Current available models for simulation of the separation process in gas-liquid membrane contactor (MC) systems consider a uniform partial membrane wetting along the membrane length (L-mem). However, transmembrane pressure changes along the L-mem. Additionally, the available models usually consider a simplified uniform pore size to represent the micro-porous MC. Additionally, not all pores in a MC have the same size. In this study, a pore-scale network model is developed to simulate the physical separation of H2S using MCs by taking to account for (i) transmembrane pressure variation and (ii) pore size distribution of MC. The model results are compared with the experimental results of H2S separation. Modeling results indicate that membrane wetting is non-uniformly distributed along L-mem. The membrane wetting ratio is maximum at the inlet of the liquid phase, and it decreases toward the liquid outlet. Also, increasing the inlet gas pressure reduces the membrane wetting ratio, and leads to higher H2S separation. Moreover, the model results indicate that shifting of the pore size distribution of MC towards smaller pore size declines the membrane wetting ratio and increases the H2S separation efficiency.