On-line optimization and choice of optimization variables for control of heat exchanger networks

The paper discusses optimal operation of a general heat exchanger network with given structure, heat exchanger areas and stream data including predefined disturbances. A method that combines the use of steady state optimization and decentralized feedback control is proposed. A general steady state model is developed, which is easily adapted to any heat exchanger network. Using this model periodically for optimization, the operating conditions that minimize utility cost are found. Setpoints are constant from one optimization to the next, and special attention is paid to the selection of measurements such that the utility cost is minimized in the presence of disturbances and model errors. In addition to heat exchanger networks, the proposed method may also be applied to other processes where the optimum lies at the intersection of constraints. 3 Author to whom correspondance should be addressed. Fax: (+47) 7359 8390, E-mail: [email protected] INTRODUCTION Methods for heat exchanger network (HEN) synthesis have been developed during the last decades and these methods aim to design a HEN that yields a reasonable trade-off between capital and operating cost in the nominal case. Since the mid 80’s several authors have also investigated flexibility of HENs, e.g. Kotjabasakis and Linnhoff (1986) which introduced sensitivity tables to find which heat exchanger areas should be increased in order to make a nominal design sufficiently flexible. In Papalexandri and Pistikopoulos (1994), HEN synthesis and flexibility are considered simultaneously using mathematical programming. The total design effort (on a systems level) required for a HEN typically involves the following three stages: a) Nominal design. Synthesize one or more networks with good properties for nominal stream data. b) Flexibility and controllability. Investigate the networks with regard to flexibility and controllability, and possibly introduce some modifications (e.g. increased area) such that at least one HEN shows satisfactory results. c) Operation. Design a control system to operate the HEN properly. This involves control structure selection and possibly some method for on-line optimization. For each step, some networks may be rejected or the designer may go back to the preceding step to find other alternatives. The steps are usually carried out in a sequential manner, however, the design may also be of a more simultaneous character, depending on the methods used. Compared to synthesis of nominal and flexible HENs, much less effort has been dedicated to find methods for the operation of HENs (step c). Mathisen et al. (1992) investigated bypass selection for control of HENs, without considering the utility consumption. In Mathisen et al. (1994) a method for operation of HENs that minimizes utility consumption is proposed. The method is based on structural properties of the network, however, the variable control configuration may result in poor dynamic performance. A method based on repeated steady state optimization is suggested by Boyaci et al. (1996), but their focus is not on the control structure for closed loop implementation. In this paper, a method for optimal operation of HENs is proposed. The method uses steady-state optimization which is carried out on-line with regular time intervals. The results of this optimization are then implemented by specifying the optimal value (setpoint) of some variable (“optimization variable”). It will be shown that the choice of optimization variables affects the performance of the (controlled) HEN when disturbances are present, and a procedure for optimal selection of these variables is presented. With the term optimal operation, we mean that the following two goals are fulfilled: • Primary goal: Satisfy targets (usually outlet temperatures). • Secondary goal: Minimize operating cost. In the following, it is assumed that the stream data (heat capacity flowrates and supply/target temperatures), network structure and heat exchanger areas are given and that the HEN is sufficiently flexible. To manipulate the network it is assumed that utility duties can be adjusted and that a variable bypass is placed across each processto-process heat exchanger. In case of stream splits, we may also assume that split fractions can be varied. The remaining part of the paper is organized as follows: First, the complete method is outlined. Then, the procedure for selection of optimization variables will be described in detail and applied to an illustrating example. Next, the steady state optimization model is presented, then the complete method is applied to an example and finally some conclusions are drawn. OUTLINE OF METHOD In order to perform a meaningful on-line optimization, it is required that there is at least one extra degree of freedom during operation, and most HENs have this feature. As an example consider the network in figure 5 where there are four manipulations (bypasses uA and uB and heater and cooler duties) to control the three outlet temperatures to their targets (primary goal). Hence we have one manipulation “in excess” which implies one degree of freedom. This extra degree of freedom can be used to minimize utility cost, i.e. to achieve the secondary goal. Note that the number of degrees of freedom during operation is different from the synthesis stage. Within the “synthesis terminology”, the HEN in figure 5 has minimum number of units and no degrees of freedom. (Constraints on ∆Tmin etc. have no relevance during operation). In some cases the degrees of freedom during operation may be less than the number of excess manipulations, however, this is not discussed any further in this paper. Figure 1 shows a schematic block diagram of the method that will be described. The optimizer contains a scalar objective function (criterion) J which indicates how well the HEN is operated, and a steady-state model of the HEN. As the objective function we will use total utility cost of the HEN. The model is optimized regularly and reference values for the optimization variables are passed to the controller K2. The reference values (setpoints) are constant in the period between each optimization.