Stochastic analysis of the effects of fluid density and viscosity variability on macrodispersion in heterogeneous porous media

Journal Article · Thu Aug 01 04:00:00 EDT 1991 · Water Resources Research; (United States)

DOI:https://doi.org/10.1029/91WR00837· OSTI ID:5885133

Welty, C ^[1]; Gelhar, L W ^[2]

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1. Drexel Univ., Philadelphia, PA (United States)
2. Massachusetts Inst. of Tech., Cambridge (United States)

Both porous medium heterogeneities and fluid density and viscosity contrasts affect solute transport in miscible fluid displacement. The effect of interaction of these processes on large-scale mixing are evaluated using spectral-based perturbation theory. A three-dimensional, statistically isotropic, exponential log permeability autocovariance is used to represent the spatial variability of the porous medium. State equations linearly relating log density and log viscosity perturbations to concentration perturbations represent the density and viscosity variability and strongly couple the flow and solute transport perturbation equations. Analytical expressions for longitudinal macrodispersivity, derived for one-dimensional mean solute transport, are functionally dependent on mean displacement distance, mean concentration and concentration gradient, density and viscosity differences, mean velocity, gravity, and correlation scale and variance of the log permeability process. Transient analysis shows that longitudinal macrodispersivity grows exponentially in time (or mean displacement distance) without bound for the case where instabilities due to viscous or gravity fingering arise (the unstable or fingering case) and that it grows at early time then decreases exponentially to an asymptotic value close to that of local dispersivity for the case where density or viscosity contrasts produce a stabilizing effect (the stable case).

• OSTI ID: 5885133
• Journal Information: Water Resources Research; (United States), Journal Name: Water Resources Research; (United States) Vol. 27:8; ISSN 0043-1397; ISSN WRERA
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
540220* -- Environment
Terrestrial-- Chemicals Monitoring & Transport-- (1990-)
AQUIFERS
DISPERSIONS
ENVIRONMENTAL TRANSPORT
FLOW MODELS
FLUID FLOW
GROUND WATER
HYDROGEN COMPOUNDS
ISOTOPE APPLICATIONS
MASS TRANSFER
MATERIALS
MATHEMATICAL MODELS
OXYGEN COMPOUNDS
PLUMES
POLLUTANTS
POLLUTION
POROUS MATERIALS
THREE-DIMENSIONAL CALCULATIONS
TRACER TECHNIQUES
VISCOSITY
VISCOUS FLOW
WATER
WATER POLLUTION