(374d) Simultaneous Chemical Process Synthesis and Heat Integration with Unknown Cold/Hot Process Streams

Kong, L., University of Wisconsin-Madison
Maravelias, C. T., University of Wisconsin-Madison
Huang, K., University of Wisconsin-Madison
Avadiappan, V., University of Wisconsin – Madison
In chemical process synthesis, the heat integration between cold and hot process streams reduces the external utility consumptions and leads to economic benefits. Sequential heat integration approaches rely on the assumption that temperatures and flow rates of process streams are known, which means that these methods can only be applied after stream conditions have been determined. On the other hand, simultaneous approaches can handle variable stream temperatures and flow rates, which means that the heat integration subsystem can be optimized along with the process and thus stream conditions. It has been shown that simultaneous approaches lead to better solutions compared to the sequential approaches [1]. While various simultaneous heat integration models have been proposed [1, 2], they require all the process streams to be classified as cold or hot streams (depending on whether the streams require heating/cooling) prior to solving the problem. However, in some cases there exists a subset of process streams that cannot be predetermined as cold or hot streams, especially in the context of superstructure optimization that involves the selection of alternative processing units. For example, the product stream from one of the two alternative reactors (A and B) is sent to one of the two alternative separation units (C and D) for purification. Units A, B, C and D might operate at different temperature ranges. Therefore, we might not be able to determine if the stream that connects the reactor and separator is a cold or hot stream before solving the problem.

Accordingly, in this work, we present a mixed-integer nonlinear programming (MINLP) optimization model for the simultaneous chemical process synthesis and heat integration with general, that is undetermined, process steams. The model extends the transshipment model proposed by Papoulias and Grossmann [3], to account for (1) streams that cannot be classified as hot or cold, and (2) variable stream temperatures and flow rates. The cold/hot stream â??identitiesâ? are represented by classification binary variables which are (de)activated based on the relative stream inlet and outlet temperatures. Variables including stream temperatures and heat loads are disaggregated into two mutually exclusive parts (cold and hot), and each part is (de)activated by the corresponding classification binary variable. The dynamic temperature intervals constructed from the variable process stream inlet temperatures are implicitly ordered from high to low temperatures and stream inlet/outlet temperatures are assigned to the correct temperature intervals. Stream heat loads at each temperature interval depend on the relative positions of stream inlet and outlet temperatures with respect to the temperatures at the interval boundaries. Preprocessing is used to reduce the size of the problem and speed up the solution process. For example, if a process stream can be predetermined as a cold stream, we can fix the corresponding classification binary variable to one, and deactivate the hot part of the disaggregated variables. It is important to note that the only nonlinearity in this model are the bilinear [flow rates]*[temperature difference] terms. Therefore, in the case that the stream flow rates or temperatures are fixed, the proposed model reduces to a MILP model; and if both of them are fixed, we recover the original transshipment model.

The proposed model is generalized to handle intermediate utilities at arbitrary temperatures. Further, the model is able to deal with both isothermal and non-isothermal phase changes. Should phase changes of pure components are present in a process stream, the original stream can be disaggregated into sub-streams and the heat integration model can be reformulated to include phase detection (i.e. decide at what phase this stream starts and ends).

The heat integration model can be integrated with a process superstructure model. To achieve this integration effectively, we discuss a series of modeling techniques that lead to simplified unit models and connectivity equations. For example, we show that the minimum number of temperature intervals needed for heat integration equals to the minimum number of process streams over all the feasible solutions, which is fewer than the total number of process streams in the original superstructure.

The proposed model is applied on several illustrative examples with variable flows and temperatures, in which some streams have unknown cold/hot classifications. Finally, we present a case study in which the proposed model is integrated with a realistic bioethanol production superstructure and is optimized based on an economic criterion [4].


1. Duran, M.A. and I.E. Grossmann, Simultaneous-Optimization and Heat Integration of Chemical Processes. Aiche Journal, 1986. 32(1): p. 123-138

2. Navarro-Amorós, M.A., et al., An alternative disjunctive optimization model for heat integration with variable temperatures. Computers & Chemical Engineering, 2013. 56: p. 12-26

3. Papoulias, S.A. and I.E. Grossmann, A Structural Optimization Approach in Process Synthesis .2. Heat-Recovery Networks. Computers & Chemical Engineering, 1983. 7(6): p. 707-721

4. Kong, L., et al., A superstructure-based framework for simultaneous process synthesis, heat integration, and utility plant design. Computers & Chemical Engineering, 2016 DOI: http://dx.doi.org/10.1016/j.compchemeng.2016.02.013.