Course Material for Lectere 1

8/21/2019 Course Material for Lectere 1

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LECTURE 1

Process Mathematical Modeling

Introduction

athematical modeling belongs to or interacts with the real world. Mathematicalmodels are developed that describe the relationship between different

quantities of different engineering system. It concern with quantitative rather

than a qualitative treatment of the process. However the term itself has a very wide field

of application from economics to engineering and science. The development of the fastercomputer and sophisticated numerical solver has made the modeling of the complete

chemical enterprise in real-time environment viable.

Modeling is a fundamental and quantitative way to understand complex systems and phenomena. Simulation is complementary to the traditional approaches of theory and

experiment. Together, they (Modeling/Simulation/optimization) make up an approach

that can deal with a wide range of physical problems and at the same time exploit the power of large-scale computing.

"A model is an idealization. Its relationship to the real problem is like that of the map of

the London tube trains to the real tube systems: a gross simplification, but one that

captures certain essentials. The map misrepresents distances and directions, but itelegantly displays the connectivity. So it is with all successful models: they unashamedly

distort the inessentials in order to capture the features that really matter. At worst, a

model is a concise description of a body of data. At best, it captures the essential physics

of the problem, it illuminates the principles that underline the key observations, and it predicts behavior under conditions which have not yet been studied."“Modeling is the physicalization of a concept, Simulation its computational realization”

The main goal of this class is to present a collection of mathematical tools for both

understanding and solving problems in fields that manipulate models of the chemical

engineering sciences.Definition: The term modeling in turn refers to the derivation of appropriate equations

that are solved for a set or system of process variables and parameters. Process Model

extracts information form the system.

In a simplified term: True representation of a physical system is called model and in

mathematical modeling system is defined by no of equations.

Mathematical modeling will provide students a broader academic exposure than what they

would normally encounter within traditional courses.

M



Process ModelProcess Model( = () ) is combination of different system (Reactor System,

Separation System, Control and Safety System and so on) of a process plant. Process

modelling is not a new concept to chemical engineer. Due to advancement of

computer base mathematical and process modelling software modelling played an

important role in design and operation by simulation and optimisation study. It arisesfrom the traditional disciplines such as transport phenomena, Chemical Kinetics, reaction

design and Thermodynamics.The variety of products made by processes of chemical technology is overwhelming; it

comprises inorganic and organic basic chemicals. The equipment (apparatus, machines,

pipelines, automation and safety systems, etc.) has to be chosen so that the investmentsmade in them yield the maximum economy. The plant must be reliable and sufficiently

flexible. The computer aided process modelling permit the chemical process to be

interpreted in a computer base software package to understand the chemical process behaviour quickly.

Figure 1 Basic Chemical Process Model

Figure 2 process model

P

Reactor

S stem

Separation

S stem

Energy System

Control and Safety System

InputOutput

Independent

variables (x)

Dependent

variables (y)

Disturbances



Brine Heater

Stage 1

Makeup Mixer Makeup Splitter

Blowdown Splitter

Stage 2 Stage NRStage NR+1 Stage NR+2 Stage NR+NJ

FEED

SEAWATER

FreshWater

Waste

Recovery stagesRejection stages

Figure 3 A typical Multi stage desalination plant

Types of Process ModelThe variety of products compromises inorganic and organic chemicals is subject to very

rapid modification according to the customer demand. The improvement of process

design, productions system can be achieved by Process modelling. Two types of process(steady state and dynamic) are prominent in chemical engineering. A steady state model

ignores the changes in process variables with time whereas the dynamic model considers

dynamic characteristics. The dynamic models are useful to understand the start-up and

shutdown characteristics of the process. So this typ

According to the modelling complexity (see figure ) we have choosen different modelling

techniques:

• Empirical Models or Regression Model/Statistical Model

• Black Box Model

• First Principle Models• Reduced model (Linearization) Transfer Function

LECTURE:



IMPORTANCE OF MODELS

Why is Modeling important?

rocess modeling is an important component of process design economically, fromthe conceptual synthesis of the process flowsheet, to the detailed design of

specialized processing equipment such as advanced reaction and separation

devices, and the design of their control systems.

For example, modeling of fuel cell power plants involves electrical, chemical and controlengineers; many projects in the upstream oil industry employ combinations of chemical,

civil and mechanical engineers; and modeling projects in the fine chemicals and

consumer goods industries require the close collaboration of physicists, chemists and

engineers. These trends point towards a unification of mathematical modeling toolsacross different disciplines of engineering and science, as a means both of facilitating

collaboration among these diverse groups, and of minimizing the costs associated with

software acquisition and deployment. This development is also beneficial to modelingsoftware development, given its ever increasing complexity and cost

Key to a good model lies in what and how simplification is introduced; it is very

important to understand what aspects of the system the model is intended to describe, andwhat are the model's limitations as a result of the simplification.

When a complex system can be simplified (reduced) to a tractable level that makes clear

the essential structure of system and how the internal constituents interact with each

other.

• Experiments are expensive• Experiments needs large efforts

• Saves time

• Computer Understand Mathematics not Process

• Model should be reuseable in different CAPE open software packages (Aspen plus, gPROMS, Hysys)

P

Figure 4 Process design



Figure 5 Application of Modelling

Some of the feature of the mathematical modeling

A physical system can be described at different level

Mathematical modeling is a way to represent the engineering system into

mathematical system.

