Pergamon Computers"chem. Engng, Vol. 21, Suppl., pp. $835-$840, 1997 © 1997 Elsevier Science Ltd All rights reserved Printed in Great Britain PII:S0098-1354(97)00153-1 0o98-1354/97$17.0o÷0 oo A formal graphical based process modeling methodology Tormod Drengstig, Stein O. Wasb¢ and Bjarne A. Foss* Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway. Abstract - In this paper we present a representation scheme for chemical unit processes. The representation is based on a topological and a phenomenological abstraction of the process. The topological abstraction decomposes the process into control volumes and boundaries. The phenomenological abstraction represents the phenomena in the process us- ing three general process characteristics, i.e. transport, reaction/generation and accumulation of mass and energy. For these entities we define a consistent set of graphical symbols that will be connected together in a network according to the modelers understanding of the process, giving a representation of the process. We further suggest to employ this representation in the development of a modeling methodology, where the symbols are related to differential and alge- braic equations in order to represent a complete and consistent mathematical model. The methodology is successfully applied to two industrial processes, a lerromanganese furnace and an aluminum electrolysis cell. The latter will he used as an example. Simulations of the aluminum cell focusing on AIFa dynamics are included. INTRODUCTION The phenomenological part describes the phenomena tak- To develop a mathematical model of a chemical process, ing place inside the topological process components, e.g. some sort of graphical sketch of the process is usually the chemical reaction or conductive heat flow. Hence, in this first step. This graphical sketch is a conceptual picture of work we focus on the development of analytical or first the process and it is used by the modeler when construct- principles mathematical models of lumped parameter sys- ing the mathematical model. Several factors influence the terns. chosen visualization of the process, e.g. 1) the properties that are believed to be important, 2) process assumptions Topologicalprocess abstraction like well mixed situation or equilibrium, 3) the complexity of the process, i.e. complex phenomena and reactions may Topological process abstraction is the abstraction or de- be difficult to represent graphically, and hence, have to be composition of a system into a network of topology corn- represented in some kind of textual or mathematical terms, ponents, i.e. devices and connections, at several differ- 4) the purpose of the model, e.g. is it to be used for control ent abstraction levels. In order to separate the compo- or design purposes, or 5) the model format, e.g. mechanis- nents at these different levels, we introduce composite tic vs. empirical, and elementary components. Composite topology compo- nents are components containing a set of composite and/or In this work, we focus on defining a consistent and for- elementary topology components, though, at the lowest mat graphical representation of chemical unit processes, level composed of elementary devices and connections. If such a formal representation can be defined, we fore- Only the elementary topology components contain a phe- see a development of a computer aided modeling tool able nomenological description. to interpret graphical symbols and guide the modeler to- wards a consistent mathematical model of her/his process. The basis for topological decomposition of plant processes A representation solely based on detailed equations is not is often guided by the physically separated unit processes necessarily the best way to obtain efficient interaction in constituting the plant. For the modularization of unit pro- communicating with other resource personal with differ- cesses themselves, there is no similar approach. The basis ent modeling knowledge and background. Hence, we be- may vary from chemical phase to temperature zone mod- lieve that a formalized graphical representation is a well ularization within the same model, depending on the pro- suited means for such communication, cess and the scope of the model. The approach employed in this work is to choose chemical phase as a modulariza- MODELING METHODOLOGY tion basis. This means that e.g. a two-phase evaporator The modeling methodology presented here is based on would be represented by one liquid and one gaseous ele- a formal graphical representation scheme. This scheme mentary device in the model representation. The complete consists of two main parts, a topological and a phe- evaporator would be a composite device containing two nomenological part. To the topological part belongs the elementary devices and one elementary connection. decomposition of the process into modules representing control volumes (devices) having accumulation proper- The graphical symbols for elementary and composite ties, and boundaries (connections) involving some kind components are given in Table 1. In order to connect the of flow between devices. This is a similar approach as topology components into a complete network, we intro- described in Marquardt (1994) and Perkins et al. (1994). duce various links or lines. These are given in Table 2. *Author to whom correspondence should be addressed. E-mail: Bjarne.Foss@itk.nmu.no $835