PREDICTION OF SOLUTE-DISPERSION IN HETEROGENEOUS POROUS-MEDIA - EFFECTS OF ERGODICITY AND HYDRAULIC CONDUCTIVITY DISCRETIZATION

The performance of a stochastic numerical modelling procedure to simulate dispersion of a conservative solute in two-dimensional heterogeneous hydraulic conductivity fields is investigated in a series of numerical experiments, the results of which are compared with theoretical predictions. Random hydraulic conductivity fields are generated with a prescribed statistical structure, a finite difference model is used to obtain the flow field and particle tracking reproduces the dispersive properties. For comparison between stochastic numerical methods and stochastic theories for solute transport, fulfilment of the ergodic requirement is necessary, consequently aspects of simulated solute plume behaviour are investigated with respect to ergodicity. Application of numerical stochastic methods is hampered by the large associated computational burden, which is affected by a range of factors, not least the level of discretisation of the hydraulic conductivity field. The experiments detailed here investigate the effects of hydraulic conductivity discretisation and the effects of initial solute source area for a range of log-permeability variances. An increasing deviation from Dagan's linear theory is observed for increasing coarseness of discretisation. A tendency to ergodic conditions is found for a smaller initial source area than previously reported.