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Summary We extend a model for gravity segregation in steady-state gas/water injection into homogeneous reservoirs for enhanced oil recovery (EOR). A new equation relates the distance gas and water flow together directly to injection pressure, independent of fluid mobilities or injection rate. We consider three additional cases: coinjection of gas and water over only a portion of the formation interval, injection of water above gas over the entire formation interval, and injection of water and gas in separate zones well separated from each other. If gas and water are injected at fixed total volumetric rates, the horizontal distance to the point of complete segregation is the same, whether gas and water are coinjected over all or any portion of the formation interval. At fixed injection pressure, the deepest penetration of mixed gas and water flow is expected when fluids are injected along the entire formation interval. At fixed total injection rate, injection of water above gas gives deeper penetration before complete segregation than does coinjection, but again exactly where the two fluids are injected does not affect the distance to the point of segregation. At fixed injection pressure, injection of water above gas is predicted to give deeper penetration before complete segregation. When injection pressure is limited, the best strategy for simultaneous injection of both phases from a vertical well would be to inject gas at the bottom of the reservoir and water over the rest of the reservoir height, with the ratio of the injection intervals adjusted to maximize overall injectivity. The 2D model applies equally to gas/water flow and to foam, and to injection of water above gas from separate intervals of a vertical well or from two parallel horizontal wells, as long as injection is uniform along each horizontal well. Sample computer simulations for foam injection agree well with the model predictions if numerical dispersion is controlled.

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We earlier presented a proof for the model of Stone (1982) for gravity segregation in steady-state, horizontal gas-liquid flow in homogeneous porous media using only the standard assumptions of the method of characteristics. We extend this method here to cases of co-injection of gas and liquid over only a portion of the formation interval, injection of water above gas over the entire formation interval, and injection of water and gas in separate zones well separated from each other. If gas and liquid are injected at fixed total volumetric rates, the horizontal distance to the point of complete segregation is the same, whether gas and liquid are co-injected over all or any portion of the formation interval. The volume of reservoir swept by gas may be affected by these different injection strategies, however, and is not directly predicted by our model. At fixed injection pressure, the deepest penetration of mixed gas and water is expected when fluids are co-injected along the entire formation interval. At fixed total injection rate, injection of water above gas gives deeper penetration before complete segregation than does co-injection, but again exactly where the two fluids are injected does not affect the distance to the point of segregation. At fixed injection pressure, injection of liquid above gas is predicted to give much deeper penetration before complete segregation. When injection pressure is limited, the best strategy for simultaneous injection of both phases would be to inject gas at the bottom of the reservoir and liquid over the rest of the reservoir height, with the ratio of the injection intervals adjusted to maximize overall injectivity. These results apply equally to gas-liquid flow and to foam. Sample computer simulations for foam injection agree well with the model predictions if numerical dispersion is controlled. Introduction A useful model for gravity segregation is that of Stone (1982), further elucidated by Jenkins (1984), for steady-state, uniform co-injection of gas and water in a homogeneous porous medium; to distinguish this case from others below, by uniform co-injection we mean injection of gas and water with uniform water fractional flow and uniform superficial velocity all along the height of the formation. Stone assumed that in this case at steady state the reservoir splits into three regions of uniform saturation, with sharp boundaries between them:an override zone with only gas flowingan underride zone with only water flowinga mixed zone with both gas and water flowing.

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