process synthesis of biodiesel production plant using artificial neural networks as the surrogate...

Pt

ID

a

ARRAA

KBSPS

1

2ttbi2

am

eeen2

t2(Iuib

0h

Computers and Chemical Engineering 46 (2012) 105– 123

Contents lists available at SciVerse ScienceDirect

Computers and Chemical Engineering

jo u rn al hom epa ge : www.elsev ier .com/ locate /compchemeng

rocess synthesis of biodiesel production plant using artificial neural networks ashe surrogate models

smail Fahmi, Selen Cremaschi ∗

epartment of Chemical Engineering, The University of Tulsa, 800 South Tucker Drive, Tulsa, OK 74104, USA

r t i c l e i n f o

rticle history:eceived 1 July 2011eceived in revised form 29 March 2012ccepted 6 June 2012vailable online 28 June 2012

eywords:iodiesel productionuperstructure optimizationrocess synthesisurrogate models artificial neural networks

a b s t r a c t

Biodiesel is an attractive biofuel because it can be used directly with the traditional petro diesel engines,either as a substitute or as a blending component. There are several alternatives that can be used toproduce biodiesel. In this work, we developed a superstructure optimization model to synthesize theoptimum biodiesel production plant, i.e., the one that gives the minimum net present sink. To reducethe computational cost of solving the resulting disjunctive programming, the surrogate models utilizingartificial neural networks (ANNs), have been developed to replace the unit operation, thermodynamicsand mixing models. The optimum solution with the alkali-catalyzed reactor (obtained in five CPU seconds)has a total net present sink of about $41 million, which differs less than one percent from the resultobtained by modeling the solution in a process simulator. However, this level of accuracy required alarge amount of data to train the ANNs.

© 2012 Elsevier Ltd. All rights reserved.

. Introduction

As the economical and exploitable fossil fuel reserves decrease, fuels from renewable sources seem more and more appealing (Hill et al.,006; Kokossis & Yang, 2010). However, in order to obtain comparable engine performance with most renewable fuels to traditional ones,he current engines should be modified (Hsieh et al., 2002; Yüksel & Yüksel, 2004). This one specific reason makes biodiesel more promisinghan other types of bio-fuel. Besides being biodegradable, non-toxic, and free from sulfur and aromatic compounds, biodiesel can be easilylended with petroleum diesel to be run in a diesel engine with little or no modifications (Kralj, 2008). Further, from the point of view of

njection system, engine performance, and resulting contaminants, biodiesel is practically similar to common diesel blends (Lujan et al.,009; Wang et al., 2000).

Biodiesel is defined by the American Society of Testing and Materials as a methyl ester of long-chained fatty acids, commonly referreds fatty acid methyl esters (FAME). FAME is commonly obtained through a transesterification of triglyceride (TG) with an alcohol, usuallyethanol (Zhang et al., 2003a, 2003b) as illustrated in Fig. 1.Some common sources for bio-oil or TG are palm (Hameed et al., 2009; Kansedo et al., 2008), microalgae (Chisti, 2008), Jatropha (Achten

t al., 2008), rapeseed (Shao et al., 2009), pennycress (Moser et al., 2009), mahua (Ghadge & Raheman, 2006), Chinese tallow kernel (Gaot al., 2009), sunflower (Pereyra-Irujo et al., 2009), Camelina sativa (Patil et al., 2009), castor (Scholz & da Silva, 2008), and soybean (Tengt al., 2009). It is also possible that the bio-oil used for FAME production is a mixture (Tapasvi et al., 2005). In a case where obtaining pureatural source is costly, waste cooking oil, which has more fatty acids in it, has also been investigated as an alternative (Bautista et al.,009; Su et al., 2008; Zhang et al., 2003a, 2003b).

Transesterification is commonly performed with a base or an acid catalyst. These two processes were investigated thoroughly from theechnical point of view (Bautista et al., 2009; Su et al., 2008; Zhang et al., 2003a, 2003b) and their economic feasibilities (Zhang et al., 2003a,003b). The TG transesterification kinetics was investigated on different solid catalysts such as calcium oxides modified with lanthanumYan et al., 2009), modified zirconia (Lopez et al., 2008), and commonly used aluminum oxide (Patil & Deng, 2009; Teng et al., 2009).t has also been suggested that carrying out the transesterification reaction in supercritical conditions with methanol can eliminate the
se of catalyst (Tan et al., 2009). As can be seen from the above examples, biodiesel production can vary due to its feedstock type and
ts reaction environment, which will consecutively impact the downstream processes. Given all these options, the synthesis of the bestiodiesel production process is a challenging problem.

∗ Corresponding author. Tel.: +1 918 631 3422; fax: +1 918 631 3268.E-mail address: [email protected] (S. Cremaschi).

098-1354/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.compchemeng.2012.06.006

dx.doi.org/10.1016/j.compchemeng.2012.06.006

http://www.sciencedirect.com/science/journal/00981354

http://www.elsevier.com/locate/compchemeng

mailto:[email protected]

dx.doi.org/10.1016/j.compchemeng.2012.06.006

106 I. Fahmi, S. Cremaschi / Computers and Chemical Engineering 46 (2012) 105– 123

Nomenclature

Operation variablesFlow molar flow rate (kg mol/h)Y binary variable� reactor’s conversion factor

ratio of required methanol over the total triglycerides� ratio of required catalyst over the total triglyceridesT temperature (K)P pressure (kPa)v volumetric flow rate (m3/h)V volume (m3)�HReac reactor’s duty (kJ/h)UAHeat product of the overall heat transfer coefficient and the heat transfer area of a heater (kJ/(h K))MSHeat mass flow rate of the heating steam of a heater (kg/h)UACool product of the overall heat transfer coefficient and the heat transfer area of a cooler (kJ/(h K))MCCool mass flow rate of the cooling water of a cooler (kg/h)� residence time (h)MW molecular weightRR reflux ratio of a distillation columnNS number of equilibrium stagesFL feed locationSR separation ratio of the light key componentDC column diameter (m)� parameter used to determine which reactant (NaOH and H2SO4) is the limiting reactant (kg mol/h)�1 excess NaOH (to be neutralized with H3PO4) (kg mol/h)�2 excess H2SO4 (to be neutralized with CaO) (kg mol/h)

required ratio between the amount of water for washing and the amount of glycerol in the liquid–liquid washer�h the change in enthalpy (kJ/(kg mol))�hvap the change in enthalpy due to evaporation (kJ/(kg mol))

Cost-related variablesReacCC reactor’s capital cost (USD)ReacUC reactor’s utilities cost (USD)HeatCC pre-reactor heater’s capital cost (USD)HeatUC pre-reactor heater’s utilities cost (USD)PostHCCC post-reactor heater/cooler’s capital cost (USD)PostHCUC post-reactor heater/cooler’s utilities cost (USD)DemColCC demethanolizer column’s capital cost (USD)DemColUC demethanolizer column’s utilities cost (USD)TGBDCC TGBD separator column’s capital cost (USD)TGBDUC TGBD separator column’s utilities cost (USD)MHTBCC MHTB separator column’s capital cost (USD)MHTBUC MHTB separator column’s utilities cost (USD)CatNeutCC catalyst neutralizer capital cost (USD)CatNeutUC catalyst neutralizer capital cost (USD)LLWCC liquid–liquid washer capital cost (USD)LLWUC liquid–liquid washer utilities cost (USD)DrierCC pre-TGBD drier capital cost (USD)DrierUC pre-TGBD drier utilities cost (USD)TCC total capital costs (USD)TUC total utilities costs (USD)ObjFunc the objective function (USD)

SubscriptsIN stream flowing in to unit operationOUT stream flowing out from unit operationWASTE stream flowing out from unit operation, but not going to be sent to other unit operationfeed feed stream of a columndistil distillate stream of a columnovhd overhead stream of a columnbot bottom stream of a columnrec recycled streamfresh fresh feedstock/external streamspec chemical species in general

I. Fahmi, S. Cremaschi / Computers and Chemical Engineering 46 (2012) 105– 123 107

TGi triglyceride i (TG1, TG2, and TG3 represent tripalmitin, triolein, and trilinolein, respectively)MEOH methanolBDi biodiesel i (BD1, BD2, and BD3 represent m-palmitate, m-oleate, and m-linoleate, respectively)GROL glycerolNaOH sodium hydroxideH2SO4 sulfuric acidCat catalyst (NaOH and H2SO4 for the second and third reactor, respectively)H3PO4 phosphoric acidNa3PO4 sodium phosphateCaO calcium oxideCaSO4 calcium sulfateH2O waterSTEAM heating steamRi reactor i (R1, R2, and R3 represent the first, second, and third reactors, respectively)PrHi pre-reactor heater connected to reactor RiPrMi pre-reactor mixer prior to pre-reactor heater PrHiEVi post-reactor expansion valve connected to reactor RiMi post-reactor mixer i (M1 and M2 for the first and second post-reactor mixer, respectively)PHi heater that is connected to post-reactor mixer MiPCi cooler that is connected to post-reactor mixer MiNHCi bypass stream that is connected to post-reactor mixer MiHECi heat exchange complex consisted of PHi, PCi, and NHCiDMCi demethanolizer column that is connected to heat exchange complex HECiPcM post-demethanolizer column mixer (prior to catalyst neutralization)Neut catalyst neutralizationLLW liquid–liquid washerdry pre-TGBD drier

Other peripherals

b&fppbrosIroo

s2ta

S

fANN ANN function

In an effort to come up with the best configuration to produce biodiesel from bio oil, some design and economical analysis work haveeen performed (Chang & Liu, 2009; Franceschini & Macchietto, 2006; Haas et al., 2006; Lim et al., 2009; López et al., 2010; van Kasteren

Nisworo, 2007; Vicente et al., 2007a, 2007b; West et al., 2008). In these works, the researchers have built a separate process modelor each process alternative and compare the resulting costs to each other. In other words, the process syntheses in these works wereerformed heuristically. However, performing analysis of the process alternatives in such a way may prevent obtaining the optimumrocess flowsheet and its design because it will be difficult to cover all possible alternatives. Theoretically, to synthesize the optimumiodiesel production plant, a superstructure optimization that covers all process alternatives should be performed. However, solving theesulting mathematical programming problem is computationally expensive if not impossible due to the complexity and non-convexityf the rigorous first-order process models. For example, the solution of the optimization problem to design a distillation column thateparates benzene and toluene required 200–500 CPU seconds with a PIII 667 MHz processor and 256 MB of RAM (Barttfeld et al., 2003).n this study, only a single distillation column was considered and feed’s condition was fully defined (Barttfeld et al., 2003). Thus, theemaining degrees of freedom come only from number of stages and feed location. This study demonstrates the high computational costf finding the optimum distillation-column design. For process synthesis, many distillation columns along with reactors and other unitperation models should be solved to find the optimum solution using superstructure optimization.

To reduce the complexity of the original problems, using surrogate models have been suggested in the field of design and processynthesis (Chambers & Mount-Campbell, 2002; Eldred & Dunlavy, 2006; Fernandes, 2006; Henao & Maravelias, 2010; Nascimento et al.,
000; Queipo et al., 2002; Sabuncuoglu & Touhami, 2002). Nascimento et al. (2000) performed a study on using neural networks, a specificype of surrogate model, as a tool to perform optimization of the chemical processes, with the nylon-6,6 polymerization process and aceticnhydride production as their case studies (Nascimento et al., 2000). For nylon-6,6 polymerization process, the neural network was used to
Fig. 1. Transesterification reaction of a triglyceride with methanol.teinbach (2007).

