Bottomhole pressure type curves for a well with a vertical hydraulic fracture under skin-effect conditions

UDK: УДК 622.276.66.001
DOI: DOI: 10.24887/0028-2448-2021-11-130-132
Key words: vertical hydraulic fracture, unsteady filtration, skin factor, skin zone, fluid loss damage zone, Laplace transform, typical curves, inverse problem
Authors: E.O. Sazonov1, I.L. Khabibullin2 1Bashneft-Dobycha LLC, RF, Ufa 2Bashkir State University, RF, Ufa

Hydraulic fracturing is currently a necessary part of the unconventional hydrocarbon reserves development. The efficiency of hydraulic fracturing is influenced by a large number of factors, one of which is the quality of the near-fracture zone of the formation, the so-called fluid loss damage zone. The flow rate and productivity index of the well significantly depend on the parameters of this zone. Therefore, it is important to have a way to estimate these parameters. The following problem was considered: in an infinite reservoir saturated with a single-phase fluid, there is a well that is intersected by a symmetric vertical hydraulic fracture along its entire thickness. The formation around the fracture has a damaged zone that has reduced reservoir properties. The hydraulic connection between the reservoir and the well is realized only through the lateral surface of the fracture. At the initial moment of time, the pressure in the formation and the fracture is the same, and the well is put into production at a constant flow rate. The solution obtained by application of the Laplace integral transform method, is presented in the form of the dependence of the bottomhole pressure on time and the hydrodynamic parameters of the system reservoir – skin zone – hydraulic fracture. This expression is essentially a ‘type curve’ equation that can be used to solve inverse problems of reservoir hydrodynamics and interpretation problems of well testing. The solution includes a parameter that can be considered as a value that determines the additional pressure drop in the skin zone, which in its meaning coincides with the skin factor.

References

1. Khabibullin I.L., Khisamov A.A., Modeling of unsteady filtration around the well with vertical hydraulic fracture (In Russ.), Vestnik Bashkirskogo gosudarstvennogo universiteta, 2017, V. 22, no. 2, pp. 309–314.

2. Khabibullin I.L., Khisamov A.A., Unsteady flow through a porous stratum with hydraulic fracture (In Russ.), Izvestiya RAN. Mekhanika zhidkosti i gaza = Fluid Dynamics, 2019, no. 5, pp. 6–14, DOI: 10.1134/S0568528119050050.

3. Nagaeva Z.M., Shagapov V.Sh., Elastic seepage in a fracture located in an oil or gas reservoir (In Russ.), Izvestiya RAN. Prikladnaya Matematika i Mekhanika = Journal of Applied Mathematics and Mechanics, 2017, V. 81, no.  3, pp. 319–329.

4.  Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

5. Cinco-Ley H., Samaniego V. F., Effect of wellbore storage and damage on the transient pressure behavior of vertically fractured wells, SPE-6752-MS, 1977, DOI: 10.2118/6752-ms.

6. Cinco-Ley H., Samaniego V.F., Transient pressure analysis: Finite conductivity fracture case versus damaged fracture case, SPE-10179-MS, 1981,  DOI: 10.2118/10179-MS

7. Lavrent'ev M.A., Shabat B.V., Metody teorii funktsiy kompleksnogo peremennogo (Methods of the theory of functions of a complex variable), Moscow: Nauka Publ., 1987, 688 p.

8. Gringarten A.C., Type-curve analysis: What it can and cannot do, Journal of Petroleum Technology, 1987, January, V. 39, no. 1, pp. 11–13, DOI: 10.2118/16388-pa.

Hydraulic fracturing is currently a necessary part of the unconventional hydrocarbon reserves development. The efficiency of hydraulic fracturing is influenced by a large number of factors, one of which is the quality of the near-fracture zone of the formation, the so-called fluid loss damage zone. The flow rate and productivity index of the well significantly depend on the parameters of this zone. Therefore, it is important to have a way to estimate these parameters. The following problem was considered: in an infinite reservoir saturated with a single-phase fluid, there is a well that is intersected by a symmetric vertical hydraulic fracture along its entire thickness. The formation around the fracture has a damaged zone that has reduced reservoir properties. The hydraulic connection between the reservoir and the well is realized only through the lateral surface of the fracture. At the initial moment of time, the pressure in the formation and the fracture is the same, and the well is put into production at a constant flow rate. The solution obtained by application of the Laplace integral transform method, is presented in the form of the dependence of the bottomhole pressure on time and the hydrodynamic parameters of the system reservoir – skin zone – hydraulic fracture. This expression is essentially a ‘type curve’ equation that can be used to solve inverse problems of reservoir hydrodynamics and interpretation problems of well testing. The solution includes a parameter that can be considered as a value that determines the additional pressure drop in the skin zone, which in its meaning coincides with the skin factor.

References

1. Khabibullin I.L., Khisamov A.A., Modeling of unsteady filtration around the well with vertical hydraulic fracture (In Russ.), Vestnik Bashkirskogo gosudarstvennogo universiteta, 2017, V. 22, no. 2, pp. 309–314.

2. Khabibullin I.L., Khisamov A.A., Unsteady flow through a porous stratum with hydraulic fracture (In Russ.), Izvestiya RAN. Mekhanika zhidkosti i gaza = Fluid Dynamics, 2019, no. 5, pp. 6–14, DOI: 10.1134/S0568528119050050.

3. Nagaeva Z.M., Shagapov V.Sh., Elastic seepage in a fracture located in an oil or gas reservoir (In Russ.), Izvestiya RAN. Prikladnaya Matematika i Mekhanika = Journal of Applied Mathematics and Mechanics, 2017, V. 81, no.  3, pp. 319–329.

4.  Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

5. Cinco-Ley H., Samaniego V. F., Effect of wellbore storage and damage on the transient pressure behavior of vertically fractured wells, SPE-6752-MS, 1977, DOI: 10.2118/6752-ms.

6. Cinco-Ley H., Samaniego V.F., Transient pressure analysis: Finite conductivity fracture case versus damaged fracture case, SPE-10179-MS, 1981,  DOI: 10.2118/10179-MS

7. Lavrent'ev M.A., Shabat B.V., Metody teorii funktsiy kompleksnogo peremennogo (Methods of the theory of functions of a complex variable), Moscow: Nauka Publ., 1987, 688 p.

8. Gringarten A.C., Type-curve analysis: What it can and cannot do, Journal of Petroleum Technology, 1987, January, V. 39, no. 1, pp. 11–13, DOI: 10.2118/16388-pa.



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