Coupling Analytical Derivatives with Adjoint Automatic Differentiation in a Modular Process Simulator

Modular process simulators are widely used in industry due to their robust and detailed unit operation models. However, their application to gradient-based process optimization remains challenging, as these simulators are typically treated as black boxes, limiting access to internal equations and derivatives. As a result, finite difference methods are commonly employed for gradient estimation, despite their sensitivity to numerical noise and poor scalability. While previous studies have demonstrated the benefits of analytical derivatives in modular simulators, these approaches have largely relied on tangent differentiation modes. This work proposes a non-intrusive methodology that couples analytical derivatives with the adjoint mode of automatic differentiation to efficiently compute gradients for process optimization in modular simulators. The approach preserves the robustness of existing simulation tools by performing simulations normally to convergence, followed by external adjoint-based derivative evaluation using analytically available sensitivities. Theoretical advantages of adjoint differentiation are thus exploited, particularly for optimization problems where the number of decision variables exceeds the number of objective outputs. The proposed framework is evaluated through a case study based on a combined heat and power cycle, using three benchmark objective functions. Gradient computation cost, robustness, and overall optimization performance are compared against forward and centered finite difference methods. Results demonstrate that the analytical adjoint approach significantly reduces gradient computation time while maintaining high robustness, achieving up to 56% reduction in computational cost compared to finite differences. These findings highlight the potential of analytical adjoint differentiation as an efficient and reliable alternative for optimization in modular process simulators.