1

m22NcCgpnsmnFoupsnmt

sinppswf

2

ddn

3

12

3

4

5

6

7

4

pit


odel the polymerization reactor with seven process variables considered as inputs and three considered as the output (Nascimento et al.,000). These three variables are used to determine the quality of the product, namely the average molecular weight (Nascimento et al.,000). In the latter case study, the objective of the optimization was to minimize the byproduct gas generation (Nascimento et al., 2000).ascimento and his group emphasized the ability of neural network as a tool for process optimization to fill the gaps in the searching gridaused by the absence of a full analytical solution and from the lack of historical data (Nascimento et al., 2000). Chambers and Mount-ampbell (2002) showed that neural networks can be used to optimize the buffer sizes for queuing and manufacturing problems. Theyenerated an artificial neural network for a generic queuing node using simulation data and combines several nodes to models the overallroduction line (Chambers & Mount-Campbell, 2002). A similar work where neural network was shown to be able to capture the stochasticature was performed by Sabuncuoglu and Touhami (2002). They concluded that the success of surrogate model highly depends on theystem characteristics (Sabuncuoglu & Touhami, 2002). Queipo et al. (2002) showed that a model that represents a heterogeneous andultiphase petroleum reservoir that normally requires a time-consuming numerical simulator to evaluate can be replaced with a neural

etwork model, and the complex distribution of permeability and porosity can be captured by a neural network (Queipo et al., 2002).ernandes (2006) used neural networks to model the Fischer–Tropsch process (Fernandes, 2006). The relationship between the amountf gasoline or diesel production and pressure, hydrogen to carbon dioxide ratio, and the space velocity, which are traditionally modeledsing complex kinetic mechanisms, is represented by a neural network and the surrogate neural network model is used to maximize theroduction amount (Fernandes, 2006). Last but not least, an example of using neural network as surrogate models in the field of processynthesis was demonstrated by Henao and Maravelias (2010). In their work, they represented each and every unit operation with neuraletworks as the surrogate models (Henao & Maravelias, 2010). They then demonstrated the feasibility of using neural network as surrogateodels with a case study of maleic anhydride production from benzene with choices of using either CSTR or PFR listed in the superstructure

hey developed (Henao & Maravelias, 2011).The work in this paper covers the process synthesis of biodiesel production plant utilizing superstructure optimization. The developed

uperstructure covers the whole plant including the reactors and the separation section to purify the product. The resulting superstructures translated into a disjunctive programming formulation. In order to reduce the computational complexity of the model, artificial neuraletworks (ANNs) are developed as the surrogate models to replace rigorous first-principle models for the unit operations and mixingoints. The details of the problem statement and methodology are described in the first two sections. The description of the biodieselroduction superstructure is presented in Section 4. The setup for the process simulator to collect the data necessary to train and test theurrogate models is explained in Section 5. This is followed by a thorough explanation of the problem formulation. The paper is concludedith the results of the optimization, summary of our experience using neural networks as surrogate models in process synthesis, and

uture directions.

. Problem statement

The problem in this paper can be stated as following: Given three transesterification process alternatives, a bio oil feedstock with aetermined composition, and prescribed constraints reflecting the requirements in the allowable operating conditions, the objective is toevelop an appropriate biodiesel production superstructure and to determine the flowsheet and operating conditions that minimize theet present sink (i.e., total capital investment and utilities costs for 10 years) in order to produce 8000 tons of biodiesel per year.

. Methodology

Overall, the methodology in this paper can be listed as follows:

. Develop the biodiesel production superstructure using one-task-one-equipment network representation (Yeomans & Grossmann, 1999).

. Develop the disjunctive programming formulation corresponding to the biodiesel superstructure with black box unit operation andmixing point models.

. Model each unit operation and mixing point in the superstructure using a commercially available process simulator. We utilized AspenHYSYS V7.1 as the process simulator.

. Identify the input and output variables for each unit operation model and construct the simulation test matrix. The levels of inputvariables for each unit operation and the mixing points for the simulation runs were generated randomly from a uniform distributionwithin the allowable ranges of the corresponding variable.

. Generate the training and test data sets for the surrogate model development for each unit operation. This was achieved by running theprocess simulator using the simulation test matrix.

. Construct the surrogate models for each unit operation and mixing point. The ANNs (i.e., the surrogate models) was trained usingtraining data sets constructed in step five. Neural Network plug-in in MATLAB was used to train the network and to obtain the networkparameters. Several ANN architectures were investigated to identify the best one. The performances of the trained ANNs were comparedusing the test data sets. The ANN that yielded the smallest sum of squared error when compared to the simulation data for the test setwas selected as the best one.

. Incorporate the developed ANNs to the disjunctive programming formulation to replace the black box models and solve the resultingoptimization problem using GAMS v23.6.2 – with DICOPT solver.

. Biodiesel production superstructure details

A feedstock of virgin oil with a composition of 50 mol% tripalmitin, 33 mol% triolein, and 17 mol% trilinolein is sent to a biodieselroduction plant to produce 8000 tons of biodiesel per year (Figs. 2 and 3). The representation style of the superstructure used in this study

s referred to as one-task-one-equipment (OTOE), where each node or block represents certain equipment that performs a certain operationo incoming arrows and yields the exiting arrows. Each arrow represents a stream that has a certain state (Yeomans & Grossmann, 1999).


Itb

ThafwpttfirttkKmh

ntagt

Fig. 2. The first half of the biodiesel production superstructure.

n Figs. 2 and 3, the equipment to perform the necessary unit operations are represented with their common process simulator diagrams,he states are represented with arrows connecting the equipment and the inlet and outlet streams of the superstructure are shown aslock arrows.

The incoming feed stream of the bio oil is mixed with the stream containing the recycled methanol as well as the fresh external methanol.his combination of bio oil and methanol can be sent to three alternative routes of transesterification, namely the supercritical methanol,omogeneous alkali-catalyzed (i.e., NaOH), and homogeneous acid-catalyzed (i.e., H2SO4) reactors. Each of these three routes consists of

pre-heater, a reactor, and an expansion valve. The catalysts for reactors that require them are sent directly to the reactor. The mixedeed streams are heated to the required temperature of the reactors and then undergoes the transesterification in the reactor. In thisork, even though the reaction pressure is considered as one of the decision variables, the compression costs were not considered in theroblem formulation because according to our preliminary analysis, these costs are considerably small, and hence negligible, comparedo the costs of other unit operations. After the reactors, the product streams are expanded to the atmospheric pressure and proceed tohe demethanolizer columns. There are several alternative mixing schemas considered for the reactor exit streams: the effluent from therst reactor (transesterification with supercritical methanol reactor, Fig. 2) can be mixed with the one from the second reactor or the thirdeactor (alkali and acid catalyzed reactors, respectively) (Fig. 2). The mixing between the second and the third reactor is not included inhe superstructure to avoid water production due to neutralization before methanol separation. A pure methanol stream is required forhe recycle and since methanol–water system has an azeotrope point, the existence of water at this point is not desired. In addition, theinetics of the transesterification reactions that was used in this study from Freedman et al. (1986), Darnoko and Cheryan (2000) andusdiana and Saka (2001) does not account for the effects of water presence during the reactions. It has also been suggested that wateray inhibit the transesterification reaction (Lepage & Roy, 1986). From both mixers, the streams can either be heated, cooled, or neither

eated nor cooled before being fed into the demethanolizer column. The superstructure of the process up to this point can be seen in Fig. 2.If either alkali or acid-catalyzed reactor is selected, the bottoms of the demethanolizer column are sent to the neutralizer unit. The

ecessary neutralizer (i.e., H3PO4 and CaO to neutralize NaOH and H2SO4, respectively) is provided as an additional stream to neutralize
he unreacted NaOH or H2SO4. The resulting salt is separated as a waste stream using a gravity separator. On the other hand, if neitherlkali nor acid-catalyzed reactor is selected, the stream can be sent directly to a multistage liquid–liquid extraction column to take out thelycerol. After the glycerol is washed away, there are two major alternatives to purify the biodiesel product. The first one is to use a drierhat will take the trace methanol and water out, and then use a distillation column to separate the biodiesel product from the remaining
Fig. 3. The second half of the biodiesel production superstructure.


Table 1Specifications for hypothetical components.

Chemical species Molecular weight Normal boiling point (K) Ideal liquid density (kg/m3) Basis component

Tripalmitin 807.30 798.6 915 TrioleinTrilinolein 879.40 815.1 925 TrioleinH3PO4 98.00 599.5 1849 H2SO4

CaO 56.08 1943.2 2498 NaOHNa3PO4 163.90 1003.0 3094 H2SO4

uar

5

t(

swcmcnd

dTttswtptk

rdwdwab3

t(atvrtrfit

6

t

CaSO4 136.10 832.8 2569 H2SO4

Na2SO4 142.00 869.0 2681 H2SO4

nreacted bio oil. The other alternative is to use a single distillation column, but with a partial condenser instead of a total one. Methanolnd water will be obtained in the vapor stream of the condenser, while the biodiesel product is obtained as the distillate product, and theemaining unreacted bio oil is recovered as the bottoms product of the column. This part of the superstructure can be seen in Fig. 3.

. Process simulator setup

In order to generate the training and test data sets, each pertinent unit operation and the mixing points are modeled individually inhe process simulator. The details of the simulation set-up used in ASPEN HYSYS are summarized in this section. Non-random two liquidNRTL) was selected as the fluid package because highly polar components are involved in the process.

Chemical components that are not available in the process simulator libraries are defined as hypothetical components. The requiredpecifications for each of these chemical species are listed in Table 1. Knowing the molecular structure of these components, their moleculareights were calculated. The values listed in Table 1 for the normal boiling point and ideal liquid density were estimated utilizing the

orresponding values for model components available in the process simulator library and assuming that they change proportionally to theolecular weight. The model components for each chemical component that is not available in the process simulator are listed on the last

olumn of Table 1. The first two components were based on triolein because they can be classified into the triglycerides group. Componentumber 4 was based on NaOH because they are both base chemical species. The rest of the components were determined based on H2SO4ue to the fact that they are similar in the range of molecular weight and their rough molecular shapes.

The kinetics for the first reactor was obtained from Kusdiana and Saka’s work (Kusdiana & Saka, 2001). It was proposed that the reactionisplays a first-order kinetics with respect to triglycerides and the rate constant was reported for different pressure and temperature values.he data was available with a temperature range of 473.15–760.15 K and a pressure between 7 and 105 MPa (Kusdiana & Saka, 2001). Evenhough Kusdiana and Saka (2001) performed the experiment with pressure range up to 105 MPa, this is not the upper bound for pressurehat we use in this work. Instead, we took the maximum value of 200 bar based on van Kasteren and Nisworo’s (2007) work on modeling theupercritical transesterification. Thus, the range of 7–20 MPa for the pressure was used in the models. According to the regression analysise performed, the pressure 200 bar corresponds to temperature of about 650 K. Thus, we use temperature range of 473.15–650.15 K in

his work. According to the available data (Kusdiana & Saka, 2001), the rate constant is strongly correlated to temperature but not toressure. Furthermore, the presented reaction pressure has a strong correlation with temperature. The available data was used to estimatehe pre-exponential factor and the activation energy of the modified Arrhenius equation. These values were used to model the reactioninetics in the process simulator.

