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7/29/2019 Bai Giang ToiUuHoa

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Phn 3: Ti u haModeling, simulation and optimization for chemical process

Instructor: Hoang Ngoc HaEmail: [email protected]

B mn QT&TBT. F. Edgar, D. M. Himmelblau. Optimization of chemical Processes.

Second edition.

Bi Minh Tr. Tiu ha (l thuyt v bi tp). NXB KHKT, H Ni, 2005.


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Introduction

The chemical industry has undergone

significant changes during the past 25 yearsdue to the

increased cost of energy

increasingly stringent environmental regulations global competition in product pricing and quality

One of the most important engineering tools foraddressing these issues is optimization

Decision-making process


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Introduction

As the power ofcomputers has increased,

the size and complexity of problems that canbe solved by optimization techniques have

correspondingly expanded

The necessary tools for solving problem

We will focus on those techniques and discusssoftware that offers the most potential for

success and gives reliable results


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Outline

Problem formulation

Nature and organization of Optimization problems Developing models for optimization (constraints or

process model)

Formulation of the objective function

Optimization theory and methods Optimization of unconstrained functions

Linear programming with constraints

Nonlinear programming with constraints

Multi-objective optimization

Applications of Optimization


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Optimization

OPTIMIZATION IS THE use of specific methods to

determine the most cost-effective and efficientsolution to a problem or design for a process

This technique is one of the major quantitative toolsin industrial decision making

A wide variety of problems in the design,

construction, operation, and analysis of chemicalplants (as well as many other industrial processes)can be resolved by optimization


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Problem formulation

Formulating the problem is perhaps the most crucial

step in optimization (from verbal statement of agiven application and organizing them into aprescribed mathematical form) The objective function (economic criterion)

The process model (constraints)

The objective function represents such factors asprofit, cost, energy, and yield in terms of the keyvariables of the process being analyzed

The process model and constraints describe theinterrelationships of the key variables


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Problem formulation

What optimization is all about

Optimization is concerned with selecting the bestvalue by efficient quantitative methods

Why optimize?

Largest production

Greatest profit

Minimum cost

The least energy usage


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Problem formulation

Examples of applications of optimization

Determining the best sites for plant location

Routing tankers for the distribution of crude and refined products

Sizing and layout of a pipeline

Designing equipment and an entire plant

Scheduling maintenance and equipment replacement

Operating equipment, such as tubular reactors, columns, andabsorbers

Evaluating plant data to construct a model of a process

Minimizing inventory charges

Allocating resources or services among several processes

Planning and scheduling construction

Example: See ref.


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Problem formulation

Main features of optimization problems

At least one objective function to be optimized

Equality constraints (equations)

Inequality constraints (inequalities)

Economic model

}Model of process

or equipment


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Problem formulation

Main features of optimization problems

Feasible solution/Feasible region

Underdetermined

Optimal solution

Overdetermined

Degrees of freedom


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Problem formulation

An optimization problem:

Minimize: f(x) objective function

Subject to: h(x) = 0 equality constraints

h(x) is a vector of equations of dim. m1g(x) is a vector of equations of dim. m2

where x = (x1 xn) X Rn

D =nx X|h(x) = 0, g(x) 0

o

g(x) 0 inequality constraint


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Problem formulation

Example: optimal scheduling

tA1 tA2

tB1 tB2


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Problem formulation

What is the objective function?

tA1 + tA2 = 365

tB1 + tB2 = 365

tAi 0

tBi 0

f(t) = tA1MA1SA1 + tA2MA2SA2+tB1MB1SB1 + tB2MB2SB2


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Problem formulation

Cc loi bi ton ti u (quy hoch ton hc)

Quy hoch tuyn tnh (QHTT)

V d thuc dng ny c Bi Ton Vn Ti

Quy hoch tham s (QHTS) l QHTT m cc h s trong

Quy hoch ng (QH): L qu trnh c nhiu giai on ni chung, hay cc qu trnh

pht trin theo thi gian ni ring

l tuyn tnhf(x), g(x), h(x)

ph thuc tham sf(x), g(x), h(x)


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Problem formulation

Cc loi bi ton ti u (quy hoch ton hc)

Quy hoch phi tuyn (QHPT)

Quy hoch ri rc (QHRR)

Quy hoch a mc tiu (QHMT) Nu trn cng mt min rng buc D ta xt nhiu hm

mc tiu khc nhau

l cc hm phi tuynf(x) hoc g(x) hoch(x)

DNu min rng buc l tp ri rc


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Translate a verbal statement or concept of

the desired objective into mathematical terms Example


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Example


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Example


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Example


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Problem formulation

The six steps used to solve optimization

problems Make a list of all of the process variables

Determine the criterion for optimization, and

specify the objective function in terms of thevariables defined in step 1 together withcoefficients (Economic model)

Using mathematical expressions, develop a valid

process or equipment model (Process model)that relates the input-output variables of theprocess and associated coefficients

Problem formulation


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Problem formulation

The six steps used to solve optimization

problems If the problem formulation is too large in scope

Break it up into manageable parts or

Simplify the objective function and model

Apply a suitable optimization technique to the

mathematical statement of the problem

Check the answers, and examine the sensitivity ofthe result to changes in the coefficients in the

problem and the assumptions


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Outline

Problem formulation

Nature and organization of Optimization problems Developing models for optimization (constraints or

process model)


Optimization theory and methods Optimization of unconstrained functions

Linear programming with constraints

Nonlinear programming with constraints

Multi-objective optimization

Applications of Optimization


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Scope of course

Optimization problems

OPTIMIZATION OF UNCONSTRAINED

FUNCTIONS: ONE-DIMENSIONAL SEARCHUNCONSTRAINED

MULTIVARIABLE OPTIMIZATION

NON LINEAR PROGRAMMINGLINEAR PROGRAMMING

MULTI-OBJECTIVE OPTIMIZATION

(OR MULTI-OBJECTIVE PROGRAMMING)

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