Correction to “Prediction of fingering in porous media”

[1] In the paper “Prediction of fingering in porous media” by Zhi Wang, Jan Feyen, and David E. Elrick (Water Resources Research 34(9), 2183–2190, 1998), the authors developed 24 specific criteria for predicting unstable flow in porous media, based on the Chuoke equation [Chuoke et al., 1959]. However, some of the results were inconsistent with predictions by others. For instance, de Rooij [2000] noted that the Wang criteria showed unstable flow for overly rapid upward flow in contrary to Philip's [1975] theory that predicted an unconditionally stable flow. These discrepancies resulted from three mistakes in the theoretical development, namely, (1) an inconsistency in the transcription of the Chuoke equation (equation (1) in the original paper), (2) a discrepancy between the definition of σ* compared to the Chuoke definition (leading to a wrong equation (3a)) and, (3) sign errors in the development of the criteria (Table 1). In the following, we give the correct development and revise the 24 stability criteria of Wang et al. [1998]. [3] Chuoke's formulation seemed ambiguous because the wetting characteristics of the fluids were not clearly defined. Therefore Wang et al. [1998] stipulated that fluid 1 be the nonwetting fluid and fluid 2 be the wetting fluid. This was based on the experimental setup by Chuoke et al. [1959]. Wang et al. [1998] also conceptualized that the macroscopic interfacial tension σ* is inherently negative for the nonwetting fluid (fluid 1) displacing the wetting fluid (fluid 2). The wettability of the displacing fluid was defined by introducing a wettability variable e, valued e = 1 for the wetting fluid displacing the nonwetting fluid, and e = −1 for the reversed displacement. Hence the interfacial tension, σ* = e∣σ*∣, is positive when e = 1 and negative when e = −1. Accordingly, equation (1) as a case for e = −1 in the analysis of Chuoke et al. [1959] was generalized into equations (2) and (3) in the paper of Wang et al. [1998]. [6] On the basis of (3), we delineated Chuoke et al.'s [1959] criterion into 24 subcriteria (as shown in Table 1) according to specific combinations of fluid properties and relative positions in porous media. Table 1 provides a direct comparison of the individual criteria with those in Table 1 of Wang et al. [1998]. [7] Note that, with these corrections, the wettable and nonwettable halves of Table 1 are now identical, indicating that parameter e does not affect the onset of instability. Moreover, rows 3 and 4 coalesce into rows 1 and 2, respectively. Therefore these identical pairs of criteria can be regrouped in terms of relative position of the heavier and lighter fluid and in terms of the viscosity contrast. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

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