Analytical and Numerical Modeling of Flow in a Fractured Gneiss Aquifer

ABSTRACT

Investigating and modeling fluid flow in fractured aquifers is a challenge. This study presents the results of a series of packer tests conducted in a fractured aquifer in Freiberg, Germany, where gneiss is the dominant rock type. Two methods were applied to acquire hydraulic properties from the packer tests: analytical and numerical modeling. MLU (Multi-Layer Unsteady state) for Windows is the analytical model that was applied. ANSYS-FLOTRAN was used to build a two-dimensional numerical model of the geometry of the layered aquifer. A reasonable match between experimental data and simulated data was achieved with the 2D numerical model while the solution from the analytical model revealed significant deviations with respect to direction.

Investigating and modeling fluid flow in fractured aquifers is a challenge. This study presents the results of a series of packer tests conducted in a fractured aquifer in Freiberg, Germany, where gneiss is the dominant rock type. Two methods were applied to acquire hydraulic properties from the packer tests: analytical and numerical modeling. MLU (Multi-Layer Unsteady state) for Windows is the analytical model that was applied. ANSYS-FLOTRAN was used to build a two-dimensional numerical model of the geometry of the layered aquifer. A reasonable match between experimental data and simulated data was achieved with the 2D numerical model while the solution from the analytical model revealed significant deviations with respect to direction.

Cite this paper

Abdelaziz, R. and Merkel, B. (2012) Analytical and Numerical Modeling of Flow in a Fractured Gneiss Aquifer.*Journal of Water Resource and Protection*, **4**, 657-662. doi: 10.4236/jwarp.2012.48076.

Abdelaziz, R. and Merkel, B. (2012) Analytical and Numerical Modeling of Flow in a Fractured Gneiss Aquifer.

References

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[14] J. Wang and K. Cui, “Numerical Study of Flow and Heat Transfer of Longitudinal-Flow Heat Exchanger,” Hebei Journal of Industrial Science & Technology, Vol. 22, No. 2, 2005, pp. 55-59.

[15] X. Gu, Q. Dong, et al., (2007). “Numerical Simulation Research on Shell-and-Tube Heat Exchanger Based on 3-D Solid Model,” Challenges of Power Engineering and Environment, Vol. 7, 2007, pp. 441-445.

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[18] F. Molina-Aiz, H. Fatnassi, et al., “Comparison of Finite Element and Finite Volume Methods for Simulation of Natural Ventilation in Greenhouses,” Computers and Elec- tronics in Agriculture, Vol. 72, No. 2, 2010, pp. 69-86. doi:10.1016/j.compag.2010.03.002

[19] D. Crandall, G. Bromhal, et al., “Numerical Simulations Examining the Relationship between Wall-Roughness and Fluid Flow in Rock Fractures,” International Journal of Rock Mechanics and Mining Sciences, Vol. 47, No. 5, 2010, pp. 784-796. doi:10.1016/j.ijrmms.2010.03.015

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[22] C. I. McDermott, R. Walsh, et al., “Hybrid Analytical and Finite Element Numerical Modeling of Mass and Heat Transport in Fractured Rocks with Matrix Diffusion,” Computational Geosciences, Vol. 13, No. 3, 2009, pp. 349-361. doi:10.1007/s10596-008-9123-9

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[26] B. Berkowitz, “Characterizing Flow and Transport in Frac- tured Geological Media: A Review,” Advances in Water Resources, Vol. 25, No. 8-12, 2002, pp. 861-884.

[27] I. Pfenner, “Bohrlochgeophysikalischer Klüftigkeitsnach- weis in Flachbohrungen unter Einbeziehung von Flowme- termessungen,” Diploma Thesis, Technische Universit?t Bergakademie Freiberg, Freiberg, 2003.

[28] F. Brassington and S. Walthall, “Field Techniques Using Borehole Packers in Hydrogeological Investigations,” Quarterly Journal of Engineering Geology & Hydrogeol- ogy, Vol. 18, No. 2, 1985, p. 181. doi:10.1144/GSL.QJEG.1985.018.02.07

[29] M. Price and A. Williams, “A Pumped Double-Packer System for Use in Aquifer Evaluation and Groundwater Sampling,” Proceedings of the Institution of Civil Engineers: Water Maritime and Energy, Vol. 101, No. 2, 1993, pp. 85-92. doi:10.1680/iwtme.1993.23589

[30] F. Driscoll, “Groundwater and Wells,” 2nd Edition, John- son Division, St. Paul, 1986.

[31] ANSYS Inc., “Fluids Analysis Guide,” User Manual, ANSYS Inc., Canonsburg, 2009.

[32] H. Lakshmininarayana, “Finite Elements Analysis: Procedures in Engineering,” Universities Press (India) Priva- te Limited, Hyderabad, 2004.

