Simulation Of Solute Transport Research Articles

Intercomparison of 3D pore-scale flow and solute transport simulation methods

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.

Simulated Preferential Water Flow and Solute Transport in Shrinking Soils

We present follow‐up work to previous work extending the classical rigid (RGD) approach formerly proposed by Gerke and van Genuchten, to account for shrinking effects (SHR) in modeling water flow and solute transport in dual‐permeability porous media. In this study we considered three SHR scenarios, assuming that aggregate shrinkage may change either: (i) the hydraulic properties of the two pore domains, (ii) their relative fractions, or (iii) both hydraulic properties and fractions of the two domains. The objective was to compare simulation results obtained under the RGD and the SHR assumptions to illustrate the impact of matrix volume changes on water storage, water fluxes, and solute concentrations during an infiltration process bringing an initially dry soil to saturation and a drainage process starting from an initially saturated soil. For an infiltration process, the simulated wetting front and the solute concentration propagation velocity, as well as the water fluxes and water and solute exchange rates, for the three SHR scenarios significantly deviated from the RGD. By contrast, relatively similar water content profiles evolved under all scenarios during drying. Overall, compared to the RGD approach, the effect of changing the hydraulic properties and the weight of the two domains according to the shrinkage behavior of the soil aggregates induced a much more rapid response in terms of water fluxes and solute travel times, as well as a larger and deeper water and solute transfer from the fractures to the matrix during wetting processes.

Groundwater Flow and Solute Transport Simulation in Eastern Al Batinah Coastal Plain, Oman: Case Study

AbstractThe Al Batinah coastal plain in the Sultanate of Oman is one of the area’s most treasured regions for the existence of fresh groundwater and agriculture. Growth of irrigation, urbanization, and industrial endeavors have resulted in a severe decline in groundwater levels in the Al Batinah coastal aquifer, leading to significant seawater intrusion in recent decades. This study examines the groundwater and seawater intrusion pattern in the eastern Al Batinah coastal plain using a groundwater flow model along with a solute transport model. Both steady and transient calibration was carried out using data from the Ministry of Regional Municipalities and Water Resources. The calibrated model was then utilized to simulate two scenarios to mitigate seawater intrusion: (1) reduction in pumping rate; and (2) artificial recharge with constant pumping. Model predictions suggest that the effect of optimizing the pumping rate and artificial recharge reducing seawater intrusion would prove to be effective in the ...

Random walk method for modeling water exchange: An application to coastal zone environmental management

This study introduces a modeling approach for simulation of water exchange based on the random walk particle tracking method. The water exchange is characterized by a water exchange matrix. The novel features of this model lie in its flexibility of operation and time saving in simulation. The feasibility of this model is demonstrated in simulation case studies conducted in the Tianjin coastal area. The model can be applied to track water exchange between water bodies in estuaries and coastal ocean for simulation and characterization of solute transport, and predict water body self-purification capacity. This model can serve as a useful tool for forecast and assessment of potential water quality issues in coastal environment.

Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix

AbstractThis work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin () to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue.

Numerical Simulation of Groundwater Flow and Solute Transport for the Northern Batinah Area, Oman

Numerical Simulation of Groundwater Flow and Solute Transport for the Northern Batinah Area, Oman

Solute Mass Exchange Between Water Phase and Biofilm for a Single Pore

Currently, there are no tractable approaches available for modeling non-equilibrium mass exchange of a solute between water phase and biofilm in porous media. The present work contributes to a quantitative description of the mass exchange of a solute over a single pore domain under a wide range of prevailing conditions. First, we developed a semiempirical model for the rate of solute mass exchange between water phase and biofilm. Then, extensive microscale simulations in a single pore were conducted. Results were averaged over a single pore domain, in order to determine a tube-scale kinetic rate coefficient as a function of various transport and biofilm properties. We illustrated the dependencies of the coefficient on a number of variables like Péclet number, Damköhler number, and biofilm volume fraction. Based on those results, we developed empirical formulae for the tube-scale mass exchange coefficient as a function of Damköhler number and biofilm volume fraction. Finally, we verified the proposed mass exchange rate against microscale simulations of solute transport in a long capillary tube. Good match was obtained over a wide range of conditions.

