U.S. Geological Survey (USGS) wtaq NOTE: Any use of trade, product or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government. NAME wtaq - A computer program for calculating drawdowns and estimating hydraulic properties for confined and water-table aquifers ABSTRACT The computer program WTAQ calculates hydraulic-head drawdowns in a confined or water-table aquifer that result from pumping at a well of finite or infinitesimal diameter. The program is based on analytical models of axial-symmetric groundwater flow in a homogeneous and anisotropic aquifer developed by Moench (1997) and Mathias and Butler (2006). The program allows for well-bore storage and well-bore skin at the pumped well and for delayed drawdown response at observation wells or piezometers. For water-table aquifers, the program allows three options for simulating drainage from the unsaturated zone: instantaneous drainage, gradual drainage, or drainage that explicitly accounts for hydraulic characteristics of the unsaturated zone (specifically, the moisture retention and relative hydraulic conductivity of the soil). WTAQ calculates dimensionless or dimensional theoretical drawdowns that can be used with measured drawdowns at observation points to estimate the hydraulic properties of confined and water-table aquifers. METHOD Program WTAQ implements the Laplace-transform solutions for drawdown at a pumped well, observation well, or observation piezometer that are given in equations 18-27 and 30-31 in Moench (1997) and equation 42 in Mathias and Butler (2006). The Laplace-transform solutions are numerically inverted to the time domain by means of either the Stehfest (1970) or de Hoog (1982) algorithms. The program calculates dimensionless or dimensional drawdowns for a given set of input conditions that are specified by the user in a data-input file. HISTORY WTAQ version 2.1 06/29/2012 - Minor bug fix to allow code to run when SIGMA is specified as 0 (for confined aquifers); previous versions stopped, with an error message, if SIGMA was specified as 0. WTAQ version 2.0 04/29/2011 - Added analytical model of Mathias and Butler (2006) for improved representation of drainage to water- table aquifers from the unsaturated zone. WTAQ version 1.2 04/29/2011 - Minor bug fix to variable name IOWS. WTAQ version 1.1 11/13/2009 - Improved internal checks for incorrect data values. WTAQ version 1.0 10/01/1999 - Initial release. DATA REQUIREMENTS To use WTAQ, the user must prepare a data-input file that contains information on the type of aquifer being simulated (confined or water table), hydraulic properties of the aquifer, characteristics of the pumped well and of all observation wells and(or) observation piezometers at which drawdowns will be calculated, and additional information for model solution. Input-data requirements are explained in the documentation reports by Barlow and Moench (1999 and 2011). OUTPUT OPTIONS Primary output is drawdown calculated as a function of time at the pumped well and at up to 25 observation-well and(or) observation-piezometer locations. A result file and plot file are generated by the program. The result file contains detailed information on the model simulation, whereas the plot file contains an abbreviated listing of model results that can be used for graphing. SYSTEM REQUIREMENTS WTAQ is written in Fortran 77. Input and result file names are queried by the program and read from the screen. The program also can be run in batch mode by redirecting program execution from the screen to a batch file that contains the names of the input and output files. DOCUMENTATION Barlow, P.M., and Moench, A.F., 1999, WTAQ--A computer program for calculating drawdowns and estimating hydraulic properties for confined and water-table aquifers: U.S. Geological Survey Water-Resources Investigations Report 99-4225, 74 p. Barlow, P.M., and Moench, A.F., 2011, WTAQ Version 2--A computer program for analysis of aquifer tests in confined and water-table aquifers with alternative representations of drainage from the unsaturated zone: U.S. Geological Survey Techniques and Methods 3-B9, 41 p. REFERENCES de Hoog, F.R., Knight, J.H., and Stokes, A.N., 1982, An improved method for numerical inversion of Laplace transforms: SIAM Journal of Scientific Computing, v. 3, no. 4, p. 1059-1071. Mathias,S.A., and Butler, A.P., 2006, Linearized Richards' equation approach to pumping test analysis in compressible aquifers: Water Resources Research, v. 42, W06408, doi:10.1029/2005WR004680, 10 p. Moench, A.F., 1997, Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer: Water Resources Research, v. 33, no. 6, p. 1397-1407. Stehfest, Harald, 1970, Numerical inversion of Laplace transforms: Communications of the Association for Computing Machinery (ACM), v. 13, no. 1, p. 47-49. CONTACTS Paul Barlow U.S. Geological Survey 10 Bearfoot Road Northborough, MA 01532 pbarlow@usgs.gov Allen Moench U.S. Geological Survey MS 496 345 Middlefield Road Menlo Park, CA 94025 afmoench@usgs.gov