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Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K0. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast κ=K/K0 and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of κ and n, are presented in Part 2. [ABSTRACT FROM AUTHOR]

In the present part the results of numerical simulations of flow and transport in media made up from circular inclusions of conductivity K that are submerged in a matrix of conductivity K0, subjected to uniform mean velocity, are presented. This is achieved for a few values of κ=K/K0 (0.01, 0.1 and 10) and of the volume fraction n (0.05, 0.1 and 0.2). The numerical simulations (NS) are compared with the analytical approximate models presented in Part 1: the composite elements (CEA), the effective medium (EMA), the dilute system (DSA) and the first-order in the logconductivity variance (FOA). The comparison is made for the longitudinal velocity variance and for the longitudinal macrodispersivity. This is carried out for n<0.2, for which the theoretical and simulation models represent the same structure of random and independent inclusions distribution. The main result is that transport is quite accurately modeled by the EMA and CEA for low κ, for which αL is large, whereas in the case of κ=10, the EMA matches the NS for n<0.1. The first-order approximation is quite far apart from the NS for the values of examined κ. [ABSTRACT FROM AUTHOR]

Saturated flow takes place in geological formations of spatially variable permeability which is regarded as a stationary random space function of given statistical moments. The flow is assumed to be uniform in the mean and the Eulerian velocity field has stationary fluctuations. Water carries solutes that react according to the nonlinear equilibrium Freundlich isotherm. Neglecting pore scale dispersion (high Peclet number), we study the behavior of an initially finite pulse injection of constant concentration. Mean flux-averaged concentration is derived in a simple manner by using the previously determined solution of transport in a homogeneous one-dimensional medium and the Lagrangian methodology developed by Cvetkovic and Dagan [5] to model reactive transport in a three-dimensional flow field. The mean breakthrough curves are computed and the combined effect of reactive parameters and heterogeneity upon reduction of the concentration peak is investigated. Furthermore, with the aid of temporal moments, we determine equivalent reaction and macrodispersion coefficients pertinent to a homogeneous medium. [ABSTRACT FROM AUTHOR]

Explores the application of stochastic approaches in modeling groundwater flow. Subsurface hydrology; Factors contributing to the slow process in subsurface hydrology; Hydrogeologic modeling.