Three-Dimensional, Transient, Saturated-Unsaturated Flow in a Groundwater Basin

A three-dimensional finite difference model has been developed for the treatment of saturated-unsaturated transient flow in small nonhomogeneous, anisotropic geologic basins. The uniqueness of the model lies in its inclusion of the unsaturated zone in a basin wide model that can also handle both confined and unconfined saturated aquifers, under both natural and developed conditions. The integrated equation of flow is solved by the line successive overrelaxation technique. The model allows any generalized region shape and any configuration of time variant boundary conditions. When applied to natural flow systems, the model provides quantitative hydrographs of surface infiltration, groundwater recharge, water table depth, and stream base flow. Results of simulations for hypothetical basins provide insight into the mechanisms involved in the development of perched water tables. The unsaturated basin response is identified as the controlling factor in determining the nature of the base flow hydrograph. Application of the model to developed basins allows one to simulate not only the manner in which groundwater withdrawals are transmitted through the aquifers, but also the changes in the rates of groundwater recharge and discharge induced by the withdrawals. For any proposed pumping pattern, it is possible to predict the maximum basin yield that can be sustained by a flow system in equilibrium with the recharge-discharge characteristics of the basin.

[1]  K. Singh,et al.  Some Factors Affecting Baseflow , 1968 .

[2]  R. Allan Freeze,et al.  The Mechanism of Natural Ground-Water Recharge and Discharge: 1. One-dimensional, Vertical, Unsteady, Unsaturated Flow above a Recharging or Discharging Ground-Water Flow System , 1969 .

[3]  C. E. Jacob.  On the flow of water in an elastic artesian aquifer , 1940 .

[4]  H. G. Weinstein,et al.  Iterative Procedure for Solution of Systems of Parabolic and Elliptic Equations in Three Dimensions , 1969 .

[5]  F. J. Fayers,et al.  The use of a high-speed digital computer in the study of the hydrodynamics of geologic basins , 1962 .

[6]  A. Liakopoulos.  RETENTION AND DISTRIBUTION OF MOISTURE IN SOILS AFTER INFILTRATION HAS CEASED , 1965 .

[7]  K. Singh.  Theoretical Baseflow Curves , 1969 .

[8]  G. Habetler,et al.  An Alternating-Direction-Implicit Iteration Technique , 1960 .

[9]  George F. Pinder,et al.  Application of the Digital Computer for Aquifer Evaluation , 1968 .

[10]  Some Practical Considerations in the Numerical Solution of Two-Dimensional Reservoir Problems , 1968 .

[11]  J. Rubin,et al.  Theoretical Analysis of Two-Dimensional, Transient Flow of Water in Unsaturated and Partly Unsaturated Soils1 , 1968 .

[12]  R. Freeze,et al.  Blueprint for a physically-based, digitally-simulated hydrologic response model , 1969 .

[13]  Flow in heterogeneous porous mediums: 1. Darcian-type description of two-phase systems , 1966 .

[14]  R. Allan Freeze,et al.  Theoretical analysis of regional groundwater flow: 1. Analytical and numerical solutions to the mathematical model , 1966 .

[15]  K. H. Coats,et al.  Comparison of Alternating-Direction and Successive Overrelaxation Techniques in Simulation of Reservoir Fluid Flow , 1969 .

[16]  J. Tóth.  A Theoretical Analysis of Groundwater Flow in Small Drainage Basins , 1963 .

[17]  H. H. Cooper.  The equation of groundwater flow in fixed and deforming coordinates , 1966 .

[18]  Robert A. Young,et al.  The temporal allocation of ground water—A simulation approach , 1970 .

[19]  W. Brutsaert,et al.  Inflow Hydrographs from Large Unconfined Aquifers , 1965 .

[20]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[21]  Don W. Green,et al.  Numerical Modeling of Unsaturated Groundwater Flow and Comparison of the Model to a Field Experiment , 1970 .

[22]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[23]  R. D. Verma,et al.  Unconfined Aquifer Seepage by Capillary Flow Theory , 1970 .

[24]  G. Hornberger,et al.  Numeric Studies of a Composite Soil Moisture Ground‐Water System , 1969 .

[25]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[26]  G. S. Taylor,et al.  Computer Methods for Transient Analysis of Water‐Table Aquifers , 1969 .