Evaluation of pumping time to receive a clean sample during fluid sampling job with wireline formation tester as well as evaluation of pumping scenarios to minimize sampling duration under existing constrains (reservoir and sandface constrains, safety etc.) are actual problems especially for fluid sampling in low-permeability formation. The article describes the digital solution allowing to simulate mud filtrate invasion in near-wellbore zone during well drilling and mud filtrate displacement by reservoir fluid during fluid sampling job with taking into account a formation damage dynamics. In this way, the software is able to evaluate depth of mud filtrate invasion and simulate both the multiphase inflow dynamics and the skin-factor dynamics during sampling job and predict sampling duration. To take into account a complex, essentially non-1D geometry of multiphase fluid flow in near-wellbore zone during fluid sampling, the special upscaling technique was developed. This upscaling technique is based on modification of 1D model by introduction of «effective» mud filtrate invasion profile and «geometry factor» which depend on ratio of vertical to horizontal permeabilities. The correlations between empirical model parameters and ratio of vertical to horizontal permeabilities were obtained by matching results of «pseudo 2D» simulations of pumping dynamics with results of 2D / 3D simulations conducted using commercial simulators ECLIPSE® and COMSOL Multiphysics®. The developed «pseudo 2D» model is computationally fast ones that allows to effectively conduct sensitivity study as well as adjust the model parameters and sampling scenario in real time in accordance with the real-time wireline formation tester measurements.