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1.
Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments.  相似文献   

2.
The matrix–fracture transfer shape factor is one of the important parameters in the modeling of fluid flow in fractured porous media using a dual-porosity concept. Warren and Root [36] introduced the dual-porosity concept and suggested a relation for the shape factor. There is no general relationship for determining the shape factor for a single-phase flow of slightly compressible fluids. Therefore, different studies reported different values for this parameter, as an input into the flow models. Several investigations have been reported on the shape factor for slightly compressible fluids. However, the case of compressible fluids has not been investigated in the past. The focus of this study is, therefore, to find the shape factor for the single-phase flow of compressible fluids (gases) in fractured porous media. In this study, a model for the determination of the shape factor for compressible fluids is presented; and, the solution of nonlinear gas diffusivity equation is used to derive the shape factor. The integral method and the method of moments are used to solve the nonlinear governing equation by considering the pressure dependency of the viscosity and isothermal compressibility of the fluid. The approximate semi-analytical model for the shape factor presented in this study is verified using single-porosity, fine-grid, numerical simulations. The dependency of the shape factor on the gas specific gravity, pressure and temperature are also investigated. The theoretical analysis presented improves our understanding of fluid flow in fractured porous media. In addition, the developed matrix–fracture transfer shape factor can be used as an input for modeling flow of compressible fluids in dual-porosity systems, such as naturally fractured gas reservoirs, coalbed methane reservoirs and fractured tight gas reservoirs.  相似文献   

3.
Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law–based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.  相似文献   

4.
A modified version of the MODFLOW/MT3DMS‐based reactive transport model PHT3D was developed to extend current reactive transport capabilities to the variably‐saturated component of the subsurface system and incorporate diffusive reactive transport of gaseous species. Referred to as PHT3D‐UZF, this code incorporates flux terms calculated by MODFLOW's unsaturated‐zone flow (UZF1) package. A volume‐averaged approach similar to the method used in UZF‐MT3DMS was adopted. The PHREEQC‐based computation of chemical processes within PHT3D‐UZF in combination with the analytical solution method of UZF1 allows for comprehensive reactive transport investigations (i.e., biogeochemical transformations) that jointly involve saturated and unsaturated zone processes. Intended for regional‐scale applications, UZF1 simulates downward‐only flux within the unsaturated zone. The model was tested by comparing simulation results with those of existing numerical models. The comparison was performed for several benchmark problems that cover a range of important hydrological and reactive transport processes. A 2D simulation scenario was defined to illustrate the geochemical evolution following dewatering in a sandy acid sulfate soil environment. Other potential applications include the simulation of biogeochemical processes in variably‐saturated systems that track the transport and fate of agricultural pollutants, nutrients, natural and xenobiotic organic compounds and micropollutants such as pharmaceuticals, as well as the evolution of isotope patterns.  相似文献   

5.
Contaminated groundwater in fractured bedrock can expose ecosystems to undesired levels of risk for extended periods due to prolonged back-diffusion from rock matrix to permeable fractures. Therefore, it is key to characterize the diffusive mass loading (intrusion) of contaminants into the rock matrix for successful management of contaminated bedrock sites. Even the most detailed site characterization techniques often fail to delineate contamination in rock matrix. This study presents a set of analytical solutions to estimate diffusive mass intrusion into matrix blocks, it is recovered by pumping and concentration rebound when pumping ceases. The analytical models were validated by comparing the results with (1) numerical model results using the same model parameters and (2) observed chloride mass recovery, rebound concentration, and concentration in pumped groundwater at a highly fractured bedrock site in Alberta, Canada. It is also demonstrated that the analytical solutions can be used to estimate the total mass stored in the fractured bedrock prior to any remediation thereby providing insights into site contamination history. The predictive results of the analytical models clearly show that successful remediation by pumping depends largely on diffusive intrusion period. The results of initial mass from the analytical model was used to successfully calibrate a three-dimensional discrete fracture network numerical model further highlighting the utility of the simple analytical solutions in supplementing the more detailed site numerical modeling. Overall, the study shows the utility of simple analytical methods to support long-term management of a contaminated fractured bedrock site including site investigations and complex numerical modeling.  相似文献   

