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1.
A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes. 相似文献
2.
Theodore D. Foster 《地球物理与天体物理流体动力学》2013,107(1):201-217
Abstract A theoretical analysis of pseudo two-dimensional, finite-amplitude, thermal convection is made for an infinite Prandtl number fluid which is subjected to a constant heat flux out of the top boundary and insulated at the bottom. For large Rayleigh numbers the convective flow becomes intermittent and the system is characterized by the following cyclic process: the formation of a thermal boundary layer by diffusion, the instability of this layer when it becomes sufficiently thick, the destruction of the layer by the convective flow, the dying down of the convection, and the reforming of the thermal boundary layer by diffusion. The periodicity and the horizontal wave number of the intermittent convective flow are found to be independent of the depth of the fluid layer but depend on the rate of cooling and the properties of the fluid. 相似文献
3.
A test case has been developed for three-dimensional simulations of variable-density flow and solute transport in discretely-fractured porous media. The simulation domain is a low-permeability porous matrix cube containing a single non-planar fracture. The initial solute concentration is zero everywhere. A constant solute concentration is assigned to the top of the domain, which increases near-top fluid density and induces downward density-driven flow. The test case is therefore comparable to downwelling of a dense brine below a saline disposal basin or a waste repository. Numerous fingers and distinct convection cells develop early in the fracture but the fingers later coalesce and convection becomes less apparent. To help test other variable-density flow and transport models, results of the test case are presented both qualitatively (concentration contours and velocity fields) and quantitatively (penetration depth, mass flux, total mass stored, maximum fracture and matrix velocity). 相似文献
4.
Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures 总被引：1，自引：0，他引：1
Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes. 相似文献
5.
《Advances in water resources》2002,25(4):439-453
A three-dimensional, reactive numerical flow model is developed that couples chemical reactions with density-dependent mass transport and fluid flow. The model includes equilibrium reactions for the aqueous species, kinetic reactions between the solid and aqueous phases, and full coupling of porosity and permeability changes that result from precipitation and dissolution reactions in porous media. A one-step, global implicit approach is used to solve the coupled flow, transport and reaction equations with a fully implicit upstream-weighted control volume discretization. The Newton–Raphson method is applied to the discretized non-linear equations and a block ILU-preconditioned CGSTAB method is used to solve the resulting Jacobian matrix equations. This approach permits the solution of the complete set of governing equations for both concentration and pressure simultaneously affected by chemical and physical processes. A series of chemical transport simulations are conducted to investigate coupled processes of reactive chemical transport and density-dependent flow and their subsequent impact on the development of preferential flow paths in porous media. The coupled effects of the processes driving flow and the chemical reactions occurring during solute transport is studied using a carbonate system in fully saturated porous media. Results demonstrate that instability development is sensitive to the initial perturbation caused by density differences between the solute plume and the ambient groundwater. If the initial perturbation is large, then it acts as a “trigger” in the flow system that causes instabilities to develop in a planar reaction front. When permeability changes occur due to dissolution reactions occurring in the porous media, a reactive feedback loop is created by calcite dissolution and the mixed convective transport of the system. Although the feedback loop does not have a significant impact on plume shape, complex concentration distributions develop as a result of the instabilities generated in the flow system. 相似文献
6.
Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 105 and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated. 相似文献
7.
The linear instability of the gradient zone of a solar pond containing a fluid-porous interface is investigated. It is found that the gradient zone can retain the same stability for lower values of the solute Rayleigh number with the introduction of a porous material compared with a purely fluid layer, whilst maintaining the same lower convective zone temperature.Interestingly, it is also shown that for certain parameter values the penetration of a porous medium into the gradient zone can cause the temperature of the lower convective zone to rise. However, for certain parameter ranges, when the fluid-porous interface is towards the top of the gradient zone, the solar pond can become highly unstable. 相似文献
8.
Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element–finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection–diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion Dm of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated. 相似文献
9.
