Estimating Transmissivity Using Specific-Capacity Data

GC0102. Estimating Transmissivity Using Specific-Capacity Data, by R. E. Mace. 44 p., 18 figs., 2 tables, 1 appendix, 2001. Print.

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About This Publication
This circular categorizes, summarizes, recommends, and provides insights into the different techniques available for relating specific capacity to transmissivity. It comprises work performed for the Edwards Aquifer Authority, the Texas Water Development Board, the Lower Colorado River Authority, and the Texas National Research Laboratory Commission.


ABSTRACT
Because specific-capacity data are useful for estimating transmissivity, they should be used whenever possible in hydrogeologic studies. Including specific-capacity data will increase the number of transmissivity estimates in aquifers, sometimes dramatically, allowing more accurate statistical and spatial descriptions of transmissivity and hydraulic conductivity. Three main approaches are used in estimating transmissivity from specific capacity data: analytical, empirical, and geostatistical. The most commonly used analytical approach is an equation derived from the Theis nonequilibrium formula, which requires corrections for well loss, vertical flow due to partial penetration, and reduced saturated thickness. The empirical approach involves empirically relating transmissivity to specific capacity measured in the same well. This approach commonly requires at least 25 data pairs but does not require a correction for turbulent well loss or vertical flow resulting from partial penetration. Geostatistical techniques are useful for estimating transmissivity from specific capacity, developing interpolated maps of transmissivity, and quantifying the estimation uncertainty. Geostatistical techniques are, however, mathematically complicated and require a substantial number of data to define semivariograms and cross-semivariograms. Techniques for estimating transmissivity from specific-capacity data have been successfully applied in many aquifers in Texas and elsewhere to provide valuable information for inputting to numerical models and for evaluating water resources.

Keywords: aquifer, ground water, hydraulic conductivity, specific capacity, transmissivity

CONTENTS

Abstract

Introduction

Specific Capacity

Analytical Methods

Solutions Based on the Dupuit-Thiem Equation

Solutions Based on the Theis Nonequilibrium Equation

Other Analytical Approaches

Empirical Methods

Statistically Derived Linear Relationships

Published Empirical Relationships

Hybrid Approaches

Geostatistical Methods

Kriging with Linear Regression

Cokriging

Kriging with Transformed Values

Other Geostatistical Approaches

Partial Penetration

Well Loss

Estimating Turbulent Well Loss from Step-Drawdown Tests

Estimating Well Loss from Time-Drawdown Tests

Graphically Estimating Well Loss

Estimating Turbulent Well Loss by Using Empirical Relationships

Estimating Well Loss by Using Pipe-Flow Theory

Incorporating Well-Loss Corrections

Fractured and Karstic Rocks

Data-Quality Issues

Other Issues

Correcting for Decreased Saturated Thickness

Including Tests Having No Reported Pumping Time or Well Radius

Including Tests Having No Measurable Drawdown

Multiple Production Zones

Recommended Approach

Conclusions

Acknowledgments

References

Symbols

Appendix A. Estimating transmissivity from specific-capacity data using the Theis and others equation inside a spreadsheet

Figures

1. Data from a pumping test on a well completed in a confined aquifer

2. Plot showing decrease in specific capacity with increasing time of pumping

3. Time for water levels to stabilize after initiation of pumping as a function of transrnissivity and storativity

4. Relationship between transmissivity and specific capacity for alluvial and fractured hard-rock aquifers using Thomasson and others approach

5. Sensitivity of specific capacity to variation in transmissivity and a parameter, C', that incorporates effects of pumping time, well radius, and storativity

6. Example of an empirical relationship between transrnissivity and specific capacity for a karstic aquifer in Texas showing the best-fit line and the 95-percent prediction intervals for the linear fit and the best-fit lines for second- and third-order polynomials

7. Empirical relationships between transmissivity and specific capacity

8. Comparison among different empirical relationships and between empirical relationships and analytical approaches

9. Relationship between measured specific capacity and pumping rate in the Edwards aquifer

10. Effect of well loss on specific capacity for dimensionless well loss, where II = CQB^-1and R_scis specific capacity corrected for well loss divided by the measured specific capacity

11. Determining B and C from step-drawdown tests, an example of estimating B and C from a step-drawdown test, and sensitivity to n for a constant B and C

12. Plot to estimate well loss from discharge rate

13. Relationship between specific capacity and well-loss constant, showing the best-fit line and 95-percent prediction intervals

14. Comparison between measured well loss and well loss estimated from an empirical relationship between specific capacity and well-loss constant and pipe-flow theory

15. Production rates for specific-capacity tests in the Edwards aquifer where there was no measurable drawdown

16. The minimum production rate required to produce at least 1 ft of drawdown for a given transrnissivity, assuming a production time of 8 h, a well radius of 4 inches, and a storativity of 10^-4

17. Empirical relationship between transrnissivity and specific capacity for the Carrizo-Wilcox aquifer of east-central Texas

18. Error comparison between the empirical approach and the analytical approach to estimating transmissivity from specific capacity in the Carrizo-Wilcox aquifer of east-central Texas

Tables

1. Summary of empirical relationships between specific capacity and transmissivity

A-1. Example spreadsheet for calculating the Theis and others equation


Citation
Mace, R. E., 2001, Estimating Transmissivity Using Specific-Capacity Data: The University of Texas at Austin, Bureau of Economic Geology, Geological Circular 01-2, 44 p.