An efficient quasi-3D particle tracking-based approach for transport through fractures with application to dynamic dispersion calculation

The quantitative study of transport through fractured media has continued for many decades, but has often been constrained by observational and computational challenges. Here, we developed an efficient quasi-3D random walk particle tracking (RWPT) algorithm to simulate solute transport through natural fractures based on a 2D flow field generated from the modified local cubic law (MLCL). As a reference, we also modeled the actual breakthrough curves (BTCs) through direct simulations with the 3D advection–diffusion equation (ADE) and Navier–Stokes equations. The RWPT algorithm along with the MLCL accurately reproduced the actual BTCs calculated with the 3D ADE. The BTCs exhibited non-Fickian behavior, including early arrival and long tails. Using the spatial information of particle trajectories, we further analyzed the dynamic dispersion process through moment analysis. From this, asymptotic time scales were determined for solute dispersion to distinguish non-Fickian from Fickian regimes. This analysis illustrates the advantage and benefit of using an efficient combination of flow modeling and RWPT.

Displacement of Br− and P22 in a Wetland Environment

Relative displacement of bromide (Br−) and coliphage P22 was analyzed in surface water and vadose zone solution from a 3-ha surface flow constructed wetland. In the vadose zone, water samples at 0.3-, 0.76-, 1.5-, and 3-m depth were collected to quantify Br− and P22 simultaneously added into the wetland influent for a transport study. When P22 was detected, Br− arrived earlier to the monitoring depths than the phage suggesting that preferential flow facilitated P22 displacement in the vadose zone. Concentrations for both tracers indicated that bacteriophage removal through the vadose zone profile was exceeding 99.21 % of the peak concentration observed in surface water samples. For transport parameter estimation, the temporal moment method (MOM) was used to calculate convective velocity (v) and longitudinal dispersion coefficient (D) from the outlet Br− breakthrough curve. The transport parameters were estimated to be 55.7 m day−1 and 1652 m2 day−1 for v and D, respectively. For P22 simulation, a first-order removal coefficient of 0.3 day−1 (R 2 = 0.943) was assessed. The observed results suggest that this method can be applied for solute transport simulation in constructed wetlands.

Impact of over-pumping and sea level rise on seawater intrusion in Gaza aquifer (Palestine)

Seawater intrusion is considered as one of the main processes that degrade water quality by raising salinity to levels exceeding acceptable drinking water standards. Over-abstraction is the main cause of seawater intrusion. Moreover, climate change and sea level rise speed up seawater intrusion. This paper presents the development of a coupled transient finite element model for simulation of fluid flow and solute transport in soils and its application to study seawater intrusion in Gaza aquifer. The effects of likely sea level rise due to climate change and over-pumping on seawater intrusion in Gaza aquifer are studied using three scenarios: rise in sea level due to climate change; decrease in piezometric head on the land side due to over-pumping; and a combination of sea level rise and over-pumping. The results show that a rise of 1 m in sea level has a significant effect on the position of the transition zone and can result in a further 0.5 km seawater intrusion in Gaza aquifer. However, the combination of sea level rise and over-pumping results in movement of the transition zone further inland (nearly 1.0 km). The results show that Gaza aquifer is subjected to severe seawater intrusion from the Mediterranean Sea and there is an urgent need to protect the aquifer from seawater intrusion.

Development and application of a solute transport model to describe field-scale nitrogen processes during autumn rains

