A three-dimensional finite-element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an "influence coefficient" technique that avoids costly numerical integration. Spatial discretization of a three-dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite-element model. The first four examples concern one-and two-dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three-dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three-dimensional situations involving seepage faces and anisotropic soil media. variably saturated flow simulation and related model development. Among these are studies by Seqol [1977], Frind and Ver•7e [1978], Reisenauer et al. [1982], and Davis and Seqol [1985]. Two modeling approaches were used in these studies. The first approach [Reisenauer et al., 1982] was formulated using the integrated finite-difference method (IFDM) with a 1790 mixed explicit-implicit Picard iterative procedure and a matrix inversion or a point successive relaxation scheme [Narasirnhan and Witherspoon , 1976]. This approach permits the use of an irregular mesh to provide a more efficient representation of a region with complex geometry than the conventional finitedifference approach. However, nodal coordinates, nodal connections, and nodal area data are required to calculate mass fluxes. The coordinates, connections, and areas must satisfy certain orthogonality constraints to ensure mass conservation. These constraints make it difficult, if not impossible, to model general curvilinear shapes. Difficulty in obtaining nonoscillatory steady state solutions without time stepping has been reported [Kincaid et al., 1984, pp. 3-37]. Also, potential problems exist in using mixed explicit-implicit time stepping with a point successive relaxation solution scheme for problems involving highly nonlinear soil properties and seepage faces.The second approach (presented by Segol [1977] and Frind and Verge [1978]) was based on the Galerkin finite-element method in conjunction with a fully implicit Picard iterative procedure and a direct matrix solver. This approach is more fl...

An approximate analytical solution describing the movement of a conservative tracer of finite volume in a radially converging flow field is proposed. The solution is divided into two phases: injection and transport. During the injection phase, an injection of chase fluid immediately following the tracer is allowed. Hydrodynamic dispersion effects are assumed to be negligible during this phase. The geometry of the tracer plume is determined by a particle‐tracking technique. During the plume transport phase, the tracer plume is approximated by a series of contiguous pulses. An approximate analytical solution for each pulse has been derived through linearization of the transport equation. The approximate solution has been verified by comparison with numerical solutions. The distribution of tracer in space and time is obtained by summing the contributions from all the pulses. Four geometrical parameters governing the geometry of the tracer plume immediately after injection are presented and discussed. The solution shows that the geometry of the initial tracer plume has an effect on the breakthrough curves. The volume of tracer and chase fluid has to be taken into account in tracer test design and data analysis. Limitations of the proposed solution are also discussed.

No abstract

No abstract

No abstract