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Representation of pressure field and fluid flows in the proximity of a horizontal well based on the instant point sources

*R.I. Nafikov, A.A. Salamatin*

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The boundary value problem of transient pressure field development around a horizontal well in a laterally infinite, inhomogeneous, anisotropic reservoir is formulated under assumption of slow spatial variation of the matrix permeability along the well axis. The well is represented as a linear fluid source/sink. The pressure distribution is expressed in the integral form on the basis of the instant point source perturbation function found explicitly. The inverse problem for fluid in/outflow density rates simulation is reduced to solution of the integral equation at a given pressure inside the well. A computational procedure is developed and implemented to predict the in/outflow rates along the well and estimate the impact of the permeability variations on the well performance. Series of calculations for constant, linear, and variable permeability cases are analyzed and compared. The difference of the obtained solution from the so-called “locally-constant” permeability approximation is demonstrated, accuracy and applicability of the latter approach are discussed.

horizontal well, variable matrix permeability, transient pressure field, in/outflow rates, method of instant point sources, inverse problem

- Borisov Yu.P., Pilatovskiy V.P., Tabakov V.P. (1964). Development of oil fields by horizontal and multilateral wells. Moscow: Nedra, 154 p. (In Russ.)
- Charnyy I.A. (1963). Underground hydrodynamics. Moscow: Gostoptekhizdat, 396 p. (In Russ.)
- Gradshteyn I.S., Ryzhik I.M. (1971). Tables of integrals, sums, series and products. Moscow: Nauka, 1108 p. (In Russ.)
- Griguletskiy V.G. (1992). Stationary oil inflow to a single horizontal well in an anisotropic reservoir. Neftyanoe khozyaystvo = Oil Industry, 10, pp. 10–12. (In Russ.)
- Karslou G., Eger D. (1964). Thermal conductivity of solids. Moscow: Nauka, 488 p. (In Russ.)
- Morozov P.E. (2009). Mathematical modeling of fluid inflow to a horizontal well in an anisotropic fractured porous reservoir. Proc. XIII AllRuss. Conf.: Modern problems of mathematical modeling. Rostov-na-Donu: YuFU Publ., pp. 368–376. (In Russ.)
- Morozov P.E. (2018). Modeling of non-stationary fluid inflow to a multisectional horizontal well. Georesursy = Georesources, 20(1), pp. 44–50. https://doi.org/10.18599/grs.2018.1.44-50
- Ozkan E., Raghavan R. (1991). New Solution for Well-Test-Analysis Problems: Part 1 – Analytical Considerations. SPE Form. Eval., 6(3), pp. 359–368. https://doi.org/10.2118/18615-PA
- Prudnikov A.P., Brychkov Yu.A., Marichev O.I. (1981). Integrals and series. Elementary functions. Moscow: Nauka, 800 p. (In Russ.)
- Soleimani B., Moradi M., Ghabeishavi A., Mousavi A. (2018). Permeability Variation Modeling and Reservoir Heterogeneity of Bangestan Carbonate Sequence, Mansouri Oilfield, SW Iran. Carbonates Evaporites, 34, pp. 143–157. https://doi.org/10.1007/s13146-018-0461-y
- Spivey J.P., Lee W.J. (1999). Estimating the Pressure-Transient Response for a Horizontal or a Hydraulically Fractured Well at an Arbitrary Orientation in an Anisotropic Reservoir. SPE Res. Eval. Eng., 2(5), pp. 462–469.
- Tikhonov A.N., Samarskiy A.A. (1999). Equations of mathematical physics. Moscow: MSU Publ., 740 p. (In Russ.)

*Radmir I. Nafikov* – Master Student, Institute of Computational Mathematics and Information Technologies

Kazan Federal University

35, Kremlevskaya str., Kazan, 420008, Russian Federation

*Artur A. Salamatin* – Cand. Sci. (Phys.-Math.), Associate Professor, Institute of Computational Mathematics and Information Technologies

Kazan Federal University

35, Kremlevskaya str., Kazan, 420008, Russian Federation

#### For citation:

Nafikov R.I., Salamatin A.A. (2023). Representation of pressure field and fluid flows in the proximity of a horizontal well based on the instant point sources. *Georesursy = Georesources*, 25(1), pp. 140–144. https://doi.org/10.18599/grs.2023.1.14