. In order to

select the proper uncertainty interval for the models of total

energy consumption, Table 4.1.1 demonstrates the possible

combinations regarding process characteristics and available

information. For instance, if it is known that a process runs under

reflux conditions and there are accurate data for the duration of

the heating and distillation operations, then an estimation of the

uncertainty range for the prediction of total energy consumption

can be made according to case 3 of Table 4.1.1, that is a relative

error between 13% and 45% with equal possibility, considering

the core of the fuzzy interval.

1000 2000 3000 4000 5000 6000

1000

2000

3000

4000

5000

6000

Model predictions [kg steam/batch]

Observ

ed m

edia

n &

batc

h−

to−

batc

h v

ariabili

ty

[kg s

team

/batc

h]

14 15

174

18

Figure 4.1.2. Model predictions (documentation based approach) against

reference values (model based plant monitoring system) for the energy losses


per equipment-product pair in the first case study (dataset-1). The batch-to-

batch variability corresponds to the 2.5 and 97.5 percentiles of the observed

energy losses over several batches.

0 20 40 60 80 100 120 1400

0.5

1

0 20 40 60 80 100 120 1400

0.5

1

Po

ssib

ility

0 20 40 60 80 100 120 1400

0.5

1

Relative error

abcd=[3 20 61 89]

abcd=[3 13 45 88]

abcd=[6 29 84 100]

abcd=[5 17 66 97]

abcd=[1 14 45 82]

abcd=[1 10 32 82]

(i)

(ii)

(iii)

Figure 4.1.3. Uncertainty estimation in the form of fuzzy intervals for relative

errors of the documentation based approach for i) Theoretical energy consump-

tion, ii) Energy losses. iii) Total energy consumption. Solid and dashed lines

correspond to different levels of available process information (i.e., solid lines

correspond to higher relative errors when there is limited or no information about

reflux taking place during distillation, and for energy losses when there is limited

or no information about the duration of unit operations). The a, d values corre-

spond to the support and the b, c values to the core of the fuzzy intervals.


Table 4.1.1. Derived fuzzy intervals from the first case study for uncertainty representation in the models for theoretical

energy consumption (Etheo), energy losses (Eloss), and total energy consumption (Etot).

Process parameters Fuzzy intervals for absolute values of relative errors (%)

Distillation Operation time* Etheo Eloss Etot

Case-1 none known (1 10 32 82) (5 17 66 97) (3 13 45 88)

Case-2 none unknown (1 10 32 82) (6 29 84 100) (3 17 53 89)

Case-3 conditions known known (1 10 32 82) (5 17 66 97) (3 13 45 88)

Case-4 conditions known unknown (1 10 32 82) (6 29 84 100) (3 17 53 89)

Case-5 conditions unknown known (1 14 45 82) (5 17 66 97) (3 16 53 88)

Case-6 conditions unknown unknown (1 14 45 82) (6 29 84 100) (3 20 61 89)

* Excluding distillation time.


4.1.5 Total Energy Consumption

By applying these uncertainty intervals for the total steam

consumption in the case of the dataset-1, the model uncertainty

can be visualized along with the batch-to-batch variability, as

shown in Figure 4.1.4. The model performance with respect to

Figure 4.1.4 can be analyzed according to three levels of model

success. The first level corresponds to a full success of the model

prediction, when both intervals cross the diagonal line. The

second and third level of success correspond to a crossing of the

diagonal line because only of the batch-to-batch variability

interval (asymmetrical interval with respect to median point

estimation) or only by the model uncertainty range (symmetrical

interval with respect to the model point estimation), respectively.

As can be seen in Figure 4.1.4 and reported in detail in Table

4.2.1, the model performance is satisfactory both in success

terms described above and in terms of typical statistical indices.

In 12 out of 18 cases, the predictions lie within the batch-to-batch

variability ranges and at the same time the model uncertainty

intervals cross the diagonal line. In two more cases there is a

second and third level success. There are, however, three cases

of model inaccuracy. The deviation of point 10 is due to the

theoretical energy consumption as discussed in Figure 4.1.1,

while for points 15 and 18 the deviation arises from the energy

loss model inaccuracy as discussed in Figure 4.1.2. With respect

to point estimations (i.e., not considering the intervals of batch-to-

batch variability and the model uncertainty intervals), the mean

absolute relative error (MARE) of the total energy consumption

model is 27%, which is acceptable for a screening methodology,


while the different forms of coefficient of determination(Willmott.

et al., 2012) lie between 0.86 and 0.89. Hence, these statistical

parameters represent a further indication of the good prediction

capabilities of the documentation based energy modeling

approach. A full list of statistical indices for the model

performance is available in the appendix (Section C.1).

2000 4000 6000 8000 10000 12000 14000 16000 18000

2000

4000

6000

8000

10000

12000

14000

16000

18000

Model predictions with fuzzy intervals (core)[kg steam/batch]

Observ

ed m

edia

n &

batc

h−

to−

batc

h v

ariabili

ty

[kg s

team

/batc

h]

10

18

15

Figure 4.1.4. Model predictions (documentation based approach) against refer-

ence values (model based plant monitoring system) for the total energy con-

sumption per equipment-product pair in the first case study (dataset-1). The

batch-to-batch variability corresponds to the 2.5 and 97.5 percentiles of the ob-

served total energy consumption over several batches. The bold segments of

the fuzzy intervals correspond to the minimal core value (b). The simple seg-

ments of the fuzzy intervals correspond to the maximal core value (c).


4.2 Case Study II

4.2.1 Dataset

In this case the reference data (dataset-2) come from two smaller

production buildings. The first is a mono-product batch plant, and

the second is a multiproduct batch plant producing four different

products, three in batch mode and one in continuous mode. The

nominal volumes for the equipments in both plants range

between 6.5 to 12 m3. In both plants all equipments operating in

batch mode and consuming steam for heating were considered

for the validation. This implies a total of 20 equipment-product

pairs for which steam consumption data from several batches

have been collected, and the median, the 2.5th and 97.5th

percentiles were calculated as reference data. The data sources

of these two buildings come from energy monitoring tools, which

follow the same principle as in the first case study. Consequently,

the quality of the reference data is equal in both case studies.

For the multiproduct plant, it was convenient to additionally

perform a top-down approach on the basis of a multi-linear

regression analysis of the overall steam consumption and the

production mass of the three chemicals produced in batch mode

in the multiproduct building according to equation 4.2.1:

3322110 mmmE ⋅+⋅+⋅+= ββββ (4.2.1)

where E is the total steam consumption of the building minus the

steam consumed by solvent regeneration processes operated in


continuous mode, m1, m2, m3 are the production mass of the

three chemicals in a given time horizon, β0 represents the base

consumption of the multiproduct building, and β1, β2, β3 represent

the specific steam consumption per product mass. Besides the

infrastructure consumption and losses, the base consumption

includes the constant consumption corresponding to the product

produced in continuous mode. The data for this analysis

corresponds to a period of three years collected on a monthly

basis. Here, it is intended to compare the performance of the

proposed process documentation based approach with a

frequently used top-down approach in batch production for

allocating energy consumption to specific products and for

estimating the total consumption of the building.

4.2.2 Total Energy Consumption

The results of the documentation based approach for the

prediction of the total energy consumption in the second case

study (dataset-2) are presented in Figure 4.2.1. Again, the

agreement between reference and predicted values is

satisfactory in most of the cases. As in the first case study, the

considerable deviations (i.e., points 6 and 12 in Figure 4.2.1)

involve distillation processes under unknown reflux conditions.

Further discussion for all individual cases is available in the

appendix (Section C.3). Comparing the model performance in the

two case studies (Table 4.2.1), it can be inferred that the model

predictions are slightly better for the first case study. This is due

to the fact that data for unit operation time were in greater extent

available in the first case study, and as it has been shown from


sensitivity analysis the unit operation time is one of the most

influential parameters on the model results. Moreover, the batch-

to-batch variability ranges are much narrower in the second case

study since the reference values correspond to a period of two

months, compared to three years in the first case study. This has

an impact on the model success cases reported in Table 4.2.1,

the number of full successes being here lower than in the first

case study. On the other hand, the number of model success

considering only the model uncertainty intervals is significantly

higher, reaching the success levels of the first case study.

Furthermore, a MARE of 37% and coefficients of determination in

the range of 0.79 to 0.83 confirm the good prediction capabilities

of the documentation based energy modeling approach for fast

screening purposes in multipurpose batch plants.

Table 4.2.1. Statistical results for the validation of the total energy consumption

model.

Statistical

parameters

Case study 1

(dataset-1)

Case study 2

(dataset-2)

successes 12* 1** 1*** 7* 1** 6***

N 18 20

MARE 0.27 0.37

dr 0.86 0.83

q2 0.86 0.79

r2 0.89 0.80

* successes within batch-to-batch variability range and within uncertainty range

(fuzzy intervals).

** successes within batch-to-batch variability range.

*** successes within uncertainty range (fuzzy intervals).


0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000

7000

8000

Model predictions with fuzzy intervals (core)[kg steam/batch]

Observ

ed m

edia

n &

batc

h−

to−

batc

h v

ariabili

ty

[kg s

team

/batc

h]

6

12

2,4,8,16,20


ence values (model based plant monitoring system) for the total energy con-

sumption per equipment-product pair in the second case study (dataset-2). The

batch-to-batch variability corresponds to the 2.5 and 97.5 percentiles of the ob-

served total energy consumption over several batches. The bold segments of

the fuzzy intervals correspond to the minimal core value (b). The simple seg-

ments of the fuzzy intervals correspond to the maximal core value (c).

4.2.3 Top-down Energy Modeling

In the second case study, the performance of the documentation

based models has also been tested against a top-down modeling

approach and reference values on chemical product and

production building basis. The steam consumption per product

shown in Table 4.2.2 was modeled by means of bottom-up

calculations with a model-based EMT installed in the plant

(bottom-up reference), with the documentation based models

(bottom-up model predictions), and also extracted from the multi-


linear regression coefficients for the top-down predictions. The

production building base consumption was in all cases equal to

the constant parameter delivered by the regression analysis. As it

can be seen in Table 4.2.2, the documentation based predictions

are much closer to the reference values for all three products

compared to the top-down approach based on the multi-linear

regression coefficients. However, when comparing in Figure 4.2.2

the performance of these different approaches for the modeling of

the production building steam consumption per month during one

year period, the top-down approach predictions present a similar

performance to the bottom-up reference values, being both in

better agreement with the steam measurements than the

documentation based bottom-up models, which systematically

underestimate the total steam consumption of the building. This,

however, is due to the fact that many operations requiring steam

are not production dependent (e.g. heating of solvents for

equipment cleaning), and therefore not part of the standard

process description. Hence, they are not captured by the

documentation based approach.

On the other hand, the “black box” top-down approach allocates

these operations to the production processes trying to match the

overall steam consumption of the building. Although this may

result in an integral success of the top-down approach model

performance, it is not suitable for allocating energy consumption

to particular products, especially if the product mass variability

over time is not high (i.e., the multi-linear regression analysis

could infer parameters which do not reflect the real specific

energy consumption per product, as it is the case in Table 4.2.2).

The documentation based bottom-up approach captures much


better these trends, although it may result in deviations for the

energy consumption at the production building level because of

unavailable information about non-standardized, non-production

dependent unit operations.

Table 4.2.2. Comparison of the bottom-up and the top-down model predictions

against reference values of steam consumption for the production of three dif-

ferent products in the multiproduct building of case study 2.

Steam consumption [kg/ kg product]*

Product Bottom-up

reference values

Bottom-up

documentation

based approach

Top-down

approach

A 0.68 0.71 1.31

B 0.61 0.48 1.69

C 9.36 4.40 0.00

* These values do not include continuous equipment and base consumption.

0 Feb Apr Jun Aug Oct Dec

400

600

800

1000

1200

1400

1600

1800

2000

2200

Time [month]

Ste

am

consum

ption o

f th

e b

uild

ing [T

o]

building

bottom−up reference

bottom−up new model

top−down

Figure 4.2.2. Monthly total steam consumption of the multiproduct building in

case study 2. Three different model predictions of steam consumption (i.e., bot-


tom-up reference values from the model-based plant monitoring tool, estima-

tions from the bottom-up documentation based approach and a top-down ap-

proach) are compared against measurements of the total steam consumption of

the building.


4.3 Case Study III

The dataset used in this case study comes from two different

chemical companies in Switzerland, one of the companies being

the same as in case study 2. Thus, part of the reference data

come from energy monitoring tools, which follow the same

principle as in the first and second case studies. However, in this

case we only consider the median steam consumption over the

different batches. The remaining data comprise estimated values

by means of rigorous modeling using Aspen Plus®

(www.aspentech.com).

Unlike the first two case studies, here we do not focus on single

equipments, but on reaction steps corresponding to the system

boundary defined in Section 3.1, namely the steam consumption

per reaction for the production of one kilogram of product. Each

of these reaction steps can involve several equipments (see

Table 4.3.1). The reactions in the dataset include acylations,

alkylations, condensations, halogenations and hydrolysis.

Table 4.3.1. Number of equipments used in the reaction synthesis path of the

products in dataset-3 (see reaction boundary defined in Section 3.1).

Product in dataset-3 Number of equipments A 4 B 4 C 1 D 3 E 2 F 4 G 8 H 1 I 1 J 2


The results presented in Figure 4.3.1 show a very good

agreement between predicted and observed values, with most of

the model predictions falling within the batch-to-batch variability

ranges and near to the diagonal. Therefore this validation shows

that the documentation based models also predict well at a more

aggregated level, namely at the reaction step level. These results

indicate that estimated values by the documentation based

approach can serve as input data for the building of the statistical

models, which were introduced in Section 3 and which results are

presented in the next section.

0 2 4 6 8 100

2

4

6

8

10

Model predictions with fuzzy intervals (core) [kg steam/kg product]

Observ

ed v

alu

es [kg s

team

/kg p

roduct]


ence values (measurements and rigorous model estimations) for the total ener-

gy consumption per product in the third case study (dataset-3). The bold seg-

ments of the fuzzy intervals correspond to the minimal core value (b). The sim-

ple segments of the fuzzy intervals correspond to the maximal core value (c).

