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Abstract This paper presents a survey of simple methods for estimating vertical sweep efficiency in improved oil recovery (IOR) by gas injection.
A useful model for gravity override in gas IOR is that of Stone and Jenkins (SPE 11130, 12632), which applies to simultaneous water-gas injection into a homogeneous reservoir. Their equations for the distance to complete segregation are rigorously correct as long as the usual assumptions of fractional-flow theory apply. Their model implies that the volume swept by gas at given injection rate is approximately the same for vertical and horizontal wells, but the injection pressure does depend on well geometry and injection interval. For a given well geometry, the distance gas can travel before segregation depends directly on injection pressure. Thus, if injection pressure is limited, it is crucial to choose an injection profile that maximizes injectivity.
Recently, Stone (SPE 91724) suggested a new method of injection: gas and water injected simultaneously but separately, with water injected higher in the interval than gas. At fixed total injection rate, injection of water above gas gives deeper penetration before complete segregation than does co-injection in two-dimensional modeling and simulations. Whether injecting water above gas or both together, using only a portion of the injection interval reduces injectivity without affecting the distance to the point of segregation.
These results apply to both gas and foam IOR as long as gas and water are injected simultaneously or in separate, small slugs.
Introduction A major problem for gas-injection improved oil recovery (IOR) is gravity segregation of injected gas and water and gravity override of gas (Lake, 1989). A useful model for gravity segregation is that of Stone (1982), extended by Jenkins (1984), for steady state, uniform co-injection of gas and water in a homogeneous reservoir. 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 and Jenkins argue that their model applies to WAG processes as well, as long as the slug size is small enough that slugs mingle and mix near the well.) Stone and Jenkins assume that at steady state the reservoir splits into three zones, each with a uniform saturation, illustrated in Fig. 1:an override zone with only gas flowing,
an underride zone with only water flowing,
a mixed zone with both gas and water flowing.
It should be emphasized that this model represents sweep efficiency at steady state: no further advance of the mixed zone would occur no matter how long gas and water were injected. There is no mobile oil anywhere in the region of interest. In the override and mixed zone oil is at gas-flood residual saturation; in the underride zone it is at waterflood residual saturation.
Starting with this and other assumptions, Stone and Jenkins derive equations for the distance Lg (in a rectangular reservoir) or Rg (in a cylindrical reservoir) that the injected gas-water mixture flows before complete segregation:
Equation (1)
Equation (2)
where Q is total volumetric injection rate of gas and water, kz vertical permeability, ??w and ??g densities of water and gas, respectively, g gravitational acceleration, W the thickness of the rectangular reservoir perpendicular to flow, and ?rtm the total relative mobility in the mixed zone. It is significant that in both cases the distance to the point of segregation scales directly with volumetric injection rate Q. In deriving these equations Stone and Jenkins also assume that horizontal pressure gradient dp/dx (or dp/dr) is the same in each zone at any given value of x or r. Jenkins (1984) further presents equations for the shape of the override, underride and mixed zones up to and beyond the point of complete gravity segregation.
It is remarkable that in Eqs. 1 and 2 the height of the reservoir and the absolute permeability in the horizontal direction do not affect the horizontal distance to the point of gravity segregation. As shown below, they do affect injection pressure.
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