Darnoko and Cheryan (2000) reported the kinetics for the second reactor, i.e., transesterification with homogenous alkali-catalyzedeaction (Darnoko & Cheryan, 2000). They listed the rate constants for the transesterification reactions explicitly, i.e., appropriate to be usedirectly in the process simulator (Darnoko & Cheryan, 2000). The rate constants for all the forward and backward intermediate reactionsere listed (Darnoko & Cheryan, 2000). In order to include this kinetic model in the process simulator, the intermediate components,iglycerides and monoglycerides, were defined as hypothetical components. The hypothetical definition for these intermediate componentsas performed in a similar manner to define the triglycerides based on the molecular weight ratio. Since the reaction kinetics data was

vailable for a specific triglyceride to methanol ratio, we let the incoming flow rate be constant with the fixed composition as prescribedy Darnoko and Cheryan (2000). The temperature range for this type of reactor is between 300 and 500 K, while the pressure is between00 and 500 kPa.

The kinetics for the third reactor was derived from Freedman and Butterfield et al.’s work (Freedman et al., 1986). The data, presented inhe graphical form, represented the weight percent of biodiesel at the reactor effluent as a function of both temperature and residence timeFreedman et al., 1986). It was specified that this weight percent was only for the resulting organic layer after being quenched with somemount of water (Freedman et al., 1986). If it can be assumed that what is left in the organic layer were the biodiesel and the unreactedriglyceride, and because the molecular weight of triglyceride is about three times of the molecular weight of biodiesel, this weight percentalue can be assumed to give roughly the percent conversion in the transesterification reactor. The temperature range for this type ofeactor is from 350.15 and 390.15 K, while the pressure ranges from 300 to 500 kPa. An ANN was not used to model this reactor becausehe kinetic expression and the parameters are not presented in the literature (Freedman et al. (1986) presented a graph that represents theelationship between the reaction conversion and temperature and residence time.). Therefore, a non-linear regression was performed tot the available data of reaction conversion as a function of temperature and residence time. Examining the available data, it was concludedhat an S-shape sigmoid function was the most appropriate equation to represent the relationship.

. Problem formulation

In this section, the detailed disjunctive programming formulation of the superstructure described in Section 4 is provided. It includeshe objective function, followed by constraints as the unit operation models and the mixing point constraints.


Table 2Cost estimation coefficients.

Coefficients Description Computation/value

CoefVCRi Coefficient to estimate vessel’s capital cost CoefVCRi =(

M&S280

)∗ 101.9 ∗ (2.18 + Fm ∗ Fp)

where M&S = 1600, Fm = 3.67, Fp ={

2.50 for R11.35 for R2 or R3

}CoefHXRi Coefficient to estimate heat exchanger’s capital cost CoefVCRi =

(M&S280

)∗ 101.3 ∗ (2.29 + Fm ∗ (Fd + Fp)) ∗

(1U

)0.65

where M&S = 1600, U = 41 kJ/(h ft2 ◦C), Fm = 3.75, Fd = 0.85,

Fp ={

0.55 for R10.25 for R2 or R3

}CoefHS Cost of heating steam $8.00 per 1000 kgCoefCW Cost of cooling water $0.07 per 1 m3

Note: when required, it is taken that the allowable temperatureincrease of the cooling water is 17 ◦C

CoefNaOH Cost of sodium hydroxide $4000/tonCoefH2SO4 Cost of sulfuric acid $40/tonCoefCaO Cost of calcium oxide $40/tonCoefH3PO4 Cost of phosphoric acid $340/ton�hSTEAM Available enthalpy change by the heating steam 3756 kJ/(kg mol) (3500 kPa from 700 K to 600 K)�hNEUT Cooling duty from the neutralization reaction 3.5 × 105 kJ/(kg mol)

6

Iyrcai

6

r

IurlFrsao

mr

�hvap,MEOH Enthalpy of vaporization of methanol at 1 atm 3.529 × 104 kJ/kg�hvap,H2O Enthalpy of vaporization of water at 1 atm 4.056 × 104 kJ/kg

.1. Objective function

The objective function that is to be minimized is the total net present sink including capital and utilities costs as expressed in Eq. (1).t is also assumed that the plant has a life of 10 years with a Modified Accelerated Cost Recovery System (MACRS) of 10%. This assumptionields a multiplying factor of 7.189 for the utilities cost. Total capital costs (TCC) is the sum of all major equipment capital costs. For theemainder of the formulation, all variables that represent capital costs have a “CC” indicator on them. The capital costs of unit operations arealculated based on the cost estimation method given in Douglas (1988). The cost estimation coefficients used in the problem formulationre listed in Table 2. Meanwhile, total utilities costs (TUC) is the sum of all utilities costs. Similarly, all variables that represent utilities costsn the formulation have a “UC” indicator on them.

ObjFunc = TCC +(

10∑n=10

1(1 + MACRS)n

)∗ TUC = TCC + 7.189 ∗ TUC (1)

.2. Reactors

The first set of constraints comes from the three reactors. Eqs. (2) and (4)–(6) express the material balances of components in eacheactor. Eq. (3) represents the methanol requirements for each reactor to run under the prescribed conditions and kinetics.

FlowTGi,OUT,Ri = (1 − �Ri) ∗ FlowTGi,IN,Ri (2)

FlowMEOH,IN,RI = ˇRi ∗∑all TGi

FlowTGi,IN,Ri (3)

FlowMEOH,OUT,RI = (ˇRi − 3 ∗ �Ri) ∗∑all TGi

FlowTGi,IN,Ri (4)

FlowBDi,OUT,Ri = 3 ∗ �Ri ∗ FlowTGi,IN,Ri (5)

FlowGROL,OUT,Ri = �Ri ∗∑all TGi

FlowTGi,IN,Ri (6)

n this formulation, Flow indicates the molar flow rate. The first subscript of Flow represents the chemical species. The general indexsed here is spec unless specific species is referred to: TGi, MEOH, BDi, and GROL for the triglycerides, methanol, biodiesel, and glycerolespectively, while Cat refers to the catalyst, which includes both NaOH and H2SO4. Special to TGi and BDi, the label i indicates to whichong chain fatty acid family group the species belong to: 1, 2, and 3 for palmitin, olein, and linolein, respectively. The second subscript oflow represents the relative position of a stream to a unit operation of interest. In this section, the second subscripts of Flow, IN and OUT,epresent the stream entering or leaving the unit operation, respectively. The third subscript of Flow specifies which unit operation thetream is attached to. Subscript Ri refers to the three transesterification reactors: R1, R2, and R3, which are supercritical, alkali-catalyzed,nd acid-catalyzed reactors, respectively. � is the transesterification reaction conversion ratio, while represents the required molar ratiof the amount of methanol and the total amount of incoming triglycerides.

The second and third reactors require sodium hydroxide and sulfuric acid as the catalyst, respectively. Eq. (7) expresses the catalysts
aterial balance in each reactor, while Eq. (8) expresses the required catalyst amount for each reactor. In Eqs. (7) and (8), � refers to the
equired molar ratio of the amount of catalyst and the total amount of incoming triglycerides.

FlowCat,IN,Ri = FlowCat,OUT,Ri (7)

1

Aflc

Itb

ocFsrd

6

ttcr


FlowCat,IN,Ri = ϕRi ∗∑all TGi

FlowTGi,IN,Ri (8)

binary variable, YRi, is assigned to each reactor Ri, whose value is equal to 1 if the corresponding reactor is included in the processowsheet and 0 otherwise. Eqs. (9)–(11) give the disjunctive programming representation of the constraints used to define each reactor’sonversion factor and pressure and temperature ranges.

⎡⎢⎢⎢⎢⎢⎢⎣

YR1

�R1 = fANN(TR1, PR1, �R1)

pR1 = 10∧(6.31 ∗ TR1 − 13.12)

7000 ≤ PR1 ≤ 20, 000

473.15 ≤ TR1 ≤ 650.15

⎤⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

¬YR1

�R1 = 0

k = 0

PR1 = 0

TR1 = 0

�R1 = 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

(9)

⎡⎢⎢⎢⎢⎣

YR2

�R2 = fANN(TR2, PR2, �R2)

300 ≤ PR2 ≤ 500

300 ≤ TR2 ≤ 500

⎤⎥⎥⎥⎥⎦ ∨

⎡⎢⎢⎢⎢⎢⎢⎣

¬YR2

�R2 = 0

PR2 = 0

TR2 = 0

�R2 = 0

⎤⎥⎥⎥⎥⎥⎥⎦

(10)

⎡⎢⎢⎢⎢⎢⎣

YR3

�R3 = 1

1 + T−1.73R3 ∗ �−35.69

R3 ∗ exp(211.81)300 ≤ PR3 ≤ 500

350.15 ≤ TR3 ≤ 390.15

⎤⎥⎥⎥⎥⎥⎦ ∨

⎡⎢⎢⎢⎢⎣

¬YR3

�R3 = 0

PR3 = 0

TR3 = 0

⎤⎥⎥⎥⎥⎦ (11)

n Eqs. (9)–(11), �, T, and P represent reactor’s residence time, temperature, and pressure, respectively. For reactors 1 and 2, the transes-erification reaction conversion ratio, �R1 and �R2 are calculated using ANNs (fANN). For the remainder of the paper, the ANN equations wille represented with fANN. The weights and biases of each of the ANNs are provided as an Appendix in the supplementary documents.

Eq. (12) represents the calculations of the capital and utilities costs for each reactor. In Eq. (12), it can be seen that the capital costf each reactor Ri, ReacCCRi, is a function of the reactor volume (VRi), while the utilities cost, ReacUCRi, is the function of the amount ofooling water, �HReacRi, necessary to keep the reactor operating isothermally. The utility costs also incorporate the amount of catalyst,lowCat,IN,Ri, for the second and third reactors. The volumetric flow rate for each reactor Ri, vRi, is estimated with an ANN function (i.e., aurrogate model) developed from the simulation data. The volume is simply the residence time (�Ri) multiplied by the volumetric flowate. The reactor’s cooling duty is also estimated using an ANN function. It is assumed that the height of the reactor is three times of itsiameter. The conversion factor 3.28 ft/m is also included in the computation of reactor’s capital cost for the purpose of unit consistency.⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YRi

1 ≤ �Ri ≤ 20

vRi = fANN(Flowspec,IN,Ri, TRi, PRi)

VRi = �Ri ∗ vRi

�HReacRi = fANN(Flowspec,IN,Ri, TRi, PRi, �Ri)

ReacCCRi = (3.28)1.868 ∗ (3)0.802(

4 ∗ VRi

3 ∗

)1.868/3∗ CoefVCRi

ReacUCRi = CoefCW ∗ �HReacRi + CoefCat ∗ FlowCat,IN,Ri⎧⎪⎨⎪⎩

∀ spec ∈ {TGi, MEOH} for R1

∀ spec ∈ {TGi, MEOH, NaOH} for R2

∀ spec ∈ {TGi, MEOH, H2SO4} for R3

⎫⎪⎬⎪⎭

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

¬YRi

�Ri = 0

vRi = 0

VRi = 0

ReacCCRi = 0

�HReacRi = 0

ReacUCRi = 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(12)

