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ORIGINAL RESEARCH

Thermodynamic Model for Fluid–Fluid Interfacial Areas in Porous Media for Arbitrary Drainage–Imbibition Sequences

^a Institute of Biogeochemistry and Pollutant Dynamics, ETH Zurich, CH-8092 Zurich, Switzerland
^b Pacific Northwest National Laboratory, P.O. Box 999, MS K9-33, Richland, WA 99352
^* Corresponding author (martin.schroth{at}env.ethz.ch).

Received 20 December 2007.

Fluid–fluid interfacial areas are important in controlling the rate of mass and energy transfer between fluid phases in porous media. We developed a modified thermodynamically based model (TBM) to predict fluid–fluid interfacial areas in porous media for arbitrary drainage–imbibition sequences. The TBM explicitly distinguishes between interfacial areas associated with continuous (free) and isolated (entrapped) nonwetting fluids. The model is restricted to two-fluid systems in which (i) no significant conversion of mechanical work into heat occurs, (ii) the wetting fluid completely wets the porous medium's solid surfaces, and (iii) no changes in interfacial area due to mass transfer between phases occur. We show example calculations for two different drainage–imbibition sequences in two porous media: a highly uniform silica sand and a well-graded silt. The TBM's predictions for interfacial area associated with free nonwetting fluid are identical to those of a previously published geometry-based model (GBM); however, predictions for interfacial area associated with entrapped nonwetting fluid are consistently larger in the TBM than in the GBM. Although a comparison of model predictions with experimental data is currently only possible to a limited extent, good general agreement was found for the TBM. As required model parameters are commonly used as inputs for or tracked during multifluid-flow simulations, the modified TBM may be easily incorporated in numerical codes.

Abbreviations: GBM, geometry-based model • NAPL, nonaqueous-phase liquid • TBM, thermodynamically based model