Pressure field in a formation with a hydraulic fracture of finite length

The pressure field in a layered, perfectly perforated, heterogeneous formation with a plane fluid flow toward a vertical hydraulic fracture is investigated using an analytical and numerical approach. Information about the pressure field is of great importance for oil and gas production, hydrogeology, and for improving the technology of extracting hydrocarbon raw materials from oil and gas hydrate deposits by pumping chemically active or radioactive solutions. An asymptotic method is used to construct an analytical solution in the leading approximation. A solution is given for the case when a critical pressure is maintained in the area of influence of injection wells on the state of the rock in the vicinity of the fracture tip, which under certain conditions corresponds to its spontaneous growth. A program is created based on the Laplace-Carson numerical image inversion algorithm, and spatiotemporal pressure distributions in the fracture and in the surrounding reservoir rock are calculated. It is shown that the pressure drop in the fracture becomes relatively quickly close to the injection pressure, and the pressure gradient tends to zero. In this case, the main pressure changes in the direction of fracture propagation are concentrated in a zone whose dimensions are significantly smaller than the dimensions of the disturbance zone in the direction transverse to the orientation of fracture. It has been established that in the collector, the pressure gradients along the path of the fracture propagation are much greater than the gradients in the areas of the reservoir that are lateral to the fracture. As a result, favorable conditions are created for crack growth. The results obtained allow us to determine the time it takes to get a critical pressure at the fracture tip, at which the process of autohydraulic fracturing begins.