Stochastic flow and transport through multifractal porous media

Stochastic theories of flow and transport in aquifers have relied on the linear perturbation approach that is accurate for flow fields with log-conductivity variance cr2 less than unity. Several studies have found that the linear perturbation ignores terms that have significant effects on the spectra of the hydraulic gradient VH and specific discharge q when (Y2 exceeds unity. In this thesis we study flow and transport when the hydraulic conductivity K is an isotropic lognormal multifractal field. Unlike the perturbation approach, results obtained are nonlinear even though several simplifying assumptions are made. The spectral density of F = in (K) for this type of field is SF (k) o kl-D where D is the space dimension. It is found that under this condition, the hydraulic gradient VH and specific discharge q are also multifractal; whose renormalization properties under space contraction involve random scaling and random rotation of the fields. Analytical expressions that are functions of D and the codimension parameter of F, CK 'are obtained for the renormalization properties and marginal distributions of VH and q . Because of the boundary conditions, the fields VH and q are anisotropic at large scales but become isotropic at very small scales. The mean specific flow decreases as the scaling range of F increases, at a rate that is dependent on D and CK. Flow simulations on a plane validate the analytical results. The multifractal properties of VH and q are used to derive their spectral density tensors, the macrodispersivities, and the effective conductivity of the medium. The spectra obtained account for the random rotation of the VH and q at smaller scales. Spectra for VH and q are anisotropic at large scales but become isotropic at small scales.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2001

Author dc:creator

• Essiam, Albert K

Advisor dc:contributor.advisor

• Daniele Veneziano.

• Civil and Environmental Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/84301

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/84301