We have extended the computational singular perturbation (CSP) method to differential algebraic equation (DAE) systems and demonstrated its application in a heterogeneous-catalysis problem. The extended method obtains the CSP basis vectors for DAEs from a reduced Jacobian matrix that takes the algebraic constraints into account. We use a canonical problem in heterogeneous catalysis, the transient continuous stirred tank reactor (T-CSTR), for illustration. The T-CSTR problem is modelled fundamentally as an ordinary differential equation (ODE) system, but it can be transformed to a DAE system if one approximates typically fast surface processes using algebraic constraints for the surface species. We demonstrate the application of CSP analysis for both ODE and DAE constructions of a T-CSTR problem, illustrating the dynamical response of the system in each case. We also highlight the utility of the analysis in commenting on the quality of any particular DAE approximation built using the quasi-steady state approximation (QSSA), relative to the ODE reference case.

我们已将计算奇异微扰 (CSP) 方法扩展到微分代数方程 (DAE) 系统，并展示了其在多相催化问题中的应用。扩展方法从考虑代数约束的简化雅可比矩阵中获得 DAE 的 CSP 基向量。我们使用多相催化中的典型问题，即瞬态连续搅拌釜反应器 (T-CSTR) 进行说明。T-CSTR 问题基本上被建模为常微分方程 (ODE) 系统，但如果使用表面物质的代数约束来近似典型的快速表面过程，则它可以转换为 DAE 系统。我们展示了 CSP 分析在 T-CSTR 问题的 ODE 和 DAE 构造中的应用，说明在每种情况下系统的动态响应。我们还强调了分析在评论使用准稳态近似 (QSSA) 相对于 ODE 参考案例构建的任何特定 DAE 近似的质量方面的实用性。