Modeling of hydraulic fracturing (HF) is the complex problem, which includes the description of many physical processes, including: the fluid flow in the fracture, deformation of the rock, fracture of the rock, proppant flow, etc. An effective solution of this problem requires a considerable number of simplifications and assumptions, which leads to various models of hydraulic fracturing. Presented article is devoted to the analysis and systematization of hydraulic fracturing models. A general system of equations for the fracturing problem is presented, and the aspects of transition from the initial equations to concrete models are considered. In this paper, we analyze both models that are traditionally used in industrial simulators (Lumped Pseudo3D, Cell-based Pseudo3D, Planar3D), and prospective models (Semi-analytical Pseudo3D, UFM Pseudo3D, Planar3D Bio, Full 3D), the implementation of which in the oil industry began recently. The basic approximations in the modeling of fracturing are considered, such as approximations of the effective continuous medium, the approximation of the small width, the incompressibility of the fracturing fluid, the approximation of small deformations and elastic mechanics, the approximation of the planar fracture shape, the approximation of the piecewise homogeneity of the formation along the vertical, the presence or absence of natural fractures network, the poroelastic effects, effects of proppant transport. It is indicated which approximations are used by each of the above-described fracture models. On this basis, conclusions about the range of applicability of certain models or fracturing simulators are drawn.
To summarize the results of analysis of the considered HF models, the systematization and hierarchy of HF models based on assumptions and limitations is proposed. The article also discusses possible directions for further development of hydraulic fracturing models.
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