A dynamic and large-scale network simulator was developed to simulate the rate-controlled immiscible displacement of two fluids in long, undisturbed soil columns. The simulator is a fast method for upscaling the hydraulic properties of heterogeneous soils and is an alternative to the conventional method where a system of partial differential equations is solved in a numerical grid. The pore space is regarded as a cubic network. Each node represents a pore network, the permeability of which is chosen randomly from a density distribution function. The macroheterogeneity of the large-scale network is quantified by the width of the node permeability distribution. The capillary pressure and relative permeability functions are obtained from either the quasistatic simulation of the displacement of water by oil in a pore-and-throat network or the inverse modeling of soil column flow tests by using the approximate multiflowpath model (MFPM). At each time step, the fluid saturation and pressure of each node are calculated, formulating mass balances at each node, accounting for capillary, viscous and gravity forces, solving the system of coupled and linear equations, calculating the instantaneous flow rates, and updating the local fluid saturations. The inlet pressure is adjusted to keep the total flow rate of injected fluid constant. Sensitivity analysis revealed that the transient responses of the axial distribution of fluid saturation, total pressure drop across the network, and sample averaged (upscaled) relative permeability functions depend on the variability of permeability distribution, spatial correlations of permeability field, capillary number, and viscosity ratio. When the microheterogeneity at the pore network scale of nodes strengthens, the flow of oil through preferential pathways is enhanced, and the upscaled water and oil relative permeabilities change drastically.

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