RESULTS CLASSIFICATION TREES 71

5 Results Classification Trees

5.1 Model Selection and Evaluation

For analyzing the performance of the classification trees we start

by considering dataset-1 (maximal 8 predictor variables, Table

3.5.1) as training set, priors based on class frequencies and three

output classes. The selection of priors did not show any consid-

erable influence on the model performance at any of the design

stages considered in this work (Appendix, Section D.1). The re-

sults of the cross validation for the five classification trees (S1 to

S5) are depicted in Figure 5.1.1 as an ROC plot. The ROC plots

presented in this paper are displayed on different axis scales,

where the specificity appears in higher resolution than the sensi-

tivity. This is important to have in mind, since a small change in

specificity implies a big shift on the x axis. As expected, an im-

provement from S1 to S5 for both training and test sets is ob-

served, since more process information is available for the mod-

els. Secondly the model performance for the training and test sets

is similar, with a difference of less than 11% and 6% for the sensi-

tivity and specificity respectively. This suggests that the models

are not overfitted.

Additionally, we assess the influence of having more predictor

variables and output classes on the model performance. For this

purpose we consider the following four different scenarios:

i. 8 candidate predictor variables (dataset-1) and 3 output classes (initial scenario)

ii. 8 candidate predictor variables (dataset-1) and 5 output


classes iii. 18 candidate predictor variables (dataset-2) and 3 output

classes iv. 18 candidate predictor variables (dataset-2) and 5 output

classes

0.08 0.1 0.12 0.14 0.16 0.180

0.2

0.4

0.6

0.8

1

S1S2

S3S4

S5

S1

S2

S3

S4S5

1− Specificity

Se

nsitiv

ity

cv−training

cv−test

random line

Figure 5.1.1. Average model performance for cross-validation training and test

sets for five stages of process design (S1 to S5), considering dataset-1

(maximal 8 predictor variables) and 3 output classes. The line denotes random

classifier performance. Models that fall into the right region defined by the

random line perform worse than random performance, and models that fall into

the left region perform better than random performance. The point in the top left

corner depicts perfect classification.

For the second scenario, we observe a similar trend to the initial

scenario (Figure 5.1.2) – when comparing model performance for

the training and test sets – but with generally lower sensitivity

values and an indication of overfitting for some design stages.


0.06 0.08 0.1 0.12 0.14 0.160

0.2

0.4

0.6

0.8

1

S1S2

S3

S4S5

S1S2

S3S4

S5

1− Specificity

Sensitiv

ity

cv−training

cv−test

random line

Figure 5.1.2. Average model performance for cross-validation training and test

sets for five stages of process design (S1 to S5), considering dataset-1

(maximal 8 predictor variables) and 5 output classes. The line denotes random

classifier performance. Models that fall into the right region defined by the

random line perform worse than random performance, and models that fall into

the left region perform better than random performance. The point in the top left

corner depicts perfect classification.

Considering now the results from the cross validation test for the

four different scenarios, we observe in Figure 5.1.3 that the

number of output classes is a more influential factor than the

addition of more predictor variables. The performance of the

models having three output classes is in most cases better,

especially in terms of sensitivity, than the models with five

classes, considering both dataset-1 and dataset-2. Being

sensitivity the true positives rate, this general trend with respect

to the number of classes was expected considering that the


probability of obtaining true positives as prediction outcomes

decreases with the number of classes.

Overall, the results of the preliminary analysis for the model

selection indicate that the case of three output classes and eight

predictor variables (dataset-1) presents the best performance and

highest interpretability due to lower model complexity. Moreover,

the additional resolution for the case of the five output classes is

also not well supported from the independent class analysis.

0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.220

0.2

0.4

0.6

0.8

1

S1S2

S3S4

S5

S1

S2S3

S4

S5

S1S2S3

S4

S5

S1

S2

S3

S4S5

1− Specificity

Sensitiv

ity

18 predictors/3 classes




random line

Figure 5.1.3. Average model performance for cross validation test set for five

stages of process design (S1 to S5) considering dataset-1 (8 candidate

predictor variables) and dataset-2 (18 candidate predictor variables) and 3 and 5

output classes. The line denotes random classifier performance. Models that fall

into the right region defined by the random line perform worse than random

performance, and models that fall into the left region perform better than random

performance. The point in the top left corner depicts perfect classification.

Up to this point we have considered the overall performance of


the classification trees. Figure 5.1.4 shows the performance of

the selected model per output class. It is interesting to notice that

while the low and high classes tend to form clusters, the middle

class is rather scattered on the plot. The low class presents high-

er sensitivity and slightly lower specificity than the high and mid-

dle classes. This can be explained considering that there are

more data points belonging to the low class than to the other

classes in a ratio of approximately 2 to 1. In general, when the

class sizes are not equal, the model favours the larger class in

terms of sensitivity and overall success rate or accuracy, but per-

forms less well regarding specificity. Following the low class, the

high class shows a better performance than the middle class.

Moreover, for the middle class we observe a performance im-

provement from S1 to S5 in terms of sensitivity, while the other

two classes improve in terms of specificity. Overall, these results

show that except for the middle class in S1, all other classes at

different stages of process design appear at the left side of the

ROC plot, indicating satisfactory model performance. On the con-

trary, the classification trees with five output classes (Figure

5.1.5), show a poor performance for the middle-low, middle, and

middle-high classes. These results also support the decision of

having three output classes instead of five. The sensitivity and

specificity values as well as the distances to the (0,1) point and

the random line for the tree output classes trees built from da-

taset-1 can be found in Table D.2.1 in the appendix.


0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

s1s2

s3

s4

s5

s1

s2

s3s4

s5

s1

s2

s3s4s5

1−Specificity

Sensitiv

ity

low

middle

high

random line

Figure 5.1.4. Model performance per class for cross validation test set for five

stages of process design (S1 to S5), considering dataset-1 (8 candidate

predictor variables) and 3 output classes. The line denotes random classifier

performance. Models that fall into the right region defined by the random line

perform worse than random performance, and models that fall into the left

region perform better than random performance. The point in the top left corner

depicts perfect classification.


0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

S1S2

S3S4

S5

S1

S2S3

S4

S5

S1

S2S3

S4

S5

S1S2

S3

S4

S5

S1

S2S3

S4

S5

1− Specificity

Sensitiv

ity

low

mid−low

mid

mid−high

high

random line

Figure 5.1.5. Model performance per class for cross-validation test set for five

stages of process design (S1 to S5), considering dataset-1 (maximal 8 predictor

variables) and 5 output classes. The line denotes random classifier

performance. Models that fall into the right region defined by the random line

perform worse than random performance, and models that fall into the left

region perform better than random performance. The point in the top left corner

depicts perfect classification.


5.2 Selection of Important Rules

The most important rules at each stage of process design are

presented in Table 5.2.1, one rule corresponding to a path in the

decision tree. For every output class the most sensitive rule was

selected as the most important one, since sensitivity was found to

be the most critical metric, especially for the middle class. To bet-

ter illustrate this procedure, Figure 5.2.1 shows the classification

tree developed for S4 with a total of seven paths corresponding

to seven rules. Three outputs are highlighted corresponding to

the three rules presented in Table 5.2.1. For instance, the path

leading to the highlighted high class output corresponds to rule-3

for S4 and can be stated as follows:

IF the reaction type is acylation OR alkylation OR complexation OR

condensation OR hydrolysis OR polymerization OR reduction, AND the

operation time is higher than 18 hours THEN the steam consumption is

high.

The performance of this model is presented in Figure 5.2.2 by

means of a resubstitution performance, where the training data is

presented on the x-axis and the predicted classes on the y-axis.

As it was previously shown in Figure 5.1.4, the S4 model is per-

forming very well for the low and high classes, and satisfactorily

for the middle class. We also see that the percentage of underes-

timations is lower than the percentage of overestimations. Con-

sidering these results, we can affirm that the S4 classification tree

can be used not only for descriptive purposes, but also for predic-

tions of steam consumption.


Table 5.2.1. Most important rules of the classification trees at the five stages of process design (S1 to S5).

Sta

ge

Ru

le

Re

actio

n

Me

ch

an

ism

Re

flu

x

Dis

tilla

tio

n

Tim

e

T m

ax

PM

I

Ste

am

dis

t

Cla

ss

S1 1 acylation (cyanur chloride) , azo-

coupling, diazotization, elimination,

halogenation, sulfonation

low

2 acylation, alkylation, complexation,

condensation, hydrolysis, polymerization,

reduction

HC,SN1,

SN2,SNAr

high

S2 1 acylation (cyanur chloride), azo-coupling,

diazotization, elimination, halogenation,

sulfonation

low



reduction

HC,SNAr no middle



yes high


reduction



sulfonation

low



reduction

HC,SN2,

SNAr

no <18 middle



reduction

>18 high



sulfonation

low



reduction

HC,SN2,

SNAr

no <18 middle



reduction

>18 high


S5 1 <80 <1.5 low

2 >80 0.5-1.5 middle

3 >1.5 high

In this table each row corresponds to one rule, each column starting from the third one to a predictor variable and the last

column to the output class. The grey areas indicate when a predictor variable is not present at the corresponding design

stage.

Considering the categorical predictor variables, reaction and mechanism, the logical rule operation for these predictors

corresponds to “OR”. The relation between the different predictors is given by the logical operator “AND”. For example, the

second rule of S1 can be formulated as follows:

IF the reaction type is equal to acylation OR alkylation OR complexation OR condensation OR hydrolysis OR polymerization OR

reduction, AND the mechanism is equal to HC OR SN1 OR SN2 OR SNAr THEN the steam consumption is high.

Reaction mechanisms are included only in cases where at least one of the reaction types can undergo through more than

one mechanism. In this way we consider the reaction mechanism as additional information to the reaction type. This choice

is consistent with the predictor importance depicted in Figure 5.2.3, which shows a higher relevance of the reaction type

compared to the mechanism at the five stages of process design.


time>18h

Tmax<93°C Tmax>93°C no distillation distillation

mechanism1** mechanism2**

reactions1* reactions2*

time<18h

PMI<4kg PMI>4kg

LOW

LOW

HIGH

MIDDLE HIGH

MIDDLELOW

Figure 5.2.1. Classification tree for the S4 design stage. The highlighted end nodes correspond to the most important rules

of S4 presented in Table 5.2.1. Rule 1 predicts low steam consumption, rule 2 predicts middle steam consumption, and rule

3 predicts high steam consumption. *Reactions1: acylation, alkylation, complexation, condensation, hydrolysis,

polymerization, reduction. Reactions2: acylation (cyanur chloride), azo-coupling, diazotization, elimination, halogenation,

sulfonation. ** Mechanism1: AN, AEN,SEAr. Mechanism2: HC, SN2, SNAr (see Table B.1.1.1 in the appendix).


0 1 3 160

low1

middle

3

high

16

Steam training dataset [kg/kg product]

Ste

am

mo

de

l cla

sse

s [

kg

/kg

pro

du

ct]

27%

95%

2%

16% 11.5%

57% 11.5%3%

77%

Figure 5.2.2. Model performance for the S4 tree in scatter plot of target values

(x-axis) versus predicted values (y-axis) (resubstitution performance)

considering dataset-1 (8 candidate predictor variables) and 3 output classes.

The data points lying inside the bold boxes on the diagonal axis represent the

data which actually belong to one class and were predicted within that class.

The points lying inside the boxes on the non diagonal bottom right area

represent underestimated values. The points lying inside the boxes on the non

diagonal top left area represent overestimated values

From Table 5.2.1, we can see that the reaction type appears in all

rules from S1 to S4, indicating a high importance of this predictor

variable. This hypothesis is confirmed by the predictor importance

plot depicted in Figure 5.2.3, where the reaction type presents the

highest importance from S1 to S4 among all attributes. The oper-

ation time, which appears in two rules in S3 and S4, suggests a

higher influence of this variable compared to other parameters.

This high influence of the time variable in S3 and S4 can also be

observed in Figure 5.2.3. On the other hand, the rules derived for

S5 follow a different pattern. The reaction type is not part of the


rules anymore, and the temperature, which was not appearing in

S3 and S4 is now included in two of the rules. The rules seem to

be dominated by the distillation steam consumption, which is not

surprising, since this is part of the target attribute, and is thus

highly correlated to it. These trends in the rules for S5 can be also

observed in the predictor importance plot in Figure 5.2.3. Summa-

rizing, we can affirm that the most sensitive rules, which were se-

lected to be the most important for the classification trees, include

the most important predictor variables.

reaction

mechanismreflu

x

distillatio

ntim

eTmax

PMI

steamDist

Pre

dic

tor

import

ance

S1

S2

S3

S4

S5

Figure 5.2.3. Predictor importance in classification trees at five stages of

process design (S1 to S5).

RESULTS PROBABILITY DENSITY FUNCTION MODELS 85

6 Results Probability Density Function Models

6.1 Model Development

Since the most important predictor variable for S1 to S4 has been

shown to be the reaction type, the decision of constructing PDF

models on this minimum process information is supported. In ad-

dition, the extracted rules served to further parameterize the PDF

models, where necessary. Table 6.1.1 shows the empirical medi-

an, minimum and maximum steam consumption values of the dif-

ferent datasets corresponding to reaction types (first column) and

the further parameterized subsets (second column). The fitted

PDF with the corresponding parameters, their median, first and

third quartiles, and 2.5th and 97.5th percentiles are also presented.

The assessment of the goodness of the fit is also given and fur-

ther discussed in Table E.1 in the appendix.


Table 6.1.1. Empirical statistics and probability density function (PDF) model results per reaction type. The values are given

in kilograms of steam consumption per kilogram of product.

