Фильтрация жидкости в неоднородном слое с коэффициентом фильтрации, изменяющимся по квадратичному закону

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Фильтрация жидкости в неоднородном слое с коэффициентом фильтрации…
Инженерный журнал: наука и инновации # 6·2017 15
Fluid filtration in an inhomogeneous porous layer
with permeability coefficient that varies according
to a quadratic law
© O.D. Algazin, A.V. Kopaev
Bauman Moscow State Technical University, Moscow, 105005, Russia
The paper considers a model problem of fluid filtration in an inhomogeneous porous layer
with the permeability coefficient which decreases with depth as the square of the distance to
the bottom. We obtained exact solutions of the corresponding boundary value problems for
two-dimensional and three-dimensional cases. As an example of applying the obtained formu-
las we give the solutions of filtering problems under the spot dam and a cascade of two spot
dams in an inhomogeneous layer with aquiclude, the solutions being expressed in elementary
functions. Moreover, we examined the source and the vertical well in the three-dimensional
inhomogeneous layer. The velocity potential in these cases is recorded in the form of integrals
of elementary functions. The solutions of the boundary value problems discussed in this arti-
cle can be applied when considering the steady electrical and thermal fields in inhomogene-
ous media, in which, respectively, the dielectric constant and coefficient of thermal conductiv-
ity change according to a quadratic law.
Keywords: fluid filtration, inhomogeneous porous layer, permeability coefficient, La-
place equation, Poisson equation, Dirichlet problem
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Estestvennye nauki — Herald of the Bauman Moscow State Technical
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DOI: 10.18698/1812-3368-2016-3-42-56
Algazin O.D., Cand. Sc. (Phys.-Math.), Assoc. Professor of the Department of Computa-
tional Mathematics and Mathematical Physics, Bauman Moscow State Technical Univer-
sity. e-mail:
Kopaev A.V., Cand. Sc. (Phys.-Math.), Assoc. Professor of the Department of Higher
Mathematics, Bauman Moscow State Technical University. e-mail: