Transport in Porous Media

, Volume 25, Issue 3, pp 283–311 | Cite as

On the movement of an LNAPL lens on the water table

  • J. Bear
  • V. Ryzhik
  • C. Braester
  • V. Entov


The penetration of light nonaqueous phase liquids (LNAPLs) in quantities that lead to an accumulation in the form of a lens above the water table is considered. First, the three-phase vertical gravity-capillary equilibrium of water, NAPL, and air above the water table is specified. The hypothesis of ‘vertical equilibrium phase distribution’ is used to derive averaged asymptotic equations describing NAPL flow as a thin lens floating above the water table. Some problems of unsteady NAPL lens movement and the development of a NAPL mound, spreading along an inclined or horizontal phreatic surface are discussed and the analytical solutions are obtained.

Key words

nonaqueous phase liquids unsaturated zone three-phase flow vertical equilibrium LNAPL lens analytical solutions 



constant in Equation (55)


constant in Equation (7)


constant in Equation (25)

e0 e1

constants in Equation (72) (75)


acceleration due to gravity


form of the moving boundary of the lens


vector of the inclination of the water table


absolute permeability of the soil

krn, krw

relative permeabilities of NAPL an water


water saturated hydraulic conductivity of the soil


initial length of the lens


exponent in the equation for NAPL relative permeability

Pa, Pn, Pw

air, NAPL water pressures

Pcaw, Pcan, Pcnw

air-water air-NAPL and NAPL-water capillary pressures


reduced capillary pressure function


characteristic capillary pressure


NAPL and water flowrates (2-d vectors)


intensity of the source.


radial coordinate √x2 + y2


function defined by Equation (61)

Sa, Sn, Sw

air and NAPL water saturations

Snr, Swr

residual NAPL, water saturations


total liquid saturation, Sn + Sw


effective saturation (Equation (2))




integrated NAPL relative permeability


integrated water relative permeability in the unsaturated zone


constant in Equation (45)


NAPL content per unit of the water table surface


water content per unit of the water table surface within the lens


dimensionless NAPL content per unit of the water table surface


the value of u at a jump

u0, u1

constants in Equations (34) and (35)

U0, U1

total NAPL quantity in a mound


characteristic velocity

x, y, z

cartesian coordinates

z1, z2

upper boundaries of the two-phase (NAPL-water) three-phase zones


lower boundary of undisturbed unsaturated zone


elevation of the upper boundary of a point above the moving water table


constant in van Genuchten equation (8)

βan, βaw

scaling coefficients in Equation (2)

β0, β1

constants in Equations (34) and (35)

γaw, γij

surface tensions


Dirac delta-function


density difference (ϱw − ϱn)


thickness of the two-phase zone (NAPL water), within the lens


total thickness of the lens


total thickness of the zone, disturbed by the presence of the lens


elevation of the moving water table


initial elevation of the water table


deviation of the water table η − η0


exponent in Equation (66)

μn, μw

NAPL water viscosities


constant in tht van Genuchten equation (8)


Boltzmann variable (r/√at)


ρw NAPL water densities


dimensionless integrated NAPL relative permeability


soil porosity

Φn, Φw

NAPL water potentials


function defined by Equation (17)


dimensionless NAPL potential


characteristic thickness Δϱ/αϱn


domain occupied by the lens in the x, y-plane


moving boundary of the lens


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • J. Bear
    • 1
  • V. Ryzhik
    • 1
  • C. Braester
    • 1
  • V. Entov
    • 2
  1. 1.Faculty of Civil EngineeringTechnion - Israel Institute of Technology HaifaHaifaIsrael
  2. 2.Laboratory of Applied Continuum Mechanics, Institute for Problems in Mechanics, RASMoscowRussia

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