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The notion of a model is widely used in almost every ﬁeld of science. The term model

is applied to entities varying from mathematical descriptions to scaled down replica’s of the

actual system. This chapter discusses some general aspects of models for and the modeling

of chemical processes. It is not intended as an in depth discussion of various techniques,

but more as an introduction into process modeling and related topics. The considerations

presented here form a basis for chapter 3, where hybrid fuzzy-ﬁrst principles modeling is

discussed.

2.1 What is a model?

A general deﬁnition of a model in an engineering environment is given by Eykhoff

(Eykhoff, 1974). He deﬁnes a model as a representation of the essential aspects of an ex-

isting system (or a system to be constructed) which presents knowledge of that system in a

usable form. This means that a model is always a simpliﬁed representation of the real sys-

tem. Such a representation can provide insight in the behaviour of the system, which does

not necessarily mean that this insight is physical . For example, if an engineer is interested in

developing a controller for a chemical reactor, he usually will want to know how the reactor

behaves dynamically. Whether this knowledge is based on physical principles or not does not

have to be relevant for his purposes.

A model is seldom a goal in itself. It is always a tool to help solving a problem, which beneﬁts

from a mathematical description of the system. Applications of models in engineering can be

found in three general areas (Eykhoff, 1974; Luyben, 1990):

Research and development. A model in research gives an interpretation of knowledge

or measurements. An example is the determination of chemical kinetic mechanisms

from laboratory or pilot-plant reaction data.

Design. Models used in design can be used to determine the correct design parameters

of a component or sub-system or can be used to study process stability, process safety,

economical aspects, etc. This means that the available knowledge has to be expressed

in such a way that it is compatible with these criteria.

Control. The control actions are based on the knowledge that is available of the system.

In addition, it is cheaper to conduct experiments concerning plant operation and control

on models than on an operating unit (which does not mean that experimental setups are

not needed at all). The control actions can for example be designed to keep the process

on normal operating conditions, to handle the process in emergency situations (such as

diagnostic systems) or to manage start-up and shut-down processes.

11

2.2 Types of models

The different applications of models and the performance criteria that result from these

have lead to many different model structures. These can be compared from different points

of view. Figure 2.1 illustrates this.

2.2.1 White box and black box models

Models that are entirely based on physical and chemical laws (thermodynamics, continu-

ity equations) are called white box,ﬁrst principles or mechanistic models. These models give

a physical insight of the system and can even be built when the system is not yet constructed.

Usually a set of (partial) differential equations supplemented with algebraic equations is used

to give a mathematical description of the model. The effort needed to build these models is

is applied to entities varying from mathematical descriptions to scaled down replica’s of the

actual system. This chapter discusses some general aspects of models for and the modeling

of chemical processes. It is not intended as an in depth discussion of various techniques,

but more as an introduction into process modeling and related topics. The considerations

presented here form a basis for chapter 3, where hybrid fuzzy-ﬁrst principles modeling is

discussed.

2.1 What is a model?

A general deﬁnition of a model in an engineering environment is given by Eykhoff

(Eykhoff, 1974). He deﬁnes a model as a representation of the essential aspects of an ex-

isting system (or a system to be constructed) which presents knowledge of that system in a

usable form. This means that a model is always a simpliﬁed representation of the real sys-

tem. Such a representation can provide insight in the behaviour of the system, which does

not necessarily mean that this insight is physical . For example, if an engineer is interested in

developing a controller for a chemical reactor, he usually will want to know how the reactor

behaves dynamically. Whether this knowledge is based on physical principles or not does not

have to be relevant for his purposes.

A model is seldom a goal in itself. It is always a tool to help solving a problem, which beneﬁts

from a mathematical description of the system. Applications of models in engineering can be

found in three general areas (Eykhoff, 1974; Luyben, 1990):

Research and development. A model in research gives an interpretation of knowledge

or measurements. An example is the determination of chemical kinetic mechanisms

from laboratory or pilot-plant reaction data.

Design. Models used in design can be used to determine the correct design parameters

of a component or sub-system or can be used to study process stability, process safety,

economical aspects, etc. This means that the available knowledge has to be expressed

in such a way that it is compatible with these criteria.

Control. The control actions are based on the knowledge that is available of the system.

In addition, it is cheaper to conduct experiments concerning plant operation and control

on models than on an operating unit (which does not mean that experimental setups are

not needed at all). The control actions can for example be designed to keep the process

on normal operating conditions, to handle the process in emergency situations (such as

diagnostic systems) or to manage start-up and shut-down processes.

11

2.2 Types of models

The different applications of models and the performance criteria that result from these

have lead to many different model structures. These can be compared from different points

of view. Figure 2.1 illustrates this.

2.2.1 White box and black box models

Models that are entirely based on physical and chemical laws (thermodynamics, continu-

ity equations) are called white box,ﬁrst principles or mechanistic models. These models give

a physical insight of the system and can even be built when the system is not yet constructed.

Usually a set of (partial) differential equations supplemented with algebraic equations is used

to give a mathematical description of the model. The effort needed to build these models is

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