EXACT SOLUTIONS OF A MODEL OF TRACER FLUID FLOW IN A VERTICAL FRACTURE
In order to intensify oil production, the injection pressure of the injected fluid increases. As a result, main auto-hydraulic fractures are formed on injection wells, which are “washed” over time by subsequent flows of injected water. These fractures can develop, join with hydraulic fractures or directly with production wells. Several fractures can propagate from the injection well. This leads to a rapid flooding of the produced product. In this regard, the problem arises of waterproofing main fractures from the side of injection wells. For water isolation of main fracture, an important task is to assess the volume of main fractures in terms of the time of arrival of the indicator fluid to the production well. In this paper, simple one-dimensional mathematical models of the laminar and turbulent flows of tracer fluid in the main fracture were developed that make it possible to estimate the volume of the fracture taking into account the influence of the permeability of its walls and the gradient of water injection pressure. For both flow regimes in a fracture, analytical solutions of the corresponding systems of equations are obtained. Pressure and flow velocity fields in laminar flow are represented in elementary functions. Similar fields in a turbulent flow are presented in a parametric form, where the parameter is the fluid acceleration. The time of arrival of the indicator fluid to the production well, both in laminar and in turbulent flows, is proportional to the difference in arctangents. The solutions obtained can be used to estimate the volumes of main fractures.