Pore-scale flow and contaminant transport in porous media

This dissertation consists of six chapters. The first one provides an introduction to the subject of this document. The next two examine and derive the mobile-immobile zone model for two different pores: a rectangular 2-D pore and an axisymmetric pore. The fourth chapter offers a numerical and laboratory experiments to study contaminant transport through a single pore. The fifth chapter focuses on whether or not fractional or Taylor dispersion controls the spread of solutes in porous media with significant presence of vortices. The final chapter studies the dynamic nature of the effective porosity. There also are three appendices.;Below, each paragraph provides an abstract of 5 consecutive dissertation chapters, chapter 2 through 6.;A new analytic solution has been derived for the diffusion into or from an immobile zone of a rectangular 2-D pore. This solution is expressed by a series of exponentials with the first term dominating all the other terms after relatively short dimensionless time of tau = Dt/a 2 > tauo ≈ 0.15, where D is molecular diffusion, t is time, and a is the pore depth. Hence for long times, tau > tau o, the analytic solution converges to a single decaying exponential and takes the form of the mobile-immobile zone (MIM) model. However, the long-time solution differs from the traditional MIM model by having an apparent initial concentration smaller than the true one. The difference represents the MIM model error, which propagates in time. This error provides a relatively small price (below 19%) for using a much simpler model instead of the exact model based on the diffusion equation. For sufficiently long times, tau > tau o, the mass-transfer coefficient is practically constant, proportional to the molecular diffusion, and inversely proportional to the square of the pore depth. For sufficiently short times, tau < tauo, the mass-transfer coefficient is time-dependent and may be significantly larger than its asymptotic value.;New analytic and semi-analytic solutions have been derived for the diffusion into or from an immobile zone of an axisymmetric pore. The analytic solution is in the form of a series of exponentials with its first term dominating the other terms after relatively short dimensionless time of tau = Dt/(R1 - Ro) 2 ≥ tauo ≈ 0.15, where D is molecular diffusion, t is time, R 1 is the pore radius, Ro is the radius of the pore entrance and exit, and (R1 - Ro) is the pore depth. Hence for long times, tau > tau o, the analytic solution converges to a single decaying exponential term and acquires the form of the mobile-immobile zone (MIM) model. However, the long-time solution differs from the traditional MIM model by having an apparent initial concentration smaller than the true one. The difference represents the MIM model error, which propagates in time. This error provides a relatively small price (below 17%) for using a much simpler model instead of the exact model based on the diffusion equation. For sufficiently long times, tau > tauo, the mass-transfer coefficient is practically constant, proportional to the molecular diffusion, and inversely proportional to the square of the pore depth. The coefficient of proportionality, named here the shape factor, is a function of pore geometry, i.e., of lambda = R1 - Ro. For sufficiently short times, tau < tauo, the mass-transfer coefficient is time-dependent and maybe significantly larger than its asymptotic value.;Solute transport through a pore is affected by its vortices. Our laboratory and numerical experiments of dye transport through a single axisymmetric pore reveal evidence of enhanced spreading and mixing by the vortex, i.e., a new kind of dispersion called here the vortex dispersion. The uptake and release of contaminants by vortices in porous media is affected by the flow Reynolds number. The larger the flow Reynolds number, the larger is the vortex dispersion, and the larger is the mass-transfer rate between the mobile zone and the vortex. The long known dependence of the mass-transfer rate between the mobile and "immobile" zones in porous media on flow velocity can be explained by the presence of vortices in the "immobile" zone and their uptake and release of contaminants.;With FLUENT software, we simulated solute transport and generated solute breakthrough curves (BTCs) along a periodically constricted pipe. We used least-square fitting to determine whether the BTC are described by fractional or Taylor dispersion. Even in significant presence of vortices, Taylor dispersion sets in after sufficiently long travel distance or travel time. However, in the pre-Taylor domain, the BTCs are described by the fractional convection-dispersion equation. This suggests a mechanism for fractional dispersion at the field scale: fractional CDE describes contaminant transport at sites for which the characteristic length of the heterogeneity is smaller than the required travel length for Taylor dispersion to set in.;The total porosity represents the ratio of the total pore volume to the sample pore volume. Similarly, the effective porosity represents the ratio of the portion of the total pore volume that participates in transmitting the fluids and/or solutes to the sample pore volume. From this portion the dead pores are excluded and so is the volume of the pores occupied by vortices. Our numerical simulations demonstrate that the effective porosity is a dynamic quantity, as the volume occupied by the vortices varies with the Reynolds number-the effective porosity is a function of groundwater velocity as well as pore morphology. It is evident that the effective porosity may vary by an order of magnitude or more for creeping flows. It may vary as much for non-creeping flows.