(592c) Modeling Multi-Stream Heat Exchangers with or without Phase Change for Simultaneous Optimization and Heat Integration

A multi-stream heat exchanger (MHEX) is a single process unit in which multiple hot and cold streams exchange heat simultaneously. MHEX are more popular in low temperature (cryogenic) applications like air separation and LNG production where the focus is on minimizing energy costs (or maximizing heat recovery from streams) using very small temperature driving forces. Unlike conventional heat exchangers which involve heat exchange between two streams, modeling MHEX is not trivial because of two reasons: a) Matches between hot and cold streams are not known a priori b) Since the matches are not known, it is not clear how to apply the criterion of minimum temperature driving force. Moreover, MHEX have complex hardware designs and the streams involved typically undergo phase change during heat transfer.

It is to be noted that a simulation-based process model for MHEX can have exactly one degree of freedom (e.g. temperature of one of the outlet hot or cold streams is unknown). This variable is determined by overall enthalpy balance (assuming MHEX does not use any hot or cold utilities and behaves like an adiabatic black box). However, the method to calculate the enthalpy of the corresponding stream depends on its phase (liquid, vapor or two phase) which again depends on its outlet temperature and hence is not known a priori. Also, there is no guarantee that the solution obtained does not involve temperature crossovers or violates the minimum temperature driving force criterion and to avoid these problems, a feasible set of input parameters needs to be specified. There are hardly any simulation or optimization based process models for MHEX available in the open literature which take care of all these issues. Optimization of flowsheets containing one or more MHEXs can be regarded as a case of simultaneous optimization and heat integration where the inlet and outlet streams conditions of MHEXs are optimized simultaneously along with the rest of the process variables in order to minimize overall cost while satisfying the constraints imposed by external process as well as feasible heat transfer constraints inherent for MHEXs.

In this paper, we propose a general nonlinear equation-oriented model for MHEX which addresses all the problems mentioned above. The proposed model for MHEX can be easily connected to models of other process units and is suitable for use in simulation and optimization of flowsheets containing MHEXs. Different models for heat integration can be incorporated depending on the objective (e.g. minimize energy cost only or simultaneously determine matches in the MHEX with or without including capital cost of MHEX).

When energy cost is the dominant factor in the objective, we propose the use of an aggregate model which is based on pinch technology for heat integration. The model equations can be considered as the solution to the following problem statement which is inverse of that used in pinch technology (Papoulias and Grossmann, 1983): Determine feasible inlet and outlet temperatures and heat capacity flowrates for a given set of hot and cold streams such that there are no utility requirements. As the concept of pinch ensures that the hot and cold composite curves are separated by HRAT (heat recovery approach temperature), the issues of temperature crossover and minimum temperature driving force are taken care of automatically without knowing the matches between hot and cold streams.

To deal with phase changes, we need to address the following two issues: a) procedure for enthalpy calculation changes with phase which is not known a priori. b) Treating heat capacity-flowrate as a constant is not a good assumption for a stream changing phase. We propose to define a priori a set of candidate streams which are capable of phase change. The streams belonging to this set are split into three substreams corresponding to superheated (SUP), two phase (2P) and subcooled (SUB) regions. This splitting is based on dew point and bubble point temperatures of the stream that may change during the course of the optimization as pressure and composition of the stream are treated as process variables and can be optimized. From the point of view of heat integration, each of the above substreams can be treated as an independent stream with an associated heat load and inlet and outlet temperatures. The inlet and outlet temperatures of substreams are assigned appropriate values using a disjunctive representation involving Boolean variables (Raman and Grossmann, 1994) where the Boolean variables are associated with the phase of parent stream at the inlet and outlet conditions. The disjunctions can be formulated either as a discrete-continuous model involving binary variables (Lee and Grossmann, 2000) or as a continuous model by solving an inner minimization problem with complementarity constraints (Raghunathan, 2004). Also, when a candidate stream does not change its phase, the inlet and outlet temperatures of irrelevant substreams are manipulated in such a way that the associated heat loads are set to zero. It is to be noted that this representation assumes that the enthalpy of the streams can be approximated as a piecewise linear function of temperature in each of three regions. If necessary, the two phase region can be split further into more segments to improve this approximation Isothermal streams can also be handled easily through an implementation strategy that decouples temperature information used for process calculations from that used for heat integration.

The capability of model is demonstrated using the PRICO (Poly Refrigerant Integrated Cycle Operations) process for LNG production (Lee et al., 2002). Although the PRICO process is a relatively simple process involving a single mixed refrigerant circulating in a simple cycle, it incorporates most of the components present in more complex LNG liquefaction processes. The proposed model is used within a mathematical programming formulation to determine the optimal operating conditions and composition of mixed refrigerant that minimizes the shaft work required for vapor compression.

References

Papoulias, S. A. and Grossmann, I. E. (1983) A Structural Optimization Approach in Proceas Synthesis. II: Heat Recovery Networks, Computers and Chemical Engineering, 7, 707-721.

Raman, R. and Grossmann, I. E. (1994). Modeling and computational techniques for logic based integer programming. Computers and Chemical Engineering, 18(7), 563-578.

Sangbum L. and Grossmann I. E. (2000) New algorithms for nonlinear generalized disjunctive programming. Computers and Chemical Engineering, 24, 2125-2141.

Raghunathan, A. (2004) PhD Thesis, Department of Chemical Engineering, Carnegie Mellon University.

Lee, G. C., Smith, R. and Zhu, X. X. (2002) Optimal Synthesis of Mixed Refrigerant Systems for Low-Temperature Processes. Industrial and Engineering Chemistry Research, 41, 5016-5028.