A spatiotemporal transport-flow framework for heavy-oil recovery: Unified Damköhler analysis of thermal, solvent, and electromagnetic mechanisms

Heavy oil and bitumen production is constrained by extremely high in situ viscosity and by the mismatch between the time required for mobility modification to propagate through the reservoir and the timescale of oil drainage. Although thermal, solvent, and electromagnetic recovery methods have been extensively studied, most existing screening approaches remain qualitative and process specific, providing limited physical guidance on when and where a given mechanism can effectively influence flow. In this work, we develop a unified Darcy-scale spatiotemporal framework that links transport-controlled propagation with constitutive viscosity modification. The effectiveness of each recovery process is evaluated using generalized space–time Damköhler numbers, which compare the characteristic timescale of local viscosity modification with the drainage timescale imposed by flow. Analytical expressions for effective propagation radius are derived for heat diffusion, electromagnetic volumetric energy deposition, and solvent transport in porous media. The framework is applied to five representative reservoir settings, including intermediate viscosity sands, thick shallow bitumen formations, deep heavy oil reservoirs, thin pay zones, and strongly heterogeneous systems. The results reveal systematic shifts in the dominant mobility modification mechanism with changes in viscosity, depth, thickness, and heterogeneity. Thick shallow reservoirs require bulk thermal mobilization, moderate viscosity systems remain controlled by sustained heating, increasing depth limits reservoir-scale thermal propagation and favors staged hybrid strategies, thin pay zones benefit from near wellbore electromagnetic conditioning, and strong heterogeneity calls for spatially.