Recent years have seen the explosive development of mixed-matrix membranes (MMMs) for a myriad of applications. In gas separation, it is desired to concurrently enhance the permeability, selectivity and physicochemical properties of the membrane. To help achieving these objectives, experimental characterization and predictive models can be used synergistically. In this investigation, a Monte Carlo (MC) algorithm is proposed to rapidly and accurately estimate the relative permeability of ideal MMMs over a wide range of conditions. The difference in diffusivity coefficients between the polymer matrix and the filler particle is used to adjust the random progression of the migrating species inside each phase. The solubility coefficients of both phases at the polymer–filler interface are used to control the migration of molecules from one phase to the other in a way to achieve progressively phase equilibrium at the interface. Results for various MMMs were compared with the results obtained with the finite difference method under identical conditions, where the results from the finite difference method are used in this investigation as the benchmark method to test the accuracy of the Monte Carlo algorithm. Results were found to be very accurate (in general, <1% error) over a wide range of polymer and filler characteristics. The MC algorithm is simple and swift to implement and provides an accurate estimation of the relative permeability of ideal MMMs. The MC method can easily be extended to investigate more readily non-ideal MMMs with particle agglomeration, interfacial void, polymer-chain rigidification and/or pore blockage, and MMMs with any filler geometry.

The permeation of gases through membranes is a fundamental process with wide-ranging applications, from gas separation and fuel cell technology to respiratory physiology. Governed by Fick’s second law of diffusion, the mathematical modelling of such transport processes often becomes analytically and computationally challenging, especially in heterogeneous, mixed matrix, or multilayered systems. To navigate these complexities, this study revisits and expands upon the use of electrical analogies as an intuitive and powerful modelling approach rooted in mid-20th-century analog computing. By leveraging the mathematical equivalence between diffusion and electrical conduction, we construct an equivalent electrical network that mirrors the transient behaviour of gas permeation across membranes. In this framework, concentration gradients are represented as voltage differences, diffusive fluxes as electrical currents, and diffusional resistances as circuit resistances. While traditional applications of electrical analogies have largely focused on steady-state phenomena, our approach enables dynamic analysis, offering conceptual clarity and computational efficiency. This methodology not only simplifies the solution of Fick’s second law but also reinforces the enduring relevance of analogical thinking in modern engineering practice. Comparative results demonstrate that the equivalent electrical circuit closely aligns with both analytical and finite difference solutions, validating its effectiveness and accuracy.