Approximate Solution of the Problem on Elastic-Liquid Filtration in a Fracture Formed in an Oil Stratum

Abstract

With the use of theoretical models of filtration liquid flows in fractures of finite and infinite lengths, formed in an oil stratum, the problem on the production of oil from a well, operating in the regimes of constant differential pressure or constant flow rate in this stratum, was solved. On the basis of approximate solution of the problem on the flow of oil from a stratum into a fracture formed in it by the method of successive changing stationary states, fairly simple analytical formulas have been obtained. A comparison of the results of numerical calculations of the practically important parameters of an oil stratum and a hydraulic fracture in it by the approximate formulas constructed and the corresponding exact formulas, which are much more complex than the approximate formulas, has shown that these results are almost identical. In particular, the errors in determining the evolution of the pressure field in a well and its flow rate by the approximate formulas did not exceed several percent. On the basis of numerical analysis of the approximate solutions obtained, the influence of the porosity and permeability of the stratum, the length of a fracture in it, and the rheological properties of the liquid saturating the stratum on the evolution of the pressure in the fracture, the flow rate of a well operating in the regime of constant differential pressure in the stratum, and the changes in the pressures in the fracture and in the well at a constant well flow rate was investigated.