Pergamon PII:S0098-1354(97)00022-7 Computers"chem. Engng, Vol. 21, Suppl., pp. S35-$40, 1997 © 1997 Elsevier Science Ltd All rights reserved Printed in Great Britain 0098-1354/97 $17.00+0.00 Process synthesis for reaction systems with cooling via finding the Attainable Region Willie Nicol, Diane Hildebrandt and David Glasser School of Process and Materials Engineering, University of the Witwatersrand, Private Bag 3, WITS, 2050, South Africa Abstract - The attainable region (AR) technique is used to find the optimum process design for an exothermic reversible reaction system where allowance is made for external cooling using two different constant temperature utilities. Heat exchange with the two utilities has different associated costs. The general optimum process structure (equipment) for the specified system was obtained via finding the attainable region. The temperature progression required for the exothermic reversible reaction was obtained by a sequence of structures. The hot reaction mixture was adiabatically reacted in a CSTR followed by a plug flow reactor then cooled down in a differential cold shot converter. This was followed with external cooling of the reactor, firstly with the hotter utility and then with the colder and more expensive utility. The optimum control of the cold shot cooling as well as the external cooling was determined using the AR technique. INTRODUCTION The attainable region (AR) technique is used in this paper to find the optimum process design for an exothermic reversible reaction system where allowance is made for external cooling using two different constant temperature utilities. Systems with exothermic reversible reactions present a reactor design challenge because the optimum reactor requires both initial high temperatures to achieve high reaction rates and low exit temperatures to achieve high equilibrium conversions. The emphasis thus falls on finding optimum ways of achieving the required falling temperature progression. In the example considered in this paper two different external cooling processes can be used to achieve the decreasing temperature progression within the optimum reactor structure. The first cooling process is with a utility at 470 K which is a fairly hot utility for the system. The cost of the heat interchange with this utility is however much cheaper compared to the cost of the other cooling process, where a utility at 300 K is used. The question now becomes how one should use the two external processes optimally in terms of synthesizing a process structure. The attainable region (AR) method is used to provide an answer to the question. Nowadays heat integration of chemical processing systems is commonly used. Different approaches, of which the pinch technology (Linnhoff et ai.,1983) is one of the favourites, are used to achieve optimal energy utilization. Using heat integration different streams (utilities as well as process streams) are assigned to different subsystems according to their energy and temperature driving force potential for heat removal or supply. It is often the case that more than one cooling/heating stream is assigned to a subsystem and it is therefore not unusual to use more than one cooling process within a certain subsystem such as a paper's examples could hence also be seen as process streams of the bigger system. The approximation is made that the cooling utility or stream stays at a constant temperature. This is only an initial design assumption and could be altered at a later stage. ATTAINABLE REGION BACKGROUND In recent years a geometric technique known as the attainable region (AR) method for synthesizing and optimizing processes structures has been developed. The initial work focused on reaction systems (Glasser et al., 1987, 1989) and was based on the idea of Horn (1961). Horn introduced the concept of the AR and defined it as the set of all possible outputs from all physically realizable reactors. Glasser and Hildebrandt (1987,1989) approached the idea of the AR from a geometric perspective. They considered a reactor as a system where the only processes occurring are reaction and mixing. They introduced geometrical interpretations of these processes and derived a set of necessary conditions for the boundary of the AR. They have also shown that once the AR is found the optimization of the problem is straightforward, provided that the objective function is an algebraic function only of the system variables. Once the AR is known, a path between the feed point and a point in the AR can be found. This path could be fairly complex combinations of reaction and mixing This combination of different processes could in turn be interpreted as a process structure (equipment). Hence by finding the AR, the reactor structures to achieve points in the AR can also be found. ATTAINABLE REGION THEORY The AR is defined as the set of values of all output variables which can be achieved by any possible steady state processes using a given feed(s). The output variables, also called the state variables, define the reaction system. Different cooling utilities may be space in which the achievable points need to be found. available, but process streams can also be used as heat A point or co-ordinate in the space is represented by a suppliers or heat removers. The different utilities in this characteristic vector c. $35