New method to determine two-liquid k-S-P relationships
In many studies involving a liquid and air, the permeability (k) function
for the liquid is determined from the capillary pressure (Pc) - saturation
(S) relation and some matching, measured, k value. The movement and therefore
the permeability of air in an air - liquid system is usually ignored. However,
if a wetting and a nonwetting liquid coexist (two immiscible liquids),
the permeability function of the nonwetting liquid must be determined as
well. Rather than using some indirect method to determine the k(Pc) relationship
of the nonwetting liquid, we propose a direct measurement technique. The
technique makes use of a uniquely designed permeability cell which allows
for steady state flow of the nonwetting liquid over a range of Pc values.
During each steady state flow condition the capillary pressure is constant
throughout the permeameter and the wetting liquid is at rest. From the
measured flow rates and the known nonwetting liquid piezometric pressures
at the top and bottom of the cell, k values can be calculated as a function
of Pc. The above technique can be applied during drainage as well as during
imbibition. The method can be extended to determine the k - Pc - S relations
with the aid of a dual-energy gamma radiation system or by keeping track
of the amount of water being displaced from the cell each time the Pc is
changed.
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Three-fluid retention involving water, PCE and air.
A classical way to obtain three-fluid retention curves in porous media
from measured two-fluid retention curves is based on the Leverett concept,
which states that the total volumetric liquid content in a water-wet porous
medium, containing water, a NAPL and air, is a function of the capilllary
pressure across the interface between the continuous NAPL and air. This
functional relationship results from the assumed condition that in a three-flui
d porous medium, the intermediate wetting fluid spreads over the water-air
interface. Application of Leverett's concept may not be valid, however,
for nonspreading NAPLs like perchlorethylene (PCE). We measured both PCE-air
and water-PCE-air retention curves using the method proposed by Dane et
al. (1992).
The following two figures (drainage and imbibition of PCE, respectively)
show the volumetric water, PCE and total liquid contents versus the capillary
pressure head across the interface between the presumably continuous PCE
and gaseous phase in the three-fluid system at one of the eight measurement
locations. For comparison, the fitted two-phase van Genuchten curves for
the same location in the twin column (with PCE and air only) are included
in the figures.
The volumetric total liquid content in the first figure appears to be
a function of the capillary pressure head across the air-PCE interface
until the head becomes about 14 cm of water. After this point the volumetric
PCE content remained fairly constant and the decrease in the total volumetric
liquid content with the presumable increase in capillary pressure between
the PCE and air was smaller in the three-fluid phase system than in the
PCE-air system. This indicates that the total liquid content was a function
of the capillary pressure head across the air-water interface (possibly
with a monolayer of PCE) rather than the capillary pressure across the
PCE-air interface. The second figure shows the PCE imbibition curve. Again
the volumetric PCE content was fairly constant until low values of hc,
when the PCE content increased rapidly, and the volumetric total liquid
content again matched the fitted two-phase retention curve.
Using Lenhard's approach and measured residual PCE values, we calculated
that at the point where PCE became discontinuous during drainage, 30 %
of the measured PCE was entrapped by water. This means that the volumetric
PCE content existing in microlenses was 0.05 or about 70 % of the total
amount of PCE present.
{more info on this topic can be found in: Hofstee et al., 1997)
Correction of laboratory retention curves
Many experimental methods for obtaining capillary pressure-volumetric
fluid content relations in porous media are affected by the occurrence
of hydrostatic pressures that create non-uniform fluid content distributions
throughout the sample of interest. Such conditions exist, e.g., in suction
apparatuses and pressure cells, which are widely used in vadose zone hydrology,
agronomy and environmental engineering, and for mercury intrusion porosimetry
routinely applied in the petroleum industry. We are interested in numerical
procedures to correct experimental data for non-uniform pressure and fluid
content distributions, thus leading to retention or pore size distribution
curves applicable to physical points. This is necessary to make the retention
information consistent with the differential theory of fluid flow in porous
media. By deconvoluting retention relations from the averaging taking
place in the sample, the correction methods we develop permit an enhanced
description of porous media - immiscible fluids systems at low capillary
pressure values.
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