.3. Pre-reactor heaters

The next set of constraints is related to the pre-reactor heaters (Fig. 2) and is shown in Eq. (13). Pre-reactor heaters are used to heat
he reactant stream to the required reactor temperature. The subscript PrHi corresponds to the pre-reactor heater that is connected tohe reactor Ri. The capital cost, HeatCCPrHi, is calculated as a function of the heater size, which is a function of the overall heat transferoefficient times its heat transfer area (UAHeatPrHi). The utilities cost, HeatUCPrHi, is directly proportional to the amount of heating steamequired (MSHeatPrHi). Both the heater’s overall heat transfer coefficient times its heat transfer area and the amount of necessary heating

siT

6

otfri

6

mctt

w

EHd


team, are ANN functions. The binary used in this formulation is the one defined for the reactor because this unit operation is only includedn the synthesized process if its corresponding reactor is selected as well. For the outlet temperature of the heater, TRi is used instead ofOUT,PrHi because these two correspond to the same variable.⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YRi

UAHeatPrHi = fANN(Flowspec,IN,PrHi, TIN,PrHi, TRi, PRi)

MSHeatPrHi = fAnn(Flowspec,IN,PrHi, TIN,PrHi,TRi, PRi)

HeatCCPrHi = (UAHeatPrHi)0.65 ∗ CoefHXRi

HeatUCPrHi = CoefHs ∗ MSHeatPrHi⎧⎨⎩

∀ spec ∈ {TGi, MEOH} for R1, PrH1

∀ spec ∈ {TGi, MEOH, NaOH} for R2, PrH2

∀ spec ∈ {TGi, MEOH, H2S04} for R3, PrH3

⎫⎬⎭

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎣

¬YRi

UAHeatPrHi = 0

MSHeatPrHi = 0

HeatCCPrHi = 0

HeatUCPrHi = 0

⎤⎥⎥⎥⎥⎥⎥⎦

(13)

.4. Expansion valves

These unit operations are used to depressurize the reactor’s effluent from the reaction pressure to the atmospheric pressure. The costf piping and valves are ignored. The subscript EVi corresponds to the expansion valve that is connected to the reactor Ri. The resultingemperature of the depressurized stream, TOUT,EVi, is obtained using an ANN function, Eq. (14). The binary in the disjunctive programmingormulation corresponds to the reactor’s binary because, similar to the pre-reactor heater, this unit operation only exists if the correspondingeactor does. For the inlet temperature of the valve, TRi is used instead of TIN,EVi because they are the same variable, and the outlet pressures not considered as one of the decision variables because it is set to be atmospheric pressure.⎡

⎢⎢⎢⎢⎢⎣

YRi

TOUT,EVi = fANN(Flowspec,IN,Evi, TRi, PRi)⎧⎨⎩

∀ spec ∈ {TGi, MEOH, BDi, GROL} for R1, EV1

∀ spec ∈ {TGi, MEOH, BDi, GROL, NaOH} for R2, EV2

∀ spec ∈ {TGi, MEOH, BDi, GROL, H2SO4} for R3, EV3

⎫⎬⎭

⎤⎥⎥⎥⎥⎥⎦ ∨[

¬YRi

TOUT,EVi = 0

](14)

.5. Post-reactor mixers

The alternatives in this case are mixing the effluent from the first reactor with the second or with the third reactor (Fig. 2). Eq. (15)akes sure that the effluent from the first reactor is either sent to the first or second mixer. Eq. (16) expresses the fact that the first mixer

an exist only if there is a stream coming from either the first or second reactors, or from both. Similarly Eq. (17) expresses the fact thathe second mixer can exist only if there is a stream coming from either the first or third reactors, or from both. The subscript Mi refers tohe post-reactor mixers: M1 and M2 for the first and second mixers, respectively.

YR1 = YR1,M1 + YR1,M2 (15)

YM1 = YR1,M1 ∨ YR2 (16)

YM2 = YR1,M1 ∨ YR3 (17)

here

YR1,M1 ={

1 if the effluent from reactor R1 is sent to mixer M10 otherwise

}

YR1,M2 ={

1 if the effluent from reactor R1 is sent to mixer M20 otherwise

}

YM1 ={

1 if mixer M1 is selected0 otherwise

}

YM2 ={

1 if mixer M2 is selected}

0 otherwise

q. (18) states that if there is only one stream coming in to the first mixer, then the outlet condition is equal to the inlet condition.owever, if there are two incoming streams, the outlet temperature, TOUT,M1, is computed with an ANN function. Similar relationships areefined for the second mixer in Eq. (19).

1

6

ntcitfoocah


⎡⎢⎢⎢⎢⎣

YR1,M1 ∧ ¬YR2

Flowspec,OUT,M1 = Flowspec,OUT,R1

TOUT,M1 = TOUT,EV1

∀ spec ∈ {TGi, MEOH, BDI, GROL}

⎤⎥⎥⎥⎥⎦ ∨

⎡⎢⎢⎢⎢⎣

¬YR1,M1 ∧ YR2


TOUT,M1 = TOUT,EV2

∀ spec ∈ {TGi, MEOH, BDI, GROL, NaOH}

⎤⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YR1,M1 ∧ YR2

Flowspec,OUT,M1 = Flowspec,OUT,R1 + Flowspec,OUT,R2

TOUT,M1 = fANN

⎛⎜⎜⎜⎜⎝

Flowspec,OUT,R1

Flowspec,OUT,R2

TOUT,EV1

TOUT,EV2

⎞⎟⎟⎟⎟⎠

{ ∀ spec ∈ {TGi, MEOH, BDI, GROL, NaOH} for R1

∀ spec ∈ {TGi, MEOH, BDI, GROL, NaOH} for R2

}

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎣

¬YR1,M1 ∧ ¬YR2

Flowspec,OUT,M1 = 0

TOUT,M1 = 0

⎤⎥⎦ (18)

⎡⎢⎢⎢⎢⎣

YR1,M2 ∧ ¬YR3


TOUT,M1 = TOUT,EV1

∀ spec ∈ {TGi, MEOH, BDI, GROL}

⎤⎥⎥⎥⎥⎦ ∨

⎡⎢⎢⎢⎢⎣

¬YR1,M2 ∧ YR3


TOUT,M1 = TOUT,EV3

∀ spec ∈ {TGi, MEOH, BDI, GROL, H2SO4}

⎤⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YR1,M2 ∧ YR3

Flowspec,OUT,M2 = Flowspec,OUT,R1 + Flowspec,OUT,R3

TOUT,M2 = fANN

⎛⎜⎜⎜⎜⎝

Flowspec,OUT,R1

Flowspec,OUT,R3

TOUT,EV1

TOUT,EV3

⎞⎟⎟⎟⎟⎠

{ ∀ spec ∈ {TGi, MEOH, BDI, GROL} for R1

∀ spec ∈ {TGi, MEOH, BDI, GROL, H2SO4} for R3

}

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎣

¬YR1,M2 ∧ ¬YR3

Flowspec,OUT,M1 = 0

TOUT,M2 = 0

⎤⎥⎦ (19)

.6. Heater and cooler complexes

The next constraints deal with the complex of heaters and coolers (Fig. 2). After mixing, a stream might be either heated, cooled oreither heated nor cooled. Eq. (20) makes sure that only one of these processes is applied to the stream. The heater, cooler, and bypasshat are connected to the post-reactor mixer Mi are grouped into a pseudo unit operation referred to as the post-reactor heat exchangeromplex, HECi. Eq. (21) states that if a heater PHi within HECi is selected (i.e., YPHi = 1) the outlet temperature has to be higher than thenlet temperature. On the other hand, if the cooler PCi within HECi is selected (i.e., YPCi = 1) the outlet temperature has to be lower thanhe inlet temperature. It is to be noted that the binary assigned for selecting neither heater nor cooler is YNHCi. As expressed in Eq. (22),or both heaters and coolers within HECi, the capital costs (PostHCCCHECi) are calculated as a function of the heat exchanger size (functionf UAHeatPHi and UACoolPCi). The heat exchangers’ UAs are ANN functions. Further, the utility cost of a heater is a function of the amountf heating steam (MSHeatPHi), which is expressed as an ANN function. Similarly, the utility cost of a cooler is a function of the amount ofooling water (MCCoolPCi), which is also an ANN function. Eq. (23) calculates the total utility costs (PostHCUCHECi) for post mixing coolersnd heaters. It is to be noted that the cost estimation coefficient for the heat exchangers is the same one used for the second pre-reactor
eater because of the similar pressure operation range.
YpHi + YpCi + YNHCi = 1 (20)

6

csol(s5iflsit

T(

aihocl

I. Fahmi, S. Cremaschi / Computers and Chemical Engineering 46 (2012) 105– 123 115⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YPHi

TOUT,HECi ≥ TIN,HECi

UAHeatPHi = fANN

(Flowspec,IN,HECi

TIN,HECiTOUT,HECi

)UACoolpCi = 0

MSHeatPHi = fANN

(Flowspec,IN,HECi

TIN,MiTOUT,HECi

)MCCoolpCi = 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YPCi

TOUT,HECi ≤ TIN,HECi

UACoolPCi = fANN

(Flowspec,IN,HECi

TIN,HECiTOUT,HECi

)UAHeatpHi = 0

MCCoolPCi = fANN

(Flowspec,IN,HECi

TIN,MiTOUT,HECi

)MSHeatpHi = 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YNHCi

TOUT,HECi = TIN,HECi

UAHeatpHi = 0

UACoolPCi = 0

MSHeatpHi = 0

MCCoolpCi = 0

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)

PostHCCCHECi = CoefHXR2 ∗ ((UAHeatPHi)0.65 + (UACoolPCi)

0.65) (22)

PostHCUCHECi = CoefHS ∗ MSHeatPHi + CoefCW ∗ MCCoolPCi (23)

.7. Demethanolizer columns

Demethanolizer columns are the distillation columns that are used to strip the majority of the unreacted methanol. The demethanolizerolumn that is connected to the heat exchanger complex HECi, is referred to with subscript DMCi. The set of constraints given in thisection also includes the ones that are used to recycle the stripped methanol back to the reactors (Fig. 2). Eq. (24) states that the majorityf the unreacted methanol goes to the distillate stream and then is recycled back. The separation ratio, SRDMCi, here is specified to be ateast 90%. The remaining methanol (following material balance) should be present in the bottoms stream as expressed in Eq. (25). Eq.26) takes care of the material balance for the remainder of the components in the feed stream. Eq. (27) states that since the distillatetream is always pure methanol, thus its temperature (Tdistil,DMCi) is the methanol’s saturated temperature (Tsat′dMethanol). The pressure of0 kPa is also selected to avoid the bottom temperature being higher than 600 K due to the fact that the available heating steam utilities

s assumed to have temperature less than 750 K. Eq. (28) states that the bottom temperature (Tbot,DMCi) is an ANN function of incomingow rate (Flowspec,feed,DMCi), feed temperature (Tfeed,DMCi), reflux ratio (RRDMCi), number of stages (NSDMCi), feed location (FLDMCi), and theeparation ratio. It is to be noted that the binary incorporated here is the binary of the post-reactor mixer because each distillation columns still in line with the mixer (Fig. 2). In this section and in Sections 6.13 and 6.14, the second subscripts of Flow, feed, distil, and bot, indicatehe distillation column’s feed, distillate, and bottoms stream, respectively.