Reaction type Paramet

erization Empirical values PDF

Model

parameters Fitted values

n median min max p1 p2 median 25th 75th 2.5th 97.5th

Acylation 33 1.6 0.0 9.3 gamma1 0.6 4.1 1.2 0.3 3.2 0.0 11.1

Time

<18h

21 0.9 0.0 6.0 gamma 0.5 3.8 0.7 0.14 2.3 0.0 9.1

Time

>18h

12 2.4 0.79 9.3 lognormal2 0.9 0.8 2.5 1.5 4.4 0.5 12.3

Acylation

(cyanur

chloride)

22 0.0 0.0 0.8 lognormal -4.1 2.9 0.0 0.0 0.1 0.0 4.9

Alkylation 33 2.5 0.0 11.8 gamma 0.6 5.2 1.7 0.5 4.2 0.0 14.4

no disti-

llation

12 1.0 0.0 3.4 gamma 0.4 2.3 0.3 0.1 1.2 0.0 5.1

disti-

llation

21 3.0 0.3 11.8 weibull3 4.9 1.5 3.8 2.1 6.1 0.4 11.7

Azo-coupling 25 0.1 0.0 5.3 gamma 0.1 6.6 0.0 0.0 0.2 0.0 6.4


Complexation 9 2.8 0.2 14.9 exponential4

0.23 3.1 1.3 6.1 0.1 16.3

Time

<18h

6 2.0 0.2 3.5 rayleigh5 1.6 1.9 1.2 2.6 0.4 4.3

Condensation 25 2.1 0.3 10.5 exponential 0.4 1.9 0.8 3.8 0.1 10.1

Tmax

<93°C

8 0.7 0.3 3.8 exponential 0.8 0.8 0.4 1.7 0.0 4.5

Tmax

>93°C

17 2.6 0.6 10.5 lognormal 1.0 0.8 2.7 1.6 4.5 0.6 11.7

Diazotization 26 0.0 0.0 0.2 exponential 18.4 0.0 0.0 0.1 0.0 0.2

Elimination 9 0.3 0.0 1.0 exponential 0.1 3.0 0.0 0.0 0.2 0.0 3.4

Halogenation 14 0.4 0.0 4.9 lognormal -0.9 1.5 0.4 0.2 1.1 0.0 6.8

Hydrolysis 9 0.8 0.0 10.4 gamma 0.3 8.3 0.4 0.0 2.2 0.0 14.2

Polymerization 18 3.0 1.2 15.9 lognormal 1.32 0.90 3.7 2.0 6.9 0.6 21.9

Time

<18h

8 1.7 1.2 3.0 lognormal 0.5 0.3 1.7 1.4 2.0 0.9 3.0

Time

>18h

10 7.7 2.8 15.9 uniform6 2.8 15.9 9.4 6.1 12.6 2.8 15.9


Reduction 14 3.6 0.1 15.8 exponential 0.2 3.1 1.3 6.2 0.1 16.6

Sulfonation 9 0.1 0.0 0.3 gamma 0.3 0.4 0.0 0.0 0.1 0.0 0.7

(1) 21

1

1

12 )(

1 p

x

p

pex

ppy

−

−

Γ= , (2)

22

21

2

)(ln

2 2

1 p

px

exp

y

−−

=π

, (3)

1

2

1 1

22

1

p

p

xp

ep

x

p

py

−−

= , (4)

xpepy 1

1−= , (5)

21

2

22

1

p

x

ep

xy

−

= ,

(6))(

1

12 ppy

−=


6.2 Model Evaluation per Reaction Type

The predictive capability of the PDF models by using the inter-

quartile ranges is depicted in Figure 6.2.1. The resubstitution per-

formance is in most cases similar among the different reaction

types (60% average of true positives) except for the polymeriza-

tion and elimination reactions which present a slightly poorer per-

formance (40% true positives), and the reduction reaction which

performs slightly better (70% true positives) than the rest. The

fact that the polymerization and elimination reactions are not pre-

dicted as well as the rest might be an indication that these two

reaction classes do not verify the hypothesis that steam con-

sumption can be predicted based only on the reaction type. In

general, the predictive capability of the PDF models is inferior to

the one of the classification trees with additional process related

predictor variables, but it can still provide useful information for an

interval estimation based on the interquartile ranges. More im-

portantly, the PDF models can provide a benchmark for labeling

chemical reaction types performed in industrial operations with

respect to their place in the distribution of the same reaction type

family. Furthermore, the PDF models allow for a more rigorous

uncertainty analysis compared to the interval estimations, by

sampling from the respective distributions.


0 2 4 6 8 10 12 14 16

*acyl,azo,dia,eli,sulfo 0

halogenation 0.4

hydrolysis 0.8

acylation 1.2

alkylation 1.7

condensation 1.9

complexation 3reduction 3.1

polymerization 3.7


Ste

am

mo

de

l m

ed

ian

[kg

/kg

pro

du

ct]

over

within

under

Figure 6.2.1. PDF model performance with target values (x-axis) versus

predicted values (y-axis) considering the interquartile ranges (resubstitution

performance). The data points colored in black fall within the model intervals.

The grey and the white colored points represent overestimated and

underestimated values respectively (see also Table 6.2.1). The line passing

through the points (0,4) and (0,4) represents perfect prediction.

*Acylation (cyanur chloride), azo-coupling, diazotization, elimination, sulfonation.

Table 6.2.1. Performance of the probability density function PDF models

considering the interquartile ranges (resubstitution validation)

Reaction within interval (%) underestimated (%) overestimated (%)

Acylation 58 27 15

Acylation

(cyanur chloride) 59 41 0

Alkylation 57 26 17

Azo-coupling 64 36 0

Complexation 56 22 22

Condensation 56 16 28

Diazotization 92 8 0

Elimination 33 67 0

Halogenation 54 15 31


Hydrolysis 56 22 22

Polymerization 39 28 33

Reduction 71 14 14

Sulfonation 56 44 0

6.3 Further Parameterization of the Models

In cases where further parameterization was performed for the

PDF models, the original dataset for a reaction type was parti-

tioned into two subsets. From the thirteen reaction models, five

were further parameterized. In all cases the partition results in

one lower and one higher interquartile interval. The lower inter-

quartile interval overlaps in most cases with the original interquar-

tile interval while decreasing its width, and the higher interquartile

interval only partially overlaps with the original interquartile inter-

val while maintaining the same width. Only for the polymerization

reaction no overlapping was observed. This is due to the gap of

values in the empirical distribution of this reaction group. After this

parameterization step, we observe that the PDF models for alkyl-

ation, condensation and polymerization maintain the same per-

centage of true positives with narrower interval predictions. Only

in the case of acylation reactions no improvement is observed

after further parameterization, since the number of true positives

decreases (Table 6.3.1). However this does not necessarily mean

that the model predictive capability deteriorates, since the corre-

sponding interval predictions are narrower and cannot be directly

compared to the parent PDF models of the same reaction type.

Overall these results support the increased resolution of the

models as a result of the further parameterization.

Theoretically, it should be possible to reach the same level of


model performance as for the classification trees of higher order

(e.g., at the S4 design stage) by continuing the parameterization

with further predictor variables for every chemical reaction type.

However, this could not be supported by the available amount of

data to obtain statistically significant results. Therefore, for predic-

tion purposes, we suggest the use of higher order classification

trees, assuming availability of the respective predictor variable

values. Nevertheless, when the input information is comparable

with the PDF models, as for instance in the cases of the S1 clas-

sification trees, a lower prediction performance compared to the

S4 classification tree is expected (Figure D.3.1 in the appendix),

which is much closer to the level of the PDF models.

Table 6.3.1. Performance of the probability density function PDF models

considering the interquartile ranges (resubstitution validation) after further

parameterization

Reaction within interval underestimated overestimated

Acylation 36% 33% 30%

Alkylation 54% 23% 23%

Complexation*

Condensation 56% 28% 16%

Polymerization 39% 28% 33%

* for the complexation reaction the resubstitution validation was not carried out,

since only the lower interval was determined. The fitting for the upper interval

was not satisfactory and thus not further considered.

APPLICATION OF THE STATISTICAL MODELS 93

7 Application of the Statistical Models

7.1 Case Study I

The classification trees and PDF models were applied to the addi-

tional case study dataset and the results are presented in Figure

7.1.1. Here the performance results are presented as stacked bar

charts divided into three sections. The first section on the bottom

represents the percentage of data which is predicted within the

model intervals. For the classification trees this is equal to the

sensitivity. The section in the middle represents the percentage of

values which are overestimated by the model, and the section on

the top, the percentage of data underestimated by the model.

From this perspective, the black lines indicate the percentage of

predicted values which are not underestimated by more than

30%, an error which is considered to be acceptable for shortcut

models in early design stages (Bumann et al., 2010, Turton R et

al., 1998).

On the top of this figure (a) we see the respective resubstitution

performance of the models (training set) and on the bottom (b)

the performance on the external case study dataset (not used for

training). In both cases we observe that the PDF models and the

S1 classification tree perform similarly within a difference range of

13%. The rest of the trends are also similar between (a) and (b),

although generally the performance of the models is approxi-

mately 10% inferior in the external data set. This can be also due

to the fact that not all steam consumption target values were de-

rived by the same modeling approach as the one used for the

training set. However, in both cases, more than 80% of the pre-


dictions were not underestimated by more than 30%. This is an

additional positive feature for the robustness of the model, in

terms of safeguarding the predictions from severe steam con-

sumption underestimation.

0

20

40

60

80

100

%

PDF S1 S2 S3 S4 S50

20

40

60

80

100

%

a)

b)

Figure 7.1.1. Average performance of the PDF models (interquartile prediction)

and classification trees (S1 to S5) for (a) resubstitution performance

(approximately 250 data points) and (b) additional industrial dataset (17 points).

The black area of the bars represents the percentage of cases which fall within

the model intervals, and the dark grey and the light grey areas the percentage of

overestimated and underestimated cases, respectively. The black lines show

the percentage of cases which are not underestimated by more than 30%.

Summarizing the results presented in this section, we suggest the

use of the PDF models especially for benchmarking and uncer-

tainty analysis. For prediction purposes the PDF models or the S1

trees should be used when the reaction type is the only available

information and a first approximate estimation of steam consump-


tion is targeted. Higher order classification trees (S4-S5) provide

satisfactory steam consumption estimations and serve as de-

scriptive models that explain which features define the level of

energy consumption (high, middle, low).

7.2 Case Study II

Here we apply the PDF models to a case study for the production

of the intermediate substance 4-(2-methoxyethyl)-phenol, which

can be produced from seven different synthesis routes (Figure

7.2.1). In a previous work a decision-making framework, which

considers environmental and economic proxy indicators for

screening of chemical batch process alternatives during early

phases of process design (Albrecht et al., 2010), was applied to

the same case study. Both methodologies allow a ranking of the

different synthesis routes.

In this example we show the procedure of estimating the steam

consumption of the different synthesis routes using the PDF

models and we compare the resulting ranking of the alternatives,

with the ranking given by the proxy indicators of (Albrecht et al.,

2010). Table 7.2.1 depicts the reaction types at every step for the

seven synthesis routes. From the thirty reactions, thirteen belong

exactly to reactions considered in the training dataset for the

model development (Figure B.1.1.1. in the appendix). Seven

reactions steps cannot be exactly match to any of the reactions in

Figure B.1.1.1, but belong to one of the reaction categories in the

training dataset (e.g. the O-Alkylation reaction with dimethyl

sulfate as reactant in step A-3). In this case in order to fill the data

gap the steam consumption is estimated considering the PDF


model for Alkylation. This is comparable to an extrapolation, since

this reaction with this reactant was not included in the training

dataset for the building of the models. Ten remaining reactions,

could not be assigned to any of the reactions included in the

training dataset (e.g. nitration in step A-1). A default value of 1.2

kg per kg of product, calculated as the average over the median

values from all PDF models, was considered in order to fill the

data gaps.

The steam consumption for a complete synthesis route can be

estimated by adding the median values derived from the PDF

models for every reaction step (see Table F.1.1 in the appendix).

The model values given in kilograms of steam per kilogram of

product, were multiplied by the corresponding reaction yield

values given in Table B.1.1.2 in the appendix, assuming

stoichiometric ratios (see Table F.1.2 in the appendix). As it can

be seen in Figure 7.2.2 and Figure 7.2.3, route E represents the

best alternative given by the PDF models as well as by the Mass

Loss Index (MLI) and the Energy Loss Index (ELI) proxy

indicators defined in the work of (Albrecht et al., 2010). The MLI is

defined in this case, as the sum of the mass ratios of all coupled

products and by products to intermediate or end product. Other

input materials into the system such as solvents, auxiliaries, etc.

are not considered in this definition of the MLI, since this

information is not available at earliest design stages. The ELI

proxy indicator is calculated on the basis of four parameters: the

concentration of water at the reactor outlet, the difference of the

boiling point temperatures between the product and the

substance which has the closest boiling point to the product, the

MLI values for each reaction step, and the reaction energy. All


these parameters are first scaled according to empirical criteria

and then weighted and aggregated to give the ELI value.

Comparing the rankings given by the PDF models and the ELI

indicator, we see that except for routes C and D the trend is the

same. Considering the MLIs, a similar ranking trend as given by

the PDF models is still observed, except for routes A and D.

Overall the ranking according to the ELI indicator presents a

higher similarity to the PDF model predictions than the MLIs. This

is consistent with the fact that an index based only on the

reaction mass yield does not necessarily correlate with energy

consumption. A fairly good correlation of a mass index, namely

the Process Mass Intensity (PMI) with an energy related indicator,

such as Global Warming Potential (GWP), has been shown in the

work of (Jimenez-Gonzalez et al., 2011). However, in this case

the mass index (PMI) includes the total mass of materials per

mass of product, for instance reactants, reagents, solvents used

for reaction and separation and catalysts, being this a more

robust, but also a more data intensive indicator than the MLI as

defined by (Albrecht et al., 2010). As it has been shown in

Section 3.5, the PMI is used as a predictor variable in

classification trees at the previously defined fourth and fifth

process design stages (S4 and S5) and not at the earliest stages

(S1 to S3), where not enough data is available. For the

classification tree (S4) the PMI was found to be an important

predictor variable (see Section 5.2), thus this result is consistent

with the work of (Jimenez-Gonzalez et al., 2011) mentioned

previously.


On the other hand, the ranking predicted by the Productivity Loss

Index (PLI) and by a composite indicator resulting from the

weighted sum of the ELI and the PLI, show a very similar trend

among each other and a different trend compared to the ranking

given by the PDF models and the ELI indicator. The PLI

considers number of reaction steps, cycle time, average product

concentration at the reactor outlet and average filling volume

(percentage of total vessel volume). Except for the number of

reaction steps, which is implicitly considered when the PDF

models are used for estimating steam consumption of a whole

synthesis route, the rest of the categories in the PLI are more

process and unit operation specific and contain less

physicochemical information compared to the ELI indicator. This

explains that the rankings given by the PDF models and the ELI

indicator follow similar trends among each other, and differentiate

from the PLI indicator ranking. In addition the PLI has a higher

weighting than the ELI on the composite proxy indicator. This

explains the similar ranking trend given by the PLI and the

composite proxy indicator.

