A Reinterpretation of Historic Aquifer Tests of Two Hydraulically Fractured Wells by Application of Inverse Analysis, Derivative Analysis, and Diagnostic Plots

Abstract

Aquifer test methods have greatly improved in recent years with the advent of inverse analysis, derivative analysis, and diagnostic plots. Updated analyses of past aquifer tests allow for improved interpretations of the data to enhance the knowledge and the predictive capabilities of the flow system. This work thoroughly reanalyzes a series of pre- and post-hydraulic fracturing, single-well aquifer tests conducted in two crystalline rock wells in New Hampshire as part of an early 1970’s study. Previous analyses of the data had relied on older manual type-curve methods for predicting the possible effects of hydraulic fracturing. This work applies inverse analysis, derivative analysis, and diagnostic plots to reanalyze the 1970’s aquifer test data. Our results demonstrate that the aquifer tests were affected by changes in flow regimes, dewatering of the aquifer and discrete fractures, and changes due to well development. Increases in transmissivities are related to well development prior to hydraulic fracturing, propagation of a single, vertical fracture hydraulically connecting the two wells after stimulation and expansion of troughs of depression. After hydraulic fracturing, the estimated total yield of the individual wells increased by 2.5 times due to the hydraulic fracturing. However, the wells may be receiving water from the same source, and well interference may affect any significant increase in their combined yield. Our analyses demonstrate the value in applying inverse analysis, derivative analysis, and diagnostic plots over the conventional method of manual type-curve analysis. In addition, our improvement in the aquifer test interpretation of the 1970’s test data has implications for more reliable estimates of sustained well yields.

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Hammond, P. and Field, M. (2014) A Reinterpretation of Historic Aquifer Tests of Two Hydraulically Fractured Wells by Application of Inverse Analysis, Derivative Analysis, and Diagnostic Plots. Journal of Water Resource and Protection, 6, 481-506. doi: 10.4236/jwarp.2014.65048.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Theis, C. (1935) The Relation between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using Groundwater Storage. Transactions, the American Geophysical Union, 16, 519-524.
http://dx.doi.org/10.1029/TR016i002p00519
[2] Cooper, H.H. and Jacob, C.E. (1946) A Generalized Graphical Method for Evaluating Formation Constants and Summarizing Well Field History. Transactions, American Geophysical Union, 27, 526-534.
http://dx.doi.org/10.1029/TR027i004p00526
[3] dos Santos, J.S., Ballestero, J.S., da Silva, T.P. and Pitombeira, E. (2011) An Analytical Model for Hydraulic Fracturing in Shallow Bedrock Formations. Groundwater, 49, 415-425.
http://dx.doi.org/10.1111/j.1745-6584.2010.00727.x
[4] Piscopo, V. and Summa, G. (2006) Experiment of Pumping at Constant-Head: An Alternative Possibility to the Sustainable Yield of a Well. Hydrogeology, 15, 679-687. http://dx.doi.org/10.1007/s10040-006-0132-2
[5] Batu, V. (1998) Aquifer Hydraulics: A Comprehensive Guide to Hydrogeologic Data Analysis. John Wiley & Sons, Inc., New York.
[6] Lebbe, L.C. (1999) Hydraulic Parameter Identification: Generalized Interpretation Method for Single and Multiple Pumping Tests. Springer-Verlag, Berlin.
[7] Duffield, G.M. (2007) AQTESOLV for Windows User’s Guide. Version 4.5, HydroSOLVE, Inc., Reston.
[8] Renard, P., Glenz, D. and Mejias, M. (2009) Understanding Diagnostic Plots for Well-Test Interpretation. Hydrogeology Journal, 17, 589-600. http://dx.doi.org/10.1007/s10040-008-0392-0
[9] Beauheim, R.L., Roberts, R.M. and Avis, J.D. (2004) Well Testing in Fractured Media: Flow Dimensions and Diagnostic Plots. Journal of Hydraulic Research, 42, 69-76. http://dx.doi.org/10.1080/00221680409500049
[10] Stewart, G.W. (1974) Hydraulic Fracturing of Drilled Water Wells in Crystalline Rocks of New Hampshire. Tech. Rep., New Hampshire Department of Resources and Economic Development, Concord.
[11] Driscoll, F.G. (1986) Groundwater and Wells. 2nd Edition, Johnson Division, St. Paul.
[12] Boulton, N.S. (1954) The Drawdown of the Water Table under Non-Steady Conditions near a Pumped Well in an Unconfined Formation. Proceedings of the Institute of Civil Engineers, 3, 564-579.
