We report highly fine-grid numerical simulations of solvent-aided bitumen leaching using propane as a solvent. These simulations allowed us to observe the detailed physics of the drainage process, which is otherwise impossible in coarse-grid simulations. Our results revealed significant fingering of the solvent into bitumen as a result of viscosity and density contrasts, which is in line with the previous experimental observation of bitumen leaching by toluene. Based on our simulation results, the drainage process undergoes two distinct infinite-acting and finite-acting periods, with more than two-thirds of the drainage taking place during the former. Interestingly, the rate of drainage of bitumen is constant during the infinite-acting period, and it is independent of formation thickness. Using the results of our simulations, we found out that the rate of drainage of bitumen is scaled linearly with formation permeability. The results of this work shed light on the fine-scale physics of the bitumen leaching process by solvents and pave the way for the development of new recovery processes.