Analogously to the point estimations, intervals of steam

consumption for every synthesis route were estimated

considering the first and third quartiles given by the PDF models.

As it is shown in Figure 7.2.5 most routes follow the same trend

considering the median values and the intervals, except route F,

which presents a slightly higher upper interval than the B route.

In order to evaluate the significance of the ranking results, a

Monte Carlo simulation was carried out to generate samples from

the PDF models corresponding to the reaction steps of the


synthesis routes, followed by an ANOVA test to analyze the

differences between the means of these samples. The data

sample for each synthesis route was obtained by adding the

sample values for each reaction step within the route. For the

reaction steps without a corresponding PDF model, a uniform

distribution was considered for the generation of the sample. The

parameters of the uniform distribution were assigned the

minimum and maximum values of 0 and 2.4 kg per kg of product

respectively. These values where derived considering the mean

value of the distribution to be the default value of 1.2 kg per kg of

product.’

In addition a boxplot diagram of the different reaction route

samples is shown in Figure 7.2.6. From visual inspection of the

boxplot, we see that we can distinguish two different groups of

synthesis routes, namely E, G, D, A with lower median values

and interval ranges, and F, B, C with higher median values and

interval ranges. The results of the ANOVA test presented in the

appendix (Section F.2) show that it is possible to further

discriminate among some routes within these two groups. While

route C is significantly different to B and F, B and F are not

significantly different among each other. Route D is not

significantly different from routes E and G, however routes E and

G are significantly different among them. Similarly, while route G

is not significantly different from routes A and D, routes A and D

are significantly different among each other.

The results depicted in this case study show the applicability of

the PDF models – considering median values or intervals – for a

fast ranking of different groups of alternative routes considering


energy consumption, when only the reaction synthesis routes are

known at early stages of process design. The PDF models

provide a similar ranking as by using a more complex indicator

such as the ELI, which requires more detailed chemical and

process information.


Figure 7.2.1. Overview of different reaction routes to produce 4-(2-methoxyethyl)-phenol, including the reaction step

numbers.


Table 7.2.1. . Reactions in the different synthesis routes of 4-(2-methoxyethyl)-phenol (presented in Figure 7.2.1*.

Route Reaction 1 Reaction 2 Reaction 3 Reaction 4 Reaction 5 Reaction 6 Reaction 7 Reaction 8

A na na alkylation reduction diazotization na

B na reduction na alkylation reduction diazotization na

C halogenation alkylation reduction na acylation reduction D halogenation na na reduction diazotization na

E acylation alkylation reduction

F na acylation na halogenation alkylation reduction diazotization na

G acylation halogenation acylation reduction

*The colored cells indicate reactions included in the model training dataset (Figure B.1.1.1. in the appendix). Non-colored

cells indicate reactions, which belong to one of the categories included in the training dataset, but which does not match to

any of the specific reaction types in Figure B.1.1.1. Na indicates reactions, which do not belong to any category in the

training dataset.


E G D A F B C0

5

10

15

Synthesis route

Ste

am

consum

ption [kg/k

g p

roduct]

Figure 7.2.2. Ranking of the different synthesis routes of 4-(2-methoxyethyl)-

phenol considering the steam consumption predictions by the PDF models.

E G D A F B C E G D A F B C0

5

10

15

Synthesis route

0

1

2

3

ELIMLI


phenol considering the MLI (y-axis on the left) and the ELI (y-axis on the right)

proxy indicators according to (Albrecht et al., 2010).


E G D A F B C E G D A F B C0

0.5

1

Synthesis route

0

0.05

0.1

PLI ELI + PLI(weighted sum)


phenol considering the PLI (y-axis on the left) proxy indicator and the weighted

sum of the ELI and PLI (y-axis on the right) indicators according to (Albrecht et

al., 2010).

E G D A F B C0

5

10

15

20

25

30

35

Synthesis route

Ste

am

consum

ption [kg/k

g p

roduct]


phenol considering the steam consumption predicted median values and

intervals by the PDF models


E G D A F B C

0

10

20

30

40

50

60

Synthesis route

Ste

am

consum

ption [kg/ kg p

roduct]

Figure 7.2.6. Boxplot of the samples corresponding to the different synthesis

routes of 4-(2-methoxyethyl)-phenol.

CONCLUSIONS AND OUTLOOK 107

8 Conclusions and Outlook

8.1 Practical Relevance and Applications

The focus of this thesis was the modeling of steam consumption

in chemical batch plants for screening purposes. Considering that

energy minimization is a key target for the chemical sector, and

that steam is the energy utility with the highest consumption and

saving potentials, although not well documented in production

documentation, we propose two main types of models of steam

consumption for different levels of data availability.

The first modeling approach is based on standard process

documentation, thermodynamic principles, rules of thumb, default

model parameters and uncertainty values to deal with severe

gaps of information. For validating this new methodology, three

case studies were carried out in multipurpose batch plants in

Switzerland. For the first two case studies the steam consumption

was modeled at the unit operation level according to the new

approach, and the results were aggregated to the equipment

level following a bottom-up procedure. The results were validated

against reference data coming from model based energy

monitoring tools installed in the plants acquiring real time process

data with high resolution (i.e., 1-minute interval). The validation

results showed generally a good agreement between reference

and predicted values and a good capability of the uncertainty

intervals to capture the batch-to-batch variability of steam

consumption. In the third case study the steam consumption

modeled at the unit operation level was aggregated to the level of

the reaction step plus work-up processes. Again even in this


case, where the level of aggregation is higher, the validation

results showed a good agreement between reference and

predicted values including the uncertainty intervals.

Therefore this approach can be used for fast screening, allocation

and monitoring of steam consumption in multipurpose batch

plants based on a static yet frequently updated information

source such as the SOP documentation with limited modeling

effort. From this perspective, it can also be used for identification

of the energy saving potential that is by setting energy

consumption targets including an estimation of the batch-to-batch

variability. To this end, this approach lies between “black-box”

top-down approaches correlating energy consumption with

production portfolio and product amounts, and detailed bottom-up

approaches based on process parameters retrieved in high

resolution time intervals resulting in more accurate yet time-

consuming models regarding their development.

The second type of shortcut models of steam consumption pro-

posed in this work are generic intervals based on statistical anal-

ysis of estimated values by the documentation approach obtained

from real production data. The statistical analysis included fitting

of probability density functions (PDFs) and classification trees to

the available data. These models can be used at different levels

of process design, the minimal required information being the re-

action type. The cross-validation results of the classification trees

show that overfitting is avoided and that there is a significant im-

provement in the prediction capability from the earliest design

stage where only the reaction type and mechanism are known, to

the latest design level where the steam consumption during distil-


lation processes is known. The resubstitution performance of the

PDF models indicates that for most reaction types, except for

polymerization and elimination, the interquartile ranges can pro-

vide satisfactory interval estimations when the reaction type is the

only available process information. Further parameterization of

the probability density functions considering additional process

information increases the model resolution. Additionally, the PDF

and the classification trees generalization capability was validated

in a case study. It was shown that, in average, more than 80% of

the predictions were not underestimated by more than 30%, be-

ing this a satisfactory performance for shortcut models in early

design stages. These models, especially the higher order classifi-

cation trees represent a potentially useful tool for estimating

steam consumption of production processes, when limited pro-

cess information is available or when overwhelming processes

have to be screened in short time. Even though the PDF models

also allow reasonable predictions of steam consumption, their

most interesting potential applications will be for providing a

benchmark framework for labelling chemical reaction types and

rigorous uncertainty analysis.

The two modeling approaches presented in this work are shortcut

models of steam consumption for different levels of process de-

tail. While the documentation based approach involves a more

rigorous modeling procedure delivering a deterministic estimated

value with an uncertainty range, the use of the statistical models

requires less input information and time effort, but results in a ge-

neric interval instead of a deterministic value. On the other hand

the statistical models serve as descriptive and explanatory tools,

besides their predictive capabilities. As it is shown in Figure 8.1.1,


depending on the application target one model might be more

convenient than the other, meaning that a compromise between

modeling time and accuracy has to be done. Summarizing we

can say that both type of models developed in this thesis are es-

pecially suitable for applications in the fields of process design,

Life Cycle Assessment (LCA) and benchmarking.

Figure 8.1.1. Decision scheme for the selection of the most suitable modeling

approach to steam consumption.


8.2 Outlook

8.2.1 Extension of the Modeling Approaches to other Process Parameters

Although the documentation based models of this study were

developed and tested for steam consumption, the extension of

this approach to other energy utilities, such as cooling water,

brine and electricity, should be straightforward as a concept,

requiring of course additional unit operation related data (e.g.,

pumping and stirring costs, condensation duties, etc.) and the

respective equations and standard parameters for the

consumption of these additional energy utilities. In this way, a

more complete energy related life cycle inventory can be

estimated for the different products of multipurpose batch plants

facilitating a fast and efficient cradle-to-gate life cycle analysis,

assuming that the production related material flows are well

documented, which is a typical case in chemical batch industry.

The same can be said for the extension of the statistical models

to other energy utilities and/or production parameters. Provided

that data of other energy utilities consumption or emissions are

available – as measurements or as estimated values (e.g.

documentation based approach) – classification trees and

probability density functions can be fitted to these data and

further selected and evaluated using the same frameworks as

proposed in this work.


8.2.2 Optimization Problem for Selection of Classification Trees

A more exhaustive model selection procedure for the

classification trees would include a systematic search of the best

set of alternatives, considering structural settings or pre-treatment

of the training dataset, and algorithmic settings.

The first level of model selection, which implies the pre-treatment

of the training dataset, includes the choice of the most suitable

predictor variables and the discretization of the target attribute

(number of intervals and interval width). In this work the data pre-

treatment was done by generating a limited number of scenarios

and assessing the model performance (see Section 3). The

second level of model selection considering algorithmic and

calculation settings include the attribute test condition to split the

dataset into smaller subsets and a measure of goodness of split,

the choice of priors, and the stopping condition to terminate the

tree-growing process. In addition to these settings, the effect of

the number of folds or partitions of the data for the cross-

validation – pruning procedure can be investigated. A rigorous

approach to handle all these structural and algorithmic

parameters in a systematic way would require the formulation of

an optimization problem.

Besides the optimization for model selection, more powerful

techniques such as random forests and other data mining

techniques (e.g., support vector machine techniques (I. Witten,

2005) can be used for building of classification models, provided

that there is enough data.

NOMENCLATURE 113

Nomenclature

Symbols

A Surface area m2

C Reflux constant kJ/min cp Heat capacity of the mixture kJ/(kg K) cpi Heat capacity of the substance kJ/(kg K) cpeq Heat capacity of the equipment kJ/(kg K) Etheo Theoretical energy consumption kJ Eloss Energy losses kJ Hs Enthalpy of steam kJ/kg K Loss coefficient kJ/(min K) m Mass of total reaction mixture kg meq Mass of the equipment kg mi Mass of substance-i kg T1 Initial temperature of reaction mixture °C T2 Final temperature of reaction mixture °C Tam Ambient temperature °C Tboil Boiling point °C Td Distillation temperature °C Th Process temperature kept constant °C Ti Temperature substance-i °C Ts Saturation temperature of steam °C t Heating time minute td Distillation time minute th Holding time minute U Heat transfer coefficient W/(m

2 K)

rH∆ Enthalpy of reaction kJ/kg

iHv∆ Enthalpy of vaporization kJ/kg

Indexes

am ambient boil boiling d distillation dist distillation eq equipment h hold temperature constant loss overall energy loss


max maximum mean mean r reaction s steam (Hs, Ts) or solvent (PMIs) theo theoretical tot total w water 1 initial (temperature) 2 final (temperature)

Abbreviations

AE Electrophilic addition AN Nucleophilic addition AEN Nucleophilic addition elimination CART Classification and Regression Trees algorithm CED Cumulative Energy Demand DIN Deutsches Institut für Normung (German Institute for Standardi-

zation) dr Refined index of agreement E elimination ELI Energy Loss Index EMT Energy Monitoring Tool FN False negatives FP False positives HC Heterogeneous catalysis LCA Life Cycle Assessment LCIA Life Cycle Impact Assessment MARE Mean Absolute Relative Error MLE Maximum Likelihood Estimation MLI Mass Loss Index N Number of data points Na Non applicable NV Nominal Volume PLI Productivity Loss Index PDF Probability Density Function PMI Process Mass Intensity PMIs Solvent Mass Intensity PMIw Water Mass Intensity q

2 Coefficient of determination

r2 Square of the correlation coefficient

Rad Radical mechanism

NOMENCLATURE 115

RAD Risk Analysis Documents ROC Receiver Operating Characteristic RME Reaction Mass Efficiency SEAr Electrophilic aromatic substitution SNAr Nucleophilic aromatic substitution SN1 Nucleophilic substitution 1 SN2 Nucleophilic substitution 2 SOP Standard Operation Procedures STEM Enamel-coated Steel STNR Stainless Steel S1 First level of process design S2 Second level of process design S3 Third level of process design S4 Fourth level of process design S5 Fifth level of process design T Temperature Tmax Maximal operation temperature Tmean Mean operation temperature TN True negatives TP True positives UO Unit Operation

Glossary

Acid base reac-tion

Indicates presence or absence of acid-base reactions (yes/ no). Acid-base processes correspond to neutralization and precipitation work-up processes (e.g. previous to mechanical separation processes)

Charge Heating of the new mass filled into the vessel to the same temperature (above 20°C) as the rest of the reaction mixture inside the vessel.

Core Core of a fuzzy set

Crystallization indicates presence or absence of crystallization processes (yes/ no)

Distillation Indicates presence or absence of distillation processes during the reaction work-up. It refers to simple evaporation or distillation under reflux conditions (yes/ no)

Evaporation Simple evaporation. It is always assumed if no reflux conditions are mentioned.

