Shadab Anwar

Lattice Boltzmann Models for Flow and Transport in Saturated Karst

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcys law-based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.

Regional scale transient groundwater flow modeling using Lattice Boltzmann methods

Lattice Boltzmann (LB) models can be used to simulate flow in porous media at scales much larger than pore size. LB-based models for such macroscopic scale porous media flow simulations are an extension of standard LB models. There are at least two alternative approaches for implementing such models. In the first approach the local velocity is altered during the collision step by incorporating an external force, F, equivalent to the damping effect of solid particles in porous media. The porous media can be permeable or impermeable depending upon the external forcing term. A sink term is introduced in the LB model to simulate a pumping well and this model is further applied to solve transient ground water well problems for confined aquifers. Directly solving the ground water flow equation with an LB model by exploiting its ability to solve the diffusion equation is another strategy. The second order transient ground water flow equation is analogous to the diffusion equation and mass diffusivity is analogous to hydraulic diffusivity. This diffusion model is used to solve transient ground water problems. Simulated results accurately match analytical solutions of the transient ground water flow equation.

Lattice Boltzmann simulation of solute transport in heterogeneous porous media with conduits to estimate macroscopic continuous time random walk model parameters

Lattice Boltzmann models simulate solute transport in porous media traversed by conduits. Resulting solute breakthrough curves are fitted with Continuous Time Random Walk models. Porous media are simulated by damping flow inertia and, when the damping is large enough, a Darcys Law solution instead of the Navier-Stokes solution normally provided by the lattice Boltzmann model is obtained. Anisotropic dispersion is incorporated using a direction-dependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard Advection-Dispersion Equation (ADE) including eddy mixing in conduits. The ADE fails to adequately fit any of these breakthrough curves.

Simultaneous heat and solute transport modeling of ground water with lattice Boltzmann methods

Recent advances in lattice Boltzmann modeling permit simulation of large-scale density-dependent ground water flow and heat/solute transport systems while retaining the advantages of ‘regular’ lattice Boltzmann methods, such as solute/heat transport at higher Reynolds numbers that can characterize flows in conduits. We model the simultaneous heat/solute problem described by Henry and Hilleke in 1972 as an extension of Henry’s classic 1964 seawater intrusion problem. We also demonstrate the method’s ‘dual domain’ modeling potential.