Alberto Bellin

Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations. 1. Analytical solutions

A first-order analytical solution for the transport of reactive solutes in physically and chemically heterogeneous porous media is derived and discussed. The solution relies on the assumption of chemical activity described by the local linear equilibrium assumption postulating the existence of a (spatially variable) retardation factor. Retardation factors and log permeabilities modeling heterogeneities are described statistically by random space functions with assigned correlation structure. Correlated as well as uncorrelated physical and chemical heterogeneities are studied. The analytical expressions derived reduce to Dagans classic solution for the case of nonreactive solute transport and obey asymptotic limits already known from the literature.

Eulerian-Lagrangian approach for modeling of flow and transport in heterogeneous geological formations

This paper presents a new Eulerian-Lagrangian method for modeling flow and transport of passive solutes in heterogeneous porous formations. The physically plausible random velocity fields are generated by a geostatistical based model. The ability of the method to correctly reproduce the velocity field statistics and to satisfy mass balance is tested and demonstrated for the case of two-dimensional flow. The method is found particularly useful in dealing with large fields where numerical, fixed grid methods such as finite difference or finite elements become very demanding from a computational point of view. The transport problem is solved in a Lagrangian framework by the particle-tracking approach which uses a suitable grid refinement to correctly handle the velocity fluctuation at any a priori defined resolution. The new method is employed to compute the probability distribution functions of the concentration and travel times and to investigate the limitations of existing methods for predicting concentrations.

Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations: 2. Numerical results

Numerical Monte Carlo simulations were conducted to assess dispersion of reactive solutes in two-dimensional physically and chemically heterogeneous porous media, using random fields with assigned correlation structure for hydraulic conductivity and linear adsorption coefficient. Conditions under which linearization of adsorption is valid are discussed. Lognormal distributions of hydraulic conductivity and adsorption coefficient were assumed. Calculations have been performed for positive and negative correlation between hydraulic conductivity and adsorption coefficient, and for uncorrelated cases. Effects of varying different properties including mean and average sorption coefficient, physical and chemical integral scale, and variance of hydraulic conductivity on dispersive behavior are shown. A larger mean sorption coefficient enhances plume spreading in uncorrelated and in negatively correlated cases. In positively correlated cases, counteracting effects of physical and chemical heterogeneity play an important role. The outcome of these counteracting effects depends on the mean, variance, and integral scales of the spatially variable properties. The analytical solutions, derived in paper 1 (Bellin et al., this issue), reveal a good agreement with the numerical results in a significant range of heterogeneiti es. The generally surprisingly good agreement of the analytical solutions with the numerically obtained results can possibly be attributed to opposing effects of nonlinearities neglected in the derivation of the analytical solutions. In the case of strong physical heterogeneity the analytical solutions perform slightly better than in the case of strong chemical heterogeneity.

The effects of recharge on flow nonuniformity and macrodispersion

The spatial, statistical structure of the fluid velocity field in the case of uniformly recharged heterogeneous aquifers is investigated, and the spatial covariances of the velocity field are derived. This information is necesary for an investigation of flow and macrodispersion using the Lagrangian formalism proposed by Dagan (1984). The resulting first two moments of the velocity are nonstationary. They are functions of a parameter β which characterizes the degree of flow nonuniformity and is related to the recharge. The displacement variances are computed and tested favorably using numerical simulations. Simple relations are developed which relate the transport parameters found for the case of uniform-in-the-average flows to nonuniform flows using a simple, nonlinear transformation of the travel time, based on β.

The impact of geo-ingeneered transient flow on transport in natural aquifers

In situ remediation is an effective technique to reduce risk caused by contaminated aquifers. However, low groundwater-flow velocity – typical in na