Ir2dinv: a finite-difference model for inverse analysis of two-dimensional linear or radial groundwater flow

Abstract We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, lr2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg–Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface.

[1]  Roger Beckie,et al.  Measurement Scale, Network Sampling Scale, and Groundwater Model Parameters , 1996 .

[2]  Mary P. Anderson,et al.  Introduction to Groundwater Modeling: Finite Difference and Finite Element Methods , 1982 .

[3]  James J. Butler,et al.  The use of slug tests to describe vertical variations in hydraulic conductivity , 1994 .

[4]  R. C. St. John,et al.  D-Optimality for Regression Designs: A Review , 1975 .

[5]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[6]  Peter Dietrich,et al.  Identification of the permeability distribution in soil by hydraulic tomography , 1995 .

[7]  A. J. Desbarats,et al.  Spatial averaging of hydraulic conductivity under radial flow conditions , 1994 .

[8]  Clifford I. Voss,et al.  Further comments on sensitivities, parameter estimation, and sampling design in one-dimensional analysis of solute transport in porous media , 1988 .

[9]  Keiji Kojima,et al.  Hydropulse Tomography for Identifying 3-D Permeability Distribution , 1993 .

[10]  C. Voss,et al.  Behavior of sensitivities in the one-dimensional advection-dispersion equation: Implications for parameter estimation and sampling design , 1987 .

[11]  Khalid Aziz,et al.  A Computer Model for Two-Phase Coning Simulation , 1974 .

[12]  James J. Butler,et al.  Sensitivity analysis of slug tests Part 2. Observation wells , 1995 .

[13]  James J. Butler,et al.  Relationship Between Pumping‐Test and Slug‐Test Parameters: Scale Effect or Artifact? , 1998 .

[14]  James J. Butler,et al.  The Role of Pumping Tests in Site Characterization: Some Theoretical Considerations , 1990 .

[15]  R. C. St.  D-Optimality for Regression Designs: A Review , 1975 .

[16]  K. Rushton,et al.  Numerical Pumping Test Analysis in Unconfined Aquifers , 1977 .

[17]  Brian R. Zurbuchen,et al.  Dipole Probe: Design and Field Applications of a Single‐Borehole Device for Measurements of Vertical Variations of Hydraulic Conductivity , 1998 .

[18]  James J. Butler,et al.  Pumping tests in nonuniform aquifers: The radially asymmetric case , 1993 .

[19]  Arlen W. Harbaugh,et al.  A modular three-dimensional finite-difference ground-water flow model , 1984 .

[20]  Jorge J. Moré,et al.  Implementation guide for MINPACK-1. [Package of Fortran subprograms for solution of systems of nonlinear equations] , 1980 .

[21]  Geoffrey C. Bohling,et al.  SUPRPUMP: An Interactive Program for Well Test Analysis and Design , 1992 .

[22]  James J. Butler,et al.  Pumping tests in networks of multilevel sampling wells: Motivation and methodology , 1999 .