Percolation characteristics of solvent invasion in rough fractures under miscible conditions

Surface roughness and flow rate effects on the solvent transport under miscible conditions in a single fracture are studied. Surface replicas of seven different rocks (marble, granite, and limestone) are used to represent different surface roughness characteristics each described by different mathematical models including three fractal dimensions. Distribution of dyed solvent is investigated at various flow rate conditions to clarify the effect of roughness on convective and diffusive mixing. After a qualitative analysis using comparative images of different rocks, the area covered by solvent with respect to time is determined to conduct a semi-quantitative analysis. In this exercise, two distinct zones are identified, namely the straight lines obtained for convective (early times) and diffusive (late times) flow. The bending point between these two lines is used to point the transition between the two zones. Finally, the slopes of the straight lines and the bending points are correlated to five different roughness parameters and the rate (Peclet number). It is observed that both surface roughness and flow rate have significant effect on solvent spatial distribution. The largest area covered is obtained at moderate flow rates and hence not only the average surface roughness characteristic is important, but coessentially total fracture surface area needs to be considered when evaluating fluid distribution. It is also noted that the rate effect is critically different for the fracture samples of large grain size (marbles and granite) compared to smaller grain sizes (limestones). Variogram fractal dimension exhibits the strongest correlation with the maximum area covered by solvent, and display increasing trend at the moderate flow rates. Equations with variogram surface fractal dimension in combination with any other surface fractal parameter coupled with Peclet number can be used to predict maximum area covered by solvent in a single fracture, which in turn can be utilized to model oil recovery, waste disposal, and groundwater contamination processes in the presence of fractures.