Evaluation of the transition characteristics of macroscopic dispersion and estimation of the non-uniform hydrogeological structure

In general, a natural aquifer has a hydrogeologically non-uniform structure. The movement of pollutants in groundwater is affected by such structural properties during transport by local advection and microscopic dispersion. The macroscopic dispersion coefficient increases linearly with travel distance or travel time at the initial stage after the pollutant is released, and then converges asymptotically to a constant value after a sufficient travel distance, longer than the integral scale of heterogeneity. For practical applications it is important to know how such macroscopic dispersion increases, when the prediction of pollutant spread is required in the transient stage. In the present study, a method for judging the convergence of macroscopic dispersion is discussed for the analytical and observed average concentration, by numerical simulations. The chi-square test for convergence of the macroscopic dispersivity is applied. Also, an evaluation procedure for the auto-regressive parameters in the model generating the random hydraulic conductivity field is proposed. This evaluation is applied for the case in which the macroscopic dispersion is estimated to be still in the growing stage. The characteristics of the proposed method are examined through application to synthetically generated random fields of hydraulic conductivity.