Effective Longitudinal Dispersivity Research Articles

Insight on the application of graphene to sandy soils to improve water holding capacity

In this study, the changes in relevant hydraulic parameters (namely hydraulic conductivity, total and effective porosity, specific retention, and longitudinal dispersivity) induced by the introduction of graphene in a calcareous sandy soil and a siliciclastic riverine soil were monitored and modelled via leaching column experiments. Constant pressure head tests were used to calculate the hydraulic conductivity of each column, while leaching experiments were run to estimate total porosity and specific retention, and for each treatment three replicates were done. Columns were then run under saturated conditions via a low flow peristaltic pump and monitored for chloride concentrations. CXTFIT 2.0 was employed to inversely model the column experiments and retrieve effective porosity and longitudinal dispersivity. Results highlighted small changes of hydraulic conductivity and porosity, induced by graphene addition for both soils. A marked increase of specific retention values was instead recorded in the amended columns respect to control ones. Chloride breakthrough curves modelling showed that graphene doubled dispersivity in the calcareous sandy soil compared to the control, while it halved dispersivity in the siliciclastic riverine soil with respect to the control. The results highlight that graphene induces positive shift in the capacity of sandy soil to retain porewater but at the same time it also alters solute transport parameters, like dispersivity, suggesting that further studies need to focus on using several exposure concentrations, durations and mode of exposure, and apply simulated field conditions or perform experiments in real field conditions, to understand the fate of unwanted compound in soils amended with graphene.

Influence of crucial reservoir properties and microbial kinetic parameters on enhanced oil recovery by microbial flooding under nonisothermal conditions: Mathematical modelling and numerical simulation

In the present study, improved mathematical and numerical models are developed in order to simulate the influence of important reservoir (effective porosity and longitudinal dispersivity), fluid and microbial kinetic (Monod half-saturation constant, substrate to biomass yield coefficient and substrate inhibition) parameters on dynamics of in-Situ microbial enhanced oil recovery (MEOR) processes using Bacillus sp. in a typical sandstone reservoir. This numerical model is a novel attempt to consider the coupled effects of heat transport and substrate-inhibition kinetics on reactive-transport of microbes, substrates and biosurfactants as against the conventional models, thus making the prediction of MEOR processes more realistic and may assist in developing suitable strategies to enhance oil recovery at field scale. In addition, the present model also investigates the changes in relative permeabilities of reservoir fluids (oil and water) and fractional flow of water under the influence of nonisothermal condition, substrate inhibition, along with variations in pore-size distribution index, oil to water viscosity ratio and crude oil API gravity within reservoir during microbial flooding for estimating residual oil recovery. The present model results match significantly well, when verified, with the existing analytical and experimental results, thus proving the model's reliability. The results suggest that under nonisothermal conditions, biosurfactant production is maximum (77.8 mg ml−1) at effective reservoir porosity 23.4%, with low substrate half-saturation constant and high substrate-to-biomass yield coefficient values of 0.018 mg ml−1 and 0.8, respectively. Though biosurfactant production is reduced by more than 80% due to substrate inhibition, which is maximum at inhibition constant value 0.1 mg ml−1, residual oil-saturation is decreased by more than 90% at the end of MEOR process, thus enhancing oil displacement, mobility and hence, improved crude oil recovery. The reactive-transport of substrates, microbes and biosurfactants at injection mean fluid velocity of 1.68 m day−1, are also found to be highly sensitive to reservoir longitudinal dispersivity (αL) and maximum biosurfactants are produced (9.74 mg ml−1) at threshold αL value, 0.37 m, which corresponds to reservoir length of 50 m. Besides, a strategy is suggested to improve the oil recovery efficiency of the present in Situ MEOR approach by characterizing the reservoir for its pore size distribution index, and formation fluids (oil and water) for their viscosity ratios and crude oil API gravities, under nonisothermal and substrate inhibition conditions.

Architects of the underworld: bioturbation by groundwater invertebrates influences aquifer hydraulic properties

The hydraulic properties of aquifers are critical to the storage and transmission of water to meet the needs of an increasingly groundwater-dependent global community. The hydraulic properties of aquifers can also influence the biota present, but inversely, invertebrate burrowing (bioturbation) may also influence the hydraulic properties and the flow of water through sediments. The aim of this study was to test whether groundwater invertebrates were capable of influencing the hydraulic properties of aquifer sediments in an experimental setting. Groundwater amphipods were added to sediment-filled laboratory columns, and the effective porosity (neff) and longitudinal dispersivity (αL) of the sediments were compared before and after 2 months of amphipod activity. The neff of columns without amphipods decreased significantly over time whereas in columns containing eight amphipods it remained relatively constant, and in columns with four amphipods it was highly variable. There was no difference in αL between columns with amphipod density or over time. These findings suggest that the amphipods were maintaining the amount of pore space that was actively contributing to transport but their activity was not influencing the distribution of flow paths, and amphipod density is critical to causing or maintaining changes in hydraulic properties.

