Grantee Research Project Results
2001 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 , Noble, Beth , Gladkikh, Mikhail
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, 2000 through September 30, 2001
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 on 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 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.In the second year, we implemented a high-resolution drainage algorithm to allow a more accurate determination of the sequence of pore-level events, as the trapped phase morphologies are potentially sensitive to the order in which pores and pore throats are drained. 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. Using sufficiently small increments in curvature in the "low resolution" algorithm yields very similar results with lower computational overhead. We also showed that theoretical predictions of irreducible wetting phase saturations compared well with experimental data reported in the literature.
A recently introduced method for measuring the area of fluid-fluid interfaces in porous media utilizes interfacial tracers. Typical tracers are water-soluble surfactants with an affinity for the water-air or water-hydrocarbon interface but have negligible solubility in the nonaqueous phase. In the past year, we have obtained clear evidence that these methods include contributions from thin films of the wetting phase. Coating the grains in pores that have been drained, these films evidently remain connected to the bulk wetting phase via pendular rings and lenses, so that tracer molecules can migrate to the film/nonaqueous phase interface. We implemented a calculation of the area of the grains in drained pores that are in contact with the nonwetting phase; when this area is added to the contributions previously computed for macroscopic phase volumes, the prediction follows experimental data very closely. The calculated film contribution is dominant at wetting phase volume fractions below 0.5. Depending on the application, however, the film area may be irrelevant because the volume of wetting phase in the film is negligible. Thus experimental techniques that do not distinguish film contributions from macroscopic contributions may yield misleading evaluations of mass-transfer rates in remediation or contamination processes.
Leveraging support from other sources, we also have completed experiments that independently support this conclusion. In water-wet packings of glass beads, we measure water/decane interfacial areas during drainage that are consistent with those of other researchers and that include the contribution of thin films. When we pack the column with oil-wet beads (glass beads treated with silane), the observed interfacial area exhibits a maximum as a function of wetting phase volume fraction. This maximum is predicted by our theoretical development described above. We also predict the maximum to be overwhelmed by the contribution of film areas, and indeed no such maximum is observed when films influence the measurement. Moreover, at the irreducible wetting phase saturation, the measured area is quantitatively consistent with the contributions from pendular ring and lens morphologies. Films apparently do not contribute in this experiment because of steric hindrance: a thin film of the wetting phase (decane) cannot accommodate the 10-to-12 carbon alkyl group of the tracer in significant quantities.
Drainage in naturally occurring porous media is a percolation process, characterized by a rapid increase in the volume fraction of nonwetting phase at a critical capillary pressure. Detailed examination of the high-resolution drainage simulations has revealed an important insight into the pore structure associated with the percolation threshold. The pores that control access to much of the pore volume are associated with pairs of grains that are separated by a distance of order 0.2R, where R is the grain radius. The pore throats associated with such clusters of pores have a "free boundary" corresponding to the gap between the grains. We hypothesize that classical estimates of the critical curvature for drainage of such throats (e.g., Haines and Mayer-Stowe-Princen) are inadequate. The macroscopic evidence for this hypothesis is that these estimates yield drainage curves that are qualitatively correct but are significantly shifted (to higher capillary pressures for the Haines estimate, to lower capillary pressures for the MSP estimate) relative to measurements. The microscopic evidence is that the advancing meniscus does not experience these pore throats individually because the free boundary allows it to become constrained by grains associated with neighboring pores. In effect, it appears that the pore throats influence the meniscus collectively. All classical invasion percolation algorithms, including those we have implemented to date, treat pore throats individually.
As part of an effort to improve the estimate of critical curvature for drainage, we recently have initiated numerical experiments with the Surface Evolver, freely available software for computing surfaces of minimal energy (http://www.susqu.edu/brakke/evolver/evolver.html). By directly accounting for the 3-D geometry of pore space in the vicinity of gaps between grains, we hope to obtain first-principles estimates of the behavior of the advancing meniscus. This should provide insight on how to refine classical estimates of critical curvature, so as to retain the computational simplicity of the invasion percolation algorithms presently in use.
Reevaluation of classical studies (Fisher, 1925; Rose, 1957) of pendular ring geometry indicates that the standard simplifying assumptions (the ring is circular in both cross-sections) may result in underestimating ring area and volume by 25 percent at the curvatures relevant in unconsolidated media. This error does not change earlier conclusions (e.g., that the wetting phase connectivity in practice is somewhere between the two limiting cases we have studied). It may serve to refine predictions of area as a function of phase volume fraction.
Future Activities:
Until the end of the contract extension granted through August 2002, we plan to conduct simulations of imbibition and calculate the area of corresponding volumes of wetting/ nonwetting phase. A novel aspect of the imbibition simulation will be the inclusion of physically derived conditions for the snapoff and subsequent trapping of nonwetting phase; previous simulations generally use ad hoc tests for trapping. We also hope to implement an evaluation of global connectivity of the wetting phase during drainage to refine the estimate of irreducible wetting phase saturation. We will continue to compare predictions for both drainage and imbibition areas to experiments obtained in our laboratories and reported in the literature.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, Physics, Mathematics, HAPS, Chemistry, 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, NAPLsRelevant Websites:
http://www.ticam.utexas.edu/CSM/EPA/area/index.htm
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http://www.ticam.utexas.edu/CSM/EPA/connectivity/index_files/v3_document.htm
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http://www.ticam.utexas.edu/CSM/EPA/critcurv/index_files/v3_document.htm
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http://www.ticam.utexas.edu/CSM/EPA/porespace/pspace2.rm
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Progress 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.