Transient solution for radial two-zone flow in unconfined aquifers under constant-head tests
Y. C. Chang
Institute of Environmental Engineering, National Chiao-Tung University, Hsinchu, Taiwan
Search for more papers by this authorCorresponding Author
H. D. Yeh
Institute of Environmental Engineering, National Chiao-Tung University, Hsinchu, Taiwan
Institute of Environmental Engineering, National Chiao Tung University, No. 1001, University Road, Hsinchu, Taiwan.===Search for more papers by this authorG. Y. Chen
Institute of Environmental Engineering, National Chiao-Tung University, Hsinchu, Taiwan
Search for more papers by this authorY. C. Chang
Institute of Environmental Engineering, National Chiao-Tung University, Hsinchu, Taiwan
Search for more papers by this authorCorresponding Author
H. D. Yeh
Institute of Environmental Engineering, National Chiao-Tung University, Hsinchu, Taiwan
Institute of Environmental Engineering, National Chiao Tung University, No. 1001, University Road, Hsinchu, Taiwan.===Search for more papers by this authorG. Y. Chen
Institute of Environmental Engineering, National Chiao-Tung University, Hsinchu, Taiwan
Search for more papers by this authorAbstract
The constant-head test (CHT) is commonly employed to determine the aquifer parameters. This test is also applied to many environmental problems such as recovering light nonaqueous phase liquids (LNAPL) and controlling off-site migration of contaminated groundwater in low-transmissivity aquifers. A well skin near the wellbore may be produced due to the well construction or development and its formation properties are significantly different from the original ones. A more appropriate description for the skin effect on the aquifer system should treat the well skin as a different formation instead of using a skin factor. Thus, the aquifer system becomes a two-zone formation including the skin and formation zones. This study presents a mathematical model developed for analyzing a two-zone unconfined aquifer system and the associated solution for CHTs at partially penetrating wells under transient state. The solution of the model may be used either to identify the in situ aquifer parameters or to investigate the effects of the wellbore storage and well skin on the head changes in unconfined aquifers under constant-head pumping. Copyright © 2010 John Wiley & Sons, Ltd.
REFERENCES
- Abdul AS. 1992. A new pumping strategy for petroleum product recovery from contaminated hydrogeologic systems: laboratory and field evaluations. Ground Water Monitoring and Remediation 12: 105–114.
- Abramowitz M, Stegun IA. 1970. Handbook of Mathematical Functions. Dover Publications: New York.
- Akindunni FF, Gillham RW. 1992. Unsaturated and saturated flow in response to pumping of an unconfined aquifer: numerical investigation of delayed drainage. Ground Water 30(6): 873–884.
- Cassiani G, Kabala ZJ, Medina MA Jr. 1999. Flowing partially penetrating well: solution to a mixed-type boundary value problem. Advances in Water Resources 23: 59–68.
- Chang YC, Yeh HD. 2009. New solutions to the constant-head test performed at a partially penetrating well. Journal of Hydrology 369: 90–97. DOI: 10.1016/j.jhydrol.2009.02.016.
- Chen CC, Chang CC. 2003. Well hydraulics theory and data analysis of the constant-head test in an unconfined aquifer with the skin effect. Water Reources Research 39(5): 1121–1135.
- Chen XH, Ayers JF. 1998. Aquifer properties determined from 2 analytical solutions. Ground Water 36(5): 783–791.
- Dagan G. 1967. A method of determining the permeability and effective porosity of unconfined anisotropic aquifer. Water Resources Research 3(4): 1059–1071.
- Hantush MS. 1964. Hydraulics of wells. In Advances in Hydroscience, vol. 1, VT Chow (ed). Academic: San Diego, CA; pp 281–432.
10.1016/B978-1-4831-9932-0.50010-3 Google Scholar
- Hawkins MF Jr. 1956. A note on the skin effect. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers 207: 356–357.
- Hiller CK, Levy BS. 1994. Estimation of aquifer diffusivity from analysis of constant-head pumping test data. Ground Water 32(1): 47–52.
- Jacob CE, Lohman SW. 1952. Nonsteady flow to a well of constant drawdown in an extensive aquifer. Eos, Transactions, American Geophysical Union 33(4): 559–569.
- Jones L, Lemar T, Tsai CT. 1992. Results of two pumping tests in Wisconsin age weathered till in Iowa. Ground Water 30(4): 529–538.
- Jones L. 1993. A comparison of pumping and slug tests for estimating the hydraulic conductivity of unweathered Wisconsin age till in Iowa. Ground Water 31(6): 896–904.
