Measurement and modeling of three-phase oil relative permeability
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Relative permeabilities for three-phase flow are commonly predicted from two-phase flow measurements using empirical models. These models are usually tested against available steady state data. However, the oil flow is unsteady state during various production stages such as gas injection after water flood. Accurate measurement of oil permeability([subscript ro]) during unsteady tertiary gas flood is necessary to study macroscopic oil displacement rate under micro scale events including double drainage, coalescence and reconnection, bulk flow and film drainage. We measure the three-phase oil relative permeability by conducting unsteady-state drainage experiments in a 0.8m water-wet sandpack. We find that when starting from capillary-trapped oil, k[subscript ro] starts high and decreases with a small change in oil saturation, and shows a strong dependence on both the flow of water and the water saturation, contrary to most models. The observed flow coupling between water and oil is stronger in three-phase flow than two-phase flow, and cannot be observed in steady-state measurements. The results suggest that the oil is transported through moving gas/oil/water interfaces (form drag) or momentum transport across stationary interfaces (friction drag). We present a simple model of friction drag which compares favorably to the experimental data. We also solve the creeping flow approximation of the Navier-Stokes equation for stable wetting and intermediate layers in the corner of angular capillaries by using a continuity boundary condition at the layer interface. We find significant coupling between the condensed phases and calculate the generalized mobilities by solving co-current and counter-current flow of wetting and intermediate layers. Finally, we present a simple heuristic model for the generalized mobilities as a function of the geometry and viscosity ratio. To identify the key parameter controlling the measured excess oil flow during tertiary gasflood, we also conduct simultaneous water-gas flood tests where we control water relative permeability and let water saturation develop naturally. The measured data and pore scale calculations indicate that viscous coupling can not explain completely the observed flow coupling between oil and water. We conclude that the rate of water saturation decrease, which controls the pore scale mechanisms including double drainage, reconnection, and film drainage significantly influences the rate of oil drainage during tertiary gas flood. Finally, we present a simple heuristic model for oil relative permeability during tertiary gas flood, and also explain how Stone I and saturation-weighted interpolation should be used to predict the permeability of mobilized oil during transient tertiary gasflood.