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.

我们以 Sabatier 反应为例，考虑通过 PDE 约束优化技术对化学微通道反应器进行优化。为了模拟微通道中的化学反应流，我们引入了一个三维和一维模型。由于这些是由偏微分方程 (PDE) 的强耦合和高度非线性系统给出的，因此我们提出了我们的软件包 cashocs，它实现了伴随方法并促进了后续优化问题的数值求解。我们以数值方式解决参数识别问题，以根据文献中给出的实验数据确定模型所需的动力学参数。所得结果与测量结果非常吻合。最后，我们提出了两个优化反应器产品产量的优化问题。首先，我们使用跟踪型成本函数来最大化反应物转化率，保持反应器的流速固定，并使用其壁温作为优化变量。其次，我们将壁温和入口气体速度作为优化变量，使用目标函数来最大化反应器中的流速，并通过状态约束来保证产品的质量。从数值上解决这些问题所获得的结果显示了改进微反应器设计的巨大潜力。使用目标函数使反应器中的流速最大化，并通过状态约束来保证产品的质量。从数值上解决这些问题所获得的结果显示出改进微反应器设计的巨大潜力。使用目标函数使反应器中的流速最大化，并通过状态约束来保证产品的质量。从数值上解决这些问题所获得的结果显示了改进微反应器设计的巨大潜力。