PORE-SCALE DILUTION OF CONSERVATIVE SOLUTES - AN EXAMPLE

We simulate flow and transport of a conservative nonsorbing tracer in an idealized periodic pore channel using finite element techniques. Th e concentration is computed; then the slowly varying concentration mea n, variance, coefficient of variation, and reactor ratio are calculate d through averaging over every cell. The coefficient of variation and reactor ratio are related and quantify the degree of dilution. Then a novel methodology is developed for the evaluation of macroscopic param eters (homogenization), including the variance decay coefficient, whic h measures the rate with which small-scale concentration fluctuations tend to diminish, and the large-time coefficient of proportionality be tween the concentration variance and the square of the mean concentrat ion variance. The methodology is based on the solution of a steady adv ection-dispersion problem in a single cell (which acts as a representa tive elementary volume); the computed result is then integrated in ord er to compute the macroscopic parameters. These parameters are compare d with the parameters computed through direct simulation on a cell-by- cell basis, and they are found to be in reasonably good agreement. Whe n the macroscopic parameters are used in the macroscopic equations, th ey produce estimates of the concentration mean and variance that are i n agreement with the results of direct simulation.