A MONTE-CARLO ASSESSMENT OF EULERIAN FLOW AND TRANSPORT PERTURBATION MODELS

Monte Carlo studies of flow and transport in two-dimensional synthetic conductivity fields are employed to evaluate first-order flow and Eul erian transport theories. Hydraulic conductivity is assumed to obey fr actional Brownian motion (fBm) statistics with infinite integral scale or to have an exponential covariance structure with finite integral s cale. The flow problem is solved via a block-centered finite differenc e scheme, and a random walk approach is employed to solve the transpor t equation for a. conservative tracer. The model is tested for mass co nservation and convergence of computed statistics and found to yield a ccurate results. It is then used to address several issues in the cont ext of flow and transport. The validity of the ist-order relation betw een the fluctuating velocity covariance and the fluctuating log conduc tivity is examined. The simulations show that for exponential covarian ce, this approximation is justified in the mean flow direction for log conductivity variance, sigma(f)(2), of the order of unity. However, a s sigma(f)(2) increases, the relation for the transverse velocity comp onent deviates from the fully nonlinear Monte Carlo results: Eulerian transport models neglect triplet correlation functions that appear in the nonlocal macroscopic flux. The relative importance of the triplet correlation term for conservative chemicals is examined. This term app ears to be small relative to the convolution flux term in mildly heter ogeneous media. As sigma(f)(2) increases or the integral scale grows, the triplet correlation becomes significant. In purely convective tran sport the triplet correlation term is significant if the heterogeneity is evolving. The exact nonlocal macroscale flux for the purely convec tive case significantly differs from that of the convective-dispersive transport. This is in agreement with recent theoretical analysis and numerical studies, and it suggests that neglecting local-scale dispers ion may lead to large errors. Localization errors in the flux term are evaluated using Monte Carlo simulations. The nonlocal in time model s ignificantly differs from the fully nonlocal model. For small variance and integral scale there is a slight difference between the fully loc alized flux and the fully nonlocal convolution flux. This is also in a greement with recent theories that suggest that moments through the se cond for the two models are nearly identical for conservative tracers. The fully localized model does not perform well in the purely convect ive cases.