Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion
- 1 June 1990
- journal article
- Published by American Geophysical Union (AGU) in Water Resources Research
- Vol. 26 (6) , 1281-1290
- https://doi.org/10.1029/wr026i006p01281
Abstract
Transport of inert solutes in natural porous formations is dominated by convection and by the large‐scale heterogeneity of permeability. A solute body inserted in the formation spreads because of the variation of velocity among and along the stream tubes which cross the plume. With neglect of the slow effect of pore‐scale dispersion the solute particles preserve their initial concentration, but the body as a whole spreads in an irregular manner (Figures 1, 2, and ). The transport theory, based on representation of permeability and velocity as random space functions, can predict the expected value and variance of concentration, but under the above conditions, the coefficient of variation may be large. In contrast, the spatial moments of the solute body are less susceptible to uncertainty, depending on the transverse dimensions of the plume and on the travel time. The first and second spatial moments are regarded as random functions of time, and their expected value and variance are derived in terms of the velocity field. The moments are assumed to satisfy the ergodic hypothesis if their coefficients of variation are negligible. The conditions which ensure the fulfillment of this requirement are examined. The “effective dispersion coefficients” are defined with the aid of the spatial moments and are shown to depend generally on the initial size of the solute body and on travel time. The results are illustrated by an analytical solution of transport in a stratified formation with the average velocity parallel to the bedding.Keywords
This publication has 22 references indexed in Scilit:
- Solute advection in stratified formationsWater Resources Research, 1989
- Theory of Solute Transport by GroundwaterAnnual Review of Fluid Mechanics, 1987
- A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracersWater Resources Research, 1986
- Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, and formation to regional scaleWater Resources Research, 1986
- Solute transport in heterogeneous porous formationsJournal of Fluid Mechanics, 1984
- Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 2. The solute transportWater Resources Research, 1982
- Dispersion resulting from flow through spatially periodic porous mediaPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1980
- Using models to simulate the movement of contaminants through groundwater flow systemsC R C Critical Reviews in Environmental Control, 1979
- Statistical Continuum TheoriesAmerican Journal of Physics, 1968
- On the dispersion of a solute in a fluid flowing through a tubeProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1956