Solvent-based processes have great potential to enhance oil recovery. The injected solvent is able to significantly reduce the viscosity of the oil and improve its mobility. In displacement processes, the frontal instability happening at the interface between solvent and oil can increase their surface contact area, while it also leads to earlier breakthrough time and less sweep efficiency if such instabilities develop too severely. Especially at very large mobility contrasts, the less viscous injected solvent can easily bypass the highly viscous heavy oil. Most of the previous studies on simulations of frontal instability are restricted to a small range of mobility ratio. In the present study, we adopted a highly accurate numerical method to simulate the detailed development of solvent fingering at extremely large mobility ratios in fully miscible displacements. At certain conditions, the case with a maximum mobility ratio as large as 22026.5 could be successfully modeled. This allowed analysis of the flow dynamics and mass transfer at such a large mobility contrast in miscible displacement processes. The breakthrough time and sweep efficiency at breakthrough were also investigated at small and extremely large values of mobility ratio through numerical simulations. With an increase in mobility ratio, the breakthrough time decreased, first very rapidly and then slowly. The breakthrough time varied as a power relationship with the mobility ratio for various Peclet numbers. Similar relationships were found for the sweep efficiency versus mobility ratio. This approach would be helpful for the accurate prediction of breakthrough time and sweep efficiency in miscible displacement under extremely large mobility contrasts.