FlowMEOH,distil,DMCi = SRDMCi ∗ FlowMEOH,feed,DMCi (24)

FlowMEOH,bot,DMCi = (1 − SRDMCi) ∗ FlowMEOH,feed,DMCi (25)

Flowspec,bot,DMCi = Flowspec,feed,DMCi

{ ∀ spec ∈ {TGi, BDi, GROL, NaOH} for DMC1

∀ spec ∈ {TGi, BDi, GROL, H2SO4} for DMC2

}(26)

Tdistil,DMCi = Tsat′dMethanol@50 kPa (27)⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YMi

Tbot,DMCi = fANN

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

Flowspec,feed,DMCi

Tfeed,DMCi

PRDMCi ∀RR ∈ [3, 6]

NSDMCi ∀ NS ∈ [3, 12], ∀ NS ∈ Z

FLDMCi ∀ FL ∈ [1, 12], ∀ FL ∈ Z, ∀ FLDMCi ≤ NSDMCi

SRDMCi ∀ SE ∈ [0.9, 1.0]

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

{ ∀ spec ∈ {TGi, MEOH, BDi, GROL, NaOH} for DMC1

∀ spec ∈ {TGi, MEOH, BDi, GROL, H2SO4} for DMC2

}

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨[

¬YMi

Tbot,DMCi = 0

](28)

he column diameter (DCDMCi), heat exchangers sizes (UAHeatDMCi and UACoolDMCi), and the heating (MSHeatDMCi) and cooling utilitiesMCCoolDMCi) are also ANN functions and can be represented with equations similar to Eq. (28).

The column diameter and heat exchangers’ size are the factors that determine the capital cost of this distillation column (DemColCCDMCi),s expressed in Eq. (29), while the heating and cooling utilities are the factors that determine the utilities cost (DemColUCDMCi), as expressedn Eq. (30). It is to be noted that the cost estimation coefficient that is used for the reboiler is the one of the alkali-catalyzed reactor pre-eater because of the similarity in the operation pressure range. Similar to the reactor’s capital cost estimation, there is a conversion factorf 3.28 ft/m in the capital cost estimation of demethanolizer column vessel. It is also to be noted that in Eq. (29), the computation of theolumn’s height is already included. It is assumed that each tray is 0.6096 m high and there is a 0.058 m space between trays. Last but noteast, it is assumed that the tray efficiency is 85%.

DemColCCDMCi = CoefVCR2 ∗ (3.28)1.868 ∗ (DCDMCi)1.066 ∗

((NSDMCi ∗ 0.6096

0.85

)+(

(NSDMCi − 1) ∗ 0.0580.85

)+ (3 ∗ DCDMCi)

)0.802

+ CoefHXR2 ∗ ((UAHeatDMCi)0.65 + (UACoolDMCi)

0.65) (29)

1

6

piohTiat

6

a(p

6

tsrdEnnfs


DemColUCDMCi = CoefHS ∗ MSHeatDMCi + CoefCW ∗ MCCoolDMCi (30)

.8. Pre-reactor mixers

Prior to the pre-reactor heater, the fresh methanol and triglycerides are mixed with the recycled methanol from the demethanolizer. There-reactor mixer that is connected to the pre-reactor PrHi is referred to as PrMi. The resulting temperature, TOUT,PrMi, of the mixed streams

s calculated using an ANN function of the flow rate of each stream as expressed in Eq. (31). It should be noted that inlet temperature is notne of the independent variables because the feedstock temperature has already been determined as 298.15 K and the recycled methanolas a saturated temperature at 50 kPa. In this section, the index rec and fresh indicate the recycle and fresh feedstock stream, respectively.he material balance constraints around the pre-reactor mixers are given in Eq. (32), which states that the amount of methanol comingnto reactor Ri is the sum of the fresh and recycled methanol that comes from the demethanolizer, and in Eq. (33), which states that themount of triglycerides coming into reactor Ri is equal to the amount of fresh triglycerides. Eqs. (34) and (35) are incorporated to maintainhe necessary TGi composition within the stream.

TOUT,PrMi = fANN(FlowMEOH,rec,PrMi, FlowMEOH,fresh,PrMi, FlowTGi,fresh,PrMi) (31)∑all Ri

FlowMEOH,IN,Ri =∑

all DMCi

FlowMEOH,bot,DMCi +∑

all PrMi

FlowMEOH,fresh,PrMi (32)

∑all Ri

FlowTGi,IN,Ri =∑

all PrMi

FlowTGi,fresh,PrMi (33)

FlowTG1,IN,Ri = 5033

∗ FlowTG2,IN,Ri (34)

FlowTG1,IN,Ri = 5017

∗ FlowTG3,IN,Ri (35)

.9. Post-column mixer

The bottoms streams from both demethanolizers are mixed before further downstream processing (Fig. 2). This post-column mixer, pseudo unit operation, is referred to as PcM. The equation sets described in this section describes this process. Eq. (36) is similar to Eq.18), except in this case the bottoms product streams from the first and second demethanolizer columns are mixed. The binary of theost-reactor mixer is used in Eq. (36) since the demethanolizer column is in line with the post-reactor mixer.⎡

⎢⎢⎢⎢⎣YM1 ∧ ¬YM2

Flowspec,OUT,PcM = Flowspec,bot,DMC1

TOUT,PcM = Tbot,DMC1

∀ spec ∈ {TGi, MEOH, BDi, GROL, NaOH}

⎤⎥⎥⎥⎥⎦ ∨

⎡⎢⎢⎢⎢⎣

¬YM1 ∧ YM2

Flowspec,OUT,PcM = Flowspec,bot,DMC2

TOUT,PcM = Tbot,DMC2

∀ spec ∈ {TGi, MEOH, BDi, GROL, H2SO4}

⎤⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YM1 ∧ YM2

Flowspec,OUT,PcM = Flowspec,bot,DMC1 + Flowspec,bot,DMC2

TOUT,PcM = fANN

⎛⎜⎜⎜⎜⎝

Flowspec,bot,DMC1

Flowspec,bot,DMC2

Tbot,DMC1

Tbot,DMC2

⎞⎟⎟⎟⎟⎠

{ ∀ spec ∈ {TGi, MEOH, BDi, GROL, NaOH} for M1, DMC1

∀ spec ∈ {TGi, MEOH, BDi, GROL, H2SO4} for M2, DMC2

}

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎣

¬YM1 ∧ ¬YM2

Flowspec,OUT,PcM = 0

TOUT,PcM = 0

⎤⎥⎦ (36)

.10. Catalyst neutralizer

After the streams from both demethanolizers’ bottoms are mixed, the resulting stream is now sent to a unit operation to neutralizehe catalyst. This unit operation is referred to as Neut. Before additional catalyst neutralizer (H3PO4 or CaO) is added, it is assumed thatodium hydroxide and sulfuric acid neutralize each other. Eq. (37) is used to determine the limiting reactant, NaOH or H2SO4, which isepresented by variable � . If neither NaOH nor H2SO4 is present in the feed stream, then Eq. (37) also states that the initial neutralizationid not occur. Eqs. (38) and (39) are used to compute the amount of leftover catalyst (�1 and �2 for NaOH and H2SO4, respectively) andq. (40) is used to compute the resulting Na2SO4 salt. Based on the leftover amount of NaOH, Eq. (41) calculates the amount of H3PO4
ecessary to neutralize it and the resulting Na3PO4 is calculated using Eq. (42). Similarly Eq. (43) calculates the necessary CaO amount toeutralize the leftover H2SO4 from the initial neutralization. The amount of CaSO4 is calculated in Eq. (44). The amount of water produced
rom the initial neutralization, acid-catalyst and also base-catalyst neutralizations are calculated using Eq. (45). Eq. (46) deals with theeparation of the resulting salts as the waste stream by the gravity separator, while the rest of the components are sent to the liquid–liquid

eT(vro

6

sitatfliw


xtraction column. The volumetric flow rate of the neutralizer feed stream, vNeut, is represented by an ANN function as shown in Eq. (47).he volume of the neutralization unit, VNeut, is obtained by multiplying the volumetric flow rate with a determined residence time (Eq.48)). This residence time, �Neut, is obtained from the similar unit operations described in Zhang et al. (2003a, 2003b). Similar to otheressels, volume is the variable used to calculate the capital cost of this unit as expressed in Eq. (49) while the utilities cost comes from theeaction’s duty, which depends on the amount of both NaOH and H2SO4 in the neutralizer feed stream (Eq. (50)). For the second subscriptf Flow in this section, WASTE refers to the resulting salt stream from the neutralization reaction.[

yR2 ∧ yR3

� = MIN(0.5 ∗ FlowNaOH,OUT,PcM, FlowH2SO4,OUT,PcM)

]∨[

¬yR2 ∧ ¬yR3

� = 0

](37)

�1 = FlowNaOH,OUT,PcM − 2 ∗ � (38)

�2 = FlowH2SO4,OUT,PcM − � (39)

FlowNa2SO4,OUT,Neut = � (40)

FlowH3PO4,IN,Neut = �13

(41)

FlowNa3PO4,OUT,Neut = �13

(42)

FlowCaO,IN,Neut = �2 (43)

FlowCaSO4,OUT,Neut = �2 (44)

FlowH2O,OUT,Neut = �1 + �2 + 2 ∗ � (45)∑all salt

Flowspec,WASTE,Neut = FlowNa3PO4,OUT,Neut + FlowCaSO4,OUT,Neut + FlowNa2SO4,OUT,Neut (46)

vNeut = fANN(Flowspec,IN,Neut, TIN,NEUT )∀ spec ∈

⎧⎪⎨⎪⎩

TGi, MEOH, BDi, GROL, NaOH(yR1 ∨ yR2) ∧ ¬yR3

TGi, MEOH, BDi, GROL, H2SO4(yR1 ∨ yR3) ∧ ¬yR2

TGi, MEOH, BDi, GROL, NaOH, H2SO4(yR1 ∧ yR3) ∨ yR1

⎫⎪⎬⎪⎭ (47)

VNeut = �Neut ∗ vNeut (48)

CatNeutCC = CoefVCR2 ∗ (3.28)1.868 ∗ (3)0.802 ∗(

4 ∗ VNeut

3 ∗

)1.868/3(49)

CatNeutUC = CoefH3PO4 ∗ MWH3PO4 ∗ FlowH3PO4,IN,Neut + CoefCaO ∗ MECaO ∗ FlowCaO,IN,Neut

+ CoefHS ∗ MWH2O

�hSTEAM∗ ((FlowNaOH,IN,Neut + FlowH2SO4,IN,Neut) ∗ �hNeut) (50)

.11. Liquid–liquid extraction column

This unit operation is used to remove the majority of the glycerol using a multi-stage stripper. In modeling this unit, we followed thepecifications provided by Zhang et al. (2003a, 2003b). Eq. (51) calculates the required amount of additional water relative to the amount ofncoming glycerol and the ratio is obtained from (Zhang et al., 2003a, 2003b). The result of the separation is expressed in Eq. (52) wherehe total amount of water and methanol has to be less than 6 mol% (Zhang et al., 2003a, 2003b). The glycerol and a small amount of waternd methanol comprise the waste stream, while the rest of the components continue for further purification. Similar to the previous unit,he volumetric flow rate of the liquid–liquid washer, vLLW, of the incoming stream is an ANN function as expressed in Eq. (53). Volumetricow rate, multiplied by a predetermined residence time, �LLW (Zhang et al., 2003a, 2003b), is used to compute the volume, VLLW, as shown

n Eq. (54). This obtained volume is the variable used to compute the capital cost, LLWCC, shown in Eq. (55), while the amount of requiredashing water is taken as the utilities cost, LLWUC, as shown in Eq. (56).