[13] Boulton, N.S. (1963) Analysis of Data from Non-Equilibrium Pumping Tests Allowing for Delayed Yield from Storage. Proceedings of the Institute of Civil Engineers, 26, 469-482. http://dx.doi.org/10.1680/iicep.1963.10409
[14] Boulton, N.S. (1973) The Influence of Delayed Drainage on Data from Pumping Tests in Unconfined Aquifers. Journal of Hydrology, 19, 157-169.
[15] Neuman, S.P. (1972) Theory of Flow in Unconfined Aquifers Considering Delayed Response of the Water Table. Water Resources Research, 8, 1031-1045. http://dx.doi.org/10.1029/WR008i004p01031
[16] Neuman, S.P. (1974) Effect of Partial Penetration on Flow in Unconfined Aquifers Considering Delayed Gravity Response. Water Resources Research, 10, 303-312. http://dx.doi.org/10.1029/WR010i002p00303
[17] Neuman, S.P. (1975) Analysis of Pumping Test Data from Anisotropic Unconfined Aquifers Considering Delayed Gravity Response. Water Resources Research, 11, 329-342. http://dx.doi.org/10.1029/WR011i002p00329
[18] Streltsova, T.D. (1975) Hydrodynamics of Groundwater Flow in a Fractured Formation. Water Resources Research, 12, 405-414. http://dx.doi.org/10.1029/WR012i003p00405
[19] Boulton, N.S. and Streltsova, T.D. (1977) Flow to a Well in an Unconfined Fractured Aquifer. In: Dilamarter, R.R. and Csallany, S.C., Eds., Hydrologic Problems in Karst Regions, University of Western Kentucky, Bowling Green, 214-227.
[20] Boulton, N.S. and Streltsova, T.D. (1977) Unsteady Flow to a Pumped Well in a Two-Layered Water-Bearing Formation. Journal of Hydrology, 35, 245-256. http://dx.doi.org/10.1016/0022-1694(77)90004-X
[21] Boulton, N.S. and Streltsova, T.D. (1977) Unsteady Flow to a Pumped Well in a Fissured Water-Bearing Formation. Journal of Hydrology, 35, 257-270. http://dx.doi.org/10.1016/0022-1694(77)90005-1
[22] Boulton, N.S. and Streltsova, T.D. (1978) Unsteady Flow to a Pumped Well in a Fissured Aquifer with a Free Surface Level Maintained Constant. Water Resources Research, 14, 527-532.
http://dx.doi.org/10.1029/WR014i003p00527
[23] Moench, A.F. (1984) Double Porosity Models for a Fissured Groundwater Reservoir with Fractured Skin. Water Resources Research, 20, 831-846.
[24] Gringarten, A.C., Ramey Jr., H.J. and Ragavan, R. (1975) Applied Pressure Analysis for Fractured Wells. Journal of Petroleum Technology, 27, 887-892.
[25] Barker, J.A. (1988) A Generalized Radial Flow Model for Hydraulic Tests in Fractured Rock. Water Resources Research, 24, 1796-1804. http://dx.doi.org/10.1029/WR024i010p01796
[26] Hantush, M.S. (1960) Modification of the Theory of Leaky Aquifers. Journal of Geophysical Research, 65, 3713-3725. http://dx.doi.org/10.1029/JZ065i011p03713
[27] Moench, A.F. (1985) Transient Flow to a Large-Diameter Well in an Aquifer with Storative Semiconfining Layers. Water Resources Research, 21, 1121-1131.
[28] Sen, Z. (1995) Applied Hydrogeology for Scientists and Engineer. CRC Press, Boca Raton.
[29] Samani, N., Pasandi, M. and Barry, D.A. (2006) Characterizing a Heterogeneous Aquifer by Derivative Analysis of Pumping and Recovery Test Data. Journal of Geological Society of Iran, 1, 29-41.
http://infoscience.epfl.ch/record/118466/files/jp142.pdf
[30] Bourdet, D., Ayoub, J.A. and Pirard, Y.M. (1989) Use of Pressure Derivative in Well-Test Interpretations. SPE Formation Evaluation, 4, 293-302. http://dx.doi.org/10.2118/12777-PA
[31] van Tonder, G.J., Botha, J.F., Wen-Hsing, C., Kunstmann, H. and Xu, Y.X. (2001) Estimation of the Sustainable Yields of Boreholes in Fractured Rock Formations. Journal of Hydrology, 241, 70-90.
http://dx.doi.org/10.1016/S0022-1694(00)00369-3
[32] Sauveplane, C. (1984) Pumping Test Analysis in Fractured Aquifer Formations: State of the Art and some Perspectives. In: Rosenshein, J. and Bennett, G.D., Eds., Groundwater Hydraulics. Water Resources Monograph 9, American Geophysical Union, Washington DC, 171-206.
