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A joint velocity-concentration PDF method for tracer flow in heterogeneous porous media.
- Source :
- Water Resources Research; 2010, Vol. 46 Issue 12, pn/a-n/a, 17p
- Publication Year :
- 2010
-
Abstract
- The probability density function (PDF) of the local concentration of a contaminant, or tracer, is an important component of risk assessment in applications that involve flow in heterogeneous subsurface formations. In this paper, a novel joint velocity-concentration PDF method for tracer flow in highly heterogeneous porous media is introduced. The PDF formalism accounts for advective transport, pore-scale dispersion (PSD), and molecular diffusion. Low-order approximations (LOAs), which are usually obtained using a perturbation expansion, typically lead to Gaussian one-point velocity PDFs. Moreover, LOAs provide reasonable approximations for small log conductivity variances (i.e., σ<subscript> Y</subscript><superscript>2</superscript> < 1). For large σ<subscript> Y</subscript><superscript>2</superscript>, however, the one-point velocity PDFs deviate significantly from the Gaussian distribution as demonstrated convincingly by several Monte Carlo (MC) simulation studies. Furthermore, the Lagrangian velocity statistics exhibit complex correlations that span a wide range of scales, including long-range correlations due to the formation of preferential flow paths. Both non-Gaussian PDFs and complex long-range correlations are accurately represented using Markovian velocity processes (MVPs) in the proposed joint PDF method. LOA methods can be generalized to some extent by presuming a certain shape for the concentration PDF (e.g., a β PDF fully characterized by the concentration mean and variance). The joint velocity-concentration PDF method proposed here does not require any closure assumptions on the shape of the marginal concentration PDF. The Eulerian joint PDF transport equation is solved numerically using a computationally efficient particle-based approach. The PDF method is validated with high-resolution MC reference data from Caroni and Fiorotto (2005) for saturated transport in velocity fields, which are stationary in space and time, for domains with σ<subscript> Y</subscript><superscript>2</superscript> = 0.05, 1, and 2 and Péclet numbers ranging from 100 to 10,000. PSD is modeled using constant anisotropic dispersion coefficients in both the reference MC computations and our PDF method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00431397
- Volume :
- 46
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Water Resources Research
- Publication Type :
- Academic Journal
- Accession number :
- 87147211
- Full Text :
- https://doi.org/10.1029/2010WR009450