6.
The structure of macroporous or aggregated soils and fractured rocks is generally so complex that it is impractical to measure the geometry at the microscale (i.e., the size and the shape of soil aggregates or rock matrix blocks, and the myriad of fissures or fractures), and use such data in geometry-dependent macroscale flow and transport models. This paper analyzes a first-order type dual-porosity model which contains a geometry-dependent coefficient, β, in the mass transfer term to macroscopically represent the size and shape of soil or rock matrix blocks. As a reference, one- and two-dimensional geometry-based diffusion models were used to simulate mass transport into and out of porous blocks of defined shapes. Estimates for β were obtained analytically for four different matrix block geometries. Values for β were also calculated by directly matching analytical solutions of the diffusion models for a number of selected matrix block geometries to results obtained with the first-order model assuming standard boundary conditions. Direct matching improved previous results for cylindrical macropore geometries, especially when relatively small ratios between the outer soil mantle and the radius of the inner cylinder were used. Results of our analysis show that β is closely related to the ratio of the effective surface area available for mass transfer, and the soil matrix volume normalized by the effective characteristic length of the matrix system. Using values of β obtained by direct matching, an empirical function is derived to estimate macroscopic geometry coefficients from medium properties which in principle are measurable. The method permits independent estimates of β, thus allowing the dual-porosity approach eventually to be applied to media with complex and mixed types of structural geometry.  相似文献   

7.
Here we use Richards Equation models of variably saturated soil and bedrock groundwater flow to investigate first-order patterns of the coupling between soil and bedrock flow systems. We utilize a Monte Carlo sensitivity analysis to identify important hillslope parameters controlling bedrock recharge and then model the transient response of bedrock and soil flow to seasonal precipitation. Our results suggest that hillslopes can be divided into three conceptual zones of groundwater interaction, (a) the zone of lateral unsaturated soil moisture accumulation (upper portion of hillslope), (b) the zone of soil saturation and bedrock recharge (middle of hillslope) and (c) the zone of saturated-soil lateral flow and bedrock groundwater exfiltration (bottom of hillslope). Zones of groundwater interaction expand upslope during periods of precipitation and drain downslope during dry periods. The amount of water partitioned to the bedrock groundwater system a can be predicted by the ratio of bedrock to soil saturated hydraulic conductivity across a variety of hillslope configurations. Our modelled processes are qualitatively consistent with observations of shallow subsurface saturation and groundwater fluctuation on hillslopes studied in our two experimental watersheds and support a conceptual model of tightly coupled shallow and deep subsurface circulation where groundwater recharge and discharge continuously stores and releases water from longer residence time storage.  相似文献   

8.
The MT3DMS groundwater solute transport model was modified to simulate solute transport in the unsaturated zone by incorporating the unsaturated‐zone flow (UZF1) package developed for MODFLOW. The modified MT3DMS code uses a volume‐averaged approach in which Lagrangian‐based UZF1 fluid fluxes and storage changes are mapped onto a fixed grid. Referred to as UZF‐MT3DMS, the linked model was tested against published benchmarks solved analytically as well as against other published codes, most frequently the U.S. Geological Survey's Variably‐Saturated Two‐Dimensional Flow and Transport Model. Results from a suite of test cases demonstrate that the modified code accurately simulates solute advection, dispersion, and reaction in the unsaturated zone. Two‐ and three‐dimensional simulations also were investigated to ensure unsaturated‐saturated zone interaction was simulated correctly. Because the UZF1 solution is analytical, large‐scale flow and transport investigations can be performed free from the computational and data burdens required by numerical solutions to Richards' equation. Results demonstrate that significant simulation runtime savings can be achieved with UZF‐MT3DMS, an important development when hundreds or thousands of model runs are required during parameter estimation and uncertainty analysis. Three‐dimensional variably saturated flow and transport simulations revealed UZF‐MT3DMS to have runtimes that are less than one tenth of the time required by models that rely on Richards' equation. Given its accuracy and efficiency, and the wide‐spread use of both MODFLOW and MT3DMS, the added capability of unsaturated‐zone transport in this familiar modeling framework stands to benefit a broad user‐ship.  相似文献   

