Analytical and numerical analysis of oil recovery by gravity drainage

In gas gravity drainage, gas enters an oil-saturated column of rock and oil drains down spontaneously under the influence of capillary and gravity forces. A one-dimensional analytical and numerical analysis of this problem is performed. The numerical model is validated by predicting previously-published experimental measurements. Then analytical expressions for oil recovery as a function of time are proposed which accurately predict numerical simulation results for different values of the dimensionless ratio of gravity to capillary forces. When gravity dominates, the oil recovery scales as a power law with time with an exponent that depends on the oil mobility, whereas when capillary forces dominate, the oil recovery has an exponential variation with time and the ultimate recovery is poorer. The analytical expressions for average recovery are used to find matrix/fracture transfer functions in a dual porosity or permeability model of gravity drainage in a fractured reservoir.