[33] Johns, R.A., Semprini, L. and Roberts, P.V. (1992) Estimating Aquifer properties by Nonlinear Least-Squares Analysis of Pump Test Response. Groundwater, 30, 68-77. http://dx.doi.org/10.1111/j.1745-6584.1992.tb00813.x
[34] Carrera, J. and Neuman, S.P. (1986) Estimation of Aquifer Parameters under Transient and Steady State Conditions: 2. Uniqueness, Stability, and Solution Algorithms. Water Resources Research, 22, 211-227.
http://dx.doi.org/10.1029/WR022i002p00211
[35] Sun, N.Z. (1994) Inverse Problems in Groundwater Modelling. Kluwer Academic Publishers, Dordrecht.
[36] Madsen, K., Nielsen, H.B. and Tingleff, O. (2004) Methods for Non-Linear Least Squares Problems. 2nd Edition, Informatics and Mathematical Modelling (IMM), Technical University of Denmark (DTU), Lyngby.
http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf
[37] Haupt, R.L. and Haupt, S.E. (2004) Practical Genetic Algorithms. 2nd Edition, John Wiley & Sons, Inc., Hoboken.
[38] Saleem, Z.A. (1970) A Computer Method for Pumping-Test Analysis. Groundwater, 8, 21-24.
http://dx.doi.org/10.1111/j.1745-6584.1970.tb01318.x
[39] Jacquard, P. and Jain, C. (1965) Permeability Distribution from Field Pressure Data. Society of Petroleum Engineers Journal, 5, 281-294. http://dx.doi.org/10.2118/1307-PA
[40] Jahns, H.O. (1966) A Rapid Method for Obtaining a Two-Dimensional Reservoir Description from Well Pressure Response Data. Society of Petroleum Engineers Journal, 6, 315-327. http://dx.doi.org/10.2118/1473-PA
[41] Sayed, S.A.S. (1990) Automated Analysis of Pumping Tests in Unconfined Aquifers of Semi-Infinite Thickness. Groundwater, 28, 108-112. http://dx.doi.org/10.1111/j.1745-6584.1990.tb02234.x
[42] Boonstra, H. and Soppe, R. (2006) Well Hydraulics and Aquifer Tests. In: Delleur, J.W., Ed., The Handbook of Groundwater Engineering, 2nd Edition, CRC Press, Taylor and Francis Group, Boca Raton, 10-1-10-35.
[43] Williamson, W.H. and Woolley, D.R. (1980) Hydraulic Fracturing to Improve the Yields of Bores in Fractured Rock. Tech. Rep. 55, Australian Water Resources Council, Australian Government Publishing Service, Canberra.
[44] Herbert, R., Talbot, J.C. and Buckley, D.K. (1993) A Study of Hydraulic Fracturing Used on Low Yielding Boreholes in the Crystalline Basement Rocks of Masvingo Province, Zimbabwe. In: Memoires of the 24th Congress, International Association of Hydrogeologists, 28th June-2nd July 1993, As (Oslo), 698-726.
[45] Gale, J.E. and MacLeod, R. (1995) Assessing the Effectiveness of Fracture Stimulation for Increasing Well Yield in Newfoundland. Tech. Rep. Canada-Newfoundland Agreement Respecting Water Resource Management, Government of Newfoundland and Labrador, Department of Environment, Water Resources Division, Environment Canada, Environmental Conservation Strategies Division.
[46] Montgomery, C.T. and Smith, M.B. (2010) Hydraulic Fracturing: History of an Enduring Technology. Journal of Petroleum Technology, 62, 26-32. http://www.spe.org/jpt/print/archives/2010/12/10Hydraulic.pdf
[47] Benzie, F., Chenier, F., Kleiman, H., McDonald, H., Surrell, J., Thomas, C. and Van Alstine, J. (1996) Hydraulic Fracturing Request Review Policy. Tech. Rep. Policy Review, Michigan Department of Environmental Quality, Lansing.
http://www.michigan.gov/documents/deq/deq-wd-gws-wcu-hydraulicfracturing_270750_7.pdf
[48] Gringarten, A.C. and Ramey, H.J. (1974) Unsteady State Pressure Distributions Created by a Well with a Single Horizontal Fracture, Partial Penetration or Restricted Entry. Journal of the Society of Petroleum Engineers, 14, 413-426.
[49] Murdoch, L.C. and Slack, W.W. (2002) Forms of Hydraulic Fractures in Shallow Fine-Grained Formations. Journal of Geotechnical and Geoenvironmental Engineering, 128, 479-487.
http://dx.doi.org/10.1061/(ASCE)1090-0241(2002)128:6(479)

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