(374g) An Algorithm for Integrated Molecular and Process Design: Physically-Driven Domain Reduction for Liquid-Liquid Extraction

Computer Aided Molecular and Process design (CAMPD) involves the simultaneous optimisation of processes and processing materials (such as mass separating agents, catalysts) [1]. In CAMPD one considers the minimisation of a process-wide objective subject to process design constraints and molecular feasibility constraints. Molecular-level (material) decisions are represented using discrete variables such as the number of groups of a given kind, whereas process variables can either be continuous or discrete. The resulting design problem is a mixed integer nonlinear problem (MINLP) which is difficult to solve for a number of reasons. The large molecular design space leads to combinatorial explosion [2]; the non-convexity of the domain can lead to poor solutions depending on the starting point; convergence failure can arise for some combinations of molecular and process variables. In particular, numerical difficulties can be encountered in the absence of a good initial guess to the highly nonlinear, and coupled, process and property models. Numerical issues can also occur if a combination of molecular and process inputs violates constraints of phase behaviour implicit in the model. For instance, an evaluation of an absorber model can fail if the stream at its liquid inlet is in the vapour state. Also, the feasible region with respect to these constraints is a function of the solvent: for example, the range of temperatures where a molecule is in the liquid state varies with the choice of solvent.

To address these challenges we have recently a developed a new algorithm for CAMPD of separation systems [3, 4]. The algorithm builds on the concept of embedding screening of molecules within an optimizer [5, 6]. Novel tests were introduced to screen both molecular and process variables, in the context of gas-liquid separation. In this approach, we first identify the process domain where the feed is stable. At each major iteration of an outer approximation (OA) algorithm [7], we find a reduced process domain for a solvent. The reduced process domain is an overestimation of the feasible region for that solvent. In a first test, the feasibility of solvent handling and storage is checked. Ina second test, the range of process variables over which the solvent and the feed can form a two-phase mixture is found. The range of process variables over which the required degree of purity of the treated stream may be attained is identified in a third test. If the solvent fails any of the tests it is eliminated. If the tests are feasible, the primal problem is solved using bounds identified by the tests and initial guesses within the reduced process domain. Information from the tests and the primal problem is used to construct the master problem for the OA algorithm.

The extension of this methodology to liquid-liquid extraction systems is presented here. The three tests, initially developed for absorption processes, are recast for the case of liquid-liquid extraction. The approach is illustrated with a case study of the separation of butanol from a fermentation broth. As the broth is dilute in butanol, separation of this mixture by distillation is highly energy intensive. Hence, an optimal solvent for extraction, and the corresponding optimal process variables, are designed using the algorithm proposed here. A group contribution equation of state, the group contribution version of the statistical associating fluid theory with a Mie potential, SAFT-γ Mie[8,9], is used in this work to predict the relevant thermodynamic properties. A systematic study of the performance of the algorithm is undertaken. The algorithm succeeds in avoiding expensive process evaluations for infeasible solvents and enhances convergence to the solution from multiple starting points.

1 Adjiman, C. S., Galindo, A., and Jackson, G. (2014). Proceedings of the 8th International Conference on Foundations of Computer-Aided Process Design FOCAPD 2014, edited by Eden M.R., Siirola J.D., Towler G.P., Computer Aided Chemical Engineering, Elsevier B.V.

2 Joback, K.G. and Stephanopoulos, G. (1995). In Advances in Chemical Engineering, 21: 257-311

3 Gopinath S, Galindo A, Jackson G, Adjiman CS (2016). Proceedings of the 26th European Symposium on Computer Aided Process Engineering, edited by Kravanja Z., Computer Aided Chemical Engineering. Elsevier B.V.

4 Gopinath S, Galindo A, Jackson G, Adjiman CS (2016). Computer-aided molecular and process design for absorption-desorption systems using physically-driven domain reduction (2016). Manuscript submitted

5 Buxton, A., Livingston, A. G., and Pistikopoulos, E. N. (1999). AIChE Journal, 45: 817-843

6 Giovanoglou, A., Barlatier, J., Adjiman, C. S., Pistikopoulos, E. N., and Cordiner, J. L. (2003). AIChE Journal, 49: 3095-3109

7 Duran, M. A. and Grossmann, I. E. (1986). Mathematical Programming, 36: 307-339

8 Papaioannou, V., Lafitte, T., Aveñdano, C., Adjiman, C. S., Jackson, G., Müller, E. A., and Galindo, A. (2014). The Journal of Chemical Physics, 140: 054107

9 Lafitte, T., Apostolakou, A., Avendaño, C., Galindo, A., Adjiman, C. S., Müller, E. A., and Jackson, G. (2013). The Journal of Chemical Physics, 139: 154504