461804 Simultaneous Chemical Process Synthesis and Heat Integration with Unknown Cold/Hot Process Streams
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 , 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 “identities” 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 .
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