Influence of the Position of a Horizontal Hydraulic Fracture on the Pressure Field in the Stratum

The authors have proposed an analytical-numerical model of filtration in a producing stratum with a horizontal fracture, that is based on the solution of a quasi-stationary problem on the filtration pressure field in a dominantvertical-permeability anisotropic porous medium divided by a disk hydrofracturing region. On the boundaries separating the fracture from the surrounding rocks, piezoconductivity equations were supplemented with conjugation conditions. The problem has been solved in a zero asymptotic approximation in the Laplace–Carson transform space. Inversion of the formulas was performed with the Iseger numerical algorithm. Results of the computational experiment have been given. It has been shown that the greatest influence of the location of the fracture on the pressure field is observed in the case where it is on one boundary of the producing bed, and from an instant of time, the location of the fissure ceases to exert an influence on the pressure field in the fracture. On the calculated pressure curves, stabilization is observed which is analogous to the existing logarithmic model for the case of a homogeneous stratum. The authors have investigated the space-time dependence of the pressure perturbation across the thickness of the bed in which hydraulic fracturing was implemented. It has been shown that the pressure difference between each point of the vertical cross section and the bottom (top) grows at small values of time. Subsequently, the pressure difference peaks and the growth is replaced by a drop. A regularity has been noted that implies that the rate of growth in the pressure difference between the fracture and the stratum′s bottom is much higher than that of drop.