Predictions of dynamic changes in reaction rates as a consequence of incomplete mixing using pore scale reactive transport modeling on images of porous media.

We present a pore scale model capable of simulating fluid/fluid reactive transport on images of porous media from first principles. We use a streamline-based particle tracking method for simulating flow and transport, while for reaction to occur, both reactants must be within a diffusive distance of each other during a time-step. We assign a probability of reaction (Pr), as a function of the reaction rate constant (kr) and the diffusion length. Firstly, we validate our model for reaction against analytical solutions for the bimolecular reaction (A+B→C) in a free fluid. Then, we simulate transport and reaction in a beadpack to validate the model through predicting the fluid/fluid reaction experimental results provided by Gramling et al. (2002). Our model accurately predicts the experimental data, as it takes into account the degree of incomplete mixing present at the sub-pore (image voxel) level, in contrast to advection-dispersion-reaction equation (ADRE) model that over-predicts pore scale mixing. Finally, we show how our model can predict dynamic changes in the reaction rate accurately accounting for the local geometry, topology and flow field at the pore scale. We demonstrate the substantial difference between the predicted early-time reaction rate in comparison to the ADRE model.

Statistical scaling of pore-scale Lagrangian velocities in natural porous media.

We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

Dynamics and stability of two-potential flows in the porous media.

The experimental and numerical results of the capillary-force-driven climb of wetting liquid in porous media, which is opposed by the gravity force, are analyzed with respect to the emergence of a multiphase flow front and flow stability of the climbing liquid. Two dynamic characteristics are used: (i) the multiphase flow front thickness as a function of time, and (ii) the capillary number as a function of Bond number, where both numbers are calculated from the harmonic average of pores radii. Throughout the climb, the influence of capillary, gravity, and viscous force variations on the flow behavior is investigated for different porous media. For a specific porous medium, a unique flow front power law function of time is observed for the capillary flow climbs with or without gravity force. Distinct dynamic flow front power law functions are found for different porous media. However, for capillary climb in different porous media, one is able to predict a unique behavior for the wetting height (the interface between wetted and dry regions of porous medium) using the capillary and Bond number. It is found that these two numbers correlate as a unique exponential function, even for porous media whose permeabilities vary for two orders of magnitude. For climbs without the gravity force (capillary spreads), the initial climb dynamics follows this exponential law, but for later flow times and when a significant flow front is developed, one observes a constant value of the capillary number. Using this approach to describe the capillary climb, only the capillary versus Bond number correlation is needed, which is completely measureable from the experiments.

Capillary climb dynamics in the limits of prevailing capillary and gravity force.

The dynamics of capillary climb of a wetting liquid into a porous medium that is opposed by gravity force is studied numerically. We use the capillary network model, in which an actual porous medium is represented as a network of pores and throats, each following a predefined size distribution function. The liquid potential in the pores along the liquid interface within the network is calculated as a result of capillary and gravity forces. The solution is general, and accounts for changes in the climbing height and climbing velocity. The numerical results for the capillary climb reveal that there are at least two distinct flow mechanisms. Initially, the flow is characterized by high climbing velocity, in which the capillary force is higher than the gravity force, and the flow is the viscous force dominated. For this single-phase flow, the Washburn equation can be used to predict the changes of climbing height over time. Later, for longer times and larger climbing height, the capillary and gravity forces become comparable, and one observes a slower increase in the climbing height as a function of time. Due to the two forces being comparable, the gas-liquid sharp interface transforms into flow front, where the multiphase flow develops. The numerical results from this study, expressed as the climbing height as a power law function of time, indicate that the two powers, which correspond to the two distinct mechanisms, differ significantly. The comparison of the powers with experimental data indicates good agreement. Furthermore, the power value from the Washburn solution is also analyzed, where it should be equal to 1/2 for purely viscous force driven flow. This is in contrast to the power value of ∼0.43 that is found experimentally. We show from the numerical solution that this discrepancy is due to the momentum dissipation on the liquid interface.

MRI velocimetry and lattice-Boltzmann simulations of viscous flow of a Newtonian liquid through a dual porosity fibre array.

Viscous flow through fibrous porous media has considerable importance in a number of industrial processes including, in particular, resin transfer molding. In this paper magnetic resonance flow imaging techniques are used to visualize flow of a Newtonian liquid through a dual porosity structure. Of particular interest in these studies is the transition in the flow as the liquid moves from the open region into the fiber array. The ability of lattice-Boltzmann simulations to predict the visualized flow fields is presented and discussed.