Instructions for Running the Analytical Code PAT (Purge Analyzer Tool) for Computation of In-Well Time of Travel of Groundwater under Pumping Conditions

Open-File Report 2019-1104
Prepared in cooperation with the U.S. Environmental Protection Agency
By: , and 



Understanding the optimal time needed to purge a well while pumping to collect a representative groundwater sample requires an understanding of groundwater flow in wells (in-well flow). Parameters that affect in-well flow include the hydraulic properties of the aquifer, well construction, drawdown from pumping, and pump rate. The time of travel relative to in-well flow is affected by the pump’s intake location. The Purge Analyzer Tool (PAT) incorporates hydraulic calculations to help assess the optimal purge times required to vertically transport groundwater in the well to the pump intake (Harte, 2017). Harte (2017) includes a discussion on the rationale for determining in-well groundwater flow and time of travel and also discusses the limitations inherent in the PAT; an understanding of the limitations is important to ensure proper use.

The PAT calculates flow by use of the Dupuit-Theim equation (Lohman, 1979) that assumes steady-state radial flow and a total inflow from the well opening or screen equal to the pumping rate (eq. 1). A bulk average hydraulic conductivity (Kavg) is derived from this relationship. Once Kavg is calculated, the program calculates incremental (layered) horizontal radial inflow into the well over user defined increments (layers). These defined increments represent the screen or well opening as a fraction of the total inflow. The amount of inflow per layer is proportional to the user-defined layered distribution of hydraulic conductivity (Klayer) because drawdown is assumed to be uniformly distributed in the well. The water budget equation that guides the solution of the PAT (eq. 1) is specified as:

Qp = Qv + QH + Qw                                     (1)


QP   is pumping rate,
Qv   is vertical flow entering the boundary of the mixing zone (Mz) from the summation of layered radial flow (∑Qhl-n) where l-n denotes number of layers,
QH   is horizontal radial flow into the mixing zone (Mz), and
Qw   is flow from wellbore storage effects.

The in-well flow is computed from the convergence of incremental (layered) radial inflows (Qhl-n) summed to the total vertical flow (QV) entering the adjacent zone to the pump intake (called mixing zone [Mz]) as shown in figure 1. The Qv is transported as one-dimensional piston flow. Within the Mz, it's assumed that flow to the pump is dominated by horizontal radial flow (QH) when the pump is in the open interval of the well. Flow from the wellbore storage (Qw) is computed from the volume of water pumped from the well at the time of the drawdown (s) measurement(s). Aquifer storage effects are unaccounted for but are likely to be problematic when (1) dewatering within the well opening occurs or (2) when the water table is close to the top of the well screen or open interval where additional flow into the upper portion of the well opening may occur. For fully saturated wells tens of feet below the water table, storage effects are likely to be more uniformly distributed across the well screen or open interval (regardless of confined or unconfined conditions). Therefore, radial inflow from storage will be less prominent under pump rates commonly used in groundwater sampling either for volumetric sampling (<3 gallons per minute) or low-flow sampling (<0.5 liters per minute).

A major benefit of the use of the PAT is the understanding of time-varying, vertical integration of captured pump water. The analytical model computes aquifer (formation) capture intervals relative to the open interval of the well. This information is displayed graphically (called aquifer fraction graphs) and can be used to assess the likely formation intervals contributing water to the sample at any time.

Suggested Citation

Harte, P.T., Huffman, B.J., Perina, T., Levine, H., and Rojas-Mickelson, D., 2019, Instructions for running the analytical code PAT (Purge Analyzer Tool) for computation of in-well time of travel of groundwater under pumping conditions: U.S. Geological Survey Open-File Report 2019–1104, 23 p.,

ISSN: 2331-1258 (online)

Table of Contents

  • Acknowledgments
  • Introduction
  • Contents of Program
  • Operation
  • Solver
  • Assumptions and Limitations
  • Applications
  • Summary
  • References Cited
  • Appendix 1. Solution Examples using Purge Analyzer Tool
  • Appendix 2. Incorporation of Stratigraphic Information in Simulation
  • Appendix 3. Additional Examples of Input and Output
Publication type Report
Publication Subtype USGS Numbered Series
Title Instructions for running the analytical code PAT (Purge Analyzer Tool) for computation of in-well time of travel of groundwater under pumping conditions
Series title Open-File Report
Series number 2019-1104
DOI 10.3133/ofr20191104
Year Published 2019
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) New England Water Science Center
Description Report: vii, 23 p.; Application Site
Online Only (Y/N) Y
Additional Online Files (Y/N) N
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