《Advances in water resources》2004,27(6):657-667
In this article, the quadrupole method is implemented in order to simulate the effects of heterogeneities on one dimensional advective and diffusive transport of a passive solute in porous media. Theoretical studies of dispersion in heterogeneous stratified media can bring insight into transport artefacts linked to scale effects and apparent dispersion coefficients. The quadrupole method is an efficient method for the calculation of transient response of linear systems. It is based here on the Laplace transform technique. The analytical solutions that can be derived by this method assists understanding of upscaled parameters relevant to heterogeneous porous media.First, the method is developed for an infinite homogeneous porous medium. Then, it is adapted to a stratified medium where the fluid flow is perpendicular to the interfaces. The first heterogeneous medium studied is composed of two semi-infinite layers perpendicular to the flow direction each having different transport properties. The concentration response of the medium to a Dirac injection is evaluated. The case studied emphasises the importance in the choice of the boundary conditions.In the case of a periodic heterogeneous porous medium, the concentration response of the medium is evaluated for different numbers of unit-cells. When the number of unit cells is great enough, depending on the transport properties of each layer in the unit cell, an equivalent homogeneous behaviour is reached. An exact determination of the transport properties (equivalent dispersion coefficient) of the equivalent homogeneous porous medium is given. 相似文献
10.
Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection. 相似文献
11.
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
12.
Results are presented from both linear stability analysis and numerical simulations of three-dimensional nonlinear convection in a Boussinesq fluid in an annular channel, under experimental boundary conditions, rotating about a vertical axis uniformly heated from below. The focus is placed on the Prandtl number Pr = 7.0, representing liquid water at room temperature. The linear analysis shows that, when the aspect ratio is sufficiently small, there exists only one stationary mode that occupies the whole fluid container. When the aspect ratio is moderate or large, however, there exist three different linear solutions: (i) the outer sidewall-localized traveling wave propagating against the sense of rotation; (ii) the inner sidewall-localized traveling wave propagating in the same sense as rotation; and (iii) both the counter-traveling waves occurring simultaneously. Guided by the result of the linear stability analysis, fully three-dimensional simulations are then performed for a channel with a moderate aspect ratio. It is found that neither the prograde nor the retrograde mode is physically realizable near threshold and beyond. The dynamics of nonlinear convection in a rotating channel are chiefly characterized by the interaction between the sidewall-localized waves and the interior convection cells/rolls, producing an interesting and unusual nonlinear phenomenon. In order to compare with the classical Rayleigh–Bénard problem without vertical sidewalls, we also study linear and nonlinear convection at exactly the same parameters but in an infinitely extended layer with periodic horizontal conditions. This reveals that both the linear instability and nonlinear convection in a rotating channel are characteristically different from those in a rotating layer with periodic horizontal conditions. 相似文献
13.
Ryan T. Bailey Eric D. Morway Richard G. Niswonger Timothy K. Gates 《Ground water》2013,51(5):752-761
A numerical model was developed that is capable of simulating multispecies reactive solute transport in variably saturated porous media. This model consists of a modified version of the reactive transport model RT3D (Reactive Transport in 3 Dimensions) that is linked to the Unsaturated‐Zone Flow (UZF1) package and MODFLOW. Referred to as UZF‐RT3D, the model is tested against published analytical benchmarks as well as other published contaminant transport models, including HYDRUS‐1D, VS2DT, and SUTRA, and the coupled flow and transport modeling system of CATHY and TRAN3D. Comparisons in one‐dimensional, two‐dimensional, and three‐dimensional variably saturated systems are explored. While several test cases are included to verify the correct implementation of variably saturated transport in UZF‐RT3D, other cases are included to demonstrate the usefulness of the code in terms of model run‐time and handling the reaction kinetics of multiple interacting species in variably saturated subsurface systems. As UZF1 relies on a kinematic‐wave approximation for unsaturated flow that neglects the diffusive terms in Richards equation, UZF‐RT3D can be used for large‐scale aquifer systems for which the UZF1 formulation is reasonable, that is, capillary‐pressure gradients can be neglected and soil parameters can be treated as homogeneous. Decreased model run‐time and the ability to include site‐specific chemical species and chemical reactions make UZF‐RT3D an attractive model for efficient simulation of multispecies reactive transport in variably saturated large‐scale subsurface systems. 相似文献
14.
An infinite horizontal layer, with vertically stratified temperature and solute concentration, is considered in the case where the viscosity is exponentially dependent on temperature, and the Prandtl number is infinite. Its linear stability is investigated when the destabilizing thermal gradient acts against a stabilizing solute gradient. The analysis is performed using horizontal Fourier and vertical Chebyshev polynomial expansions. For the constant viscosity case, the laws well established in the free boundary configuration are seen to be directly suitable for the rigid one. In the variable viscosity case, characterised by a given viscosity contrast c, the scaling laws with c are settled extrapolating to the double diffusive situation the approach initiated by Stengel et al. (1982). In contrast with the constant viscosity case, the critical wave number is found to be strongly dependent on the solutal Rayleigh number in the marginal oscillatory obtained at large contrast values. 相似文献
15.
