Modeling, simulation and optimization for chemical process

Phần 3: Tối ưu hóaModeling, simulation and optimization for chemical process

Instructor: Hoang Ngoc HaEmail: [email protected]

Bộ môn QT&TB

T. F. Edgar, D. M. Himmelblau. Optimization of chemical Processes. Second edition.

Bùi Minh Trí. Tối ưu hóa (lý thuyết và bài tập). NXB KHKT, Hà Nội, 2005.

CuuDuongThanCong.com https://fb.com/tailieudientucntt

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Introduction

The chemical industry has undergonesignificant changes during the past 25 yearsdue to the

increased cost of energyincreasingly stringent environmental regulationsglobal competition in product pricing and quality…

One of the most important engineering tools for addressing these issues is optimization

Decision-making process


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Introduction

As the power of computers has increased, the size and complexity of problems that canbe solved by optimization techniques have correspondingly expanded

The necessary tools for solving problemWe will focus on those techniques and discusssoftware that offers the most potential for success and gives reliable results


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Outline

Problem formulationNature and organization of Optimization problemsDeveloping models for optimization (constraints or process model)Formulation of the objective function

Optimization theory and methodsOptimization of unconstrained functionsLinear programming with constraintsNonlinear programming with constraintsMulti-objective optimization

Applications of Optimization


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Optimization

OPTIMIZATION IS THE use of specific methods to determine the most cost-effective and efficient solution 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 a given application and organizing them into a prescribed mathematical form)

The objective function (economic criterion)The process model (constraints)

The objective function represents such factors as profit, cost, energy, and yield in terms of the keyvariables of the process being analyzedThe process model and constraints describe theinterrelationships of the key variables


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Problem formulation

What optimization is all aboutOptimization is concerned with selecting the bestvalue by efficient quantitative methods

Why optimize?Largest productionGreatest profitMinimum costThe least energy usage…


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Problem formulation

Examples of applications of optimizationDetermining the best sites for plant locationRouting tankers for the distribution of crude and refined productsSizing and layout of a pipelineDesigning equipment and an entire plantScheduling maintenance and equipment replacementOperating equipment, such as tubular reactors, columns, andabsorbersEvaluating plant data to construct a model of a processMinimizing inventory chargesAllocating resources or services among several processesPlanning 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 processor 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. m1

g(x) is a vector of equations of dim. m2

where x = (x1 · · ·xn) ∈ X ⊂ Rn

D =nx ∈ X|h(x) = 0, g(x) ≥ 0

og(x) ≥ 0 inequality constraints


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Problem formulation

Example: optimal scheduling

tA1tA2

tB1tB2


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Problem formulation

What is the objective function?

tA1+ tA2

= 365

tB1+ tB2

= 365

tAi ≥ 0tBi ≥ 0

f(t) = tA1MA1

SA1+ tA2

MA2SA2

+tB1MB1

SB1+ tB2

MB2SB2


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Problem formulation

Các loại bài toán tối ưu (quy hoạch toán học)Quy hoạch tuyến tính (QHTT)

Ví dụ thuộc dạng này có Bài Toán Vận TảiQuy hoạch tham số (QHTS) là QHTT mà các hệ số trong

Quy hoạch động (QHĐ):Là quá trình có nhiều giai đoạn nói chung, hay các quá trìnhphát triển theo thời gian nói riêng

là tuyến tínhf(x), g(x), h(x)

phụ thuộc tham sốf(x), g(x), h(x)


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Problem formulation

Các loại bài toán tối ưu (quy hoạch toán học) Quy hoạch phi tuyến (QHPT)

Quy hoạch rời rạc (QHRR)

Quy hoạch đa mục tiêu (QHĐMT)Nếu trên cùng một miền ràng buộc D ta xét nhiều hàmmục tiêu khác nhau

là các hàm phi tuyếnf(x) hoặc g(x) hoặch(x)

DNếu miền ràng buộc là tập rời rạc


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Formulation of the objective function

Translate a verbal statement or concept ofthe desired objective into mathematical termsExample


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Formulation of the objective function

Example


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Problem formulation

The six steps used to solve optimizationproblems

Make a list of all of the process variablesDetermine the criterion for optimization, andspecify the objective function in terms of thevariables defined in step 1 together withcoefficients (Economic model)Using mathematical expressions, develop a validprocess 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 optimizationproblems

If the problem formulation is too large in scopeBreak it up into manageable parts orSimplify the objective function and model

Apply a suitable optimization technique to themathematical statement of the problemCheck the answers, and examine the sensitivity ofthe result to changes in the coefficients in theproblem and the assumptions


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Outline

Problem formulationNature and organization of Optimization problemsDeveloping models for optimization (constraints or process model)Formulation of the objective function

Optimization theory and methodsOptimization of unconstrained functionsLinear programming with constraintsNonlinear programming with constraintsMulti-objective optimization

Applications of Optimization


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Scope of course

Optimization problems

OPTIMIZATION OF UNCONSTRAINEDFUNCTIONS: ONE-DIMENSIONAL SEARCH

UNCONSTRAINEDMULTIVARIABLE OPTIMIZATION

NON LINEAR PROGRAMMINGLINEAR PROGRAMMING

MULTI-OBJECTIVE OPTIMIZATION (OR MULTI-OBJECTIVE PROGRAMMING)


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Modeling, simulation and optimization for chemical process

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