Release:

2019, Vol. 5. №3Title:

The problem of the flow of fluid to an imperfect drill hole
For citation:
Filippov A. I., Akhmetova O. V., Kovalsky A. A., Gubaydullin M. R. 2019. “The problem of the flow of fluid to an imperfect drill hole”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 5, no 3, pp. 97-117. DOI: 10.21684/2411-7978-2019-5-3-97-117

About the authors:

Aleksandr I. Filippov, Dr. Sci. (Tech.), Professor, Department of General Scientific Disciplines, Ufa State Petroleum Technical University branch in Salavat; Professor, Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, filippovai@rambler.ruOksana V. Akhmetova, Dr. Sci. (Phys.-Math.), Head of the Department of General and Theoretical Physics, Sterlitamak branch of the Bashkir State University; eLibrary AuthorID, ahoksana@yandex.ru

Aleksei A. Kovalsky, Cand. Sci. (Phys.-Math.), Director, Sterlitamak Branch of the Bashkir State University; eLibrary AuthorID, aakov68@mail.ru

Marat R. Gubaydullin, Junior Researcher, Sterlitamak Branch of the Bashkir State University; eLibrary AuthorID, Web of Science ResearcherID, fir_bmf@mail.ru

Abstract:

This article studies seepage flows arising from the selection of hydrocarbons from imperfect drill-holes. The authors observe the problem of pressure field in a homogeneous isolated isotropic homogeneous reservoir perforated in the range, completely contained in the layer of a common width.

To construct an analytical asymptotic solution, the single-layer initial problem is replaced by an equivalent three-layer symmetric, including the piezoconductivity equations for the perforated, covering, and underlying non-perforated layers, the initial and boundary conditions; on the conditional boundary of the perforated and non-perforated layers, the conditions of pressure and flow equality are specified (conjugation conditions). The solution of the problem is assumed to be regular — the value of the desired function, and, if necessary, its derivative at infinity is zero.

The problem is formulated in dimensionless quantities for the functions of the pressure deviation from its unperturbed distribution, normalized to the amplitude value of the depression. To solve the problem, the authors have developed an asymptotic method of a formal parameter. The solution of the problems for the zero and first coefficients of the asymptotic expansion is found in the space of the Laplace — Carson images in the variable *t*.

Based on the formulas obtained and the Darcy law, the authors construct graphical dependencies for the vertical and horizontal components of the fluid velocity filtered from the periphery to the well.

The computational experiment illustrates that there are no vertical flows at the exit to the well in the perforated part of the reservoir, and when removed from the well, these flows are different from zero, which indicates the presence of interlayer flows even in homogeneous imperfect drill holes. In the center of the perforated layer, such flows are absent, since the transverse velocity component vanishes. At the same time, the inflow in an imperfect drill hole is uneven, and the maximum modulus of the horizontal velocity component on all curves is reached at the boundary of the perforation interval.

Keywords:

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