Tracer Tests in Stratified Alluvial Aquifers: Predictions of Effective Porosity and Longitudinal Dispersivity versus Field Values

Tracer tests in aquifers are key tests to delineate protection perimeters around drinking water wells. They help to determine field values of effective porosity, ne, and longitudinal dispersivity, αL, from curve fitting to a breakthrough curve (BTC). It is difficult to predict ne, but correlations obtained with field or numerical tracer tests may be used to predict αL. The BTCs of field tracer tests differ from those predicted by the advection-dispersion theory in three ways: (1) early arrival with smaller than expected ne, (2) scale-dependent αL, and (3) a long thick tail. In this article, physical principles are used to obtain new closed-form predictive equations for ne and αL in stratified alluvial aquifers. The new equations give ne and αL for the hydraulically equivalent homogeneous aquifer. The predicted values for ne are shown to fit the field values of seven well-documented field tracer tests. The new equations explain the ne field values and can explain field values of αL for stratified aquifers, their variation with distance, and the variance of the ln(K) distribution. If the tracer is injected for a limited time, the predicted BTC also displays the three usual features of field data, which simply result from a lognormal K-distribution. The new equations and their experimental verification correctly elucidate some difficulties due to aquifer heterogeneity and improve our ability to predict groundwater movements in the subsurface.

Methodology of determining effective porosity and longitudinal dispersivity of aquifer and the application to field tracer injection test in Southern Hanoi, Vietnam