A new generic, three-dimensional, solute transport component was developed into FLUSH, which is a hydrological model developed for Nordic conditions. Water flow and solute transport descriptions in FLUSH follow the dual-permeability concept, which divides the total soil pore space into mobile soil matrix and macropore systems. The solute transport model was parameterized to simulate the main processes of nitrogen (N) cycle in clayey, subsurface-drained soils during autumn periods after the harvest. The model simulates transport of nitrate and ammonium N, as well as mineralization, nitrification, and denitrification. Reactions in soil are affected by temperature and moisture, as simulated by FLUSH. Ammonium can adsorb on soil particles in both pore systems, while organic N is described in simulations as an immobile solute in the soil matrix. One-dimensional version of the model was applied to two subdrained field sections (1.3 and 3.4 ha) in the Nummela experimental field in southern Finland during two autumn periods (2008 and 2011). The model was able to replicate the measured dynamics of nitrate N concentrations in drain discharge during both the periods. Concentrations were the most dependent on drain discharge dynamics and the rate of nitrification. Measured and simulated ammonium concentrations in drain discharge were about 10 times smaller than nitrate concentrations, even though the levels of N input with initial values and deposition for both inorganic fractions were similar. Successful solute transport simulation results further increase the confidence in the description of the water flow processes in FLUSH.

Geochemical evolution and residence time of porewater in low-permeability rocks of the Michigan Basin, Southwest Ontario

Drill cores collected from an 860-m-thick Paleozoic (Cambrian to Devonian) sedimentary sequence of the Michigan Basin in southwest Ontario, Canada, were used to develop vertical profiles of natural tracers in porewater from the sedimentary sequence and build a conceptual model regarding processes and timing of solute migration. In this paper, the conceptual model is quantitatively assessed with numerical simulations of diffusion-dominated solute transport (Cl− and 18O). The conceptual model suggests that the tracer profiles result from mixing between a deep shield brine with isotopic characteristics consistent with water–rock interaction over a long period of geologic time, Ordovician seawater at intermediate depth, and an overlying hypersaline brine formed by evaporation of seawater in a restricted basin during the Silurian. Between the peak of basin consolidation at 300MaBP and the Pleistocene (2.6MaBP), salinity and isotopic concentration gradients are thought to have driven mixing, dominantly by diffusion. Water isotope data indicate that in the Pleistocene, melt water infiltrated to a maximum depth of 330m in the Silurian Salina Formation, likely in response to transient glacial loading and elevated sub-glacial hydraulic pressures. Also in the Pleistocene, over-pressured conditions in deep regions of the basin drove high-salinity brine eastward in the basal Cambrian aquifer, interrupting pre-existing tracer-diffusion profiles.A base case set of boundary and initial conditions provides a good fit between simulated and measured tracer profiles, but requires effective diffusion coefficients (De) in the Ordovician limestones that are lower than the average values obtained in laboratory measurements by as much as a factor of 10. The base-case values are still within the overall range of measured values. At the formation scale, relatively low in-situ De values are attributed to the intermittent occurrence of gas and liquid hydrocarbons in the Ordovician carbonate units and the effect of lithostatic confining pressure; neither of which are accounted for in the laboratory measurements but both would have the effect of decreasing De for aqueous solutes. The numerical model is most sensitive to the formation-specific De values and geologically reasonable variations in initial and boundary conditions have a relatively small influence on the results. Additional simulations indicate that hydraulic disturbance and ingress of meltwater during the Pleistocene can explain second-order features observed in the measured tracer profiles. This work provides supporting evidence for previous research indicating that the porewater residence time in the Ordovician sequence approaches the age of the rocks.

Effects of tidal fluctuations and spatial heterogeneity on mixing and spreading in spatially heterogeneous coastal aquifers

AbstractWe study the combined effect of heterogeneity in the hydraulic conductivity field and tidal oscillations on the three‐dimensional dynamics of seawater intrusion in coastal aquifers. We focus on the quantification of its impact on solute mixing and spreading of the freshwater–seawater interface. Three‐dimensional Monte Carlo realizations of log‐normally distributed permeability fields were performed, and for each realization, numerical variable density flow and solute transport simulations were conducted. Mixing is characterized by the spatial moments of concentration. The enhanced solute mixing is quantified by an effective dispersion coefficient. The simulations show that heterogeneity produces an inland movement of the toe location along with a significant widening of the transition zone, which is linearly proportional to the product of the arithmetic mean of the correlation lengths in the three spatial dimensions (λa) and the permeability field variance ( ). We find that once tidal oscillations are included, as the degree of heterogeneity increases, the combined effect of heterogeneity and tidal oscillations on mixing and spreading of the interface reduces. This is explained by the fact that an increase in the log‐permeability variance induces an increase in both the effective permeability and the spatial connectivity, which implies a more uniform hydraulic response to tidal forcing and, as a result, the degree of mixing decreases. This study also identifies that the mixing behavior induced by tidal oscillations in heterogeneous coastal aquifers is controlled by the effective tidal mixing number ( ) which depends on the amplitude, the period, the storativity, and the effective horizontal permeability.

