Effect Of Transverse Dispersion Research Articles

Transverse mixing zone under dispersion in porous media: Effects of medium heterogeneity and fluid rheology

The addition of an environmental remediation modifier—polymer solution—to a Newtonian fluid expands the distribution of remediation agents injected in situ into saturated aquifers (affecting plume velocity and deformation), enhancing remediation efficiency. However, the effect of the flow properties of the polymer solution on the macroscopic transverse dispersion remains poorly understood. In this work, a transparent thin-layer two-dimensional sandbox was constructed to simulate the aquifer, and the transverse distribution range of colored solute—permanganate solution and viscous shear-thinning fluid (permanganate solution + xanthan gum)—was captured in real-time by a camera device during transport in porous media. The boundary dispersion coefficient was obtained by fitting a breakthrough curve of the boundary concentration, while the overall plume dispersion coefficient was determined via image moment analysis. The effects of fluid rheology and heterogeneity on the transverse mixing of the plume were analyzed, and the mechanism of viscoelasticity-induced transverse dispersion and mixing enhancement was summarized. The results indicated that the anisotropic stress generated by polymer fluid deformation at high water velocity increased the fluctuation and transverse distribution of the plume, while higher-viscosity polymers increased the initial extrusion swelling and additional compressive stress, covering a larger area. Xanthan gum enhanced the transverse distribution of the plume mainly through initial injection-extrusion expansion effect, viscoelastic stability of the post-injection part, and streamline crossing attributed to elastic turbulence. This study also verified that the shear-thinning fluid enhanced the effect of transverse dispersion and mixing under heterogeneous conditions, providing insights applicable to groundwater remediation.

Enhanced solute transport in porous media due to pH-dependent adsorption and transverse dispersion

The process of pH-dependent adsorption/desorption controls the transport of solutes in reactive porous media, the greater the adsorption the slower the solute migration. Earlier works show that in the presence of longitudinal hydrodynamic dispersion and pH-dependent adsorption, a fast solute transport phenomenon may arise. However, the effect of transverse dispersion on this fast transport phenomenon has not been investigated, yet.In this paper, we report an experimental and modeling work on the fast transport of strontium (Sr2+) through a reactive porous medium made of sand and hydrous ferric oxide (HFO) coated sand, where both longitudinal and transverse dispersion were important. A reactive transport model for an incompressible fluid was developed combining surface complexation with mass conservation equations for a solute and the acidity (difference between the concentration of total proton and hydroxide ions). The model was used to design and describe experiments run in a column-flood system and in a two-dimensional (2D) bead-pack. Results show that when an alkaline solution containing Sr2+ is injected into a 2D bead-pack containing HFO-coated sand and equilibrated with an acidic solution, a Sr2+ plume forms which comprises: (i) a retarded front due to the adsorption of Sr2+ onto the porous medium; (ii) a fast wave (or pulse) ahead of the retarded front due to longitudinal dispersion and traveling at the average fluid velocity; and (iii) a continuous leakage from the retarded front due to transverse dispersion.The results of this work confirm that pH-dependent adsorption/desorption process in conjunction with longitudinal dispersion causes fast wave, i.e., a solute migration which is faster than expected if the interplay between pH and dispersion is neglected. Furthermore, transverse dispersion in the presence of a pH gradient gives rise to a plume composed of a leakage from the retarded front connected to the fast wave.

Development of scaling criteria for steam flooding EOR process

The development of new scaling criteria for steam flooding process is presented in this paper. The mathematical development is done by using modified Darcy’s law, constitutive relationships, constraints, and the initial and boundary conditions. Dimensional and inspectional analyses are used to develop sets of dimensionless groups by incorporating rock and fluid memory concept. The variety of scaling criteria and their comparative advantages and limitations are discussed. Currently available scaling criteria development for steam flooding processes used the same fluid, same porous media in model and prototype. However, it requires a high-pressure model with different porous media, which causes difficulties in scaling properties, and therefore, largely depends on pressure and the porous media itself. In this paper, different methods are presented which permit scaling of all properties dependent on pressure or temperature by relaxing the requirements of geometric similarity. A set of relaxed scaling criteria is determined to satisfy a major mechanism. A comparative study of different approaches and their relative merits and demerits are discussed. Approach 2 (same fluids, same pressure drop, same porous medium, and geometric similarity) seems to be the most appropriate for the steam flooding process; however, gravitational forces cannot be scaled properly with this approach. Approach 3 (same fluids, same pressure drop, same porous media, and relaxed geometric similarity) is suitable for this process if the effect of transverse dispersion is considered negligible. Finally, a table is developed which can act as a guideline to select an appropriate approach that best scales a major mechanism for a specific steam flooding recovery process.