FlowH2O,IN,LLW (for washing) = ∗ FlowGROL,IN,LLW (51)

FlowH2O,OUT,LLW FlowMEOH,OUT,LLW∑all specFlowspec,OUT,LLW

≤ 0.06 (52)

vLLW = fANN(Flowspec,IN,LLW , TIN,LLW )∀ spec ∈ {TGi, MEOH, BDi, GROL, H2O} (53)

VLLW = �LLW ∗ vLLW (54)

LLWCC = CeofVCR2 ∗ (3.28)1.868 ∗ (3)0.802 ∗(

4 ∗ VLLW

3 ∗

)1.868/3(55)

LLWCU = CoefCW ∗ (FlowH2O,IN,LLW (for washing)) (56)

1

6

drot(add(s

6

ottta

(

u


.12. Pre-TG-BD-column drier

The first alternative for the final product purification step is to send the stream from the liquid–liquid extraction column to a chain of arier that will take out the methanol and water and a distillation column that will separate the biodiesel from the unreacted triglycerides;eferred to as TGBD column for the remainder of this paper. This alternative is represented by a binary variable, YTGBD, which is equal tone if this sequence is selected in the final process, 0 otherwise. This section details the constraints about the drier. The formulation forhe column will follow in the next sections. The volumetric flow rate of the incoming stream, vdry, is estimated with an ANN function (Eq.57)). Notice that in this part, glycerol is still one of the components considered in this unit operation despite the fact that it was removedt the liquid–liquid extraction column. This is because the amount of water in the drier feed stream (in addition to the amount produceduring the neutralization reaction) is dependent on the amount of glycerol. The second and third parts of Eq. (57) follow the same styleescribed for the previous unit where the volume (Vdry) is computed and then used to compute the capital cost (DrierCC). The utilities costDrierUC) is calculated based on the amount of heating steam required to vaporize the amounts of methanol and water in the drier feedtream (Eq. (57)).⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

YTGBD

vdry = fANN(Flowspec,IN,dry, TIN,dry)∀ spec ∈ {TGi, MEOH, BDi, GROL, H2O}Vdry = �dry ∗ vdry

DrierCC = CorgVCR2 ∗ (3.28)1.868 ∗ (3)0.802 ∗(

4 ∗ Vdry

3 ∗

)1.868/3

DrierUC = CoefHS

�hSTEAM∗(

FlowMEOH,IN,dry ∗ MWMEOH

�hvap,MEOH+ FlowH2O,IN,dry ∗ MWH2O

�hvap,H2O

)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨

⎡⎢⎢⎢⎢⎢⎢⎣

¬YTGBD

vdry = 0

Vdry = 0

DrierCC = 0

DrierUC = 0

⎤⎥⎥⎥⎥⎥⎥⎦

(57)

.13. TG-BD column

This distillation column is used to purify the biodiesel product and separate the unreacted triglycerides. The feed stream of this unitperation is the exit stream of the drier that removes the excess methanol and water. Eq. (58) states that the majority of the biodiesel goeso the distillate, while as shown in Eq. (59), the rest is recovered in the bottoms stream. At least 90% of the biodiesel (SRTGBD) is recovered ashe distillate product. Eq. (60) dictates that all unreacted triglycerides should end up in the bottoms product of the column. Eq. (61) showshat the distillate temperature is calculated using an ANN function with the following inputs: inlet stream conditions and the column’srchitecture, which are reflux ratio, number of stages, feed location, and separation ratio.

FlowBDi,distil,TGBD = SRTGBD ∗ FlowBDi,feed,TGBD (58)

FlowBDi,bot,TGBD = (1 − SRTGBD) ∗ FlowBDi,feed,TGBD (59)

FlowTGi,bot,TGBD = FlowTGi,feed,TGBD (60)⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Tdistil,TGBD = fANN

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

YTGBD

Flowspec,feed,TGBD

Tfeed,TGBD

RRTGBD∀ RR ∈ [3, 6]

NSTGBD∀ NS ∈ [3, 12], ∀ NS ∈ Z

FLTGBD ∀ FL ∈ [1, 12], ∀ FL ∈ Z, ∀ FLTGBD ≤ NSTGBD

SRTGBD ∀ SR ∈ [0, 9, 1.0]

∀ spec ∈{

TGi, BDi}

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨[

¬YTGBD

Tdistil,TGBD = 0

](61)

ANN functions are also used to represent the bottom temperature (Tbot,TGBD), column diameter (DCTGBD), heat exchangers’ sizesUAHeatTGBD and UACoolTGBD), and the heating (MSHeatTGBD) and cooling (MCCoolTGBD) utilities.

The column and heat exchanger size are used to compute the capital cost (TGBDCC) as shown in Eq. (62), while Eq. (63) states that thetilities cost of the column (TGBDUC) is a function of the amount of heating steam and cooling water.

TGBDCC = CoefVCR2 ∗ (3.28)1.868 ∗ (DCTGBD)1.066 ∗((

NSTGBD ∗ 0.60960.85

)+(

(NSTGBD − 1) ∗ 0.0580.85

)+ (3 ∗ DCTGBD)

)0.802

+ CoefHXR2 ∗ ((UAHeatTGBD)0.65 + (UACoolTGBD)0.65) (62)

TGBDUC = CoefHS ∗ MSHeatTGBD + CoefCW ∗ MCCoolTGBD (63)

6

a

t

tostt

S(ca

S

Ll

E(

7

r

7

I


.14. Methanol–water-TG-BD (MHTB) column

The second alternative to purify the product includes a single distillation column with a partial condenser (Fig. 3). Methanol and waterre obtained as vapor stream from the partial condenser and the biodiesel product is collected as the distillate stream. The alternative of

his unit operation is represented by a binary variable, YMHTB ={

1 if this column is selected in the final flowsheet0 otherwise

}. Eq. (64) states that

he majority of the methanol and water in the feed should go to the overhead stream, while Eq. (65) states that the biodiesel product isbtained in the distillate stream. Eqs. (66) and (67) states that the rest of the methanol, water, and biodiesel are collected as the bottomstream along with the unreacted triglycerides as shown in Eq. (68). Eq. (69) shows that the distillate temperature is an ANN function ofhe column feed conditions and the column’s architecture, which are reflux ratio, number of stages, feed location, and separation ratio. Inhe second subscript of Flow in this section, index ovhd refers to the overhead vapor stream of the partial condenser.

Flowspec,ovhd,MHTB = SRMHTB ∗ Flowspec,feed,MHTB∀ spec ∈ {MEOH, H2O} (64)

FlowBDi,distil,MHTB = SRMHTB ∗ FlowBDi,feed,MHTB (65)

Flowspec,bot,MHTB = (1 − SRMHTB) ∗ Flowspec,feed,MHTB∀ spec ∈{

MEOH, H2O}

(66)

FlowBDi,bot,MHTB = (1 − SRMHTB) ∗ FlowBDi,feed,MHTB (67)

FlowTGi,bot,MHTB = FlowTGi,feed,MHTB (68)⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

Tdistil,MHTB = fANN

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

YMHTB

Flowspec,feed,MHTB

Tfeed,MHTB

RRMHTB ∀ RR ∈ [3, 6]

NSMHTB ∀ NS ∈ [3, 12], ∀ NS ∈ Integer

FLMHTB ∀ FL ∈ [1, 12], ∀ FL ∈ Integer, ∀ FLMHTB ≤ NSMHTB

SRMHTB ∀ SR ∈ [0, 9, 1.0]

∀ spec ∈{

TGi, MEOH, BDi, H2O}

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∨[

¬YMHTB

Tdistil,MHTB = 0

](69)

imilar to the distillate temperature (Tdistil,MHTB), bottom temperature (Tbot,MHTB), column diameter (DCMHTB), condenser and reboiler’s sizesUAHeatMHTB and UACoolMHTB), and heating (MSHeatMHTB) and cooling utilities (MCCoolMHTB) are calculated via ANN functions as well. Theolumn diameter and the heat exchangers’ sizes are then utilized to calculate the capital cost (MHTBCC) as shown in Eq. (70), while themount of heating steam and cooling water are used to compute the utilities cost (MHTBUC) as expressed in Eq. (71).

MHTBCC = CoefVCR2 ∗ (3.28)1.868 ∗ (DCMHTB)1.066 ∗((

NSMHTB ∗ 0.60960.85

+(

(NSMHTB − 1) ∗ 0.0580.85

)+ (3 ∗ DCMHTB)

))0.802

+ CoefHXR2 ∗((

UAHeatMHTB

41

)0.65

+(

UACoolMHTB

41

)0.65)

(70)

MHTBUC = CoefHS ∗ MSHeatMHTB + CoefCW ∗ MCCoolMHTB (71)

ince the TGBD and MHTB column cannot be selected together, the sum of their binaries has to add up to one as expressed in Eq. (72):

YTGBD + YMHTB = 1 (72)

ast but not least, we need to include the cost of the fresh feedstock of the main reactants, triglycerides and methanol. This calculation isisted in Eq. (73).

RawMatCost = CoefMEOH ∗∑

all PrMi

FlowMEOH,fresh,PrMi + CoefTGi ∗∑

all,PrMi

∑allTGi

FlowTGi,fresh,PrMi (73)

qs. (1)–(73) constitute a disjunctive programming formulation. We obtained the corresponding Mixed Integer Nonlinear ProgrammingMINLP) model using Big-M approach.

. Results and discussion

The first part of this section covers the result of the optimization problem and the second part discusses the overview and challengesegarding the development and utilization of ANNs for superstructure optimization.

.1. Result of the optimization problem

The optimization problem was solved using GAMS V23.6.2 in a computer with Windows 7 Professional 64-bit operating system, Dualntel E5405 2.0 GHz processors, and 8 GB RAM memory. The MINLP solver used was DICOPT. The resulting MINLP formulation has 1732


Table 3Optimal results from various initial guesses.