Equipment It refers to reactors, storage tanks, decanters, etc. Evaporation (classification trees)

Indicates presence or absence of evaporation processes (yes/ no). Evaporation refers to simple evaporation occurring during the reaction synthesis or any work-up step


Heat Heating of the total mass inside the vessel to a final temperature above 20°C.

Hold Keep the process temperature constant. Last reaction Indicates if the considered reaction is the last one of the

synthesis route (yes/no) Mechanical Indicates presence or absence of mechanical processes

(yes/ no). Mechanical processes include filtration, centrifugation and washing work-up processes

Mechanism Reaction mechanism defined according to Table B.1.1.1 Miscellaneous Indicates presence or absence of miscellaneous processes

(yes/ no). Miscellaneous, are work-up processes which cannot be classified in any of the already mentioned categories (e.g. dilution of the reaction mixture and stirring at high temperature)

Reaction Energy produced or consumed due to exothermic or endothermic chemical reactions.

Reaction type Reaction type defined according to Figure B.1.1.1 Reflux (classifi-cation trees)

Indicates presence or absence of reflux conditions during the reaction synthesis or during the reaction work-up (yes/ no)

Reflux Distillation under reflux conditions, with C being a constant fitted to measurement data of steam consumption of recovery of butanol under strong reflux conditions.

Steamdist Steam consumption during distillation processes Support Support of a fuzzy set Time Sum over time in hours required for heating of the reaction

mixture, solvent evaporation, keeping the temperature constant above the atmospheric temperature under reflux conditions or not, during the reaction synthesis and work-up processes within the defined boundary system

Vessel See equipment.

APPENDIX 117

Appendix

A Supporting Information to Chapter 2


A.1 Uncertainty as Simple and Fuzzy Intervals

In contrast to classical sets where for each object there are only

two possibilities, namely belonging to the set or not, a fuzzy set is

a set of objects without clear boundaries, meaning that it can

contain elements with a partial membership. If X is the universe of

all elements in consideration and A is a subset of X, each

element x Є X is associated with a membership value to the

subset A. This degree of membership of elements in a fuzzy set

is expressed by real numbers in the unit interval [0,1], that is by a

membership function µA(x):

[ ]{ }1 0, )( ,);(,( ∈∈= xXxxxA AA µµ (a.1.1)

The closer µA(x) is to 1, the more x is considered to belong to A.

Therefore, fuzzy sets are suitable for expressing gradual

transitions from membership to non-membership. Fuzzy intervals

are fuzzy sets where the membership function usually consists of

an increasing and decreasing part, and possibly flat parts. Among

the different distributions which can be used to assess

membership functions, triangular and trapezoidal functions are

often selected due to their simplicity. In this work, we propose the

use of trapezoidal fuzzy intervals (Figure A.1.1) with a

membership function given by equation (a.1.2):

APPENDIX 119

Figure A.1.1. Trapezoidal fuzzy interval.

( )

≤

≤≤−

−

≤≤

≤≤−

−

≤

=

xd

dxccd

xd

cxb

bxaab

ax

ax

dcbaxA

,0

,

,1

,

,0

,,,,µ (a.1.2)

This membership function can be interpreted as a possibility

distribution function, which is the degree of plausibility between

zero and one of a particular interval (Zadeh, 1999).

Consequently, a fuzzy variable is associated with a possibility

distribution in the same manner as a random variable is

associated with a probability distribution. The interval between a

and d, which is called the support, covers all values that are

plausible or possible, whereas the range from b to c is called the

core and covers the most plausible values of the fuzzy interval.


The fuzzy approach for the expression of model uncertainty can

be used in different ways. The trapezoidal membership function

can provide information about the uncertainty distribution, namely

central tendency and skewness, but it can also lead to a simple

interval approach defined by the core and the support.

APPENDIX 121

B Supporting Information to Chapter 3


B.1 Classification of Chemical Reactions

B.1.1 Reaction Types Included in the Training Dataset

Notation used for the list of reactions in Figure B.1.1.1

• Unless specified in observations, R symbolizes hydrogen,

alkyl chains, aromatic ring(s), or any functional group as

substituent.

• R’, R’’, R’’’, etc are used to indicate the presence of

different substituents.

• Unless specified in observations, X symbolizes a halogen

atom.

• Catalysts, solvents, auxiliaries and reaction conditions are

not specified.

• A definition of the reaction mechanisms are found in Table

B.1.1.1.

APPENDIX 123

APPENDIX 125

APPENDIX 127

APPENDIX 129

APPENDIX 131

Figure B.1.1.1. List of reaction types included in the training dataset.


Table B.1.1.1. Reaction mechanisms corresponding to the reaction types

presented in Figure B.1.1.1.

Abbreviation Mechanism Observation

AE electrophilic addition AN nucleophilic addition AEN nucleophilic addition

elimination

E elimination HC heterogeneous catalysis This is not a chemical

mechanism, but a way of grouping together reactions that involve heterogeneous catalysis and complex reaction mechanisms, e.g. reductions with hydrogen

SEAr electrophilic aromatic substitution

SNAr nucleophilic aromatic substitution

SN1 nucleophilic substitution 1 SN2 nucleophilic substitution 2 Rad radical mechanism

Table B.1.1.2. Reaction yield descriptive statistics corresponding to the training

dataset for the statistical models.

Reaction type median minimum maximum

Acylation 88% 42% 96% Acylation (cyanur chloride) 90% 71% 95% Alkylation 85% 60% 100% Azo-coupling 90% 73% 97% Complexation 90% 85% 90% Condensation 79% 55% 95% Diazotization 90% 73% 97% Elimination 90% 71% 90% Halogenation 91% 78% 97% Hydrolysis 89% 66% 97% Reduction 81% 40% 95% Sulfonation 90% 60% 97% Polymerization na na na

APPENDIX 133

Table B.1.1.3. Process parameter descriptive statistics corresponding to the training dataset for the statistical models.

Reaction type Time [h] Tmax [°C] Tmean [°C] PMI PMIs PMIw

mean

min

max

mean

min

max

mean

min

max

mean

min

max

mean

min

max

mean

min

max

Acylation 14 0 42 87 20 185 51 16 94 10.4 1.2 54.7 4.6 0.0 34.9 2.9 0.0 44.2

Acylation* 1 0 9 40 17 70 25 8 56 9.6 4.2 28.4 0.0 0.0 0.0 5.2 0.0 21.8

Alkylation 17 0 42 95 0 185 52 0 107 8.4 1.1 42.3 3.7 0.0 34.6 1.8 0.0 9.1

Azo-coupling 13 1 40 44 0 130 25 0 47 13.9 0.5 46.6 0.0 0.0 0.0 10.2 0.0 36.2

Complexation 13 1 35 100 75 150 69 58 88 16.3 3.3 64.9 0.0 0.0 0.0 11.3 1.1 52.6

Condensation 3 0 16 101 35 170 62 25 107 9.6 1.2 32.0 3.6 0.0 9.2 2.5 0.0 19.5

Diazotization 3 0 15 37 20 55 22 14 28 10.0 3.3 44.8 0.0 0.0 0.0 6.3 0.0 28.9

Elimination 0 0 2 34 0 70 22 0 50 11.8 1.1 22.0 0.0 0.0 0.0 4.7 0.0 19.7

Halogenation 15 2 46 68 20 103 48 12 89 6.3 1.3 13.4 2.7 0.0 10.8 0.8 0.0 9.1

Hydrolysis 9 2 24 75 25 102 47 14 80 16.9 3.0 58.8 2.8 0.0 10.6 9.5 0.0 42.7

Polymerization 32 7 84 89 72 102 64 47 85 4.3 1.9 6.5 1.5 0.1 3.4 1.6 0.0 3.9

Reduction 14 0 29 74 35 105 36 20 49 15.4 1.1 43.8 8.2 0.0 39.6 3.6 0.0 23.1

Sulfonation 11 3 18 59 23 120 40 20 82 6.0 2.5 18.9 0.0 0.0 0.2 1.3 0.0 11.5

* cyanur chloride.


B.1.2 One-way Anova

Acylation Reactions

Table B.1.2.1. Descriptive statistics for the dependent variable steam

consumption and the grouping variable acylation reaction type. The values are

given in kg of steam per kg of product

Reaction Mean Standard deviation

Number of points

C-Acylation* 4.94 0.91 4 N-Acylation 2.79 2.48 23 N-Acylation (cyanur chloride)

0.18 0.26 22

O-Acylation 1.36 1.34 10 Total 1.72 2.19 59

* C-Acylation reactions were not included in the training dataset since they were

significantly different to the rest of the acylation reactions and the total number

of points (4) was too low to perform statistical analysis on this group (see

multiple comparisons in Table B.1.2.5).

Table B.1.2.2. Test of homogeneity of variances

Levene statistic degrees of freedom 1

degrees of freedom 2

Sig.*

8.76 3 55 .00

* Since the significance value is less than 0.05 we can say that the variances of

the different acylation reaction sub-groups are different. Therefore, the

assumption of homogeneity of variances has been violated.

Table B.1.2.3. One-way anova test results for the acylation reactions.

Source of variation

Sum of squares

degrees of freedom

Mean square

F Sig.*

Between Groups

121.01 3 40.34 14.23 .00

Within Groups

155.96 55 2.84

APPENDIX 135

Total 276.97 58

* Since the assumption of homogeneity of variances has been violated, we also

look at the Brown-Forsythe and Welch alternative F-ratios, which have been

derived to be robust in this cases (Field, 2009).

Table B.1.2.4. Robust test of equality of means.

Statistic* degrees of freedom 1

degrees of freedom 2**

Sig.***

Welch 40.74 3 10.51 .00 Brown-Forsythe 19.92 3 33.82 .00

* Asymptotically F distributed. ** Adjusted residual degrees of freedom. *** Both

test statistics are highly significant, thus we can say that there is a significant

difference among the different acylation reaction types. Therefore we proceed

with a multiple comparison to compare pairwise all different combinations of

groups.

Table B.1.2.5. Multiple comparisons using the Games-Howell procedure

(Jaccard et al., 1984)*.

Reaction (I) Reaction (J) Mean diffe-rence (I-J)

Stan-dard error

Sig.** CI 95% Lower bound

CI 95% Upper bound

C-Acylation N-Acylation 2.15* 0.69 0.04 0.13 4.18

N-Acylation (cyanur chloride)

4.76* 0.46 0.01 2.59 6.93

O-Acylation 3.57* 0.62 0.00 1.60 5.55

N-Acylation C-Acylation -2.15* 0.69 0.04 -4.18 -0.13


2.61* 0.52 0.00 1.16 4.05

O-Acylation 1.42 0.67 0.17 -0.40 3.24



C-Acylation -4.76* 0.46 0.01 -6.93 -2.59

N-Acylation -2.61* 0.52 0.00 -4.05 -1.16

O-Acylation -1.18 0.43 0.08 -2.51 0.14

O-Acylation C-Acylation -3.57* 0.62 0.00 -5.55 -1.60

N-Acylation -1.42 0.67 0.17 -3.24 0.40


1.18 0.43 0.08 -0.14 2.51

* This procedure is recommended in cases when there is a doubt that the

population variances are equal (see Table B.1.2.2) (Field, 2009).

** The underlined values correspond to significance levels of less than 0.05,

thus they indicate which reaction pair are significantly different between each

other.

Alkylation Reactions

Table B.1.2.6. Descriptive statistics for the dependent variable steam

consumption and the grouping variable alkylation reaction type. The values are

given in kg of steam per kg of product


N

C-Alkylation 0.83 1.22 7 N-Alkylation 3.48 2.73 18 O-Alkylation 4.01 3.44 17 S-Alkylation 2.51 1.13 3 Total 3.12 2.99 35

Table B.1.2.7. Test of homogeneity of variances



Sig.*

APPENDIX 137

2.32 3 31 .095

* Since the significance value is more than 0.05 we can say that the variances of

the different acylation reaction sub-groups are NOT different. Therefore, the

assumption of homogeneity of variances has not been violated.

Table B.1.2.8. One-way anova test results for the alkylation reactions.

Source of variation

Sum of squares

degrees of freedom

Mean square

F Sig.

Between Groups

52.24 3 17.41 2.14 0.12

Within Groups

252.70 31 8.15

Total 304.94 34

* Since the observed significance value is more than .05 we can say that there

is NOT a significant difference among the different alkylation reaction types.

Symbols and abbreviations

CI Confidence interval Degrees of freedom 1

Number of different groups to which the sampled cases belong minus one


Total number of cases in all groups minus the number of different groups to which the sampled cases belong

F Quantile of the F-test distribution N Number of data points Sig Level of significance


B.2 Classification Tree

B.2.1 Predictor Importance

The following formulas give a formal definition of predictor im-

portance

N

tR

I

N

t

i

i

∑=

∆

= 1

)(

(b.2.1.1)

)()()()( RL tRtRtRtR −−=∆ (b.2.1.2)

)(gdi)()( ttPtR ⋅= (b.2.1.3)

∑−=

t

tP )(1gdi(t) 2 (b.2.1.4)

totaln

tntP

)()( = (b.2.1.5)

where Ii is the impurity of predictor i, t is the node where predictor

i is tested, N is the total number of nodes where predictor i is

tested, R(t) is the risk of the parent node, R(tL) is the risk of the

child node on the left, R(tR) is the risk of the child node on the

right, gdi(t) is the Gini index at node t, P(t) is the node probability,

n(t) is the proportion of observations from the original data that

satisfy the conditions for the node and ntotal is the total number of

observations from the original data.

APPENDIX 139

B.3 Probability Density Function Models

B.3.1 Maximum Likelihood Estimation

There are different methods of estimating population parameters,

such as the method of moments, maximum likelihood, least-

squares and Bayes estimators. The maximum likelihood (MLE)

method is the most common statistical method of parameter es-

timation, resulting in statistically efficient solutions with parameter

values having minimum variance.

It finds the model parameters that maximize the likelihood func-

tion, namely the parameters corresponding to the probability den-

sity function (PDF) that makes the observed data the most likely

to have happened. Whereas the PDF is a function of the data

given a particular set of parameter values (Figure B.3.1.1, top),

the likelihood function is a function of the parameter given a par-

ticular set of observed data defined in the parameter scale. The

likelihood of multiple observations is defined as the product of the

likelihoods of the individual observations in equation b.3.1.1 be-

low, and accordingly the log-likelihood (presented as negative

log-likelihood in Figure B.3.1.1, bottom) as the sum of the likeli-

hoods of the individual observations in equation b.3.1.2.

