Asymptotic Analysis of the Inflow to a Fracture in an Oil–Gas Reservoir with Bottom Water

A model of oil inflow to a well in a fractured reservoir with a vast gas cap and an underlying water layer is presented in the conditions of gravity-induced segregation of fluids. Using an asymptotic analysis of the equations it was possible to simplify the description of the seepage process before and after the water and gas breakthrough into the well and at a distance from it, as well as to estimate the possibility of waterless and gasless extraction in the conditions of the stabilization of phase fractions in the total rate. It is shown that the hydrostatic equilibrium model can be used in the large-scale approximation fairly far from the well. It is noted that in most practical cases the finite-conductance effect of a fracture is negligible in the large-scale approximation, so that the model of an infinitely permeable fracture can be applied. The equations for determining gas and water fractions in the production after the breakthrough of the water and gas cones in the vicinity of the sink were derived on the flow scale. Finally, the coupling of the models presented makes it possible to describe adequately the inflow to the well before and after the breakthrough of the water and gas cones. The plausibility of the models presented is confirmed by the comparison of the calculated results with the actual data.