Article is devoted to mathematical modeling of the fracturing mechanics and software development for fracturing simulation and decision making support in design and conduct of fracturing treatments. We discuss the basic software elements for modeling hydraulic fracturing, the existing mathematical models of hydraulic fracturing process (KGD, PKN, Radial, Cell-based-Pseudo3D, Lumped-Pseudo3D, Planar3D), history of development, characteristics and limitations. It is noted the practical importance for the fracturing planning tasks and risk minimization to correctly describe the fracture height growth, this pushed the development of Pseudo3D (P3D) and Planar3D (PL3D) models.
We show the general mathematical formulation of hydraulic fracturing process, based on coupled solution of the formation elasticity equations, fluid hydrodynamics and proppant transport. In details discussed the mathematical formulation for Planar3D model and common assumptions that are made. Software interface examples are shown for common methods of fracturing injection tests analysis and hydraulic fracturing design simulation on the example of corporate fracturing simulator. Typical functional requirements for hydraulic fracturing simulators are given. It is noted that the combination in a one fracturing simulator Planar3D and Cell-based-P3D models provides a flexible software solution to specific geological conditions and requirements for the calculation speeds. It has been shown that for certain geological conditions fracturing simulations using Planar3D and Pseudo3D models may vary in term of evaluating hydraulic fracture geometry. The attention made that the task of speed increasing for Planar3D-models is the actual point of application for scientific and engineering community efforts.
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