Accuracy of Mathematical Model with Regard to Safety Analysis of Chemical Reactors* A. MOLNÁR, J. MARKOŠ, and Ľ. JELEMENSKÝ Department of Chemical and Biochemical Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, SK-812 37 Bratislava e-mail: attila@chtf.stuba.sk Received 31 January 2002 Interest in discovering multiple steady-state solutions for reaction processes grew exponentially by the existence of the first computers. Modern process simulators can find multiple solutions only by the expenditure of much effort. Three mathematical models with different accuracy are introduced and a simple comparison of model’s accuracy is made with regard to safety analysis of continuous stirred tank reactor. The first two models are based on standards in chemical reactor design; the third one is an internal model of CSTR in HYSYS simulation program. Furthermore, OLE automation interface is also used to access the existing physical property packages of HYSYS. Chemical production in which chemical reactions take place at extreme condition (high temperature or pressure) requires a detailed analysis of possible dan- gerous situations, which may lead to industrial acci- dents with endangering of lives and health not only of workers, but also of civilians. From the viewpoint of operation safety, the attention should be focused on chemical reactors, especially multiple steady states, their characteristics; causes and ways of switching be- tween them are of a great importance. Liljenroth [1] first mentioned the existence of mul- tiple steady states at the beginning of the 20th cen- tury. The study of multiple steady states of a con- tinuous stirred tank reactor in which a single re- action occurs has been the subject of research of many authors. Many mathematical criteria have been proposed, but the usability of these analytical tech- niques and criteria is limited for simple situations [2— 4]. A paper by Heerden [5] on autothermic reactors contains an argument for stability from the slopes of the heat generation and removal curves. For the first time, Bilous and Amundson [2] treated the re- actor as a dynamical system. By using Lyapunov’s method of linearization, a pair of algebraic conditions for local stability was given. The authors considered a scheme of two consecutive reactions and showed that up to five steady states might be expected un- der some conditions. Numerical continuation methods based on predictor-corrector procedure are used for solving complex system of equations these days [6, 7]. Process modeling often consumes a lot of time. Especially when the model requires new calculations with various initial conditions that must be entered manually. The integrated environment for chemical process simulation and design, like HYSYS, is a com- bination of stand-alone models, which helps users to take control of their time [8, 9]. The identification of multiple steady states of continuous stirred tank reac- tors by HYSYS is insufficient, even though this is the primary step when identifying the possible risky states of a reactor. The program can identify only some of the steady states (with expenditure of much effort). Moreover, neither the system stability nor the num- ber of steady states could be predicted by means of HYSYS simulator [10, 11]. THEORETICAL One of the qualitative characteristics of safety anal- ysis is the accuracy of mathematical model. Numerous engineering equations have a form of nonlinear alge- braic or differential equations, which may have one or more solutions. Omitting special kind of equations, one is not able to solve these equations without nu- merical or iterative calculations. During modeling or projection, a simplified model in its analytical form is often used. In most cases, the dependence of vari- ous characteristics of physicochemical parameters on temperature and composition is neglected, like ther- mal capacity, density, mixing heat, mixing volume, etc. *Presented at the 29th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 27—31 May 2002.