Experimental investigation of compound-specific dilution of solute plumes in saturated porous media: 2-D vs. 3-D flow-through systems.

Dilution of solute plumes in groundwater strongly depends on transverse mixing. Thus, the correct parameterization of transverse dispersion is of critical importance for the quantitative description of solute transport. In this study we perform flow-through laboratory experiments to investigate the influence of transport dimensionality on transverse mixing. We present a high-resolution experimental setup to study solute dilution and transverse dispersion in three-dimensional porous media. We conduct multi-tracer experiments in the new 3-D setup and compare the results with the outcomes of analogous tracer experiments performed in a quasi 2-D system. We work under steady-state flow and transport conditions and consider a range of velocities relevant for groundwater flow (0.5-8 m/day). Transverse dispersion coefficients are determined from high-resolution concentration profiles at the outlet of the flow-through chambers (7×7 ports in the 3-D setup and 7 ports in the quasi 2-D system), considering conservative tracers with significantly different aqueous diffusion coefficients, namely fluorescein and dissolved oxygen. To quantify dilution in the 2-D and 3-D systems, we experimentally determine the flux-related dilution index using the flow rates and the concentrations measured at the inlet and outlet ports, and we propose semi-analytical expressions to predict its evolution with travel distance in uniform groundwater flow. The experimental results in the quasi 2-D and 3-D flow-through systems are consistent and show a compound-specific behavior of the transverse dispersion coefficient and its non-linear dependence on the seepage velocity in both setups. The degree of dilution and the compound-specific effects of transverse dispersion are considerably more pronounced in 3-D than in quasi 2-D transport systems.

Evaluation of transverse dispersion effects in tank experiments by numerical modeling: Parameter estimation, sensitivity analysis and revision of experimental design

Transverse dispersion represents an important mixing process for transport of contaminants in groundwater and constitutes an essential prerequisite for geochemical and biodegradation reactions. Within this context, this work describes the detailed numerical simulation of highly controlled laboratory experiments using uranine, bromide and oxygen depleted water as conservative tracers for the quantification of transverse mixing in porous media. Synthetic numerical experiments reproducing an existing laboratory experimental set-up of quasi two-dimensional flow through tank were performed to assess the applicability of an analytical solution of the 2D advection-dispersion equation for the estimation of transverse dispersivity as fitting parameter. The fitted dispersivities were compared to the “true” values introduced in the numerical simulations and the associated error could be precisely estimated. A sensitivity analysis was performed on the experimental set-up in order to evaluate the sensitivities of the measurements taken at the tank experiment on the individual hydraulic and transport parameters. From the results, an improved experimental set-up as well as a numerical evaluation procedure could be developed, which allow for a precise and reliable determination of dispersivities. The improved tank set-up was used for new laboratory experiments, performed at advective velocities of 4.9m d−1 and 10.5m d−1. Numerical evaluation of these experiments yielded a unique and reliable parameter set, which closely fits the measured tracer concentration data. For the porous medium with a grain size of 0.25–0.30mm, the fitted longitudinal and transverse dispersivities were 3.49×10−4m and 1.48×10−5m, respectively. The procedures developed in this paper for the synthetic and rigorous design and evaluation of the experiments can be generalized and transferred to comparable applications.

Effect of transverse dispersion on solute transport in a vertical dipole flow test with a tracer