In general numerical algorithms optimize the log-likelihood

function instead of the likelihood function, in order to avoid very

small numbers which could exceed computational precision. In

addition the MLE algorithm implemented in MATLAB1 for

convenience minimizes the negative log-likelihood function, which

is equivalent to finding the maximum likelihood estimates. In the

example of Figure B.3.1.1, the minimum negative log-likelihood is


found at p1=0.2=1/µ, with a mean value of µ=5. Parameter p1

defines then the PDF shown on top of Figure B.3.1.1.

1 2 3 4 5 6 7 8 9

2500

3000

3500

4000

4500

5000

parameter 1/p1

Ne

ga

tive

Lo

g−

like

liho

od

0 5 10 15 20 25 30 35 40 450

0.05

0.1

0.15

0.2

data x

Pro

ba

bili

ty d

en

sity

mean or expected value=1/p1

negative log−likelihood of 1/p1=5

Figure B.3.1.1. Exponential probability density function xpx epf 1

1−= with

parameter p1 (top), joint negative Log-likelihood of the parameters over an independent random sample X (bottom).

);()( 11 pxfpL iXi

n ∏= (b.3.1.1)

∑=

i

iXn pxfpL );(log)(log 11 (b.3.1.2)

1 Statistics Toolbox

TM.

APPENDIX 141

B.3.2 Goodness of Fit

B.3.2.1 Conventional Test Statistics

Tests of goodness of fit are used to assess whether or not a

sample of measurements from a random variable can be

represented by a selected theoretical probability density function.

The most commonly used tests are the Chi-Square, the

Kolmogorov-Smirnoff and the Anderson-Darling tests. They

provide a probability that random data generated from the fitted

distribution would have produced a goodness-of-fit statistic value

as low as that calculated for the observed data (Ayyub and

McCuen, 1997). The best fit among different candidate

distributions is reflected by the lowest value of a given test

statistic.

Chi-square Statistic

The Chi-Square statistic χ2 compares the histogram of the

observed data with the expected histogram obtained from the

fitted distribution, and is calculated as follows,

{ }∑

=

−=

N

iiE

iEiO

1

22

)(

)()(χ (b.3.2.1)

Where,

O(i)= number of observations in bin i E(i)=expected number of observations in bin i from the fitted distribution N=number of classes in the histogram


Kolmogorov-Smirnoff Statistic

The Kolmogorov-Smirnoff statistic Dn is based on the maximum

vertical distance between the fitted cumulative distribution

function and the empirical cumulative distribution.

[ ])()(max xFxFD nn −= (b.3.2.2)

Where,

Dn is the Kolmogorov-Smirnoff distance n= total number of data points F(x)=fitted distribution function Fn(x)= i/n i=cumulative rank of data point

Anderson-Darling Statistic

The Anderson-Darling-statistic is a more elaborated version of the

Kolmogorov-Smirnoff statistic with an improved performance on

fitting the tails of a distribution.

∫+∞

∞−

Ψ−= dxxfxxFxFA nn )()()()(22 (b.3.2.3)

{ })(1)()(

xFxF

nx

−=Ψ (b.3.2.4)

Where,

n=number of data points F(x) =fitted distribution function f(x)=density function of fitted distribution Fn(x)= i/n i =cumulative rank of data point

APPENDIX 143

Despite the fact that these test statistics are omnipresent in

modeling literature, they suffer some important limitations. The

Chi-Square test requires a very large number of observations for

providing accurate results, and suffers from the dependency on

the number of histogram classes used with the associated

uncertainty in making a correct choice. The Kolmogorov-Smirnoff

and the Anderson-Darling tests assume that the hypothesized

distribution is known a priori which is seldomly met in reality,

where the distribution parameters are often estimated from the

observed data. In addition, none of these statistics accounts for

model complexity penalizing for the number of parameters used.

Thus these test statistics do not prevent overfitting.

B.3.2.2 Akaike Information Criterion

The Akaike Information Criterion (AIC) is an approach used for

selecting a model from a set of models. It is based on information

theory, which derives from Boltzmann’s concept of entropy. The

selected model minimizes the information lost when a model is

used to approximate reality (distance between reality and a

model). Akaike proposed a formal relationship between

information theory and likelihood theory (equation b.3.2.5), where

the maximized log-likelihood accounts for the accuracy of the

parameter estimates, and K (number of free parameters

estimated within the model) accounts for model complexity or

compensation for the bias (penalty component), thus helping to

avoid overfitting. The model with minimum AIC value is selected

as the best model to fit the data.

KLAIC 2log2 +−= (b.3.2.5)


Where,

logL=maximized log-likelihood (see Appendix B.3.1). K=number of free parameters in the model.

The AIC allows relative model comparison by means of the

Akaike weights wi, which normalize the model likelihoods such

that they sum 1 and treat them as probabilities. The Akaike

weights can be interpreted as the probability that model i is the

best model for the data (equation b.3.2.6, where the numerator is

the relative likelihood for each model).

∑=

∆−

∆−

=R

i

i

i

iw

1

)2

exp(

)2

exp(

(b.3.2.6)

AICAIC ii min−=∆ (b.3.2.7)

AICi=AIC of model-i R= number of competing models

APPENDIX 145

C Supporting Information to Chapter 4


C.1 Sensitivity Analysis

In order to quantify the effects of input parameter variations on

the model results, a sensitivity analysis was performed for the

dataset-1. The input parameters considered for the theoretical

energy consumption include the information about reflux

conditions during distillation, reaction mass and temperature

increase inside the reactor. Additionally, variations in

physicochemical properties of the substances, such as heat

capacity and enthalpy of vaporization, and equipment

characteristics such as mass and heat capacity of the reactor,

have also been considered. For the energy losses, the operation

time, the area of the reactor and the difference between the

temperature inside the reactor and the ambient temperature were

considered. The original input parameters, as extracted from the

SOP were corrected according to the actual process parameters

extracted from the EMT. The energy modeling was then

calculated again by means of the documentation based approach

considering the mentioned corrections one at each time.

Additionally, a model run was performed considering all

corrections simultaneously, approaching in this way the real

process conditions.

For the evaluation of the model performance after the mentioned

input corrections, some descriptive statistics and various

diagnostic measures are reported in Table C.1.1. As model error

measures the mean absolute error (MAE), the mean absolute

relative error (MARE), and the root mean squared error (RMSE)

were used, decomposed into a systematic (RMSEs) and an

unsystematic (RMSEu) part. The RMSEs describes the linear

APPENDIX 147

bias produced by the model, whereas the RMSEu may be

considered as a measure of precision. Besides these error

measures, various indices of agreement between model

predictions and reference values were calculated, that is the

square of the correlation coefficient (r2), the coefficient of

determination (q2) and refined indices of agreement (d1, d2, dr)

(Willmott. et al., 2012). As can be seen in Table C.1.1, the MARE,

MAE and RMSE differ and present a decrease with respect to the

start input only for reflux considerations for the theoretical energy,

and operation time for energy losses. Regarding the indices of

agreement, the highest values and thus a better agreement

between observed and predicted values also correspond to reflux

considerations and operation time. Since these evaluation criteria

indicate a reduction of the error and an increase of the prediction

capabilities only for reflux conditions and operation time, both

parameters are considered as influential on the model results.


Table C.1.1. Statistical evaluation of the documentation based approach model for the theoretical energy, energy losses, and total energy consumption in the case of dataset-1, during sensitivity analysis scenarios for the model input parameters (start: original parameters from the process documentation, reflux: reflux conditions during distillation, properties: physico-chemical properties of the substances and equipment characteristics, mass: reaction mass, dT: temperature increase during process operation, all: all parameters simultaneously). The units are given in kg of steam/ batch.

Theoretical energy Energy losses Total energy

Para-meter

start reflux prop mass dT all start time prop dT all reflux +time

N 18 18 18 18 18 18 18 18 18 18 18 18

mean_r 2801 2801 2801 2801 2801 2801 1439 1439 1439 1439 1439 4252

mean_m 2047 2390 1944 2163 2040 2380 770 1199 1363 751 1897 3589

sd_r 3109 3109 3109 3109 3109 3109 1441 1441 1441 1441 1441 4530

sd_m 1977 2457 2028 2020 1961 2460 1100 1443 2211 1097 2526 3762

a 538 263 421 656 557 256 -71.84 -5.51 -140 -62.25 84.06 250

b 0.54 0.76 0.54 0.54 0.53 0.76 0.58 0.84 1.04 0.57 1.26 0.79

MARE 0.29 0.25 0.29 0.34 0.34 0.27 0.56 0.42 0.61 0.56 0.66 0.27

MAE 946 604 990 951 990 615 744 536 978 765 1010 1030

RMSE 1884 1067 1954 1888 1918 1088 1121 838 1577 1163 1805 1658

RMSEs 1583 835 1623 1534 1613 843 886 331 99 919 585 1155

RMSEu 1020 664 1088 1101 1038 687 687 770 1574 714 1707 1190

APPENDIX 149

d2 0.85 0.96 0.84 0.85 0.84 0.96 0.81 0.91 0.78 0.79 0.76 0.96

d1 0.79 0.87 0.78 0.79 0.78 0.87 0.68 0.78 0.64 0.67 0.65 0.85

dr 0.82 0.88 0.81 0.82 0.81 0.88 0.68 0.77 0.58 0.67 0.57 0.86

q2 0.61 0.88 0.58 0.61 0.60 0.87 0.36 0.64 -0.27 0.31 -0.66 0.86

r2 0.72 0.92 0.70 0.69 0.70 0.92 0.59 0.70 0.46 0.55 0.52 0.89

Symbols and abbreviations

a Intercept of a least-squares regression line between predicted and observed variables b Slope of a least-squares regression line between predicted and observed variables dr Refined index of agreement d1 Refined index of agreement d2 Refined index of agreement MAE Mean Absolute Error MARE Mean Absolute Relative Error mean_r Mean value of the reference dataset mean_m Mean value of the model dataset N Number of data points q


r2

Square of the correlation coefficient RMSE Root mean squared error RMSEs Systematic root mean squared error RMSEu Unsystematic root mean squared error sd_m Standard deviation of the model dataset sd_r Standard deviation of the reference dataset


C.2 Statistic Evaluation of the Documentation based

Approach Model Performance

Comparing the results of the theoretical energy predictions shown

in Tables C.1.1 and C.2.1, it is interesting to notice that for all the

cases of dataset-1, the systematic portion of the error RMSEs is

bigger than the unsystematic part RMSEu, whereas for dataset-2

the opposite direction is observed. This can be explained by the

fact that some corrections were made in the input parameters for

the theoretical energy calculation of dataset-1, whereas for

dataset-2 this was not the case. Therefore, even though the high

RMSEs for the first case study showed that there is a potential for

improvement of the theoretical energy model performance by

means of a more detailed process modeling with less

assumptions and default values, the RMSEs for the second case

study indicated a low portion of systematic error and, hence, a

good accuracy of the model based only on process

documentation without any further corrections of the default input

parameters and assumptions.

On the other hand, the RMSEs and RMSEu for the energy losses

present the opposite trend, being the ratio of unsystematic error

to total error higher for the first case study and lower for the

second. A high RMSEu to RMSE ratio reveals the difficulty of

modeling the energy losses in an accurate way, even when the

operation time is known, and suggests that it would be difficult to

further improve the results by means of a more detailed modeling.

On the contrary, a low RMSEu to RMSE ratio like for case study 2

implies that there is bias produced by the model. Since the loss

constant (Kloss) was chosen among two different proposed values

APPENDIX 151

(Bieler et al., 2004), according to the performance on dataset-1,

when this constant is applied to a different production plant, it

may tend to produce a systematic error and increase the bias in

the results. Finally, it should be noted that for both datasets the

MARE and the three indices of agreement confirm the expected

trend of higher prediction capability for modeling of theoretical

energy, followed by total energy and energy losses.

Table C.2.1. Statistical evaluation of the documentation based approach model

for the theoretical energy, energy losses, and total energy consumption in the

case of dataset-2. The units are given in kg of steam/ batch.

Statistical parameters

Theoretical energy

Energy losses Total energy

N 20 20 20

mean_r 1183 622 1805

mean_m 1247 396 1642

sd_r 1201 819 1897

sd_m 1378 403 1738

a -2.24 156.89 163.05

b 1.06 0.38 0.82

MARE 0.31 2.46 0.37

MAE 300 337 546

RMSE 533 595 843

RMSEs 91 542 372

RMSEu 526 245 757

d2 0.95 0.74 0.94

d1 0.86 0.67 0.82

dr 0.86 0.72 0.83

q2 0.79 0.45 0.79

r2 0.85 0.61 0.80


Symbols and Abbreviations

a Intercept of a least-squares regression line between predicted and observed variables

b Slope of a least-squares regression line between predicted and observed variables

dr Refined index of agreement d1 Refined index of agreement d2 Refined index of agreement MAE Mean Absolute Error MARE Mean Absolute Relative Error mean_r Mean value of the reference dataset mean_m Mean value of the model dataset N Number of data points q


r2

Square of the correlation coefficient RMSE Root mean squared error RMSEs Systematic root mean squared error RMSEu Unsystematic root mean squared error sd_m Standard deviation of the model dataset sd_r Standard deviation of the reference dataset

APPENDIX 153

C.3 Observed and Predicted Steam Consumption

Tables C.3.1 and C.3.2 show the observed and the predicted

theoretical energy, energy losses and total energy values for the

first and second case study, respectively. Additionally, the relative

errors and the success of the predicted results considering also

the uncertainty ranges and batch-to-batch variability are shown

for each individual case. The problematic cases which were

pointed out in the main text (Figure 4.1.1, Figure 4.1.2, Figure

4.1.4, Figure 4.2.1) are highlighted, since they present

considerable deviation from the observed values and the model

uncertainty ranges fail to capture the observed batch-to-batch

variability. These cases are discussed in detail in the following

sub-sections.

