(494c) Synthesis of Two-Dimensional Reactor Network Based On Transfer Fundamentals

A reactor system, which is the core of process in typical refining and petrochemical industry, often depends critically the economic and environmental performance of process.  And it provides essential conditions for design and control on following separation and heat exchange processes.

The reactor network synthesis is largely focused on establishing the structure which involves determining the types, sizes, interconnections and nominal operating conditions.  In the past decades, most researches on the reactor network synthesis can be classified into two significant categories: superstructure optimization and targeting based on Attainable Region.

Traditionally, synthesis of reactor network, whose objective function commonly optimize maximization of yield, or minimization of total volume, is usually based on PFR, CSTR, DSR, even CFR models (Lakshmanan & Biegler, 1996; Schweiger & Floudas 1999).  Though, Peclet number is considered to describe a non-ideal reactor instead of those ideal models (Achenie & Biegler, 1986; Zhou & Manousiouthakis, 2006).  Actually, Peclet number describes only back-mixing in axial direction, but axial and radial directions in reactors are influenced by each other.  Therefore, a practical reactor model which contains velocity distribution, heat transform, and mass transform in both axial and radial directions is more significant on industrial applications.

In this work, a two-dimensional model based on transfer fundamentals is proposed to approximate to a practical reactor, and then a state space framework (Bagajewicz & Manousiouthakis, 1992, 1998) composed by series two-dimensional models and distribution network (DN) is constructed for the synthesis of reactor networks.  That state space superstructure aims at developing a systematic framework which contains all possible initial reactor networks.  Moreover, heat transfer rate equation is considered as a constraint in a non-isothermal reactor system, because the same volume with variable parameters, such as length and diameter, will lead to different areas which work on heat transfer effect.  Compared with describing Total Annual Cost (TAC) through traditional coefficient method (Zhou & Manousiouthakis, 2008), we also apply a more detailed objective function, which involves installed cost, catalyst cost, and utility cost, to obtain economical optimal design.

Once detailed kinetics of reaction is formulated in a reactor model, ordinary differential equations (ODEs) make synthesis problems hard to solve. Especially, while two-dimensional reactors are considered, partial differential equations (PDEs) make formulations more complex.  Therefore, a mixed-integer dynamic optimization (MIDO) problem constituted by partial differential equations is proposed.  Discretization, such as finite element and central difference methods, is employed to transform differential equations into algebraic equations, and then a reactor model becomes a nonlinear programming (NLP) problem.  The state space framework organizes every reactor to develop all possible structures of network, but gives rising to a MINLP model.  Through the decomposition strategy as well as the discretization algorithm, the MIDO problem is simplified into a nonlinear programming problem.

Two cases illustrated in this paper are both collaborations between academia and industry with a potential future impact.  Epoxidation of propylene by hydrogen peroxide to produce propylene-oxide (HPPO), whose by-products are propylene glycol methyl ether and oxygen, is a new process.  A propylene-oxide reactor network is designed by our proposed approach.  With increasing environmental and safe concerns in process design, the generation of wasteful and dangerous byproducts is limited in the reactor network.  This also avoids expensive treatment and separation costs downstream in the process.  This is totally a liquid reactor system, which solved by IPOPT in AMPL environment.  Alkylation of toluene by methanol to produce p-xylene is the other example optimized by the proposed approach.   And this case is a vapor-only reactor system, which means both mole flow and volume flow are changed with length of a reactor.  The second case is solved in GAMS environment which shows the feasibility of the proposed approach.

Liquid and vapor reactor systems are both illustrated to achieve optimal decision variables simultaneously, includes length, diameter, interconnections and operating conditions.  Temperature and concentration distribution on axial and radial directions are attained at the same time through the approach proposed, which is demonstrated to be effective.

Literature Cited

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