Numerical Indicator for Flow Through Heterogeneous Permeable Media

摘要

This paper suggests a numerical indicator to examine the nature of miscible displacements in heterogeneous permeable media. We compare miscible displacements through assigning a numerical value to the governing flow regime. Previous studies point out that the competition between effects is the cause of developing various types of flow regimes (dispersive, fingering, gravity override, and channeling). However, the distinction between the flow patterns is only possible qualitatively (visually) so far; therefore, the visual traditional method fails to properly characterize displacements with a similar flow pattern and lacks the capability of evaluating the displacement performance as the flow regime changes. We adopt the notion of the correlation coefficient function and use the progression of the mixing zone to assign the numerical values to the flow regimes. The correlation coefficient function of the lengths of the mixing zone calculated between two different times represents the tendency to propagate linearly with time. On the other hand, the correlation coefficient function of the squared length of the mixing zone corresponds to linear growth with Time . Using the arithmetic average of the correlation coefficient functions over successive time intervals, we introduce a flow regime indicator to study the nature of miscible floods. We use a simulation approach to validate the numerical indicator. The numerical values assigned to the flow patterns are consistent with the visual identification of flow patterns. We conclude that the pattern attributed value is an effective measure of the mixing zone development in heterogeneous permeable media for the the limited cross flow. The suggested procedure identifies the type of flow regime at any stage of displacement and helps monitor evolution of the mixing zone. The latter is important in prediction of displacement performance. Through this study, we investigate the relation between the attributed numerical values and the displacement performance.