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 -