Groundwater field pumping out and tracer injection test had been carried out at Nghiem Xuyen commune, Thuong Tin district, Hanoi where salinized and fresh groundwater boundary exist in the Pleistocene aquifer. The test was executed with pumping out rate of 9l/sec and tracer injection rate of 0.7l/sec of water with the salt concentration of 5g/l. The interpretation and analysis of the groundwater solute transport parameters by the field pumping out and tracer injection test is a rather complicated and delicate task due to the variability of the temporal boundary conditions. The test results have shown that although the tracer injection time is rather long (up to 60 hours), the tracer breakthrough curve of the tracer concentration of the pumped out water has its very specific characteristic shape, however with some variation due to the test invisible variability of conditions. The results of the parameter identification based on the method of least squares have given effective porosity of 0.32 and longitudinal dispersivity of 2.5m (which give the hydrodynamic dispersion of from D=250m2/day right outside the pumping well screen to D=18m2/day right outside the injection well screen). The minimal sum of squares of the differences between the observed and model normalized tracer concentration is 0.00119, which is corresponding to the average absolute difference between observed and model normalized concentrations of 0.0355 (while 1 is the worse and 0 is the best). The results have also shown that the maximal tracer concentration right outside the pumping out well screen is 6.1 times greater than the tracer concentration of the pumped out water. The distortion flow coefficient αW (the ratio between the flow rate through the injection well section without its presence) and the groundwater flow into the tracer injection well is from 18.66 (at the early testing time) to 10.76 (at the later testing time).References Bear J. and Verruijt A., 1987. Modeling groundwater flow and pollution, D. Reidel Publishing Company, Dordrecht, Holand, 414pp. Brouyère S. 2008. Modeling tracer injection and well-aquifer interactions: a new mathematical and numerical approach. Water Resour. Res, 39(3), 1070-1075. Drost, W., D. Klotz, A. Koch, H. Moser, F. Neumaier, and W. Rauert, 1968. Point dilution methods of investigating ground water flow by means of radioisotopes. Water Resour. Res., 4(1), 125-146. Fetter C.W., 2001. Applied Hydrogeology. Prentice Hall Inc. New Jersey 07458, 598pp. Hall, S.H., 1996. Practical single-well tracer methods for aquifer testing, In: Tenth National Outdoor Action Conference and Exposition, National Groundwater Association, Colombus, Ohio, USA, 11pp. Huyakorn P.S., and Pinder G. F., 1983. Computational Methods in Subsurface Flow. Academic Press, New York, 473pp. Nguyen Van Hoang, 2016. Modeling of pollutant transport in water environment. Vietnam Academy of Science and Technology Publishers, 201pp. Nguyen Van Hoang (project head) (2014-2017). Science and Technology Proposal: Study on the finite element modeling software for simulation of groundwater flow and solute transport by groundwater-application to aquifer in Central plain of Vietnam" codded ĐT.NCCB-ĐHƯD.2012-G/04 supported by NAFOSTED-MOST. Nguyen Van Hoang, Dinh Van Thuan, Nguyen Duc Roi, Le Duc Luong, 2012. Study on the impact of the Tri An reservoir on its downstream groundwater level regime. Vietnam Journal of Earth Sciences, 34(4), 465-476. Nguyen Van Hoang, Pham Lan Hoa, Le Thanh Tung, 2014. Study on the accuracy of the numerical modeling of the groundwater movement due to spatial and temporal discretization. Vietnam Journal of Earth Sciences, 36(4), 424-431. Nguyen Van Hoang and Nguyen Duc Roi, 2015. Finite element method in estimation of lag time of rainfall recharge to Holocene groundwater aquifer in Hung Yen province. Vietnam Journal of Earth Sciences, 37(4), 355-362. Nguyen Van Hoang, Nguyen Thanh Cong, Pham Lan Hoa, Le Thanh Tung, 2016. Study on the characteristics of salinity transport in 2D cross-section unconfined aquifer. Vietnam Journal of Earth Sciences, 38(1), 66-78. Novakowski, K.S., 1992. An evaluation of boundary conditions for one-dimensional solute transport, 1, Mathematical development. Water Resour. Res., 28(9), 2399-2410. Polubarinova-Kotrina P. IA., 1977. Theory of Groundwater. Moscow Science Publishers. 664pp. Tong Thanh Tung, 2015. Specialized report: Interpretation and analysis of aquifer parameters for pumping test at group-well test CHN5 in Nghiem Xuyen-Thuong Tin-Hanoi. Project "Groundwater protection in large cities (city: Hanoi)". Vietnam National Center for Water Resources Planning and Investigation-MoNRE, 16pp. Trieu Duc Huy (Project head), 2015. Science and Technology Proposal: Groundwater protection in large cities (city: Hanoi) approved by MoNRE Minister in Decision 1557/QD-BTNMT dated 30th Aug. 2013. Vietnam National Center for Water Resources Planning and Investigation-MoNRE. Vitaly A. Zlotnik and John David Logan, 1996. Boundary Conditions for Convergent Radial Tracer Tests and Effect of Well Bore Mixing Volume. Papers in the Earth and Atmospheric Sciences, 159pp. Zienkiewicz O. C. and Morgan K., 1983. Finite Elements and Approximation. Academic Press, 328p.

On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow

Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective–dispersive transport model, considered as “virtual truth”, with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the “virtual truth” and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized.

Estimation of flow and transport parameters for woodchip-based bioreactors: II. field-scale bioreactor

To reduce nitrate-N from tile drains, subsurface bioreactors using woodchips as a carbon source for denitrification have been installed for the past two decades. The objectives of this study were to estimate effective porosity, longitudinal and transverse dispersivity, and first- or zero-order decay coefficients for a field-scale bioreactor with woodchips as the carbon source. In a field-scale bioreactor (6.1 m by 6.1 m) installed at Decatur, IL nitrate-N concentrations were monitored in 16 monitoring wells installed at 1.5 m intervals and 0.75 m from each corner. An interpolation method was used for transient, two-dimensional groundwater flow, and the Random Walk Method which does not introduce numerical dispersion errors was used for two-dimensional nitrate-N transport. Nonlinear techniques for fitting the numerical solution to the observed breakthrough curves were used to estimate the transport parameters for the field-scale bioreactor. The longitudinal and transverse dispersivity, the first-order decay coefficient, and the effective porosity were estimated as 10.2 cm, 1.13 cm, 0.01 h−1, and 0.79, respectively. Under a pulse of nitrate-N, high reduction rate of nitrate-N in mass (approximately 47% for 269.9 g nitrate-N of the input mass) was observed at the outlet of the field-scale bioreactor at 4.4 h of hydraulic retention time. This result suggests that field-scale bioreactors using woodchips as a carbon source may be used to provide significant nutrient reduction from tile-drained fields.