《Advances in water resources》2007,30(4):966-983
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
16.
17.
Abstract Stability analysis is formulated for a two-layer fluid model in which the upper and lower layers are convectively stable and unstable, respectively. With discontinuities in viscosity and conductivity at the interface, the exchange of stability does not generally hold and overstability is possible. A detailed analytical treatment is presented for the case of small viscosity and conductivity in which viscous and conducting boundary layers are formed at the interface. The usual damping effect due to the energy dissipation by viscosity and thermal conductivity exists irrespective of whether the mode is the convection or the gravity wave, but, for larger horizontal wave lengths, the effect of the boundary layer can become more important. The jump in the thermal conductivity in the boundary layer can give rise to overstability of the gravity wave in agreement with Souffrin and Spiegel (1967). The jump in the viscosity provides a self-catalytic action for the unstable flow if the viscosity is assumed to be the nonlinear turbulent viscosity due to the motion itself. The effect, however, is not strong enough to overcome the usual viscous damping. 相似文献
18.
Geothermal fields and hydrothermal mineral deposits are manifestations of the interaction between heat transfer and fluid
flow in the Earth’s crust. Understanding the factors that drive fluid flow is essential for managing geothermal energy production
and for understanding the genesis of hydrothermal mineral systems. We provide an overview of fluid flow drivers with a focus
on flow driven by heat and hydraulic head. We show how numerical simulations can be used to compare the effect of different
flow drivers on hydrothermal mineralisation. We explore the concepts of laminar flow in porous media (Darcy’s law) and the
non-dimensional Rayleigh number (Ra) for free thermal convection in the context of fluid flow in hydrothermal systems in three dimensions. We compare models
of free thermal convection to hydraulic head driven flow in relation to hydrothermal copper mineralisation at Mount Isa, Australia.
Free thermal convection occurs if the permeability of the fault system results in Ra above the critical threshold, whereas a vertical head gradient results in an upward flow field. 相似文献
19.
The transport of contaminants in aquifers is usually represented by a convection-dispersion equation. There are several well-known problems of oscillation and artificial dispersion that affect the numerical solution of this equation. For example, several studies have shown that standard treatment of the cross-dispersion terms always leads to a negative concentration. It is also well known that the numerical solution of the convective term is affected by spurious oscillations or substantial numerical dispersion. These difficulties are especially significant for solute transport in nonuniform flow in heterogeneous aquifers. For the case of coupled reactive-transport models, even small negative concentration values can become amplified through nonlinear reaction source/sink terms and thus result in physically erroneous and unstable results. This paper includes a brief discussion about how nonpositive concentrations arise from numerical solution of the convection and cross-dispersion terms. We demonstrate the effectiveness of directional splitting with one-dimensional flux limiters for the convection term. Also, a new numerical scheme for the dispersion term that preserves positivity is presented. The results of the proposed convection scheme and the solution given by the new method to compute dispersion are compared with standard numerical methods as used in MT3DMS. 相似文献
20.
Three-dimensional grids representing a heterogeneous, ground water system are generated at 10 different resolutions in support of a site-scale flow and transport modeling effort. These grids represent hydrostratigraphy near Yucca Mountain, Nevada, consisting of 18 stratigraphic units with contrasting fluid flow and transport properties. The grid generation method allows the stratigraphy to be modeled by numerical grids of different resolution so that comparison studies can be performed to test for grid quality and determine the resolution required to resolve geologic structure and physical processes such as fluid flow and solute transport. The process of generating numerical grids with appropriate property distributions from geologic conceptual models is automated, thus making the entire process easy to implement with fewer user-induced errors. The series of grids of various resolutions are used to assess the level at which increasing resolution no longer influences the flow and solute transport results. Grid resolution is found to be a critical issue for ground water flow and solute transport. The resolution required in a particular instance is a function of the feature size of the model, the intrinsic properties of materials, the specific physics of the problem, and boundary conditions. The asymptotic nature of results related to flow and transport indicate that for a hydrologic model of the heterogeneous hydrostratigraphy under Yucca Mountain, a horizontal grid spacing of 600 m and vertical grid spacing of 40 m resolve the hydrostratigraphic model with sufficient precision to accurately model the hypothetical flow and solute transport to within 5% of the value that would be obtained with much higher resolution. 相似文献