Reducing the ambiguity of karst aquifer models by pattern matching of flow and transport on catchment scale

Abstract. Assessing the hydraulic parameters of karst aquifers is a challenge due to their high degree of heterogeneity. The unknown parameter field generally leads to a high ambiguity for flow and transport calibration in numerical models of karst aquifers. In this study, a distributed numerical model was built for the simulation of groundwater flow and solute transport in a highly heterogeneous karst aquifer in south-western Germany. Therefore, an interface for the simulation of solute transport in one-dimensional pipes was implemented into the software COMSOL Multiphysics® and coupled to the three-dimensional solute transport interface for continuum domains. For reducing model ambiguity, the simulation was matched for steady-state conditions to the hydraulic head distribution in the model area, the spring discharge of several springs and the transport velocities of two tracer tests. Furthermore, other measured parameters such as the hydraulic conductivity of the fissured matrix and the maximal karst conduit volume were available for model calibration. Parameter studies were performed for several karst conduit geometries to analyse the influence of the respective geometric and hydraulic parameters and develop a calibration approach in a large-scale heterogeneous karst system. Results show that it is possible not only to derive a consistent flow and transport model for a 150 km2 karst area but also to combine the use of groundwater flow and transport parameters thereby greatly reducing model ambiguity. The approach provides basic information about the conduit network not accessible for direct geometric measurements. The conduit network volume for the main karst spring in the study area could be narrowed down to approximately 100 000 m3.

Impact of space‐time mesh adaptation on solute transport modeling in porous media

AbstractWe implement a space‐time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of nonreactive transport experiments in laboratory‐scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space‐time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space‐time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery‐based error estimator which enables us to properly select the size, shape, and orientation of the mesh elements. Adaptation of the time step is performed through an ad hoc local reconstruction of the temporal derivative of the solution via a recovery‐based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a nonuniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space‐time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space‐time discretization.

Practical finite analytic methods for simulation of solute transport with scale-dependent dispersion under advection-dominated conditions

The practical finite analytic (PFA) method was applied to the solution of the one-dimensional advection equation with scale-dependent dispersion equation (ASDE) for solute transport in porous media under advection-dominated (high Peclet number) conditions. A triangular explicit PFA (EPFA) with three different approaches (EPFA 1, 2 and 3) and the Crank–Nicolson (CN) centered and upwind techniques were developed to solve the ASDE with a dispersivity with linear dependence on transport distance. In EPFA 1, to get more accurate results for the ASDE, the existing PFA method was developed and combined with the FD method. In EPFA 2 the original PFA method was employed to check its accuracy for modeling the ASDE without any modifications. Finally, in EPFA 3, based on the current PFA solution, new formulations are proposed to evaluate the accuracy of this approach. For all conditions, EPFA 3 has the best behavior in comparison with other numerical techniques for different linear functions for distance dependence of dispersivity.

Combined biofouling and scaling in membrane feed channels: a new modeling approach

A mathematical model was developed for combined fouling due to biofilms and mineral precipitates in membrane feed channels with spacers. Finite element simulation of flow and solute transport in two-dimensional geometries was coupled with a particle-based approach for the development of a composite (cells and crystals) foulant layer. Three fouling scenarios were compared: biofouling only, scaling only and combined fouling. Combined fouling causes a quicker flux decline than the summed flux deterioration when scaling and biofouling act independently. The model results indicate that the presence of biofilms leads to more mineral formation due to: (1) an enhanced degree of saturation for salts next to the membrane and within the biofilm; and (2) more available surface for nucleation to occur. The impact of biofilm in accelerating gypsum precipitation depends on the composition of the feed water (eg the presence of NaCl) and the kinetics of crystal nucleation and growth. Interactions between flow, solute transport and biofilm-induced mineralization are discussed.