Summary Vertical dipole flow test with a tracer (DFTT) have been proposed as an in situ method to determine the longitudinal dispersivity from analysis of the breakthrough curves (BTCs) in the extracted screened interval by assuming that only the longitudinal dispersion has an effect on the BTCs. However, the tracer must undergo transverse dispersion before it enters the extracted screened interval and will certainly influence BTCs in the extracted screened interval. The purpose of this study is to investigate the effect of the transverse dispersion on the BTCs in the extracted screened interval during a vertical DFTT and to examine the applicable condition of a DFTT in determining the longitudinal dispersivity. A previously developed mathematical model for reagent transport in a vertical circulation flow field is modified and used for the investigation. Simulation results demonstrate that the transverse dispersion exerts significant effects on the BTCs in the extracted screened interval in an aquifer with a large hydraulic conductivity anisotropy ratio and a large longitudinal dispersivity. The selection of operational parameters including the interval location, lengths of the screened interval and interval distances does not significantly promote the applying condition of the DFTT for determining the longitudinal dispersivity. I t suggests that longitudinal dispersivity cannot be solely determined by analysis of the BTCs, simply because the BTCs are simultaneously affected by both the longitudinal and transverse dispersions. One should note that the DFTT can only be applied to evaluate the longitudinal dispersivity in an aquifer with a small hydraulic conductivity anisotropy ratio or a small longitudinal dispersivity.

Soliton deflexion for(1 + 3)D Kadomtsev-Petviashvili Equation

Two types of soliton deflexion of (1+3)D Kadomtsev–Petviashvili (K–P) equation are considered. Using the Hirota bilinear form and the new technique of “homoclinic test”, a type of exact periodic soliton solution of the K–P equation with positive transverse dispersion effects is obtained. Another type of periodic soliton solution is found by means of the periodic soliton solution of the K–P equation with negative transverse dispersion effects and a temporal and spatial transformation. It is also investigated that the equilibrium solution u0=-16 is an unique deflexion point, periodic soliton of traveling in different spatial directions will be interchanged with the solution varying from one side of -1/6 to the other side.

Enhancement of mass transport and separation of species by oscillatory electroosmotic flows

Mass transport driven by oscillatory electroosmotic flows (EOF) in a two-dimensional micro-channel is studied theoretically. The results indicate that the velocity and concentration distributions across the channel-width become more and more non-uniform as the Womersley number W , or the oscillation frequency, increases. It is also revealed that, with a constant tidal displacement, the total mass transport rate increases with the Womersley number W due to both the stronger convective and the transverse dispersion effects. The total mass transport rate also increases with the tidal displacement (with a fixed oscillation frequency) because of the associated stronger convective effects. The cross-over phenomenon of the mass transport rates for different species becomes possible with sufficiently large Debye lengths and at sufficiently large values of W . Consequently, with proper choices of the Debye length, oscillation frequency and tidal displacement, oscillatory EOF may become a good candidate for the first-step separation of the mass species.

Stochastic determination of three‐dimensional capture zones for a fully penetrating well

A stochastic methodology is used to investigate transport of a conservative solute by steady flow to a fully penetrating pumping well in a three‐dimensional heterogeneous formation. The spatially variable hydraulic conductivity is modeled as a stationary random function of anisotropic two‐point covariance. Although mean transport is radial, heterogeneity produces three‐dimensional velocity fluctuations which are shown to affect solute recovery and the capture zone distribution. Expressions accurate to the first order in log conductivity variance σY2 are derived for travel time variance, capture zone extent, and solute recovery under the following simplifying assumptions: (1) the vertical integral scale of conductivity is much less than the horizontal integral scale, (2) the depth of the formation is much greater than the vertical integral scale of conductivity, (3) the well bore diameter is much smaller than the horizontal scale of conductivity, (4) longitudinal and lateral local dispersion are negligible while the effect of transverse dispersion is examined. Travel time variance στ2 for transport in convergent flow in a three‐dimensional aquifer is shown to be greater than στ2 in either constant mean flow in a three‐dimensional formation or radially convergent flow in a heterogeneous two‐dimensional medium. Transverse dispersion between layers in a sedimentary formation is found to increase mixing between flow paths leading to a marginal reduction in travel time variance. Because of negative correlation between mass flux and travel time, solute retrieval at the well occurs earlier from a constant flux solute source than from an instantaneous plume. The relationship between initial plume length and relative plume spreading is illustrated for simple plume geometries.

A Programming Model for River Quality Management under Transverse Mixing

The objective of river quality management is to achieve a given water quality standard at certain control stations by cutting down the pollutant load in the basin at the lowest cost. Conventional programming models, however, cannot guarantee the satisfaction of the quality standard at each drinking water intake when transverse mixing occurs in the river, because they focus on the average concentration of the cross sections, while the raw water is usually drawn from the sides of the river. In this paper, a programming model is proposed to deal with waste load allocation problems. The effect of transverse dispersion on the quality at drinking water intakes is taken into account by introducing an index which represents the degree of mixing in a river. This has made it possible to link the sewage system planning with the improvement of drinking water quality. The results of model application show that the priority of sewage treatment in a river basin is quite different from those advanced by the conventional models, it is suggested that a change of the traditional strategy of waste load allocation is necessary for better quality of drinking water supply.

