Grantee Research Project Results
2000 Progress Report: Theoretical Evaluation of the Interfacial Area between Two Fluids in Soil
EPA Grant Number: R827116Title: Theoretical Evaluation of the Interfacial Area between Two Fluids in Soil
Investigators: Bryant, Steven , Johnson, Anna
Current Investigators: Bryant, Steven
Institution: The University of Texas at Austin
EPA Project Officer: Aja, Hayley
Project Period: October 1, 1998 through September 30, 2001 (Extended to November 30, 2002)
Project Period Covered by this Report: October 1, 1999 through September 30, 2000
Project Amount: $246,378
RFA: Exploratory Research - Physics (1998) RFA Text | Recipients Lists
Research Category: Land and Waste Management , Air , Safer Chemicals
Objective:
The overall rate of mass transfer between immiscible phases (e.g., NAPL and water) in porous media is a critical parameter in several applications of environmental interest, such as contamination and remediation of groundwater. The rate of mass transfer between these phases depends upon the thermodynamic driving force as well as the area of the interface between the two phases. The interfacial area is very difficult to measure, however, because it depends strongly on the geometry of the pore space confining the fluids, and this area can be highly irregular in granular porous media. This project will develop a novel mathematical modeling technique to predict the area from first principles.
Progress Summary:
The area of the interface between two immiscible phases in a porous medium depends on the geometric configuration of the phases. This configuration is governed by the pressure difference between the phases, the geometry of the pore space, and the history of fluid displacement within the medium. In the first year of this project, we developed methods to compute this configuration in the random, dense packing of equal spheres described by Finney, which serves as a physically representative analogue of simple porous media. We extended existing algorithms for simulating drainage in order to locate and to quantify trapped volumes of wetting phase. Two trapping criteria were evaluated: "poor" connectivity, where trapping occurs as pendular rings at grain contacts and as lenses within pore throats associated with grain contacts, and "intermediate" connectivity, where trapping occurs only at grain contacts. The contribution of the isolated wetting phase to total interfacial area depends strongly on the assumed degree of connectivity.
The present evaluation of wetting phase trapping is entirely local, meaning it depends only on the phase configuration in the pores and throats associated with a grain contact. The results are therefore potentially sensitive to the order in which pores and pore throats are drained, so in the past year we implemented a high-resolution drainage algorithm to allow a more accurate determination of the sequence of pore-level events. The previous algorithm calculated the equilibrium configuration of the phases at specified increments in capillary pressure. The order in which pores were drained was purely systematic; each pore has an index, and the pores were tested at each curvature simply by looping over the indices. In the high-resolution simulation, a list of all pores that are candidates for drainage is created. A pore is a candidate for drainage if it contains wetting phase and is connected to neighbors containing non-wetting phase. The candidate pore that has the lowest critical curvature is then drained. This is a more accurate way of determining the drainage pathway. Global curvature is only incremented when there are no candidate pores that can be drained at the current global curvature. This method provides a better representation of "Haines jumps," a situation that occurs when there are several connected pores that have critical curvatures less than the current global curvature. As soon as one of those pores is drained, they will all be drained in a chain reaction called a Haines jump. Simulations with this algorithm showed that the curvature at which pendular rings and lenses were trapped at grain contacts and in pore throats did indeed differ from that computed in the previous approach. Because the phase area and volume are not strongly sensitive to small changes in curvature, however, both approaches yield very similar results if sufficiently small increments in curvature are used in the "low resolution" algorithm.
We also have compared the irreducible wetting phase saturations from both simulations to experimental data reported in the literature (Morrow, Chemical Engineering Science 1970;25:1799-1814) for a variety of porous media. When "poor" connectivity is assumed, the irreducible wetting phase saturation that we calculate is around 9.2 percent, whereas when we assume "intermediate" connectivity, the irreducible saturation is around 2.4 percent. Morrow's data are clustered around 8 percent, suggesting that the actual connectivity lies between the extremes that we have studied.
This year we also investigated several different methods of estimating
critical curvature for drainage of a pore throat. The original drainage code
uses Haines' estimation of critical curvature, which assumes that the interface
is spherical as it passes through the pore throat. This yields a critical
curvature of Ccrit = 2/ri, where ri is the radius of the largest circle that can
be inscribed in the void area at the most constricted part of the pore throat.
Recently, we have implemented an algorithm that uses the Meyer-Stowe-Princen
(MSP) estimation for critical curvature, which takes the "radius" of the
interface to be the ratio of the area of liquid supported by surface tension to
the solid perimeter. The critical curvature is then Ccrit = 1/ri. Mason and
Morrow (Journal of Colloid and Interface Science 1984;100:519-535) computed the
MSP estimate for pore throats between cylindrical rods. We took this estimate
one step further and developed a "3-D" MSP estimation, which takes into account
the spherical grains of our model porous medium. Initial results indicate that
all three curvature estimates yield drainage curves that follow the same
drainage path as experimental data and that their irreducible wetting phase
saturations also are close to experimental results; however, the curvature at
which drainage takes place for each estimate does not match experimental
results. The drainage curve using the Haines' estimate is about 1 curvature unit
higher than observed, while the drainage curves using the MSP and 3-D MSP
estimates are about 1 curvature unit lower.
Future Activities:
The bracketing of experimentally observed trapped wetting phase saturations is a very encouraging result. Since it appears that the wetting phase connectivity within typical unconsolidated porous media falls between our "poor" and "intermediate" connectivity assumptions, we plan to compute directly the global wetting phase connectivity so that a more accurate identification of trapped wetting phase can be made. We also will continue to refine our critical curvature estimate, so that we can more accurately predict the saturation-capillary pressure curve for drainage. We hypothesize that "cooperative" drainage, in which the interface enters a pore via two adjacent throats simultaneously, may be the reason that our single-throat algorithms fail to predict the saturation-pressure curve, even with refined estimates of critical curvature. We also hope to begin evaluating interfacial area during imbibition (displacement of non-wetting phase by wetting phase) and the influence of contact angle on area and volume.
Journal Articles:
No journal articles submitted with this report: View all 15 publications for this projectSupplemental Keywords:
remediation, NAPL, chemical transport, physics., RFA, Scientific Discipline, Air, Toxics, Waste, Mathematics, Physics, Chemistry, HAPS, chemical mixtures, Groundwater remediation, Engineering, Chemistry, & Physics, fate and transport, soil , porus media, NAPL, chemical transport modeling, interfacial phenomena, mass transfer, interwall partitioning tracer tests, groundwater contamination, mathematical formulations, NAPLsProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.