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.
1. Meyer B.R., Design formulae for 2-D and 3-D vertical hydraulic fractures: Model comparison and parametric studies, SPE 15240, 1986.
2. Meyer B.R., Cooper G.D., Nelson S.G., Real-time 3-D hydraulic fracturing simulation: Theory and field case studies, SPE 20658, 1990.
3. Clifton R.J., Brown U., Wang J-J., Multiple fluids, proppant transport, and thermal effects in three-dimensional simulation of hydraulic fracturing, SPE 18198, 1988.
4. Kurashlga Mlchlo, Clifton R.J., Integral equations for the problem of a 3d crack in an infinite, fluidfilled, poroelastic solid, SPE 19386, 1989.
5. Barree R.D., A practical numerical simulator for three-dimensional fracture propagation in heterogeneous media, SPE 12273, 1983.
6. Aksakov A.V., Borshchuk O.S., Zheltova I.S. et al., Corporate fracturing simulator: from a mathematical model to the software development (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2016, no. 11, pp. 35-40.
7. Pitakbunkate T., Yang M., Valko P.P., Economides M.J., Hydraulic fracture optimisation with a p-3D model, SPE 142303, 2011.
8. Paderin G.V., Modified approach to incorporating hydraulic fracture width profile in unified fracture design model, SPE 182034, 2016.
9. Weng X., Kresse O., Cohen C.-E. et al., Modeling of hydraulic-fracture-network propagation in a naturally fractured formation, SPE 140253-PA, 2011.
10. Boronin S.A., Osiptsov A.A., Desroches J., Displacement of yield-stress fluids in a fracture, International Journal of Multiphase Flow, 2015, V. 76, pp. 47–63.
11. Golovin S.V., Baykin A.N., Stationary dipole at the fracture tip in a poroelastic medium, International Journal of Solids Structures, 2015, V. 69–70, pp. 305–310.
12. Clifton R.J., Wang J.J., Modeling of poroelastic effects in hydraulic fracturing, SPE 21871-MS, 1991.