Effect of transverse dispersion on solute transport in soils : Leij, F J; Dane, J H J HydrolV122, N1/4, Jan 1991, P407–422

Effect of transverse dispersion on solute transport in soils : Leij, F J; Dane, J H J HydrolV122, N1/4, Jan 1991, P407–422

The effect of transverse dispersion on solute transport in soils

Most theoretical and experimental investigations of solute transport involve one-dimensional problems (i.e. soil column studies), whereas in reality many soil pollution problems concern transport and flow in more than one dimension. This study investigates two-dimensional transport, with emphasis on the contribution of transverse dispersion to solute transport. Three problems were studied with a finite element code. The first problem involved one-dimensional flow parallel to the interface of two layers with differing pore-water velocity. The early arrival of the solute at the end of the low-permeability layer and the increase in solute spreading for both layers, as a result of transverse dispersion, were demonstrated. The two other problems concerned transport of a pollutant from a point source and a diffuse source, respectively, located at the soil surface. The magnitude of the transverse dispersion coefficient influenced the region to which the pollution extended as well as the intensity of the pollution.

Discussion of the Use of Capillary Tube Networks in Reservoir Performance Studies

Abstract The paper is presented as a discussion of the work of Simon and Kelsey on the use of capillary tube networks in reservoir performance studies. The author believes that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions that are too optimistic for reservoir-scale predictions that are too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. The reason for this is that the networks are too small to permit proper scaling of longitudinal and transverse dispersion effects. Hence, as early a breakthrough as will occur with fully developed viscous fingers is not observed. Introduction It appears to us that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions which are much too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. We believe that the principal reason for this is that the Simon-Kelsey networks are too small to permit proper scaling of longitudinal and transverse proper scaling of longitudinal and transverse dispersion effects. Hence, the authors do not observe as early a breakthrough as will occur with fully developed viscous fingers. Since the authors oil recovery predictions are too optimistic for any given degree of heterogeneity, but decrease with increasing heterogeneity, Simon and Kelsey have attributed too great a degree of heterogeneity to some of the laboratory models involved in previously reported work in attempting to match the observed recovery data. Data derived from the models themselves indicate a much lesser degree of heterogeneity. MODELLING OF PORE STRUCTURE AND THE H FACTOR The mathematical model of reservoir displacement processes described by Simon and Kelsey is related processes described by Simon and Kelsey is related to the capillary network model of pore structure devised by Fatt. However, Fatt intended his model to describe the capillary pressure and relative permeability properties of small samples of reservoir rock, rather than large-scale oil reservoirs. Fatt emphasized the relationship between the form of the network as expressed by his connectivity number, 8, and the degree of similarity of the capillary pressure and relative permeability curves for his model to those of typical reservoir rocks. Fatt found that similarity required a value of 8 in the interval from 7 to 25. This is the average number of other tubes connected to the two ends of a given tube. It means that from 4 to 13 flow channels meet at each junction, on the average. For this reason, Fatt favored the use of a triple hexagonal network (B = 10) in which six tubes meet at each junction. This judgment of natural rock pore structure is supported by more recent scanning electron microscope studies. Simon and Kelsey used the double hexagonal network (B = 7) in part of the work reported in Ref. 1; but the remainder and the second article are based on a diamond grid (B = 6). Fact also found that a reciprocal relationship between tube radius and tube length was required to simulate actual rock permeability-porosity relationships. Simon and Kelsey permeability-porosity relationships. Simon and Kelsey have instead used tubes of constant length. A wide distribution of cube radii was found by Fatt to be necessary to simulate the capillary pressure curves of consolidated porous media. Pore radius distributions are typically log-normal, and the distributions used by Fatt were of this shape. They are not flat-topped distributions such as that used by Simon and Kelsey to define a heterogeneity factor, H, as the ratio of the maximum to the minimum channel radius. However, it is easy to derive for such a flat-topped distribution that the fractional average deviation for a total number of flow channels, N, is given by the following equations: ............(1a) ............(1b) SPEJ P. 352