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459968 Towards a Computational Platform for General Flowsheet Synthesis

**Towards a computational platform for general flowsheet synthesis**

Qi Chen^{1}, Ignacio Grossmann^{1}

^{1}Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

**ABSTRACT**

Synthesis of chemical process flowsheets is a fundamental challenge of the chemical engineering discipline [1]. Recently, low energy prices and new feedstocks introduced by the US shale boom have spurred renewed interest in process design. At the same time, sustainability concerns provide impetus for computer-aided design in the emerging areas of bio-feedstocks, carbon capture systems, and process intensification. Superstructure optimization facilitates a unified basis for tackling synthesis problems across this wide range of interest areas, and from green-field design to retrofit operations [2]. However, despite substantial progress in superstructure optimization, particularly in subsystems like heat exchanger network synthesis and separation sequences, there has been limited adoption of these methods in industry [3]. One driver for this has been lack of a general purpose software platform for performing superstructure synthesis.

In this paper, we present progress towards development of such a platform. A general purpose solution poses both modeling and implementation challenges with a combination of nonlinear, nonconvex equations (frequently arising from mixing/splitting and concave cost functions) and discrete design decisions. We adopt a Generalized Disjunctive Programming (GDP) modeling approach, with optional processing units represented by a disjunction between presence and absence of the unit [4]. We then decompose the problem using logic-based outer-approximation (LOA) [4,5] in order to reduce dimensionality through the reduced-space nonlinear programs (rNLPs) resulting from a fixed configuration of the process network. Furthermore, these rNLPs avoid zero-flow singularities in absent process units by excluding them from the subproblem model. Outer-approximation with equality relaxation (OA/ER) cuts [6] derived from the subproblems communicate information to a mixed-integer linear (MILP) master problem, which selects a new network configuration. The algorithm then repeats until a termination condition is reached. In this work, we propose a modeling distinction between interconnection (e.g. mixers and splitters) and processing nodes in the MILP master problem. We use rigorous underestimators such as polyhedral envelopes for linearizing interconnection nodes rather than OA/ER cuts as before. Since flow rates through interconnection nodes tend to vary more in different process configurations than other types of nodes, rigorous underestimators reduce the likelihood that the optimal solution will be excluded prematurely. This modification yields improved performance both in superstructures predominantly defined by interconnections as well as those driven by complex processing units. We also replace concave cost functions by linear underestimators to predict lower bounds for the case of linear input-output models for the units. Furthermore, in order to improve the robustness of the optimizations, we investigate several strategies for initialization for the rNLPs, the impact of modeling with flows, compositions, and split fractions, and the addition of valid inequalities.

We implement this framework in the high level programming language Python using the Pyomo [7] modeling environment that allows direct formulation of the GDP for superstructure optimization in terms of equations, disjunctions and logic propositions. This combination allows for a true object-oriented modeling paradigm. With the Pyomo Block feature, entire groups of model constraints can be dynamically activated or deactivated for LOA with one line of code. We also demonstrate the ability to perform programmatic application of OA cuts, piecewise McCormick envelopes, multi-parametric disaggregation, and linear underestimators with Python function calls.

The proposed platform is applied to a set of literature case studies, including water treatment network design [8], flowsheet synthesis for the hydrodealkylation of toluene [9], and production of methanol [4]. Computational results demonstrate the ability to readily model superstructure optimization models, and to quickly find near-optimal solutions to a range of synthesis problems.

**References**

[1] L.T. Biegler, I.E. Grossmann, A.W. Westerberg, Systematic methods of chemical process design, Prentice Hall PTR, 1997.

[2] I.E. Grossmann, G. Guillen-Gosalbez, Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes, Comput. Chem. Eng. 34 (2010) 1365–1376. doi:10.1016/j.compchemeng.2009.11.012.

[3] G.J. Harmsen, Industrial best practices of conceptual process design, Chem. Eng. Process. Process Intensif. 43 (2004) 677–681. doi:10.1016/j.cep.2003.02.003.

[4] M. Türkay, I.E. Grossmann, Logic-based MINLP algorithms for the optimal synthesis of process networks, Comput. Chem. Eng. 20 (1996) 959–978. doi:10.1016/0098-1354(95)00219-7.

[5] M.A. Duran, I.E. Grossmann, An outer-approximation algorithm for a class of mixed-integer nonlinear programs, Math. Program. 36 (1986) 307. doi:10.1007/BF02592064.

[6] J. Viswanathan, I.E. Grossmann, A combined penalty function and outer-approximation method for MINLP optimization, Comput. Chem. Eng. 14 (1990) 769–782. doi:10.1016/0098-1354(90)87085-4.

[7] W.E. Hart, C. Laird, J.-P. Watson, D.L. Woodruff, Pyomo – Optimization Modeling in Python, Springer US, Boston, MA, 2012. doi:10.1007/978-1-4614-3226-5.

[8] R. Karuppiah, I.E. Grossmann, Global optimization for the synthesis of integrated water systems in chemical processes, Comput. Chem. Eng. 30 (2006) 650–673. doi:10.1016/j.compchemeng.2005.11.005.

[9] G.R. Kocis, I.E. Grossmann, Computational Experience With Dicopt Solving Minlp Problems in Process Systems-Engineering, Comput. Chem. Eng. 13 (1989) 307–315. doi:10.1016/0098-1354(89)85008-2.

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