An analytical solution for linear waterflood including the effects of capillary pressure
In this paper the authors develop exact solutions for a model linear (one-dimensional (1D)) waterflood that includes the effects of capillary pressure. They show that at constant injection rates an exact solution is possible for a water/oil displacement process. Explicit analytical expressions for the oil saturation distribution as a function of position and time are derived that account for the effects of capillary pressure. The solution is expressed in terms of F and a dimensionless parameter, ..beta../sup 2/, that denotes the relative magnitude of viscous to capillary terms. At high injection rates (..beta -->..infinity), the solution reduces to the familiar Buckley Leverett expressions, including the shock front solution when F greater than or equal to 1. From the analytical results one can calculate the capillary effects on the performance of the model waterflood. This work finds applications in two areas. First, it can be used to describe explicitly the performance of the model waterflood at low injection rates (small ..beta..), where the existing approximate solutions fail to account for the large capillary terms. Second, it can be used to check approximate analytical (such as the Buckley-Leverett), asymptotic, and numerical solutions.
- Research Organization:
- Univ. of Southern California
- OSTI ID:
- 5804667
- Journal Information:
- SPEJ, Soc. Pet. Eng. J.; (United States), Vol. 23:1
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
WATERFLOODING
FLOW RATE
MATHEMATICAL MODELS
ANALYTICAL SOLUTION
CAPILLARY FLOW
ENHANCED RECOVERY
OIL FIELDS
OIL SATURATION
OIL WELLS
ONE-DIMENSIONAL CALCULATIONS
RESERVOIR PRESSURE
FLUID FLOW
FLUID INJECTION
GEOLOGIC DEPOSITS
MINERAL RESOURCES
PETROLEUM DEPOSITS
RECOVERY
RESOURCES
SATURATION
WELLS
020300* - Petroleum- Drilling & Production