(666c) An Algorithm for Integrated Design of Organic Rankine Cycles

Uku Erik Tropp, David H. Bowskill, Smitha Gopinath, George Jackson, Amparo Galindo, Claire S. Adjiman

Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London

Organic Rankine Cycles (ORCs) are able to utilize waste heat or low quality heat to generate power. Thus, the use of ORCS can lead towards sustainable and environmentally friendly energy systems. The optimal operating conditions of the ORC depend on the specifications of the process (for e.g., temperature of the heat source), constraints of the system (for e.g., amount of coolant available) and the choice of working fluid. Optimal cycles may be designed by simultaneously choosing the fluid and the operating conditions, subject to the constraints. Such an integrated design of materials (molecules) and processes is also referred to as Computer Aided Molecular and Process design (CAMPD) [1]. In the ORC CAMPD, process decisions are usually continuous, whereas material (molecular) decisions are inherently discrete. The ORC working fluid (a pure-component is considered here) may be represented by the number of occurrences in the molecule of each functional group (in a given set of groups) and the connectivity between these occurring groups. Given a property prediction method, that translates the molecular composition of the fluid to physico-chemical properties of interest in the ORC model, the CAMPD problem may be formulated. The resulting design problem is a mixed integer nonlinear problem (MINLP) which is prone to non-convergence for a number of reasons.

The ORC process model (equality constraints of the design problem) consists of a number of non-convex coupled equations, while property prediction models tend to be highly nonlinear. Further, as the choice of working fluid changes, across optimizations, many molecules may be infeasible with respect to the process model, which could result in non-convergence of optimizations (especially if simulator-based optimization is used). For example, a chosen molecule may have a critical point that is lower than the range of allowable pressures and temperatures and can thus not be condensed into a liquid in the cycle. In other scenarios, a molecule with a boiling point which is higher than that of the hot source cannot be obtained as a vapour at the outlet of the evaporator. An attempt to evaluate the vapour properties of such a stream can result in numerical failure.

To address the challenge of non-convergence and improve computational performance, we extend an algorithm [2, 3] which was recently developed for CAMPD of separation systems. The algorithm builds on the concept of embedding screening of molecules within an iterative MINLP optimizer [4, 5], such as Outer-Approximation [6]. Within this algorithm, each molecule generated by the master problem passes through a sequence of tests, before the evaluation of the primal problem for that molecule. The aim of the tests is to identify a priori regions within the process domain that are infeasible for a given molecule. If the entire domain is infeasible for a molecule, the molecule may be eliminated without evaluation of the primal problem, and information on the violated constraints are added to the master problem. For a molecule that passes the tests, the tests generate bounds on the feasible process domain for that molecule.

In this work, we develop tests specific to the design of ORC systems. The tests produce bounds on allowable operating pressures of the ORC for every feasible molecule. The tests also eliminate molecules whose phase behaviour (critical point, vapour pressure and so on) make them infeasible in the ORC. The algorithm is applied to solve three case studies of integrated ORC working fluid and process design. The SAFT-γ Mie [7] equation of state is used for prediction of thermodynamic properties of the working fluid. We find that the bounds obtained by the tests are useful in reducing the process domain and enable convergence of the primal problem. Without these bounds, the evaluation of the primal problem fails for certain molecules. The use of the algorithm enhances the robustness of the design problem, allowing one to obtain (locally) optimal solutions from a variety of starting points, which is useful as the problem is non-convex. Thus, the algorithm facilitates the use of rigorous process and property prediction models for the design of ORCs.

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