No. Binaries (Y) Total cost (USD) Solution time (CPU s)

Reactor Mix alternatives HEC1 HEC2 Downstream

R1 R2 R3 R1,M1 R1,M2 PC1 NHC1 PH1 PC2 NHC2 PH2 TGBD MHTB

1 0 1 0 0 0 0 1 0 0 1 0 1 0 4.1068E+07 5.3022 1 1 0 0 1 0 1 0 0 1 0 1 0 4.2811E+07 9.9923 1 1 0 0 1 0 1 0 0 1 0 0 1 4.4905E+07 5.2404 1 1 1 1 0 0 1 0 0 0 1 1 0 4.6440E+07 9.6435 0 1 0 0 0 1 0 0 0 1 0 1 0 4.7159E+07 5.1976 0 1 0 0 0 0 0 1 1 0 0 0 1 4.7646E+07 8.4727 0 1 1 0 0 0 1 0 0 1 0 1 0 4.7909E+07 11.4548 0 1 1 0 0 0 0 1 1 0 0 1 0 4.8199E+07 7.8949 1 0 1 0 1 1 0 0 0 1 0 1 0 4.9727E+07 8.019

10 1 0 1 1 0 1 0 0 0 1 0 0 1 5.2627E+07 3.24411 1 1 1 0 1 1 0 0 0 0 1 1 0 5.2907E+07 8.27012 1 1 1 0 1 0 1 0 0 1 0 1 0 5.3301E+07 10.24913 1 1 1 0 1 0 0 1 1 0 0 1 0 5.3398E+07 7.89314 1 1 1 1 0 1 0 0 0 1 0 1 0 5.3983E+07 10.81115 1 0 0 1 0 0 1 0 0 1 0 1 0 5.4136E+07 14.61716 1 1 1 1 0 0 0 1 1 0 0 1 0 5.4282E+07 23.43217 1 1 1 1 0 0 0 1 0 1 0 1 0 5.4516E+07 9.17218 1 1 1 0 1 0 1 0 0 0 1 0 1 5.5512E+07 5.16419 1 0 0 1 0 0 1 0 1 0 0 1 0 5.5670E+07 11.31220 1 1 1 1 0 0 1 0 0 1 0 1 0 5.6041E+07 10.09421 1 1 1 1 0 1 0 0 0 1 0 0 1 5.6416E+07 12.84122 0 1 1 0 0 0 0 1 0 0 1 1 0 5.6986E+07 10.32823 1 0 1 0 1 0 0 1 0 0 1 1 0 5.8606E+07 10.59224 1 1 0 0 1 0 1 0 1 0 0 1 0 5.8653E+07 8.39425 0 1 0 0 0 0 1 0 0 0 1 1 0 5.8764E+07 11.27926 1 1 0 0 1 1 0 0 0 0 1 1 0 5.8764E+07 8.29827 1 1 0 0 1 0 1 0 0 0 1 1 0 5.8776E+07 7.05528 1 0 1 1 0 1 0 0 1 0 0 1 0 5.8778E+07 18.61829 1 1 0 0 1 1 0 0 1 0 0 1 0 5.8816E+07 7.64430 1 1 0 0 1 1 0 0 0 1 0 1 0 5.8824E+07 5.68131 1 0 0 1 0 1 0 0 0 1 0 1 0 5.8846E+07 10.21832 1 0 0 0 1 0 0 1 1 0 0 1 0 5.8851E+07 11.18533 0 0 1 0 0 0 0 1 1 0 0 1 0 5.8872E+07 13.07234 0 0 1 0 0 1 0 0 0 1 0 1 0 5.8923E+07 8.12735 0 1 0 0 0 0 1 0 1 0 0 1 0 5.9014E+07 7.95636 1 0 1 1 0 0 1 0 1 0 0 1 0 6.0387E+07 5.11637 1 1 0 0 1 1 0 0 1 0 0 0 1 6.0515E+07 13.19838 1 1 0 0 1 0 0 1 0 1 0 1 0 6.0610E+07 8.73639 1 1 0 0 1 0 0 1 0 0 1 0 1 6.0706E+07 16.14540 1 1 1 1 0 1 0 0 0 0 1 1 0 6.1231E+07 5.38641 1 1 0 0 1 0 1 0 1 0 0 0 1 6.2516E+07 11.46842 1 1 0 0 1 0 0 1 0 1 0 0 1 6.3198E+07 5.94443 1 1 1 0 1 0 0 1 0 0 1 0 1 6.5019E+07 10.67044 1 0 0 0 1 0 1 0 0 0 1 1 0 6.8399E+07 6.95945 1 0 1 1 0 0 1 0 0 0 1 0 1 7.0140E+07 4.99246 1 0 0 0 1 0 1 0 1 0 0 1 0 1.0414E+08 5.648

cgots

scbwo

7

tad

47 1 0 0 0 1 0 1 0 0 1 0 1 0 1.0417E+08 4.08648 1 0 1 0 1 0 1 0 0 0 1 0 1 1.1065E+08 12.482

onstraints and 1711 variables. The optimization problem is solved many times with different initial points. The initial guesses wereenerated by enumerating all possible combinations of the independent binaries. All continuous variables were initialized at the middlef their upper and lower values. Of the 198 initializations, 48 of them yielded local optimal solutions. The solution time ranged from 1.0o 23.4 CPU seconds for all initializations (including the ones that were infeasible). The results of all local optimal solutions along with theolution times are given in Table 3. The data in Table 3 is sorted in increasing order of the net present sink.

The details of the lowest net present sink solution are presented as follows. This optimum solution was obtained in about five CPUeconds, and it dictates using only the second reactor, i.e., alkali-catalyzed transesterification reaction. Following the demethanolizerolumn, the neutralizer unit and liquid–liquid extraction column separate glycerol, the biodiesel should be purified using the drier followedy distillation. The net present sink of the optimum solution is USD 41.06 million. The optimum flowsheet can be seen in Fig. 4. This flowsheetas also modeled in the process simulator and the resulting net present sink of the simulation model was USD 41.45 million, which differs

nly 0.96% from the superstructure optimization solution.

.2. The usage of artificial neural networks in superstructure optimization

Using ANN as surrogate models to reduce the model complexity in superstructure optimization problems is quite promising due tohe fact that the methodology is straight forward: gather the training sets from process simulator, train the ANN to fit the gathered data,nd attach the ANNs to the disjunctive program to solve the optimization problem. Regardless of which unit operation the ANN will beeveloped for, there is no difference in the surrogate model development methodology. In addition, the end-user does not have to postulate


dtotCopwbnap

rieaiawevicscdActaotctt

g

8

ab

Fig. 4. The optimum flowsheet.

ifferent predetermined mathematical relationships when shifting to modeling different unit operations. However, one still has to postulatehe ANN’s architecture, namely the number of layers and number of neurons in each layer and sometimes it might be time consuming tobtain the right ANN architecture. Nevertheless, our work suggests that ANN reduces the computational cost significantly, i.e., the solutiono the superstructure optimization problem to synthesize the optimum biodiesel production plant was obtained in approximately fivePU seconds. However, one might argue that this short computational time is rather an indication that the initial guess is near the localptimum. Despite this possibility, our study shows that even the longest solution time required to solve this whole process synthesisroblem is still lower than the time needed to solve a single distillation column problem that uses the first-principal relationship evenith using today’s available computing resources (Barttfeld et al., 2003; Kraemer et al., 2009; Caballero & Grossmann 2010). It should also

e noted that the problem presented in Barttfeld et al. (2003), Kraemer et al. (2009) and Caballero and Grossmann (2010) consider onlyumber of trays and feed location as the decision variables. In our problem, for each distillation column, the feed composition, flow rate,nd temperature are decision variables. This observation suggests that ANN can be utilized to reduce the computational cost of solvingrocess synthesis problems.

One of the challenges faced using ANN for superstructure optimization is the surrogate models reduced accuracy within the low-endegion: a region where the output values are close to their smallest allowable values. In addition, there are several other challenges we facedn developing ANN as the surrogate models for unit operations. As an example, consider the development of surrogate models for the heatxchangers. Let’s assume that we are trying to develop an ANN that will be used to predict the heat transfer area. Then inputs of the ANNre the inlet and exit stream compositions, and their pressures and temperatures. Physically we know that there has to be a temperaturencrease or decrease over the heat exchanger. Therefore, unlike the rest of the input variables, it is not possible to randomize both inletnd outlet temperatures at the same time to obtain the simulation test matrix. In a cooler, for example, the variable that is randomizedithin range is the outlet temperature. Then, the inlet temperature cannot be randomized within the known allowable range. Instead for

ach data point of the outlet temperature, it has a new minimum value, the outlet temperature. In other words, even though these twoariables are independent of each other when viewed from the ANN’s perspective, the data that is used to train it is not independent,.e., there is a constraint that connects them. Therefore, it can be clearly seen that although one input variable, outlet temperature for theooler, still maintains the uniform distribution in the training data set, the other one, the inlet temperature for our example, does not. Thiskews the output variables distribution in training data set. The resulting distribution difference between variables makes training theorresponding ANN rather challenging. In such cases, the distribution difference required us to generate rather large amounts of trainingata sets such that the ANN can capture the underlying phenomena that map the inputs to the output. An example for comparison: theNN for the volumetric flow rate of the stream coming into a reactor only requires 700 training data points, but the one for the post-reactorooler, both the size and amount of water, requires 8000 training data points. At this point it is also worth noting that a method to reducehe model’s dimensionality, such as Principal Component Analysis, although tested, in general could not be applied in process synthesispplications due to the independent nature of the composition data in the input streams. In order to tackle this distribution difference,ther than collecting more training data points, we also applied a mathematical modification (e.g., powered to a certain value) to theraining data points such that the distribution of the dependent input variable (feed stream temperature for our example) becomes aslose as possible to a uniform distribution. The parameters that were used to measure how close the distribution is toward uniform arehe mean and the standard deviation. It was shown that after the modification, the ANN training showed better results than compared tohe raw variables.

One last important limitation of any surrogate model is the fact that the surrogate model is as accurate as the data that is used toenerate it. Therefore, it is imperative to have accurate training data points.

. Conclusions and future direction

Biodiesel is an interesting and rather promising type of biofuel because it can be produced from the abundance source of bio oilnd it is compatible with the current petro diesel engines, either used as a pure substitute or as a blending complement. Producingiodiesel is commonly done by the transesterification of bio oil, in a form of triglycerides or fatty acid, with methanol. There are several

1

pasi

muarsiac

dttt

A

A

2

R

AB

B

C

CCCDDEFF

FG

G

HH

HHH

H

K

K

K

KKLL

L

L

L


rocess alternatives for transesterification, such as using homogeneous catalysts, utilizing solid catalysts, or using supercritical methanols one of the reactants without any catalysts. To synthesize the optimum biodiesel production plant, a simultaneous optimization of theuperstructure that maps all of the process alternatives needs to be performed. The resulting MINLP formulation, which is highly nonlinear,s quite costly to solve if it is solvable.

In this paper, surrogate models are used to tackle superstructure optimization of biodiesel production. Among many kinds of surrogateodels, ANN is utilized due to its ability to reduce the model’s complexity without losing its representativeness. The solution shows that

sing the alkali-catalyzed transesterification reactor gives us the optimum process flowsheet. The fact that this problem was solved in onlybout five CPU seconds shows that using ANNs as surrogate models to reduce the model’s complexity for the purpose of process synthesis isather promising. However, this was not achieved without challenges. Large amounts of training data sets or points need to be gathered forome unit operations such that the ANN can capture the underlying model accurately. In addition, the difference in distribution betweennput variables, mainly due to the physics and sizing relationship requirements, also makes the ANN training somewhat challenging. Inn effort to tackle such circumstances, we modified the training data points using mathematical transformations such that they will be aslose as possible to a uniform distribution. This improves the accuracy of the ANN predictions.

As a future direction, an improvement on how to develop a method to build ANN that fits the training data well with as few trainingata points as possible regardless of the existence of distribution difference between variables will be considered. It should be noted thathe optimum solution is dependent on the model parameters such as the cost and composition of the bio oil, cost of methanol as well ashe catalyst, the capacity of the plant and utility costs. As a future direction, a through sensitivity analysis will be performed to understandhe impact of these parameters on the suggested process flowsheet and operating conditions.

cknowledgement

The financial support by the Graduate School at the University of Tulsa is acknowledged.

ppendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.compchemeng.012.06.006.

eferences

chten, W. M. J., Verchot, L., Franken, Y. J., Mathijs, E., Singh, V. P., Aerts, R., et al. (2008). Jatropha bio-diesel production and use. Biomass and Bioenergy, 32(12), 1063–1084.arttfeld, M., Aguirre, P. A., & Grossmann, I. E. (2003). Alternative representations and formulations for the economic optimization of multicomponent distillation columns.

