Solute Dispersion In Porous Media Research Articles

Dynamic Fluid Connectivity Controls Solute Dispersion in Multiphase Porous Media Flow

AbstractSolute transport in multiphase flow through porous media plays a central role in many natural systems and geoengineering applications. The interplay between fluid flow and capillary forces leads to transient flow dynamics and phase distributions. However, it is not known how such dynamic flow affects the dispersion of transported species. Here, we use highly resolved numerical simulations of immiscible two‐phase flow to investigate dispersion in multiphase flows. We show that repeated activation and deactivation of different flow pathways under the effect of capillary forces accelerates the spreading of solutes compared to single phase flow. We establish the transport laws under dynamic multiphase flows by linking the dispersion coefficient to the Bond number, the ratio of the force driving the flow and the surface tension. Our results determine the controlling factors for solute dispersion in porous media, opening a range of applications for understanding and controlling transport in porous geological systems.

Dynamic Dispersion Coefficient of Solutes Flowing in a Circular Tube and a Tube-Bundle Model

Mathematical formulations have been proposed and verified to determine dynamic dispersion coefficients for solutes flowing in a circular tube with fully developed laminar flow under different source conditions. Both the moment analysis method and the Green's function are used to derive mathematical formulations, while the three-dimensional (3D) random walk particle tracking (RWPT) algorithm in a Cartesian coordinate system has been modified to describe solute flow behavior. The newly proposed formulations have been verified to determine dynamic dispersion coefficients of solutes by achieving excellent agreements with both the RWPT results and analytical solutions. The differences among transverse average concentration using the Taylor model with and without dynamic dispersion coefficient and center-of-mass velocity are significant at early times but indistinguishable when dimensionless time (tD) approaches 0.5. Furthermore, compared to solutes flowing in a 3D circular tube, dispersion coefficients of solutes flowing in a two-dimensional (2D) parallel-plate fracture are always larger for a uniform planar source; however, this is not always true for a point source. Solute dispersion in porous media represented by the tube-bundle model is greatly affected by pore-size distribution and increases as standard deviation of pore-size distribution (σ) increases across the full-time scale.

Gas–Solute Dispersivity Ratio in Granular Porous Media as Related to Particle Size Distribution and Particle Shape

Measurements of solute dispersion in porous media is generally much more time consuming than gas dispersion measurements performed under equivalent conditions. Significant time savings may therefore, be achieved if solute dispersion coefficients can be estimated based on measured gas dispersion data. This paper evaluates the possibility for estimating solute dispersion based on gas dispersion measurements. Breakthrough measurements were carried out at different fluid velocities (covering the same range in Reynolds number), using O2 and NaCl as gas and solute tracers, respectively. Three different, granular porous materials were used: (1) crushed granite (very angular particles), (2) gravel (particles of intermediate roundness) and (3) Leca® (almost spherical particles). For each material, 21 different particle size fractions were used. Gas and solute dispersion coefficients were determined by fitting the advection–dispersion equation to the measured breakthrough curves and in turn used to calculate gas and solute dispersivities as a function of mean particle size (D m) and particle size range (R) for the 63 particle size fractions considered. The results show that solute and gas dispersivities are related and that their ratio depends on both R and D m. Based on these observations a simple model for predicting the dispersivity ratio from D m and R, was proposed.

Assessment of a UV Excited Fluorescent Dye Technique for Estimating Solute Dispersion in Porous Media

Dyes are important tracers to investigate subsurface water movement and solute transport processes. Laboratory tracer experiments with a fluorescent dye, Brilliant Sulfaflavine, are carried out in a two-dimensional water flow tank uniformly packed with glass beads over a wide range of steady state water flow rates. Under ultraviolet (UV) illumination conditions the fluorescent dye emits visible light and is imaged by a digital camera. An imaging processing technique based on UV excited spatial distributions of the fluorescent dye tracer allows to link with a spatial moment approach to identify the longitudinal and transverse microdispersivities. The experimental results show that the mean values of longitudinal and transverse microdispersivities range from 0.095 cm to 0.40 cm and from 0.027 cm to 0.061 cm, respectively. Laboratory study is extended by a random walk particle tracking approach to reconstruct the estimated microdispersivity transitions, demonstrating a good agreement between the experimental and numerical results in homogeneous porous formations of concern. The methodology applied herein represents a potentially valuable tool in the assessment of microdispersion phenomena in porous media.

New stochastic model for dispersion in heterogeneous porous media: 1. Application to unbounded domains

A new model of solute dispersion in porous media that avoids Fickian assumptions and that can be applied to variable drift velocities as in non-homogeneous or geometrically constricted aquifers, is presented. A key feature is the recognition that because drift velocity acts as a driving coefficient in the kinematical equation that describes random fluid displacements at the pore scale, the use of Ito calculus and related tools from stochastic differential equation theory (SPDE) is required to properly model interaction between pore scale randomness and macroscopic change of the drift velocity. Solute transport is described by formulating an integral version of the solute mass conservation equations, using a probability density. By appropriate linking of this to the related but distinct probability density arising from the kinematical SPDE, it is shown that the evolution of a Gaussian solute plume can be calculated, and in particular its time-dependent variance and hence dispersivity. Exact analytical solutions of the differential and integral equations that this procedure involves, are presented for the case of a constant drift velocity, as well as for a constant velocity gradient. In the former case, diffusive dispersion as familiar from the advection–dispersion equation is recovered. However, in the latter case, it is shown that there are not only reversible kinematical dispersion effects, but also irreversible, intrinsically stochastic contributions in excess of that predicted by diffusive dispersion. Moreover, this intrinsic contribution has a non-linear time dependence and hence opens up the way for an explanation of the strong observed scale dependence of dispersivity.

Solute dispersion in a variably saturated sand

The understanding of solute dispersion in unsaturated porous media is still nascent. This work focuses on the measurement of solute dispersion in porous media at various levels of pore‐volume saturation and on the parameterization of longitudinal dispersivity in terms of the saturation ratio and a soil's textural characteristics. The dispersion coefficient was determined in partly saturated columns packed with Toyoura sand or glass beads under steady state flow. A 0.0282 N sodium chloride solution was used as a nonreactive tracer in a series of laboratory experiments in which, for a fixed water content, the average pore‐water velocity was varied. The column experiments showed that the dispersion coefficient increases linearly with increasing water velocity for a fixed water content and that the slope of the dispersion coefficient versus water velocity relationship diminishes as the water content is increased. The Peclet number (Pe) was fitted to the experimental tracer data by a nonlinear function Pe = aSrb, in which Sr is the saturation ratio and a and b are textured‐dependent parameters. The dispersivity (α, in centimeters) of the test columns' porous media was then estimated in terms of the saturation ratio and the median grain size (d50, in centimeters) by the power law α = d50/Pe = d50/aSrb, which provides a specific functional relationship among a porous medium's dispersion properties, the saturation ratio, and the medium's textural characteristics.

Longitudinal dispersion in porous media with variable porosity

An analytical procedure is developed in the present paper for predicting the solute dispersion in porous media with variable porosity and constant volumetric seepage flow rate. Several porosity equations which may represent the possible porosity variation as a function of spatial coordinate are suggested and used to test how well the predicted solute concentration by using a constant average porosity is when compared to the prediction using a prescribed porosity function. It is found that the predictions by using an average porosity are within 15% of those using a linear or a slightly curved porosity function. However, the discrepancy between them is very substantial as the porosity function becomes a strong non-linear one. For this instance, prediction of the solute concentration using an average porosity is rather poor and a numerical method is needed if a reliable prediction is to be obtained.