[33] F. Li, F. Wang, et al., “Simulation Study on Two-Di- mensional Diversion Duct by ANSYS Method,” Interna- tional Conference on Artificial Intelligence and Compu- tational Intelligence, Sanya, 23-24 October 2010, pp. 427- 431.

[34] K. A Al-Sahib, A. N. Jameel, et al., “Investigation into the Vibration Characteristics and Stability of a Welded Pipe Conveying Fluid,” Jordan Journal of Mechanical and Industrial Engineering, Vol. 4, No. 3, 2010, p. 378.

[35] P. Ben-Tzvi, R. B. Mrad, et al., “A Conceptual Design and FE Analysis of a Piezoceramic Actuated Dispensing System for Microdrops Generation in Microarray Applications, Mechatronics, Vol. 17, No. 1, 2007, pp. 1-13. doi:10.1016/j.mechatronics.2006.08.001

[36] S. Viswanathan, “Finite Element Analysis of Interaction between Actin Cytoskeleton and Intracellular Fluid in Prechondrocytes and Chondrocytes Subjected to Compressive Loading,” Master Thesis, West Virginia University, Morgantown, 2004.

[1] P. Dietrich, “Flow and Transport in Fractured Porous Media,” Springer Verlag, Berlin, 2005. doi:10.1007/b138453

[2] D. Ford and P. W. Williams, “Karst Hydrogeology and Geomorphology,” Wiley, Hoboken, 2007.

[3] C. V. Theis, “The Relation between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using Ground-Water Storage,” American Geophysical Union Transactions, Vol. 16, 1935, pp. 519-524.

[4] J. E. Warren and P. J. Root, “The Behavior of Naturally Fractured Reservoirs,” Old SPE Journal, Vol. 3, No. 3, 1963, pp. 245-255.

[5] H. Kazemi, “Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fracture Distribution,” Old SPE Journal, Vol. 9, No. 4, 1969, pp. 451-462.

[6] A. Odeh, “Unsteady-State Behavior of Naturally Fractured Reservoirs,” Old SPE Journal, Vol. 5, No. 1, 1965, pp. 60-66.

[7] M. S. Hantush and R. G. Thomas, “A Method for Analyzing a Drawdown Test in Anisotropic Aquifers,” Water Resources Research, Vol. 2, No. 2, 1966, pp. 281-285. doi:10.1029/WR002i002p00281

[8] T. Streltsova, “Hydrodynamics of Groundwater Flow in a Fractured Formation,” Water Resources Research, Vol. 12, No. 3, 1976, pp. 405-414. doi:10.1029/WR012i003p00405

[9] D. N. Jenkins and J. K. Prentice, “Theory for Aquifer Test Analysis in Fractured Rocks under Linear (Non-Ra- dial) Flow Conditions, Ground Water, Vol. 20, No. 1, 1982, pp. 12-21. doi:10.1111/j.1745-6584.1982.tb01325.x

[10] Z. Sen, “Aquifer Test Analysis in Fractured Rocks with Linear Flow Pattern,” Ground Water, Vol. 20, No. 1, 1986, pp. 72-78. doi:10.1111/j.1745-6584.1986.tb01461.x

[11] A. J. B. Cohen, “Hydrogeologic Characterization of a Fractured Granitic Rock Aquifer, Raymond, California,” Lawrence Berkeley Laboratory, Berkeley, 1993.

[12] J. D. Gernand and J. P. Heitman, “Detailed Pumping Test to Characterize a Fractured Bedrock Aquifer,” Ground Water, Vol. 35, No. 4, 1997, pp. 632-637. doi:10.1111/j.1745-6584.1997.tb00128.x

[13] T. Schweisinger, E. Svenson and L. C. Murdoch, “Transient Changes in Fracture Aperture during Hydraulic Well Tests in Fractured Gneiss,” University of Georgia, Athens, 2005.

[14] J. Wang and K. Cui, “Numerical Study of Flow and Heat Transfer of Longitudinal-Flow Heat Exchanger,” Hebei Journal of Industrial Science & Technology, Vol. 22, No. 2, 2005, pp. 55-59.

[15] X. Gu, Q. Dong, et al., (2007). “Numerical Simulation Research on Shell-and-Tube Heat Exchanger Based on 3-D Solid Model,” Challenges of Power Engineering and Environment, Vol. 7, 2007, pp. 441-445.

[16] K. Cen, Y. Chi, et al., “Challenges of Power Engineering and Environment,” Proceedings of the International Con- ference on Power Engineering, Vol. 1, 2007, p. 1860.

[17] T. Z. Slack, “Hydromechanical Interference Slug Tests in a Fractured Biotite Gneiss,” Master Thesis, Clemson Uni- versity, Clemson, 2010.

