TY - JOUR
T1 - Leaky-layer seepage
T2 - The Verigin function revisited
AU - Kacimov, A. R.
AU - Obnosov, Yurii V.
N1 - Funding Information:
Acknowledgements This study was supported by Sultan Qaboos University, project CL/SQU-UAEU/0/3/02 and the Russian Foundation for Basic Research, grant 06-01-81019-Bel_a. Helpful comments by O.Strack, two anonymous referees and discussions with F.Marketz (Petroleum Development Oman - Shell) are appreciated.
PY - 2008
Y1 - 2008
N2 - An explicit analytical solution to the problem of steady Darcian seepage into a constant-head subsurface gallery (a straight line segment) placed in a homogeneous rock under a leaky layer of silt deposited in a reservoir is obtained. The third-type boundary condition (linear relation between the head and normal component of the Darcian velocity) along the interface between sediments and rock is tackled by the Verigin function, which satisfies the mixed boundary-value problem conditions in a domain obtained by a conformal mapping of the physical plane (quadrangle) onto an auxiliary plane. This function has three integrable singularities and, unlike Verigin's attempt to construct the second conformal mapping, we use a Signorini-type integral representation. The gallery flow rate is plotted as a function of the gallery size, location under the leaky layer, and the leakage factor, which combines the hydraulic conductivities of the rock and silt, the difference in hydraulic head between the reservoir bottom above the leaky layer and the gallery contour and the silt thickness.
AB - An explicit analytical solution to the problem of steady Darcian seepage into a constant-head subsurface gallery (a straight line segment) placed in a homogeneous rock under a leaky layer of silt deposited in a reservoir is obtained. The third-type boundary condition (linear relation between the head and normal component of the Darcian velocity) along the interface between sediments and rock is tackled by the Verigin function, which satisfies the mixed boundary-value problem conditions in a domain obtained by a conformal mapping of the physical plane (quadrangle) onto an auxiliary plane. This function has three integrable singularities and, unlike Verigin's attempt to construct the second conformal mapping, we use a Signorini-type integral representation. The gallery flow rate is plotted as a function of the gallery size, location under the leaky layer, and the leakage factor, which combines the hydraulic conductivities of the rock and silt, the difference in hydraulic head between the reservoir bottom above the leaky layer and the gallery contour and the silt thickness.
KW - Analytic functions
KW - Boundary-value problems
KW - Leaky layer
KW - Seepage
UR - http://www.scopus.com/inward/record.url?scp=55649101613&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=55649101613&partnerID=8YFLogxK
U2 - 10.1007/s10665-008-9223-5
DO - 10.1007/s10665-008-9223-5
M3 - Article
AN - SCOPUS:55649101613
SN - 0022-0833
VL - 62
SP - 345
EP - 354
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 4
ER -