9.
Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant.  相似文献   

10.
The advance of a chemical weathering front into the bedrock of a hillslope is often limited by the rate weathering products that can be carried away, maintaining chemical disequilibrium. If the weathering front is within the saturated zone, groundwater flow downslope may affect the rate of transport and weathering—however, weathering also modifies the rock permeability and the subsurface potential gradient that drives lateral groundwater flow. This feedback may help explain why there tends to be neither “runaway weathering” to great depth nor exposed bedrock covering much of the earth and may provide a mechanism for weathering front advance to keep pace with incision of adjacent streams into bedrock. This is the second of a two‐part paper exploring the coevolution of bedrock weathering and lateral flow in hillslopes using a simple low‐dimensional model based on hydraulic groundwater theory. Here, we show how a simplified kinetic model of 1‐D rock weathering can be extended to consider lateral flow in a 2‐D hillslope. Exact and approximate analytical solutions for the location and thickness of weathering within the hillslope are obtained for a number of cases. A location for the weathering front can be found such that lateral flow is able to export weathering products at the rate required to keep pace with stream incision at steady state. Three pathways of solute export are identified: “diffusing up,” where solutes diffuse up and away from the weathering front into the laterally flowing aquifer; “draining down,” where solutes are advected primarily downward into the unweathered bedrock; and “draining along,” where solutes travel laterally within the weathering zone. For each pathway, a different subsurface topography and overall relief of unweathered bedrock within the hillslope is needed to remove solutes at steady state. The relief each pathway requires depends on the rate of stream incision raised to a different power, such that at a given incision rate, one pathway requires minimal relief and, therefore, likely determines the steady‐state hillslope profile.  相似文献   

11.
By implementing the moisture-based form of Richards’ equation into the geochemical modelling framework PHREEQC, a generic tool for the simulation of one-dimensional flow and solute transport in the vadose zone undergoing complex geochemical reactions was developed. A second-order, cell-centred, explicit finite difference scheme was employed for the numerical solution of the partial differential equations of flow and transport. In this scheme, the charge-balanced soil solution is treated as an assembly of elements, where changes in water and solute contents result from fluxes of elements across cell boundaries. Therefore, water flow is considered in terms of oxygen and hydrogen transport.  相似文献   

12.
Owing to the mathematical similarities between heat and mass transport, the multi-species transport model MT3DMS should be able to simulate heat transport if the effects of buoyancy and changes in viscosity are small. Although in several studies solute models have been successfully applied to simulate heat transport, these studies failed to provide any rigorous test of this approach. In the current study, we carefully evaluate simulations of a single borehole ground source heat pump (GSHP) system in three scenarios: a pure conduction situation, an intermediate case, and a convection-dominated case. Two evaluation approaches are employed: first, MT3DMS heat transport results are compared with analytical solutions. Second, simulations by MT3DMS, which is finite difference, are compared with those by the finite element code FEFLOW and the finite difference code SEAWAT. Both FEFLOW and SEAWAT are designed to simulate heat flow. For each comparison, the computed results are examined based on residual errors. MT3DMS and the analytical solutions compare satisfactorily. MT3DMS and SEAWAT results show very good agreement for all cases. MT3DMS and FEFLOW two-dimensional (2D) and three-dimensional (3D) results show good to very good agreement, except that in 3D there is somewhat deteriorated agreement close to the heat source where the difference in numerical methods is thought to influence the solution. The results suggest that MT3DMS can be successfully applied to simulate GSHP systems, and likely other systems with similar temperature ranges and gradients in saturated porous media.  相似文献   

13.
A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field.  相似文献   

14.
In this paper we describe the transport of pollution in groundwater in the neighbourhood of a well in a uniform background flow. We compute the rate at which contaminated particles reach the well as a function of the place of the source of pollution. The motion of a particle in a dispersive flow is seen as a random walk process. The Fokker-Planck equation for the random motion of a particle is transformed using the complex potential for the advective flow field. The resulting equation is solved asymptotically after a stretching transformation. Finally, the analytical solution is compared with results from Monte Carlo simulations with the random walk model. The method can be extended to arbitrary flow fields. Then by a numerical coordinate transformation the analytical results can still be employed.  相似文献   

