Molecular separation of pharmaceutical contaminants from water has been recently of great interest to alleviate their detrimental impacts on environment and human well-being. As the novelty, this investigation aims to develop a mechanistic modeling approach and consequently its related CFD-based simulations to evaluate the molecular separation efficiency of ibuprofen (IP) and its metabolite 4-isobutylacetophenone (4-IBAP) from water inside a porous membrane contactor (PMC). For this purpose, octanol has been applied as an organic phase to extract IP and 4-IBAP from the aqueous solution due to high solubility of solutes in octanol. Finite element (FE) technique is used as a promising tool to simultaneously solve continuity and Navier-Stokes equations and their associated boundary conditions in tube, shell and porous membrane compartments of the PMC. The results demonstrated that the application of PMC and liquid-liquid extraction process can be significantly effective due to separating 51 and 54% of inlet IP and 4-IBAP molecules from aqueous solution, respectively. Moreover, the impact of various operational / functional parameters such as packing density, the number of fibrous membrane, the module length, the membrane porosity / tortuosity, and ultimately the aqueous solution flow rate on the molecular separation efficiency of IP and 4-IBAP is studied in more details.