TY - JOUR
T1 - How much floating light nonaqueous phase liquid can a phreatic surface sustain? Riesenkampf's scheme revisited
AU - Kacimov, Anvar
AU - Obnosov, Yurii
AU - Al-Maktoumi, Ali
AU - Al-Balushi, Mohammed
PY - 2011/11/1
Y1 - 2011/11/1
N2 - Steady, Darcian, one-phase, phreatic surface flow of groundwater into a
horizontal well with a pancake lens of light nonaqueous phase liquid
(LNAPL) accumulated in the water table trough is studied by the method
of complex analysis. A sharp interface model assumes groundwater capped
by two isobaric limbs (groundwater-vadose zone interfaces) of a free
surface with an in-between cambered segment of an immiscible LNAPL-water
interface, along which pressure is hydrostatically increasing with the
depth of the LNAPL "channel." The complex potential polygon is mapped
onto an auxiliary half plane where the complex physical coordinate of
the flow domain is represented in terms of singular integrals as a
solution of the Keldysh-Sedov problem. The shapes of semi-infinite
"wings" of the water table contacting the vadose zone gas and of a
finite length LNAPL-groundwater interface are found from parametric
equations that involve the sink strength and location with respect to
the pancake surface, the ordinate of the lowest trough point, and the
volume of LNAPL accreted in the lens. Critical conditions, corresponding
to the lens contour cusping toward the sink, are found. The Riesenkampf
solution contains a free parameter, which is fixed by specifying either
a point on the free surface or the volume of the trough-intercepted
LNAPL.
AB - Steady, Darcian, one-phase, phreatic surface flow of groundwater into a
horizontal well with a pancake lens of light nonaqueous phase liquid
(LNAPL) accumulated in the water table trough is studied by the method
of complex analysis. A sharp interface model assumes groundwater capped
by two isobaric limbs (groundwater-vadose zone interfaces) of a free
surface with an in-between cambered segment of an immiscible LNAPL-water
interface, along which pressure is hydrostatically increasing with the
depth of the LNAPL "channel." The complex potential polygon is mapped
onto an auxiliary half plane where the complex physical coordinate of
the flow domain is represented in terms of singular integrals as a
solution of the Keldysh-Sedov problem. The shapes of semi-infinite
"wings" of the water table contacting the vadose zone gas and of a
finite length LNAPL-groundwater interface are found from parametric
equations that involve the sink strength and location with respect to
the pancake surface, the ordinate of the lowest trough point, and the
volume of LNAPL accreted in the lens. Critical conditions, corresponding
to the lens contour cusping toward the sink, are found. The Riesenkampf
solution contains a free parameter, which is fixed by specifying either
a point on the free surface or the volume of the trough-intercepted
LNAPL.
KW - LNAPL
KW - holomorphic functions
KW - horizontal well
KW - phreatic surface
KW - Hydrology: Groundwater hydraulics
KW - Hydrology: Groundwater hydrology
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U2 - 10.1029/2010WR010369
DO - 10.1029/2010WR010369
M3 - Article
AN - SCOPUS:81755176144
SN - 0043-1397
VL - 47
JO - Water Resources Research
JF - Water Resources Research
IS - 11
M1 - W11521
ER -