15.
Recharge areas of spring systems can be hard to identify, but they can be critically important for protection of a spring resource. A recharge area for a spring complex in southern Wisconsin was delineated using a variety of complementary techniques. A telescopic mesh refinement (TMR) model was constructed from an existing regional-scale ground water flow model. This TMR model was formally optimized using parameter estimation techniques; the optimized "best fit" to measured heads and fluxes was obtained by using a horizontal hydraulic conductivity 200% larger than the original regional model for the upper bedrock aquifer and 80% smaller for the lower bedrock aquifer. The uncertainty in hydraulic conductivity was formally considered using a stochastic Monte Carlo approach. Two-hundred model runs used uniformly distributed, randomly sampled, horizontal hydraulic conductivity values within the range given by the TMR optimized values and the previously constructed regional model. A probability distribution of particles captured by the spring, or a "probabilistic capture zone," was calculated from the realistic Monte Carlo results (136 runs of 200). In addition to portions of the local surface watershed, the capture zone encompassed areas outside of the watershed--demonstrating that the ground watershed and surface watershed do not coincide. Analysis of water collected from the site identified relatively large contrasts in chemistry, even for springs within 15 m of one another. The differences showed a distinct gradation from Ordovician-carbonate-dominated water in western spring vents to Cambrian-sandstone-influenced water in eastern spring vents. The difference in chemistry was attributed to distinctive bedrock geology as demonstrated by overlaying the capture zone derived from numerical modeling over a bedrock geology map for the area. This finding gives additional confidence to the capture zone calculated by modeling.  相似文献   

16.
In northern peatlands, subsurface ice formation is an important process that can control heat transport, groundwater flow, and biological activity. Temperature was measured over one and a half years in a vertical profile in the Red Lake Bog, Minnesota. To successfully simulate the transport of heat within the peat profile, the U.S. Geological Survey’s SUTRA computer code was modified. The modified code simulates fully saturated, coupled porewater-energy transport, with freezing and melting porewater, and includes proportional heat capacity and thermal conductivity of water and ice, decreasing matrix permeability due to ice formation, and latent heat. The model is verified by correctly simulating the Lunardini analytical solution for ice formation in a porous medium with a mixed ice–water zone. The modified SUTRA model correctly simulates the temperature and ice distributions in the peat bog. Two possible benchmark problems for groundwater and energy transport with ice formation and melting are proposed that may be used by other researchers for code comparison.  相似文献   

17.
Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This paper develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. The result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.  相似文献   

18.
A steady/quasi-steady model is developed for predicting flow into a partially penetrating well with skin zone in a confined aquifer overlying an impervious layer. The model takes into account flow through the bottom of the wellbore, finite skin thickness and finite horizontal and vertical extent of the aquifer. Moreover, the solution can be easily extended to include the mixed-type boundary condition at the well face, where a Dirichlet in the form of a specified hydraulic head and a Neumann in the form of zero flux coexist at the same time at different portions of the well face. The validity of the proposed solution is tested by comparing a few results obtained from the developed model with corresponding results obtained by analytical and numerical means. The study shows that, among other factors remaining constant, both the horizontal and vertical extent of an artesian aquifer, thickness of the skin zone, bottom flow and conductivity contrast of the skin and formation zones, play an important part in deciding flow to a well dug in the aquifer, and hence these factors must be considered while analyzing the problem. The model proposed here can be used to estimate skin thickness as well as hydraulic conductivities of the skin and formation zones of a well with skin zone in an artesian aquifer underlain by an impervious layer by utilizing pumping test data falling in the steady or quasi-steady state of a typical pumping test. As the proposed solution is of a general nature in the sense that it can handle, apart from partial penetration and bottom flow, the finite size skin zone and finite horizontal and vertical extent of an artesian aquifer together with the mixed-type boundary condition at the well face, it is hoped that the predictions coming out of the model will be more realistic than those obtained using solutions developed with more stringent assumptions.  相似文献   

19.
Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.  相似文献   

20.
Cleanup standards for volatile organic compounds in thick vadose zones can be based on indirect risk (transport to ground water) when contamination is below depths of significant direct risk. At one Arizona Superfund site, a one-dimensional vadose zone transport model (VLE-ACH) was used to estimate the continued transport of VOCs from the vadose zone to ground water. VLEACH is a relatively simple and readily available model that proved useful for estimating indirect risk from VOCs in the vadose zone at this site. The estimates of total soil concentrations used as initial conditions for VLF.ACH incorporated a variety of data from the site. Soil gas concentrations were found to be more useful than soil matrix data for estimating total soil concentrations at this arid-zone site. A simple mixing cell model was used with the VLEACH-derived mass loading estimates from the vadose zone over time to estimate the resulting changes in ground water concentrations. For this site, the results of the linked VLEACH/mixing cell simulations indicate it is likely that the federal MCI. for TCE will be exceeded in underlying ground water if remedial action on I he vadose zone is not pursued.  相似文献   

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