The vapour extraction (VAPEX) process, as a nonthermal process, may be suitable for the recovery of heavy oil and bitumen. In this process, the injected solvent diffuses into the heavy oil/bitumen, reduces its viscosity, and drains it to the producing well. The VAPEX process is more acceptable than other processes because of its environmental friendliness, low capital and operating costs, and suitability for thin reservoirs. Most of the efforts in the modelling of the VAPEX process have concentrated on the application of fluid-flow equations to the solvent and the diluted oil inside each gridblock used in the simulation of the VAPEX. This is adequate when very fine gridblocks are chosen to simulate the process in which the boundary layer (transition zone) occurs over a number of gridblocks. Fine gridblocks, however, require a large amount of simulation time, which is not applicable for field-scale simulation even with today's computing power. To deal with this problem, a new approach is introduced that is based on the application of the fluid-flow equations to three phases: solvent, diluted oil, and heavy oil/bitumen. With this approach, it becomes possible to have mobile solvent, mobile live oil, and immobile or slow-moving heavy oil/bitumen inside a gridblock. The main feature of the proposed model is its ability to capture the boundary layer within a gridblock, making very fine gridblocks unnecessary in the simulation of the VAPEX process. In addition, this approach can be applied to model the viscous fingering inside gridblocks.