• Mathematical model formulate the physical system that are directly related to physical and chemical quantities.

• The modeling procedure is an adaptive procedure in which information gained

from each step is used to improve in the next try (Model Validation).

•

Model may be used for predicting the future behavior of system reconstructing the past behavior of the system (Neural fuzzy model) and understanding better

operating conditions by using control.

• Mathematical model can handle IPDAE system using the modern flowsheeting packages.

A modern chemical plant consists of interconnected units such as heat exchangers,

reactors, distillation columns, mixers etc. with high degree of integration to achieveenergy efficiency. Design and operation of such complex plants is a challenging problem.

One of the today’s modeling concept the model should be reusable through different

software packages



Figure 6 Mixer model

Figure 7 gPROMS Model is used in Aspentech



LECTURE:

MODELS DVELOPMENT

HOW TO BUILD A MODEL The Steps followed for development of Engineering Model

• Background : contains essential information which is unique to that particular

case study/project

• Problem Statement: Explain the objectives and to state what is given and what isrequired.

• Model Formulation: breaks the problem down and formulates it mathematically

in terms of governing equations/inequalities and relevant boundary/initial

conditions• Mathematical/Numerical Solution: A mathematical solution (if this is possible)

and/or, failing that, possible numerical solutions. depends upon the mathematicalsolver of the software package reformulate the problem

• Model Validation: is key to any model solution and could involve solutions

using alternative numerical techniques or the use of the computer, including

software packages, to back up the results obtained in the previous section.• Interpretation and Conclusions: interprets the results and draws major

conclusions giving, in some cases, suggestions for further extensions.

• Computer Algorithms discusses and, in some cases, gives details of anyimportant algorithms or software which have been used in the solution techniques.

Figure 8 A mathematics routes to solving engineering problems



Model Assumption:

Model Assumption: the complexity of Model depends on the types of assumption

considered the mathematical and computational difficulties occurring in solving the

model equations (computing time, store location) are reasons for the modelsimplifications required in the majority of cases. It also leads to appropriate type of

modeling techniques.Remember that Key to a good model lies in what and how simplification is introduced; it is

very important to understand what aspects of the system the model is intended to describe,and what are the model's limitations as a result of the simplification.



Hierarchical model decomposition

This is much easier than constructing a very large model for the entire flowsheet (as you

see in the flowsheet packages you find different equipment model pallet and you connect

them to build the flowsheet packages). It contain the declarations of all parameters,variable and equations for the entire flowsheet. However, modern modeling concept is to

divide the different section of the process flowsheet and connect together to develop the

Master model. The model for a complex process is constructed progressively in anumber of hierarchical levels. This Master model may be Process flowsheet or Process

enterprise (where scheduling and Supply chain study is conducted with simultaneouslyconducted control).



LECTURE:

Computer Aided Process Engineering

ver the past decade there has been an increasing demand for suitable material inthe area of mathematical modeling as applied to science, engineering, business

and management. Recent developments in computer technology and related

software have provided the necessary tools of increasing power and sophistication which

have significant implications for the use and role of mathematical modeling in the abovedisciplines. In the past, traditional methods have relied heavily on expensive

experimentation and the building of scaled models, but now a more flexible and cost

effective approach is available through greater use of mathematical modeling andcomputer simulation.

Due to the advancement of the microcomputers, the models are now directly connected to

the plant operation to carry out the plant performance calculations, generate managementinformation and also to perform limited alarm diagnostic. With the improvement of the

microcomputers and availability of the cheaper microcomputers, process modeling using

the microcomputers has become cost effective.

Any experimental work is expensive and the real plant operation is an expensive and time

consuming. Computer aided modeling, simulation and optimization saves the time andmoney by providing the fewer configuration of the experimental work. In addition,

computer simulation, optimization saves the money in design and operation. The long-term performance and reliability of individual plant vary from plant to plant and day today for various reasons such as operating conditions, scaling and fouling of heat transfer

surfaces in boilers and different desalination units. Therefore, better operations of the

existing plant depend on the better understanding of the different parameters of the plant.

Simulation helps to visualize the ultimate picture and trends of various conditions ofexisting plant as well as those of a new situation of the plant.

O

Model

Physical

property

packages

Equipmentmodel/Unit

model

Numerical

Solver

R

E

S

U

L

Figure 9 The general concept to develop the chemical Engineering Model using Flowsheeting

Packages



The typical modelling approach (Figure 10) in recent years for simulation and

optimisation uses numerical solvers. The numerical solvers may involve SQP basedmethods or any other non-gradient based optimiser such as GA, SA algorithm and in

simulation the solver may involve Newton-Raphson method, etc.

Figure 10 Typical Simulation and Optimization Architecture

Here is a list of related Commercial commonly used software for modelling, simulation

and optimisation in Chemical Industries:

1. GAMS

2. ASPEN HySys3. gPROMS

4. Simulink / MATLAB

5. GAMS

6. Berkeley Madonna and othersProcess mathematical model is a collection of (set) of equations that describe some aspect

of the chemical system under investigation. For many complex chemical processes the

model result is set of nonlinear equation requiring numerical solution. The most commonway to deal with this is to program the equations using the modelling software such as

gPROMS, Aspen Custom Builder or other engineering Software such as Matlab.

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