C.3.1 Theoretical Energy Consumption

Errors concerning distillation processes undergoing reflux, like it

is the case for the equipments 10 and 16 in Table C.3.1, and 6

and 17 in Table C.3.2, are a consequence of the assumption of a

standard value of energy consumption during reflux conditions.

This standard value was derived by averaging measurements of

steam consumption under strong reflux of butanol for 27 batches

(Bieler et al., 2004). Obviously, this shortcut model does not

account for different and perhaps extremely high or low reflux

ratios and it also does not consider the substance specific

enthalpies of vaporization. Therefore, an improvement of the

model predictions for processes undergoing reflux could be

achieved by explicitly including the reflux ratio in the energy

calculations, whenever it is available. On the other hand, errors

which arise from the use of default values for the heat capacity,


for instance in case of equipment 4 in Table C.3.1, can be

reduced by considering the substance specific heat capacities.

After these corrections the relative error for the theoretical energy

consumption reduces to 3%. Another case of model deviations

from observed energy consumption values is the one of

simultaneous heating and cooling due to suboptimal temperature

control system. This is the case for equipment 2 in Table C.3.2.

Finally, the inaccuracy of the temperature during distillation is one

of the causes of the high relative error for equipment 14 in Table

C.3.2. In this case the relative error reduces from 86 to 56% after

the temperature correction.

C.3.2 Energy Losses

Energy losses at low process temperatures are not very well

captured by the documentation based approach, as it is the case

for equipments 4 and 15 in Table C.3.1 and equipments 15 and

16 in Table C.3.2. In the first two cases, the initial temperature of

the reaction mass is around 15°C, while the final temperature

reaches approximately 30°C, and in the last two cases the

average temperature remains between 40 and 48°C. Considering

that the energy losses according to the documentation based

approach are proportional to the temperature difference between

the ambient temperature and the average temperature inside the

reactor, a low temperature difference implies very low energy

losses. For the equipments 4 and 15 (Table C.3.1) the heat

exchange area of the equipment was identified as the source of

error in the model predictions. After replacing standard default

area values by specific area information, the relative errors

reduced to 16% and 4% respectively. In addition to the area,

APPENDIX 155

inaccuracies in the temperature inside the reactor were also

leading to error in the energy losses estimations of equipments

14 and 17 (Table C.3.1). After corrections of both parameters, the

relative errors were reduced to -40% and -3%. For equipment 5 in

Table C.3.2, the high relative error is produced mainly by

temperature inaccuracies in the process documentation, and after

correction the relative error was reduced to 36%. Therefore, for

most problematic cases the failures of the model predictions

could be explained based on inaccuracies of the model input

values and the respective relative errors were reduced after

appropriate correction. However, there are two cases which

remain unclear. For equipment 12 in Table C.3.2, there are

reasons to believe, based on the trend of the sensor data of

steam consumption, that there might be a problem with the

observed value (measurement). Finally, no specific input

inaccuracy could be detected for equipment 6 in Table C.3.2. In

this case, a model uncertainty according to the support instead of

the core of the fuzzy interval would be more appropriate.


Table C.3.1. Detailed assessment of the documentation based approach model predictions of the theoretical energy, energy

losses, and total energy consumption for all individual points in the case of dataset-1 (*ok: within batch-to-batch variability

range (success), ko: outside batch-to-batch variability range (no success), **ok: within fuzzy uncertainty range (success),

ko: outside uncertainty range (no success)). The units are given in kg of steam/ batch.


Eq

ua

tio

n

Ob

se

rve

d

me

dia

n

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del

pre

dic

tion

Assess-

me

nt*

Re

lative

e

rro

r %

Ob

se

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d

me

dia

n

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del

pre

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tion

Assess-

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nt*

Re

lative

e

rro

r %

Ob

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d

me

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del

pre

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tion

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me

nt*

Assess-

me

nt*

*

Re

lative

e

rro

r %

1 390 445 ok 14 437 473 ok 8 815 918 ok ok 13

2 257 435 ok 69 259 7 ko -97 529 443 ok ok -16

3 832 842 ok 1 296 364 ok 23 1129 1205 ok ok 7

4 2239 3321 ko 48 1310 2178 ko 66 3552 5499 ko ok 55

5 603 720 ok 19 408 475 ok 16 1016 1195 ok ok 18

6 183 178 ok -2 206 126 ok -39 384 305 ok ok -21

7 109 146 ok 34 210 267 ok 27 314 412 ok ok 32

8 7094 6485 ok -9 3520 3860 ok 10 10652 10345 ok ok -3

9 74 13 ok -82 144 34 ok -76 211.5 47 ok ko -78

APPENDIX 157

10 7703 4088 ko -47 4556.5 3679 ok -19 12468 7767 ko ko -38

11 7131 6550 ok -8 2648 2094 ok -21 9779 8644 ok ok -12

12 1687 1941 ok 15 1362 1960 ok 44 3006 3901 ok ok 30

13 743 627 ok -15 283 300 ok 6 1023 927 ok ok -9

14 890 1017 ok 14 607 109 ko -82 1497 1126 ok ok -25

15 3722 2798 ok -25 1495 541 ko -64 5233 3339 ko ko -36

16 9543 7662 ko -20 3685 4296 ok 17 13209 11958 ok ok -9

17 1486 1376 ok -7 833 399 ko -52 2312 1775 ok ok -23

18 5068 4103 ok -19 3262 441 ko -86 8351 4544 ko ko -46


Table C.3.2. Detailed assessment of the documentation based approach model predictions of the theoretical energy, energy

losses, and total energy consumption for all individual points in the case of dataset-2 (*ok: within batch-to-batch variability

range (success), ko: outside batch-to-batch variability range (no success), **ok: within fuzzy uncertainty range (success),

ko: outside uncertainty range (no success)). The units are given in kg of steam/ batch.


Eq

ua

tio

n

Ob

se

rve

d

me

dia

n

Mo

del

pre

dic

tion

Assess-

me

nt*

Assess-

me

nt*

*

Re

lative

e

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r %

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d

me

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me

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Assess-

me

nt*

*

Re

lative

e

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d

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pre

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tion

Assess-

me

nt*

Assess-

me

nt*

*

Re

lative

e

rro

r %

1 2544 2775 ok ok 9 781 959 ok ok 23 3325 3734 ok ok 12

2 373 106 ko ko -72 28 51 ok ok 85 401 157 ko ko -61

3 408 609 ok ko 49 457 692 ok ok 52 864 1301 ko ok 50

4 117 59 ko ko -50 74 58 ok ok -21 191 117 ko ko -39

5 3554 3547 ok ok 0 1646 780 ko ko -53 5200 4327 ko ok -17

6 3229 2071 ko ko -36 1408 488 ko ko -65 4637 2559 ko ko -45

7 216 188 ok ok -13 -7 13 ok ok -282 209 201 ok ok -4

8 77 95 ok ok 24 133 10 ko ko -93 210 105 ko ko -50

APPENDIX 159

9 0 0 ok ok 0 0 0 ok ok 0 0 0 ok ok 0

10 1618 1331 ok ok -18 769 389 ok ok -49 2387 1721 ok ok -28

11 291 381 ko ok 31 24 143 ko ko 496 295 524 ko ok 78

12 2427 2580 ok ok 6 3262 1142 ko ko -65 5689 3722 ko ko -35

13 458 514 ok ok 12 191 225 ok ok 18 649 739 ko ok 14

14 225 418 ko ko 86 106 95 ok ok -11 330 513 ko ok 55

15 1619 1183 ok ko -27 375 108 ko ko -71 1994 1291 ok ko -35

16 118 90 ok ok -24 307 97 ko ko -69 425 187 ko ko -56

17 2904 4641 ko ko 60 883 1027 ok ok 16 3787 5668 ko ok 50

18 2068 2965 ko ok 43 1583 902 ok ok -43 3652 3867 ok ok 6

19 1106 1161 ok ok 5 400 730 ok ok 82 1506 1891 ko ok 26

20 314 276 ok ok -12 39 1 ko ko -97 353 277 ko ok -22


D Supporting Information to Chapter 5

APPENDIX 161

D.1 Prior Selection

One of the settings of the CART algorithm (L. Breiman et al.,

1984) is the selection of the prior probabilities (priors). The priors

refer to the probability of each class previous to any empirical ev-

idence. Priors are calculated by default in MATLAB1 based on the

class frequencies. Besides growing trees using default priors, we

set all priors to be equal (uniform priors) in order to evaluate the

influence of the prior selection on the model performance.

0.1 0.12 0.14 0.16 0.18 0.20

0.2

0.4

0.6

0.8

1

S1

S2S3S4S5

S1S2

S3 S4

S5

1− Specificity

Sensitiv

ity

frequency priors

uniform priors

Figure D.1.1. Average model performance for cross validation test set for five

stages of process design (S1 to S5) for dataset-1 (8 candidate predictor

variables) and 3 output classes considering frequency-based and uniform priors.

The line denotes random classifier performance. Models that fall into the right

region defined by the random line perform worse than random performance, and

models that fall into the left region perform better than random performance. The

point in the top left corner depicts perfect classification.

1 Statistics Toolbox

TM.


D.2 Performance of Classification Trees per Output Class

Table D.2.1. Test cross validation performance of the classification models at

five stages of process design (S1 to S5) built from dataset-1, depicted per

output class.

Stage Class Sensitivity Specificity Accuracy D1* D2*

S1 low 0.90 0.59 0.75 0.42 0.49 middle 0.00 1.00 0.78 1.00 0.00 high 0.66 0.78 0.75 0.40 0.44

S2 low 0.89 0.79 0.84 0.24 0.68 middle 0.31 0.94 0.80 0.69 0.25 high 0.72 0.81 0.79 0.34 0.53

S3 low 0.85 0.80 0.82 0.25 0.65 middle 0.40 0.90 0.79 0.61 0.30 high 0.67 0.84 0.79 0.37 0.51

S4 low 0.90 0.75 0.83 0.27 0.65 middle 0.40 0.91 0.80 0.61 0.31 high 0.70 0.90 0.85 0.32 0.60

S5 low 0.80 0.81 0.80 0.28 0.61 middle 0.65 0.79 0.76 0.41 0.44 high 0.69 0.98 0.91 0.31 0.67

* D1 is the Euclidean distance to the random line and D2 is equal to the

Euclidean distance to the point (0,1).

APPENDIX 163

D.3 Average Model Performance of the S1 Tree

0 1 3 160

low1

middle

3

high

16


Ste

am

mo

de

l cla

sse

s [

kg

/kg

pro

du

ct]

51%

94% 49% 36%

64%6%

Figure D.3.1. Average model performance of the S1 tree (resubstitution

validation), considering dataset-1 (maximal 8 predictor variables) and 3 output

classes. The training data is presented on the x axis and the predicted classes

on the y axis. The data points lying inside the bold boxes on the diagonal axis

represent the data which actually belong to one class and were predicted within

that class. The points lying inside the boxes on the non diagonal bottom right

area represent underestimated values. The points lying inside the boxes on the

non diagonal top left area represent overestimated values.


D.4 Classification Trees

Table D.4.1. Classification tree for the S1 design stage

Node Parent node

Rule

1 0 IF the reaction type is acylation OR alkylation OR complexation OR condensation OR hydrolysis OR polymerization OR reduction THEN go to internal node 2 ELSEIF reaction type is acylation (cyanur chloride) OR azo-coupling OR diazotization OR elimination OR halogenation OR sulfonation THEN go to terminal node 3

2 1 IF the reaction mechanism is AN OR SEAr OR AEN THEN go to terminal node 4 ELSEIF the reaction mechanism is HC OR RAD OR SN1 OR SN2 OR SNAr THEN go to terminal node 5

3 1 low steam consumption 4 2 low steam consumption 5 2 high steam consumption

APPENDIX 165

Table D.4.2. Classification tree for the S2 design stage.

Node Parent node

Rule


2 1 IF distillation does not take place THEN go to internal node 4 ELSEIF distillation takes place go to terminal node 5

3 1 low steam consumption 4 2 IF the reaction mechanism is AN OR SEAr OR AEN OR SN2 THEN go to terminal node 6 ELSEIF the

reaction mechanism is HC OR RAD OR SNAr THEN go to terminal node 7

5 2 high steam consumption 6 4 low steam consumption 7 4 middle steam consumption



Node Parent node

Rule


2 1 IF time is lower than 18 hours THEN go to internal node 4 ELSEIF time is higher than 18 hours go to terminal node 5

3 1 low steam consumption 4 2 IF the reaction mechanism is AN OR SEAr OR AEN THEN go to terminal node 6 ELSEIF the reaction

mechanism is HC OR RAD OR SN2 OR SNAr THEN go to terminal node 7 5 2 high steam consumption

6 4 IF Tmax is lower than 93°C then go to terminal node 8 ELSEIF Tmax is higher than 93°C THEN go to terminal node 9

7 4 IF distillation does not take place THEN go to terminal node 10 ELSEIF distillation takes place go to terminal node 11

8 6 low steam consumption 9 6 middle steam consumption

10 7 middle steam consumption 11 7 high steam consumption

APPENDIX 167


Node Parent node

Rule


2 1 IF time is lower than 18 hours THEN go to internal node 4 ELSEIF time is higher than 18 hours go to terminal node 5

3 1 low steam consumption 4 2 IF the reaction mechanism is AN OR SEAr OR AEN THEN go to internal node 6 ELSEIF the reaction

mechanism is HC OR RAD OR SN2 OR SNAr THEN go to internal node 7

5 2 high steam consumption 6 4 IF Tmax is lower than 93°C then go to terminal node 8 ELSEIF Tmax is higher than 93°C THEN go to

internal node 9

7 4 IF distillation does not take place THEN go to terminal node 10 ELSEIF distillation takes place go to terminal node 11

8 6 low steam consumption

9 6 IF PMI is lower than 4 THEN go to terminal node 12 ELSEIF PMI is higher than 4 THEN go to terminal node 13

10 7 middle steam consumption

11 7 high steam consumption 12 9 low steam consumption



Table D.4.5. Classification tree for the S5 design stage

Node Parent node

Rule

1 0 IF Steamdist is lower than 1.5 kg THEN go to internal node 2 ELSEIF Steamdist is higher than 1.5 kg THEN go to terminal node 3

2 1 IF Tmax is lower than 79°C then go to terminal node 4 ELSEIF Tmax is higher than 79°C THEN go to internal node 5

3 1 high steam consumption 4 2 low steam consumption 5 2 IF Steamdist is lower than 0.5 kg THEN go to internal node 6 ELSEIF Steamdist is higher than 0.5 kg

THEN go to terminal node 7 6 5 IF the reaction type is acylation OR alkylation OR condensation OR halogenations OR hydrolysis OR

sulfonation THEN go to terminal node 8 ELSEIF reaction is complexation OR azo-coupling OR polymerization OR reduction THEN go to terminal node 9

7 5 middle steam consumption 8 6 low steam consumption


APPENDIX 169

E Supporting Information to Chapter 6


E.1 Goodness of Fit of PDF Models

APPENDIX 171

0 5 100

10

20Acylation

gam

0 5 100

20

40Acylation (cyanur chloride)

exp

0 5 10 150

10

20Alkylation

exp

0 2 4 60

20

40Azo−coupling

exp

0 5 10 15 200

5

10Complexation

gam

0 5 10 15 200

5

10Condensation

exp

0 0.05 0.1 0.15 0.20

20

40Diazotization

exp

0 0.5 1 1.50

5Elimination

logn

0 5 100

5

10

Halogenation

logn

0 5 10 150

5

10Hydrolysis

exp

0 5 10 15 200

5

10

Polymerizationlo

gn

0 5 10 15 200

5

10Reduction

exp

0 0.1 0.2 0.3 0.40

5

unif

Sulfonation

Figure E.1.1. Histograms of the steam training data and the corresponding superimposed fitted probability distributions.