Parametric Studies on Saltwater Intrusion into Coastal Aquifers for Anticipate Sea Level Rise

Saltwater intrusion into coastal aquifers is a global issue, exacerbated by increasing demands for freshwater in coastal regions. This study investigates into the parametric analysis on saltwater intrusion in a conceptual, coastal, unconfined aquifer considering wide range of freshwater draft and anticipated sea level rise. The saltwater intrusion under various circumstances is simulated through parametric studies using MODFLOW, MT3DMS and SEAWAT. The MODFLOW is used to simulate the groundwater flow system under changing hydro-dynamics in coastal aquifer. To simulate solute transport MT3DMS and SEAWAT is used. The saltwater intrusion process has direct bearing on hydraulic conductivity and inversely related to porosity. It may also be noted that increase in recharge rate considered in the study does not have much influence on saltwater intrusion. Effect of freshwater draft at locations beyond half of the width of the aquifer considered has marginal effect and hence can be considered as safe zone for freshwater withdrawals. Due to the climate change effect, the anticipated rise in sea level of 0.88 m over a century is considered in the investigation. This causes increase in salinity intrusion by about 25%. The combined effect of sea level rise and freshwater draft considered indicated significant increase in saltwater intrusion into coastal aquifers up to 57%.

Efficiency enhancement of optimized Latin hypercube sampling strategies: Application to Monte Carlo uncertainty analysis and meta-modeling

The majority of literature regarding optimized Latin hypercube sampling (OLHS) is devoted to increasing the efficiency of these sampling strategies through the development of new algorithms based on the combination of innovative space-filling criteria and specialized optimization schemes. However, little attention has been given to the impact of the initial design that is fed into the optimization algorithm, on the efficiency of OLHS strategies. Previous studies, as well as codes developed for OLHS, have relied on one of the following two approaches for the selection of the initial design in OLHS: (1) the use of random points in the hypercube intervals (random LHS), and (2) the use of midpoints in the hypercube intervals (midpoint LHS). Both approaches have been extensively used, but no attempt has been previously made to compare the efficiency and robustness of their resulting sample designs. In this study we compare the two approaches and show that the space-filling characteristics of OLHS designs are sensitive to the initial design that is fed into the optimization algorithm. It is also illustrated that the space-filling characteristics of OLHS designs based on midpoint LHS are significantly better those based on random LHS. The two approaches are compared by incorporating their resulting sample designs in Monte Carlo simulation (MCS) for uncertainty propagation analysis, and then, by employing the sample designs in the selection of the training set for constructing non-intrusive polynomial chaos expansion (NIPCE) meta-models which subsequently replace the original full model in MCSs. The analysis is based on two case studies involving numerical simulation of density dependent flow and solute transport in porous media within the context of seawater intrusion in coastal aquifers. We show that the use of midpoint LHS as the initial design increases the efficiency and robustness of the resulting MCSs and NIPCE meta-models. The study also illustrates that this relative improvement decreases with increasing number of sample points and input parameter dimensions. Since the computational time and efforts for generating the sample designs in the two approaches are identical, the use of midpoint LHS as the initial design in OLHS is thus recommended.

A robust coupled model for solute transport driven by severe flow conditions

This paper introduces a computationally efficient model that solves a 4 × 4 matrix form of the hyperbolic conservation laws consisting of the 2D shallow water and advection-diffusion equations. The model allows automatic shock-capturing due to the implementation of a finite volume Godunov-type scheme featured with an HLLC approximate Riemann solver. The numerical scheme is also able to provide well-balanced solutions and maintain non-negative water depth and solute concentration for applications involving wetting and drying over complex domain topographies. Implemented on a simplified adaptive grid system, the model can save 3–17 times of computational cost without compromising solution accuracy for those simulations with predominant localised complex hydrodynamic or flow features, as demonstrated by the numerical experiments. Therefore, the current model provides a potential tool for efficient simulation of large-scale solute transport as well as flow hydrodynamics during a highly transient flood event caused by dam failure or flash flooding.