###### On the influence of the model of leakage into the reservoir during hydraulic fracturing by compressive liquid

UDC: 532.546+519.63

DOI: 10.33285/2782-604X-2023-2(595)-25-30

Authors:

KANEVSKAYA REGINA D.^{1},

KOCHUEVA OLGA N.^{1},

FEDYUNINA DARIA D.^{1}
^{1} National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: compressible fluid hydraulic fracturing, leakage model, hydraulic fracture pressure

Annotation:

The article investigates the problem of modeling leakage into the reservoir during hydraulic fracturing (HF) using a fracturing fluid based on liquefied hydrocarbon gas. To calculate the mass leakage of a hydraulic fracturing compressible fluid through the walls of the fracture into the reservoir, the solution of the nonlinear piezoconductivity equation with a variable boundary condition in a one-dimensional formulation is considered. It is assumed that the coordinate is orthogonal to the direction of the fracture propagation, which corresponds to a plane-parallel flow. A solution is obtained, which is a generalization of Carter's empirical formula. A numerical model of hydraulic fracture propagation in a porous medium has been developed, which includes two processes: filtration of a compressible fracturing fluid in the formation and its flow inside the fracture. The problem is considered at a constant pressure of the injected hydraulic fracturing fluid at the bottom of the well, while modeling the fracture growth the Perkins – Kern model is used. The fracture growth equation takes into account seepage leaks into the reservoir based on the obtained solution; it is assumed that leaks are determined by the current pressure in the fracture in each of its sections. The results obtained in the course of seepage leaks calculation based on the solution found, which takes into account the growth of the boundary value of pressure with time in the course of hydraulic fracturing according to a power law, and according to the Carter formula at a constant pressure at the boundary, are comparatively analyzed.

Bibliography:

1. SUG dlya GRP. Razrabotka netraditsionnykh zapasov uglevodorodov pri pomoshchi tekhnologii GRP s primeneniem v kachestve zhidkostey razryva szhizhennykh uglevodorodnykh gazov / V.A. Tsygankov, K.V. Strizhnev, L.A. Magadova, A.V. Nen'ko // Delovoy zhurnal Neftegaz.RU. – 2019. – № 6(90). – S. 56–61.

2. Zheltov Yu.P., Khristianovich S.A. O gidravlicheskom razryve neftenosnogo plasta // Izv. AN SSSR. Otd-nie tekhn. nauk. – 1955. – № 5. – S. 3–41.

3. Nordgren R. Propagation of vertical hydraulic fractures // SPE J. – 1972. – Vol. 12, Issue 4. – P. 306–314. – DOI: 10.2118/3009-PA

4. Geertsma J., de Klerk F. A rapid method of predicting width and extent of hydraulic induced fractures // J. of Petroleum Technology. – 1969. – Vol. 21, Issue 12. – P. 1571–1581. – DOI: 10.2118/2458-PA

5. Sneddon I.N. Integral transform methods // Mechanics of fracture. Vol 1. Methods of analysis and solution of crack problems / Ed. G.C. Sih. – Leyden: Springer Nordhoff Int., 1973. – P. 315–367.

6. Matematicheskie modeli gidrorazryva plasta / D.V. Esipov, D.S. Kuranakov, V.N. Lapin, S.G. Chernyy // Vychislitel'nye tekhnologii. – 2014. – T. 19, № 2. – S. 33–61.

7. Carter R.D. Appendix I. Derivation of the general equation for estimating the extent of the fractured area // Drilling and Production Practice / G.C. Howard, C.R. Fast (Eds.). – N.Y.: American Petroleum Institute, 1957. – P. 261–270.

8. Barenblatt G.I., Entov V.M., Ryzhik V.M. Dvizhenie zhidkostey i gazov v prirodnykh plastakh. – M.: Nedra, 1984. – 208 s.

9. Perkins T.K., Kern L.R. Widths of hydraulic fractures // J. of Petroleum Technology. – 1961. – Vol. 13, Issue 9. – P. 937–949. – DOI:10.2118/89-PA