Abstract
We consider the optimization of a chemical microchannel reactor by means of PDE-constrained optimization techniques, using the example of the Sabatier reaction. To model the chemically reacting flow in the microchannels, we introduce a three- and a one-dimensional model. As these are given by strongly coupled and highly nonlinear systems of partial differential equations (PDEs), we present our software package cashocs which implements the adjoint approach and facilitates the numerical solution of the subsequent optimization problems. We solve a parameter identification problem numerically to determine necessary kinetic parameters for the models from experimental data given in the literature. The obtained results show excellent agreement to the measurements. Finally, we present two optimization problems for optimizing the reactor’s product yield. First, we use a tracking-type cost functional to maximize the reactant conversion, keep the flow rate of the reactor fixed, and use its wall temperature as optimization variable. Second, we consider the wall temperature and the inlet gas velocity as optimization variables, use an objective functional for maximizing the flow rate in the reactor, and ensure the quality of the product by means of a state constraint. The results obtained from solving these problems numerically show great potential for improving the design of the microreactor.
Highlights
The Sabatier process, named after the French chemists Paul Sabatier and Jean-Baptiste Senderens who reported it in 1902 [1], is given by the reversible exothermic reactionCO2 + 4H2 CH4 + 2H2O, H 0 ≈ −165 kJ/mol. (1.1)This reaction has been investigated, e.g., in the context of in situ resource utilization on mars [2,3], for life-support systems on the ISS [4], and it is used for power-to-gas applications [5,6], and cogeneration systems [7,8]
Microchannel geometries are interesting for chemical reactions as the large specific surface area of the microchannels allows for high performance of catalytic reactions as well as precise temperature management by means of appropriate temperature control systems
The purpose of this paper is to investigate the optimization of such a microchannel reactor for the Sabatier reaction using techniques from partial differential equations (PDEs)-constrained optimization
Summary
The Sabatier process, named after the French chemists Paul Sabatier and Jean-Baptiste Senderens who reported it in 1902 [1], is given by the reversible exothermic reaction. Throughout this paper, we consider the same setting as in [11,29], where a microchannel reactor for the Sabatier reaction is investigated by means of experiments and simulations To model this reactor mathematically, we introduce the following two models. We derive a one-dimensional model from the first one using a homogenization procedure similar to [19] As both models are given by strongly coupled and highly nonlinear systems of PDEs, we use our software package cashocs [30] for the numerical solution of the subsequent optimization problems. We consider the inlet gas velocity of the reactor and its wall temperature as optimization variables and use a objective functional for maximizing the mass flow rate in the reactor In this case, the quality of the product is ensured by use of a state constraint for the CO2 conversion.
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