This work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized Integral Transform Technique (GITT) is applied using approximate non-converged solutions of the 3D model, by adopting low truncation orders in the eigenfunction expansions. Second, the Coupled Integral Equations Approach (CIEA) provides a reduced mathematical model for the average concentrations, which leads to inherently approximate solutions. The AEM approach through the Bayesian framework is illustrated in the simultaneous estimation of kinetic and diffusion coefficients of the transesterification reaction. For this purpose, the fully converged GITT results with higher truncation orders for the 3D partial differential model are employed as reference results to define the approximations errors. The results highlight that either the non-converged solutions via GITT or the reduced model solution obtained via CIEA, when taking into account the model error, are robust and cost-effective alternatives for the inverse analysis of nonlinear convection–diffusion-reaction problems.

这项工作推进了近似误差模型方法，用于在 3D 微反应器中使用大豆油和甲醇进行生物柴油合成的逆向分析。考虑了两种降低计算成本的混合数值分析方法来为三维非线性耦合扩散-对流-反应模型提供近似的正向问题解决方案。首先，通过在特征函数展开中采用低截断阶数，使用 3D 模型的近似非收敛解应用广义积分变换技术 (GITT)。其次，耦合积分方程方法 (CIEA) 为平均浓度提供了简化的数学模型，这导致了固有的近似解。通过贝叶斯框架的 AEM 方法在酯交换反应的动力学和扩散系数的同时估计中得到了说明。为此，使用具有更高截断阶数的 3D 偏微分模型的完全收敛 GITT 结果作为参考结果来定义近似误差。结果强调，无论是通过 GITT 的非收敛解还是通过 CIEA 获得的简化模型解，当考虑到模型误差时，对于非线性对流-扩散-反应问题的逆向分析，都是稳健且具有成本效益的替代方案。具有更高截断阶数的 3D 偏微分模型的完全收敛 GITT 结果用作参考结果来定义近似误差。结果强调，无论是通过 GITT 的非收敛解还是通过 CIEA 获得的简化模型解，当考虑到模型误差时，对于非线性对流-扩散-反应问题的逆向分析，都是稳健且具有成本效益的替代方案。具有更高截断阶数的 3D 偏微分模型的完全收敛 GITT 结果用作参考结果来定义近似误差。结果强调，无论是通过 GITT 的非收敛解还是通过 CIEA 获得的简化模型解，当考虑到模型误差时，对于非线性对流-扩散-反应问题的逆向分析，都是稳健且具有成本效益的替代方案。