0 5 100

0.5

1gam

Acylation

0 5 100

0.5

1

exp

Acylation (cyanur chloride)

0 5 10 150

0.5

1

exp

Alkylation

0 2 4 60

0.5

1

exp

Azo−coupling

0 5 10 150

0.5

1

gam

Complexation

0 5 10 150

0.5

1

exp

Condensation

0 0.05 0.1 0.15 0.20

0.5

1

exp

Diazotization

0 0.5 10

0.5

1

logn

Elimination

0 2 4 60

0.5

1

logn

Halogenation

0 5 10 150

0.5

1

exp

Hydrolysis

0 5 10 15 200

0.5

1

logn

Polymerization

0 5 10 15 200

0.5

1

exp

Reduction

0 0.1 0.2 0.3 0.40

0.5

1

uniform

Sulfonation

Data

Model

Figure E.1.2. Cumulative distribution functions of the steam training data and the corresponding statistical populations.

APPENDIX 173

0 5 10 15 200

10

20

ga

m

Acylation

0 1 2 3 4−10

0

10

exp

Acylation (cyanur chloride)

0 5 10 15−20

0

20

exp

Alkylation

0 1 2 3−10

0

10

exp

Azo−coupling

0 5 10 150

10

20

ga

m

Complexation

0 5 10 150

10

20

exp

Condensation

0 0.05 0.1−0.2

0

0.2

exp

Diazotization

0 2000 4000 6000−2000

0

2000

log

n

Elimination

0 2 4 60

5

log

n

Halogenation

0 2 4 60

10

20

exp

Hydrolysis

0 10 20 30−50

0

50lo

gn

Polymerization

0 5 10 150

10

20

exp

Reduction

0 0.1 0.2 0.3 0.40

0.2

0.4

un

ifo

rm

Sulfonation

Figure E.1.3. Q-Q plots of the steam training data (y-axis) against the corresponding statistical populations (x-axis).


Table E.1.1. Goodness of the fit assessment of the PDF models.

Reaction type parameterization fitted PDF n χ2 p(χ2) D p(D) AD p(AD) weight delta Acylation gamma 33 4.44 0.49 0.11 0.74 na na 0.81 0.00

Time<18h gamma 21 8.75 0.07 0.20 0.32 na na 0.85 0.00 Time>18h lognormal 12 2.00 0.37 0.22 0.53 0.44 0.24 0.24 0.00

Acylation

(cyanur chloride) lognormal 22 7.54 0.11 - - - - 0.43 0.00

Alkylation gamma 33 6.58 0.25 0.15 0.38 na na 0.78 0.00

no distillation gamma 12 - - 0.28 0.22 na na 0.76 0.00 distillation weibull 21 2.5 0.65 - - 0.17 0.81 0.33 0.00

Azo-coupling gamma 25 6.1 0.19 - - na na 0.99 0.00

Complexation exponential 9 0.9 0.82 0.14 0.99 0.19 0.98 0.66 0.00 time<18h rayleigh 6 0.42 0.81 0.22 0.88 na na 0.38 0.00

Condensation exponential 25 4.45 0.49 0.14 0.64 0.52 0.42 0.34 0.00 Tmax<93°C exponential 8 3.59 0.31 0.26 0.58 0.62 0.30 0.49 0.00 Tmax>93°C lognormal 17 1.36 0.72 0.15 0.77 0.30 0.54 0.33 0.00

Diazotization exponential 10 1.32 0.72 0.32 0.22 1.11 0.08 0.35 0.05

Elimination gamma 9 - - - - na na 0.93 0.00

APPENDIX 175

Halogenation lognormal 14 3.6 0.31 0.10 0.99 0.19 0.87 0.53 0.00

Hydrolysis gamma 9 1.04 0.59 0.40 0.09 na na 0.88 0.00

Polymerization lognormal 18 3.36 0.34 0.15 0.78 0.56 0.13 0.40 0.00

time<18 lognormal 8 1.6 0.45 0.24 0.67 0.41 0.26 0.20 1.56 time>18 uniform 10 na na 0.23 0.60 na na 0.70 0.00

Reduction exponential 14 7.52 0.11 0.20 0.57 0.52 0.41 0.60 0.00

Sulfonation gamma 9 - - 0.34 0.21 na na 0.89 0.00

Symbols

n number of data points (degrees of freedom) na non applicable χ2 Chi-Square statistic p(χ2) p-value associated with the Chi-Square statistic D Kolmogorov-Smirnov statistic p(D) p-value associated with the Kolmogorov-Smirnov statistic AD Anderson-Darling statistic p(AD) p-value associated with the Anderson-Darling statistic weight Weight of evidence in favor of the model being the actual best model (Akaike weight) delta Measure of the Akaike Information Criterion of the model relative to the best model


The test statistics presented in this table are obtained from the

Chi-Square-, the Kolmogorov-Smirnoff and the Anderson-Darling

goodness of fit tests (Vose, 2008). These non-parametric tests

return a probability that a randomly drawn dataset from the fitted

distribution might have generated a test statistic at least as low as

the one observed. The null hypothesis that the data originate

from the hypothesized distribution is rejected, if the p-value is

lower than the pre-specified significance level α and the best fit

among different candidate distributions is reflected by the lowest

value of a given test statistic. The reported test statistics in this

table have a p-value greater than a significance level of 5% (p-

value > 0.05). The test statistics corresponding to a significance

level lower than 5% are not reported. A higher p-value implies

that the probability of getting the corresponding statistic from a

sample of the same size is higher. Besides these conventional

test statistics, the Akaike Information Criterion (AIC) has been

used to select the optimal distribution. The AIC is a measure of

the relative quality of a statistical model for a dataset. Compared

to conventional test statistics, AIC is superior in selecting the

optimal distribution, since they account for model complexity,

penalizing distributions with more parameters, and are better

suited for relative model comparison by means of the Akaike

weights and delta. The best model has a delta equal to cero, and

the biggest weight among all compared models.

APPENDIX 177

F Supporting Information to Chapter 7


F.1 Modeling results – Case Study II

Table F.1.1. Steam consumption estimatins (kg /kg product) for the reactions presented in Figure 7.2.1, considering the

median values of the PDF models.

Route Reaction 1 Reaction 2 Reaction 3 Reaction 4 Reaction 5 Reaction 6 Reaction 7 Reaction 8 Total

A 1.2 1.2 1.7 3.1 0 1.2 8.4

B 1.2 3.1 1.2 1.7 3.1 0 1.2 10.3 C 0.4 1.7 3.1 1.2 1.2 3.1 10.7

D 0.4 1.2 1.2 3.1 0 1.2 5.9

E 1.2 1.7 3.1 6

F 1.2 1.2 1.2 0.4 1.7 3.1 0 1.2 10

G 1.2 0.4 1.2 3.1 5.9

Table F.1.2. Steam consumption estimations (kg /kg product) for the reactions presented in Figure 7.2.1, considering the

median values of the PDF models and the corresponding reaction yields (Table B.1.1.2) and stoichiometric ratios.

Route Reaction 1 Reaction 2 Reaction 3 Reaction 4 Reaction 5 Reaction 6 Reaction 7 Reaction 8 Total

A 0.8 1.2 2.2 4.6 0.0 1.4 10.2

B 0.9 3.0 1.1 2.2 4.6 0.0 1.4 13.2 C 0.3 1.7 5.1 1.7 1.4 4.2 14.3

D 0.2 1.4 1.8 4.5 0.0 1.4 9.3

E 0.8 2.2 4.2 7.3

F 0.9 1.1 1.5 0.6 3.0 4.6 0.0 1.4 13.0

G 0.8 0.4 1.9 4.2 7.3

APPENDIX 179

Table F.1.3. Environmental and economic proxy indicators for multi-objective

screening of chemical batch process alternatives during early design stages*.

Route ELI PLI ELI+PLI (weighted sum)

A 1.70 0.56 0.06

B 2.11 0.59 0.06

C 1.49 0.69 0.06

D 2.23 0.74 0.07 E 0.61 0.68 0.06

F 2.07 0.68 0.07

G 1.04 0.82 0.07

* (Albrecht et al., 2010)

F.2 One-way Anova – Case Study II

Table F.2.1. Descriptive statistics for the dependent variable steam

consumption and the grouping variable synthesis route. The values are given in

kg of steam per kg of product.


Number of points

A 14.72 8.83 1000

B 19.59 13.04 1000

C 23.47 16.20 1000 D 12.83 8.15 1000

E 12.40 8.51 1000

F 20.86 12.62 1000

G 13.89 11.43 1000

Total 16.82 12.28 7000

Table F.2.2. Test of homogeneity of variances



Sig.*

72.38 6 6993 .00

* Since the significance value is less than 0.05 we can say that the variances of

the different acylation reaction sub-groups are different. Therefore, the

assumption of homogeneity of variances has been violated.


Table F.2.3. One-way anova test results.

Source of variation

Sum of squares

degrees of freedom

Mean square

F Sig.*

Between Groups

116578.52 6 19429.75 144.77 0.00

Within Groups

938533.03 6993 134.21

Total 1055111.55 6999

* Since the assumption of homogeneity of variances has been violated, we also

look at the Brown-Forsythe and Welch alternative F-ratios, which have been

derived to be robust in this cases (Field, 2009).

Table F.2.4. Robust test of equality of means.

Statistic* degrees of freedom 1

degrees of freedom 2**

Sig.***

Welch 130.40 6 3091.15 0.00 Brown-Forsythe 144.77 6 5649.75 0.00

* Asymptotically F distributed. ** Adjusted residual degrees of freedom. *** Both

test statistics are highly significant, thus we can say that there is a significant

difference among the different synthesis routes. Therefore we proceed with a

multiple comparison to compare pair wise all different combinations of groups.

Table F.2.5. Multiple comparisons using the Games-Howell procedure (Jaccard

et al., 1984)*.

Reaction (I) Reaction (J) Mean diffe-rence (I-J)

Stan-dard error

Sig.** CI 95% Lower bound

CI 95% Upper bound

A B -4.86 0.50 0.00 -6.33 -3.39 C -8.74 0.58 0.00 -10.46 -7.02 D 1.90 0.38 0.00 0.77 3.02 E 2.32 0.39 0.00 1.17 3.46 F -6.14 0.49 0.00 -7.58 -4.70 G 0.83 0.46 0.53 -0.52 2.18 B A 4.86 0.50 0.00 3.39 6.33 C -3.88 0.66 0.00 -5.82 -1.94 D 6.76 0.49 0.00 5.32 8.20 E 7.18 0.49 0.00 5.73 8.64 F -1.27 0.57 0.28 -2.97 0.42

APPENDIX 181

G 5.70 0.55 0.00 4.08 7.32 C A 8.74 0.58 0.00 7.02 10.46 B 3.88 0.66 0.00 1.94 5.82 D 10.63 0.57 0.00 8.94 12.33 E 11.06 0.58 0.00 9.35 12.77 F 2.60 0.65 0.00 0.69 4.52 G 9.58 0.63 0.00 7.72 11.43 D A -1.90 0.38 0.00 -3.02 -0.77 B -6.76 0.49 0.00 -8.20 -5.32 C -10.63 0.57 0.00 -12.33 -8.94 E 0.42 0.37 0.92 -0.68 1.52 F -8.03 0.48 0.00 -9.44 -6.63 G -1.06 0.44 0.20 -2.37 0.25 E A -2.32 0.39 0.00 -3.46 -1.17 B -7.18 0.49 0.00 -8.64 -5.73 C -11.06 0.58 0.00 -12.77 -9.35 D -0.42 0.37 0.92 -1.52 0.68 F -8.46 0.48 0.00 -9.88 -7.04 G -1.49 0.45 0.02 -2.82 -0.16 F A 6.14 0.49 0.00 4.70 7.58 B 1.27 0.57 0.28 -0.42 2.97 C -2.60 0.65 0.00 -4.52 -0.69 D 8.03 0.48 0.00 6.63 9.44 E 8.46 0.48 0.00 7.04 9.88 G 6.97 0.54 0.00 5.38 8.56 G A -0.83 0.46 0.53 -2.18 0.52 B -5.70 0.55 0.00 -7.32 -4.08 C -9.58 0.63 0.00 -11.43 -7.72 D 1.06 0.44 0.20 -0.25 2.37 E 1.49 0.45 0.02 0.16 2.82 F -6.97 0.54 0.00 -8.56 -5.38

* This procedure is recommended in cases when there is a doubt that the

population variances are equal (see Table F.2.2) (Field, 2009).

** The underlined values correspond to significance levels of less than 0.05,

thus they indicate which reaction pair are significantly different between each

other.


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