Measurement and prediction of the relationship between capillary pressure, saturation, and interfacial area in a NAPL‐water‐glass bead system

<jats:p>In this work, the constitutive relationship between capillary pressure (<jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub>), saturation (<jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub>), and fluid‐fluid interfacial area per volume (IFA) is characterized using computed microtomography for drainage and imbibition experiments consisting of a nonaqueous phase liquid and water. The experimentally measured relationship was compared to a thermodynamic model that relates the area under the <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> curve to the total IFA, <jats:italic>a</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub>, and the capillary‐associated IFA, <jats:italic>a</jats:italic><jats:sub><jats:italic>nw</jats:italic></jats:sub>. Surfaces were fit to the experimental and modeled <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> − <jats:italic>a</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub> and <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> − <jats:italic>a</jats:italic><jats:sub><jats:italic>nw</jats:italic></jats:sub> data in order to characterize the relationship in three dimensions (3D). For the experimental system, it was shown that the <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> − <jats:italic>a</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub> relationship does not exhibit hysteresis. The model is found to provide a reasonable approximation of the magnitude of the 3D surfaces for <jats:italic>a</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub> and <jats:italic>a</jats:italic><jats:sub><jats:italic>nw</jats:italic></jats:sub>, with a mean absolute percent error of 26% and 15%, respectively. The relatively high mean absolute percent errors are primarily the result of discrepancies observed at the wetting‐ and nonwetting‐phase residual saturation values. Differences in the shapes of the surfaces are noted, particularly in the curvature (arising from the addition of scanning curves and presence of <jats:italic>a</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> hysteresis in the predicted results) and endpoints (particularly the inherent nature of thermodynamic models to predict significant <jats:italic>a</jats:italic><jats:sub><jats:italic>nw</jats:italic></jats:sub> associated with residual nonwetting‐phase saturation). Overall, the thermodynamic model is shown to be a practical, inexpensive tool for predicting the <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> − <jats:italic>a</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub> and <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> − <jats:italic>a</jats:italic><jats:sub><jats:italic>nw</jats:italic></jats:sub> surfaces from <jats:italic>P</jats:italic><jats:sub><jats:italic>c</jats:italic></jats:sub> − <jats:italic>S</jats:italic><jats:sub><jats:italic>w</jats:italic></jats:sub> data.</jats:p>