For lateral flow tests, the numerical pore-scale modeling of capillary action, and the resulting fluid propagation through the porous membrane, remains challenging due to limited computational resources. To meet this challenge, a computing resource efficient macroscopic flow model is employed, which incorporates effective properties of the porous membrane. However, since diagnostic membranes consist of complex open-pored microstructures, a quantitative determination of all important effective properties is difficult. Especially when it comes to the macroscopic modeling of the capillary-driven fluid flow through the structure, too little attention is paid to the effective pore radius. Most commonly, it is determined by fitting to experimental data and subsequently, flow predictions are based on liquid spreading experiments. This work replaces the commonly applied fitting procedures by a simulation-based correlation between structure parameters and the effective pore radius. Furthermore, a systematic methodology for the determination of all important effective pore-scale properties, based on numerical simulations instead of experimental data, is shown. For the investigation, both computer tomographic high-resolution images (nano-CT) and algorithmically generated models serve as three dimensional digital twins of the membrane containing the microstructural geometrical informations. As a main result, a correlation-based and efficient prediction of capillary-driven fluid flow in diagnostic membranes, over multiple scales, is presented. This advanced approach facilitates the feasibility to predict the propagation process in any open-pored, porous membrane microstructure. With this work, effective pore sizes can be determined without fitting procedures; and by combining generation algorithms with the macroscopic flow model, a major contribution to the efforts towards virtual material design is achieved.