Estimation of laboratory-scale dispersivities using an annulus-and-core device

This paper investigates the use of two-dimensional radial column experiments to estimate longitudinal, and transverse dispersivity at the laboratory scale. The experimental device is an device: it is based on a classical column system, of which the inlet reservoir is divided into three independent concentric zones, allowing non-uniform tracer injection. The outlet reservoir is similarly adapted, so that information on the radial distribution of concentration becomes available through mean effluent concentration measurements in each annular zone. In this study, we only investigated continuous tracer injections through the central inlet zone. An analytical solution to a similar problem was available in the literature, and was adapted to compute effluent concentrations. The influence of the simplified boundary conditions of the solution was assessed by means of a numerical model. A general methodology is suggested to obtain transport parameters from breakthrough curve analysis, involving (i) the determination of effective porosity and longitudinal dispersivity from the full averaged breakthrough curve using classical one-dimensional tools and (ii) the determination of transverse dispersivity from the breakthrough curves recorded in the annular zones. Preliminary experiments were performed on a glass bead porous medium, on a gravel sand and on a natural medium sand. It is found that the rapidity of the test, its low cost, and the ability to simultaneously estimate three transport parameters comes at the price of potentially larger experimental errors. Transverse dispersivities were found to be higher than values previously reported in the literature, probably as a result of plume meandering, which cannot be detected nor corrected when using annulus-and-core devices. (C) 2008 Elsevier B.V. All rights reserved.

Nonergodic solute transport in physically and chemically heterogeneous porous media

The time‐dependent ensemble average of the first‐order longitudinal second spatial moment, 〈S11′R〉, of nonergodic plumes of a sorbing solute in linear equilibrium and the effective longitudinal dispersivity, γ11′R, were evaluated for the line sources of different lengths normal or parallel to the uniform mean velocity, μ, in two‐ and three‐dimensional physically and chemically heterogeneous and statistically isotropic media. Physical and chemical heterogeneity is described with a random hydraulic conductivity field K(x) and a random retardation factor field R(x), respectively. The retardation factor is defined as 1 + Kd(x), where Kd(x) is the distribution coefficient. The fields K(x) and Kd(x) are assumed to be lognormally distributed and correlated. Three correlation models between Y = log K and W = log Kd are considered: the perfectly positive correlation (model A), the perfectly negative correlation (model B), and no correlation (model C). The values of Z11′R, which is defined as 〈 S11′R〉 minus its initial value, and γ11′ R for all three correlation models increase as the length of a line source l increases. As l→ ∞, Z11′R or γ11′R approach their respective ergodic limits X11′R or α11′R. The asymptotic longitudinal dispersion due to the physical and chemical heterogeneity is Fickian for a line source normal to μ and non‐Fickian for a line source parallel to μ. The positive correlation between Y and W reduces Z11′R and γ11′R, the negative correlation enhances Z11′R and γ11′R, and no correlation slightly enhances Z11′R and γ11′R, in comparison with nonreactive Z11′ and γ11′. The larger the value of the mean retardation factor, the large its effect on Z11′R and γ11′R. The three‐dimensional Z11′R and γ11′R are slightly larger than their respective two‐dimensional counterparts.

Testing and parameterizing a conceptual solute transport model in saturated fractured tuff using sorbing and nonsorbing tracers in cross-hole tracer tests

Two cross-hole tracer tests involving the simultaneous injection of two nonsorbing solute tracers with different diffusion coefficients (bromide and pentafluorobenzoate) and one weakly sorbing solute tracer (lithium ion) were conducted in two different intervals at the C-wells complex near the site of a potential high-level nuclear waste repository at Yucca Mountain, NV. The tests were conducted to (1) test a conceptual radionuclide transport model for saturated, fractured tuffs near Yucca Mountain and (2) obtain transport parameter estimates for predictive modeling of radionuclide transport. The differences between the responses of the two nonsorbing tracers and the sorbing tracer (when normalized to injection masses) were consistent with a dual-porosity transport system in which matrix diffusion was occurring. The concentration attenuation of the sorbing tracer relative to the nonsorbing tracers suggested that diffusion occurred primarily into matrix pores, not simply into stagnant water within the fractures. The K d values deduced from the lithium responses were generally larger than K d values measured in laboratory batch sorption tests using crushed C-wells cores. This result supports the use of laboratory-derived K d values for predicting sorbing species transport at the site, as the laboratory K d values would result in underprediction of sorption and hence conservative transport predictions. The tracer tests also provided estimates of effective flow porosity and longitudinal dispersivity at the site. The tests clearly demonstrated the advantages of using multiple tracers of different physical and chemical characteristics to distinguish between alternative conceptual transport models and to obtain transport parameter estimates that are better constrained than can be obtained using only a single tracer or using multiple nonsorbing tracers without a sorbing tracer.

