This paper presents a formalized method of testing hydraulic fracturing simulators for a planar fracture, validating the robustness of the implemented physical and mathematical models. In this set of tests, the main accent is made on implementation of the basic laws of hydraulic fracturing: equations of elasticity, the law of mass conservation, the equation of lubrication, leak-offs model, fracture propagation criterion. All tests are done with the dimensionless parameters of the hydraulic fracturing. Scaling of the equations leads to the universality of the given tests. Dimensionless parameters determine fracture form, fracture fluid effectivity and the fracture propagating regime. Different practical cases with the same dimensionless parameters have the same scaled parameters. Therefore, the test into the dimensionless parameters is more universal, than ordinary practical case. Also, the modeling of the different practical cases with the same dimensionless parameters helps to determine value of relative errors of the calculation scheme. Verification of the mathematical model is carried out both by comparison with known analytical and semi-analytical solutions for specific cases (Radial, PKN models) and by compliance with fundamental physical laws. The fracture leak-offs and fracture fluid effectivity is validated by the well-known Nolte-function, which represented in the dimensionless form. This set of tests is the basis for a universal system of fracture simulator tests and will allow to objectively compare existing commercial and non-commercial simulators with existing benchmarks, as well as with each other.
References
1. Khasanov M.M., Paderin G.V., Shel' E.V. et al., Approaches to modeling hydraulic fracturing and their development (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2017, no. 2, pp. 37–41.
2. Irwin G.R., Fracture mode transition for a crack traversing a plate, Journal of Basic Engineering, 1960, V. 82, no. 2, pp. 417–423
3. Shel E. et al., Retrospective analysis of hydrofracturing with the dimensionless parameters: Comparing design and transient tests, SPE 191707-18RPTC-MS, 2018.
4. Perkins T.K. et al., Widths of hydraulic fractures, Journal of Petroleum Technology, 1961, V. 13, no. 9, pp. 937–949.
5. Economides M.J. et al., Reservoir stimulation, Englewood Cliffs, NJ: Prentice Hall, 1989, pp. 356–358.
