This project provides a mechanistic, first-principles framework for modeling and optimizing enzymatic cascades immobilized within porous particles. It explicitly models coupled reaction-diffusion phenomena inside the pores and the surrounding batch reactor.

By migrating the original SciPy-based numerical approach to a Pyomo-based algebraic modeling implementation, this framework allows for complex, large-scale dynamic optimization. Key enhancements in this repository include:

• Time-dependent Enzyme Deactivation: Optional integration of first-order decay kinetics to simulate simultaneous enzyme deactivation over time.
• Advanced Spatial Immobilization Distributions (SIDs): Expanded parametrizations that support flexible spatial patterns, including egg-shell, egg-white, and egg-yolk-type distributions.
• Robust Solver Integration: Automatic collocation discretization and integration with large-scale non-linear solvers (like IPOPT) for efficient optimization.

This project builds upon the theoretical foundation and initial codebase established by Paschalidis et al.:

• Main Paper: L. Paschalidis, S. Arana-Peña, V. Sieber, and J. Burger, "Mechanistic modeling, parametric study, and optimization of immobilization of enzymatic cascades in porous particles," React. Chem. Eng., vol. 8, no. 9, pp. 2234–2244, 2023.
• Original SciPy Repository: TUM-CS-CTV/ImmobilizationMPO

To improve the numerical stability of the boundary-value and initial-value problems during optimization, dimensional variables are scaled into dimensionless forms. The standard conversion equations used in this framework's dimensionless approach are:

$$\xi = \frac{x}{L}$$

where $x$ is the dimensional pore depth and $L$ is the total pore length.

$$u_{i} = \frac{S_{i}}{S_{\text{ref}}}$$

where $S_{i}$ is the concentration of component $i$, and $S_{\text{ref}}$ is a reference concentration, typically $S_{1,0}(t=0)$.