Time-Dependent Dispersion of Nonergodic Plumes in Two-Dimensional Heterogeneous Aquifers

The time-dependent second spatial moment Z(t) ≡<S(t)>−S(0) and the effective dispersivity γ(t), defined as (1/2μ)[d<S>/dt], of nonergodic plumes are evaluated in two-dimensional (2D) statistically isotropic media under a uniform mean velocity μ, and the first-order approximation of the particle displacement, to study the effect of initial plume size on Z(t) and γ(t), where <S(t)> is the ensemble average of the second spatial moments, S(t), of a solute plume about its center of mass, and S(0) is the initial value of S(t). It is found that the aspect ratio ι2/ι1 of an area source plays an important role in the dispersive behavior of a nonergodic plume, where ι2 and ι1 are the normalized lengths (with respect to the correlation scale of log-hydraulic conductivity) of the source normal and parallel to μ, respectively. When ι2/ι1≥ 1, both the longitudinal and transverse second spatial moments Z11 and Z22 increase at early time, and at large time Z11 becomes proportional to time, or the effective longitudinal dispersivity γ11 approaches a constant while Z22 becomes constant or γ11 approaches zero. When ι2/ι1< 1, Zii and γii (i= 1, 2) increase at early time. At late time, however, they behave in a fundamentally different manner: Z11 increases monotonically to approach a constant, or γ11 decreases gradually to zero while Z22 reaches a peak and then decreases to zero, or γ22 falls below zero, i.e., becomes negative, and increases again to approach zero. Comparison of the first-order theoretical results with a Monte Carlo simulation shows good agreements for plumes with large initial sizes in less heterogeneous media.

Transport of conservative chemical through an unsaturated two‐dimensional Miller‐similar medium with steady state flow

Numerical simulation of water flow in a two‐dimensional, macroscopically homogeneous, Miller‐similar medium showed the existence of a network of flow channels with two complementary states separated by a critical point [Roth, 1995]. The consequences of this for solute transport are explored by numerical simulations using particle tracking. It is found that many experimentally observed features of transport through soil are reproduced qualitatively by these simulations. Analyzing the results reveals that in the corresponding effective medium the travel distance for the transition to convection‐dispersion and the effective dispersivity depend on the water flux. In particular, the effective longitudinal dispersivity, which is often assumed to be a material constant of the porous structure, is found to vary by more than an order of magnitude with a minimum near the critical point. The simulations further demonstrate that the local structure of the velocity field and the subscale hydrodynamic dispersion are of minor importance for the field‐averaged transport process.

Nonergodic Solute Transport in Three‐Dimensional Heterogeneous Isotropic Aquifers

The general expressions for the time‐dependent ensemble averages of the second spatial moments 〈A〉 and the effective dispersivities γ, defined as (½μ)(d;〈A〉/dt) where μ is the magnitude of the mean flow velocity μ, are evaluated in order to study the effect of initial plume size on 〈A〉 and γ in three‐dimensional heterogeneous isotropic aquifers under the first‐order approximation to the particle displacement. The results confirm previous findings that 〈A〉 and γ generally approach their respective ergodic limits X and α as the size of a source increases, where X and α are the single particle displacement covariance and the associated dispersivity, and that the transverse lengths of a source are more important than the longitudinal length for the ergodic condition to be met. The longitudinal dispersion of a nonergodic plume becomes Fickian or the effective asymptotic longitudinal dispersivity is constant at late time as long as one of the initial lateral lengths of the plume is nonzero, while the transverse dispersion is always non‐Fickian and the effective asymptotic transverse dispersivities are always zero regardless of the initial plume size. The most important and interesting findings are, when the longitudinal length l1 of an initial plume is larger than the lateral lengths l2 and l3, both effective longitudinal and transverse dispersivities γii (i= 1, 2, 3) increase to their respective peaks at early time, then γ11 decreases toward an asymptotic constant, whose value depends on the values of l2 and l3 (γ11 → 0 if l2 = l3 = 0), whereas γ22 and γ33 decrease to below zero (i.e., become negative), increase again, and finally approach zero independent of the lateral lengths of the source. Comparison of the current study with a numerical simulation shows good agreement between the calculated and simulated longitudinal second spatial moments.

Effective porosity and longitudinal dispersivity of sedimentary rocks determined by laboratory and field tracer tests

Effective porosity and longitudinal dispersivity of sedimentary rocks determined by laboratory and field tracer tests