Recently, the steam-over-solvent injection in fractured reservoirs (SOS-FR) method was proposed as a potential solution for efficient heavy-oil/bitumen recovery in oil-wet naturally fractured reservoirs. The method is based on initial injection steam (Phase 1), followed by solvent (Phase 2). In the third cycle (Phase 3), steam is injected again to recover more oil and retrieve the solvent. Solvent retrieval during the third cycle was observed to be fast if the temperature is at approximately the boiling point of the solvent. This process is controlled by efficient matrix recovery and the mechanics of the process need to be clarified to further determine the efficient application conditions for the given matrix and oil characteristics. Single-matrix behaviour during the process was numerically modelled for static: conditions and the results were matched with the experimental observations. The physics of the recovery mechanism was analyzed through visual inspection of saturation and concentration profiles in each cycle. The major observation was the substantial effect of gravity in oil recovery when the matrix were exposed to solvent. Special attention was given to the solvent retrieval late and amount in Phase 3 and the permeability reduction caused by asphaltene precipitation in Phase 2. This phenomenon was modelled using a permeability function changing with spatial coordinates and time (i.e., k=f(x,y,z,t). It was observed that permeability reduction caused by asphaltene precipitation is significant and needs to be taken into account in the modelling process. After showing the effect of the matrix size on the oil recovery and solvent retrieval, an upscaling analysis was performed. The log-log relationship between the time value to reach ultimate recovery and the matrix size yielded a straight-line relationship with a non-integer exponent less than two for all three phases of the process. The observed straight-line relationship (and the exponent values obtained) is highly encouraging to extend the study to obtain a universal scaling relationship.