[18] F. Molina-Aiz, H. Fatnassi, et al., “Comparison of Finite Element and Finite Volume Methods for Simulation of Natural Ventilation in Greenhouses,” Computers and Elec- tronics in Agriculture, Vol. 72, No. 2, 2010, pp. 69-86. doi:10.1016/j.compag.2010.03.002

[19] D. Crandall, G. Bromhal, et al., “Numerical Simulations Examining the Relationship between Wall-Roughness and Fluid Flow in Rock Fractures,” International Journal of Rock Mechanics and Mining Sciences, Vol. 47, No. 5, 2010, pp. 784-796. doi:10.1016/j.ijrmms.2010.03.015

[20] K. Hemker and V. Post, “MLU for Windows,” MLU Users Guide, 2011.

[21] R. Walsh, C. McDermott, et al., “Numerical Modeling of Stress-Permeability Coupling in Rough Fractures,” Hydro- geology Journal, Vol. 16, No. 4, 2008, pp. 613-627. doi:10.1007/s10040-007-0254-1

[22] C. I. McDermott, R. Walsh, et al., “Hybrid Analytical and Finite Element Numerical Modeling of Mass and Heat Transport in Fractured Rocks with Matrix Diffusion,” Computational Geosciences, Vol. 13, No. 3, 2009, pp. 349-361. doi:10.1007/s10596-008-9123-9

[23] A. Myrttinen, T. Boving, et al., “Modeling of an MTBE Plume at Pascoag, Rhode Island,” Environmental Geology, Vol. 57, No. 5, 2009, pp. 1197-1206.

[24] K. Pruess, C. Oldenburg, et al., “TOUGH2 User’s Guide, Version 2.0,” Lawrence Berkeley National Laboratory, Berkeley, 1999.

[25] K. Pruess and J. García, “Multiphase Flow Dynamics during CO2 Disposal into Saline Aquifers,” Environmental Geology, Vol. 42, No. 2, 2002, pp. 282-295.

[26] B. Berkowitz, “Characterizing Flow and Transport in Frac- tured Geological Media: A Review,” Advances in Water Resources, Vol. 25, No. 8-12, 2002, pp. 861-884.

[27] I. Pfenner, “Bohrlochgeophysikalischer Klüftigkeitsnach- weis in Flachbohrungen unter Einbeziehung von Flowme- termessungen,” Diploma Thesis, Technische Universit?t Bergakademie Freiberg, Freiberg, 2003.

[28] F. Brassington and S. Walthall, “Field Techniques Using Borehole Packers in Hydrogeological Investigations,” Quarterly Journal of Engineering Geology & Hydrogeol- ogy, Vol. 18, No. 2, 1985, p. 181. doi:10.1144/GSL.QJEG.1985.018.02.07

[29] M. Price and A. Williams, “A Pumped Double-Packer System for Use in Aquifer Evaluation and Groundwater Sampling,” Proceedings of the Institution of Civil Engineers: Water Maritime and Energy, Vol. 101, No. 2, 1993, pp. 85-92. doi:10.1680/iwtme.1993.23589

[30] F. Driscoll, “Groundwater and Wells,” 2nd Edition, John- son Division, St. Paul, 1986.

[31] ANSYS Inc., “Fluids Analysis Guide,” User Manual, ANSYS Inc., Canonsburg, 2009.

[32] H. Lakshmininarayana, “Finite Elements Analysis: Procedures in Engineering,” Universities Press (India) Priva- te Limited, Hyderabad, 2004.

[33] F. Li, F. Wang, et al., “Simulation Study on Two-Di- mensional Diversion Duct by ANSYS Method,” Interna- tional Conference on Artificial Intelligence and Compu- tational Intelligence, Sanya, 23-24 October 2010, pp. 427- 431.

[34] K. A Al-Sahib, A. N. Jameel, et al., “Investigation into the Vibration Characteristics and Stability of a Welded Pipe Conveying Fluid,” Jordan Journal of Mechanical and Industrial Engineering, Vol. 4, No. 3, 2010, p. 378.

[35] P. Ben-Tzvi, R. B. Mrad, et al., “A Conceptual Design and FE Analysis of a Piezoceramic Actuated Dispensing System for Microdrops Generation in Microarray Applications, Mechatronics, Vol. 17, No. 1, 2007, pp. 1-13. doi:10.1016/j.mechatronics.2006.08.001

[36] S. Viswanathan, “Finite Element Analysis of Interaction between Actin Cytoskeleton and Intracellular Fluid in Prechondrocytes and Chondrocytes Subjected to Compressive Loading,” Master Thesis, West Virginia University, Morgantown, 2004.