Computers & Chemical Engineering, 27(3), 363–383.autista, L. F., Vicente, G., Rodriguez, R., & Pacheco, M. (2009). Optimisation of FAME production from waste cooking oil for biodiesel use. Biomass and Bioenergy, 33(5),

862–872.aballero, J. A., & Grossmann, I. E. (2010). S. Pierucci, & G. B. Ferraris (Eds.). Hybrid simulation-optimization algorithms for distillation design. Computer Aided Chemical

Engineering, 28, 637–642.hambers, M., & Mount-Campbell, C. A. (2002). Process optimization via neural network metamodeling. International Journal of Production Economics, 79(2), 93–100.hang, A.-F., & Liu, Y. A. (2009). Integrated process modeling and product design of biodiesel manufacturing. Industrial & Engineering Chemistry Research, 49(3), 1197–1213.histi, Y. (2008). Biodiesel from microalgae beats bioethanol. Trends in Biotechnology, 26(3), 126–131.arnoko, D., & Cheryan, M. (2000). Kinetics of palm oil transesterification in a batch reactor. Journal of the American Oil Chemists’ Society, 77(12), 1263–1267.ouglas, J. M. (1988). Conceptual Design of Chemical Processes. New York: McGraw-Hill.ldred, M. S., & Dunlavy, D. M. (2006). Formulations for surrogate-based optimization with data fit, multifidelity, and reduced-order models.ernandes, F. A. N. (2006). Optimization of fischer-tropsch synthesis using neural networks. Chemical Engineering & Technology, 29(4), 449–453.ranceschini, G., & Macchietto, S. (2006). Validation of a model for biodiesel production through model-based experiment design. Industrial & Engineering Chemistry Research,

46(1), 220–232.reedman, B., Butterfield, R., & Pryde, E. (1986). Transesterification kinetics of soybean oil 1. Journal of the American Oil Chemists’ Society, 63(10), 1375–1380.ao, Y.-y., Chen, W.-w., Lei, H., Liu, Y., Lin, X., & Ruan, R. (2009). Optimization of transesterification conditions for the production of fatty acid methyl ester (FAME) from

Chinese tallow kernel oil with surfactant-coated lipase. Biomass and Bioenergy, 33(2), 277–282.hadge, S. V., & Raheman, H. (2006). Process optimization for biodiesel production from mahua (Madhuca indica) oil using response surface methodology. Bioresource

Technology, 97(3), 379–384.aas, M. J., McAloon, A. J., Yee, W. C., & Foglia, T. A. (2006). A process model to estimate biodiesel production costs. Bioresource Technology, 97(4), 671–678.ameed, B. H., Lai, L. F., & Chin, L. H. (2009). Production of biodiesel from palm oil (Elaeis guineensis) using heterogeneous catalyst: An optimized process. Fuel Processing

Technology, 90(4), 606–610.enao, C. A., & Maravelias, C. T. (2010). S. Pierucci, & G. B. Ferraris (Eds.). Surrogate-based process synthesis. Computer Aided Chemical Engineering, 28, 1129–1134.enao, C. A., & Maravelias, C. T. (2011). Surrogate-based superstructure optimization framework. AIChE Journal, 57(5), 1216–1232.ill, J., Nelson, E., Tilman, D., Polasky, S., & Tiffany, D. (2006). Environmental, economic, and energetic costs and benefits of biodiesel and ethanol biofuels. Proceedings of the

National Academy of Sciences, 103(30), 11206–11210.sieh, W.-D., Chen, R.-H., Wu, T.-L., & Lin, T.-H. (2002). Engine performance and pollutant emission of an SI engine using ethanol-gasoline blended fuels. Atmospheric

Environment, 36(3), 403–410.ansedo, J., Lee, K. T., & Bhatia, S. (2008). Feasibility of palm oil as the feedstock for biodiesel production via heterogeneous transesterification. Chemical Engineering and

Technology, 31(7), 993–999.okossis, A. C., & Yang, A. (2010). On the use of systems technologies and a systematic approach for the synthesis and the design of future biorefineries. Computers & Chemical

Engineering, 34(9), 1397–1405.raemer, K., Kossack, S., & Marquardt, W. (2009). Efficient optimization-based design of distillation processes for homogeneous szeotropic mixtures. Industrial & Engineering

Chemistry Research, 48(14), 6749–6764.ralj, A. K. (2008). Heat integration between two biodiesel processes using a simple method. Energy and Fuels, 22(3), 1972–1979.usdiana, D., & Saka, S. (2001). Kinetics of transesterification in rapeseed oil to biodiesel fuel as treated in supercritical methanol. Fuel, 80(5), 693–698.epage, G., & Roy, C. C. (1986). Direct transesterification of all classes of lipids in a one-step reaction. Journal of lipid research, 27(1), 114–120.im, Y., Lee, H.-s., Lee, Y.-W., & Han, C. (2009). Design and economic analysis of the process for biodiesel fuel production from transesterificated tapeseed oil using supercritical

methanol. Industrial & Engineering Chemistry Research, 48(11), 5370–5378.opez, D. E., Goodwin, J. G., Jr., Bruce, D. A., & Furuta, S. (2008). Esterification and transesterification using modified-zirconia catalysts. Applied Catalysis A: General, 339(1),

76–83.óıpez, D. E., Mullins, J. C., & Bruce, D. A. (2010). Energy life cycle assessment for the production of biodiesel from rendered lipids in the United States. Industrial & Engineering

Chemistry Research, 49(5), 2419–2432.ujan, J. M., Tormos, B., Salvador, F. J., & Gargar, K. (2009). Comparative analysis of a DI diesel engine fuelled with biodiesel blends during the European MVEG-A cycle:

Preliminary study (I). Biomass and Bioenergy, 33(6–7), 941–947.

http://dx.doi.org/10.1016/j.compchemeng.2012.06.006

http://dx.doi.org/10.1016/j.compchemeng.2012.06.006

M

N

PP

P

Q

S

SS

SS

T

T

Tv

V

VW

WYY

YZ

Z


oser, B. R., Knothe, G., Vaughn, S. F., & Isbell, T. A. (2009). Production and evaluation of biodiesel from field pennycress (Thlaspi arWense L.) oil. Energy and Fuels, 23(8),4149–4155.

ascimento, C. A. O., Giudici, R., & Guardani, R. (2000). Neural network based approach for optimization of industrial chemical processes. Computers & Chemical Engineering,24(9–10), 2303–2314.

atil, P. D., & Deng, S. (2009). Transesterification of camelina sativa oil using heterogeneous metal oxide catalysts. Energy & Fuels, 23(9), 4619–4624.atil, P. D., Gude, V. G., & Deng, S. (2009). Biodiesel production from jatropha curcas, waste cooking, and camelina sativa oils. Industrial and Engineering Chemistry Research,

48(24), 10850–10856.ereyra-Irujo, G. A., Izquierdo, N. G., Covi, M., Nolasco, S. M., Quiroz, F., & Aguirrezabal, L. A. N. (2009). Variability in sunflower oil quality for biodiesel production: A simulation

study. Biomass and Bioenergy, 33(3), 459–468.ueipo, N. V., Pintos, S., Rincón, N., Contreras, N., & Colmenares, J. (2002). Surrogate modeling-based optimization for the integration of static and dynamic data into a reservoir

description. Journal of Petroleum Science and Engineering, 35(3–4), 167–181.abuncuoglu, I., & Touhami, S. (2002). Simulation metamodelling with neural networks: An experimental investigation. International Journal of Production Research, 40,

2483–2505.cholz, V., & da Silva, J. N. (2008). Prospects and risks of the use of castor oil as a fuel. Biomass and Bioenergy, 32(2), 95–100.hao, P., He, J., Sun, P., & Jiang, S. (2009). Process optimisation for the production of biodiesel from rapeseed soapstock by a novel method of short path distillation. Biosystems

Engineering, 102(3), 285–290.teinbach, A. (2007). A Comprehensive Analysis of Biodiesel. Biodiesel Magazine, 4(11).u, C.-H., Fu, C.-C., Gomes, J., Chu, I. M., & Wu, W.-T. (2008). A heterogeneous acid-catalyzed process for biodiesel production from enzyme hydrolyzed fatty acids. AIChE

Journal, 54(1), 327–336.an, K. T., Lee, K. T., & Mohamed, A. R. (2009). Production of FAME by palm oil transesterification via supercritical methanol technology. Biomass and Bioenergy, 33(8),

1096–1099.apasvi, D., Wiesenborn, D., & Gustafson, C. (2005). Process model for biodiesel production from various feedstocks. Transactions of the American Society of Agricultural

Engineers, 48(6), 2215–2221.eng, G., Gao, L., Xiao, G., & Liu, H. (2009). Transesterification of soybean oil to biodiesel over heterogeneous solid base catalyst. Energy & Fuels, 23(9), 4630–4634.an Kasteren, J. M. N., & Nisworo, A. P. (2007). A process model to estimate the cost of industrial scale biodiesel production from waste cooking oil by supercritical

transesterification. Resources, Conservation and Recycling, 50(4), 442–458.icente, G., Martínez, M., & Aracil, J. (2007a). Optimisation of integrated biodiesel production. Part I. A study of the biodiesel purity and yield. Bioresource Technology, 98(9),

1724–1733.icente, G., Martínez, M., & Aracil, J. (2007b). Optimisation of integrated biodiesel production. Part II: A study of the material balance. Bioresource Technology, 98(9), 1754–1761.ang, W. G., Lyons, D. W., Clark, N. N., Gautam, M., & Norton, P. M. (2000). Emissions from nine heavy trucks fueled by diesel and biodiesel blend without engine modification.

Environmental Science & Technology, 34(6), 933–939.est, A. H., Posarac, D., & Ellis, N. (2008). Assessment of four biodiesel production processes using HYSYS.Plant. Bioresource Technology, 99(14), 6587–6601.

an, S., Kim, M., Salley, S. O., & Ng, K. Y. S. (2009). Oil transesterification over calcium oxides modified with lanthanum. Applied Catalysis A: General, 360(2), 163–170.eomans, H., & Grossmann, I. E. (1999). A systematic modeling framework of superstructure optimization in process synthesis. Computers & Chemical Engineering, 23(6),

709–731.
üksel, F., & Yüksel, B. (2004). The use of ethanol-gasoline blend as a fuel in an SI engine. Renewable Energy, 29(7), 1181–1191.hang, Y., Dube, M. A., McLean, D. D., & Kates, M. (2003a). Biodiesel production from waste cooking oil: 1. Process design and technological assessment. Bioresource Technology,
89(1), 1–16.hang, Y., Dube, M. A., McLean, D. D., & Kates, M. (2003b). Biodiesel production from waste cooking oil: 2. Economic assessment and sensitivity analysis. Bioresource Technology,

90(3), 229–240.

process synthesis of biodiesel production plant using artificial neural networks as the surrogate...

Documents