- Markle JM, Rowe RK. 1995. A model for the constant-head pumping test conducted in vertically fractured media. International Journal for Numerical and Analytical Methods in Geomechanics 19: 457–473.
- Mathias SA, Bulter AP. 2006. Linearized Richard's equation approach to pumping test analysis. Water Resources Research 42: W06408. DOI:10.1029/2005WR004608.
- Mishra S, Guyonnet D. 1992. Analysis of observation-well response during constant-head testing. Ground Water 30(4): 523–528.
- Moench AF. 1994. Specific yield as determined by type-curve analysis of aquifer-test data. Ground Water 32(6): 949–957.
- Moench AF. 2004. Importance of the vadose zone in analyses of unconfined aquifer test. Ground Water 42(2): 223–233.
- Moench AF. 2008. Analytical and numerical analyses of an unconfined aquifer test considering unsaturated zone characteristic. Water Resources Research 44: W06409. DOI: 10.1029/2006WR005736.
- Murdoch LD, Franco J. 1994. The analysis of constant drawdown wells using instantaneous source functions. Water Resources Research 30(1): 117–127.
- Narasimhan TN, Zhu M. 1993. Transient flow of water to a well in an unconfined aquifer: applicability of some conceptual models. Water Resources Research 29(1): 179–191.
- Neuman SP. 1972. Theory of flow in unconfined aquifers considering delayed response of the water table. Water Resources Research 8(4): 1031–1045.
- Neuman SP. 1974. Effects of partial penetration on flow in unconfined aquifers considering delayed aquifer response. Water Resources Research 10(2): 303–312.
- Novakowski KS. 1989. A composite analytical model for analysis of pumping tests affected by wellbore storage and finite thickness skin. Water Resources Research. 25(9): 1937–1946.
- Novakowski KS. 1993. Interpretation of the transient flow rate obtained from constant-head tests conducted in situ in clays. Canadian Geotechnical Journal 30: 600–606.
- Nwankwor GI, Gillham RW, van der Kamp G, Akindunni FF. 1992. Unsaturated and saturated flow in response to pumping of an unconfined aquifer: field evidence of delayed drainage. Ground Water 30(5): 690–700.
- Pasandi M, Samani N, Barry DA. 2008. Effect of wellbore storage and finite thickness skin on flow to a partially penetrating well in a phreatic aquifer. Advances in Water Resources 31: 383–398.
- Perina T, Lee TC. 2003. General well function for pumping from a confined, leaky, or unconfined aquifer. Journal of Hydrology 317: 239–260.
- Renard P. 2005. Approximate discharge for constant head test with recharging boundary. Ground Water 43: 439–442.
- Rice JB. 1998. Constant drawdown aquifer tests: an alternative to traditional constant rate tests. Ground Water Monitoring and Remediation 18(2): 76–78.
- Rudd NC, Kabala ZJ. 1997. Response of a partially penetrating well in a heterogeneous aquifer: Integrated well-face vs. uniform well-face flux boundary conditions. Journal of Hydrology 194: 76–94.
- Shanks D. 1955. Non-linear transformations of divergent and slowly convergent sequence. Journal of Mathematics and Physics 34: 1–42.
10.1002/sapm19553411 Google Scholar
- Sneddon IN. 1972. The Use of Integral Transforms. McGraw-Hill: New York; 540 pp.
- Stehfest H. 1970. Numerical inversion of Laplace transforms. Communications of the ACM 13: 47–49.
- Singh SK. 2007. Simple approximation of well function for constant drawdown variable discharge artesian wells. Journal of Irrigation and Drainage Engineering 133(3): 282–285.
- Tartakovsky GD, Neuman SP. 2007. Three-dimensional saturated-unsaturated flow with axial symmetry to a partially penetrating well in a compressible unconfined aquifer. Water Resources Research 43: W01410. DOI: 10.1029/2006WR005153.
- Uraiet AA, Raghavan R. 1980. Unsteady flow to a well producing at a constant pressure. Journal of Petroleum Technology 32(10): 1803–1812.
- van Everdingen AF. 1953. The skin effect and its influence on the productive capacity of wells. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers 198: 171–176.
- Wilkinson WB. 1968. Constant head in situ permeability tests in clay strata. Geotechnique 18(2): 172–194.
- Yang SY. Yeh HD. 2002. Solution for flow rates across the wellbore in a two-zone confined aquifer. Jornal of Hydraulic Engineering ASCE 128(2): 175–183.
- Yang SY, Yeh HD. 2005. Laplace-domain solutions for radial two-zone flow equations under the conditions of constant-head and partially penetrating well. Journal of Hydraulic Engineering ASCE 131(3): 209–216.
- Yang SY, Yeh HD. 2006. A novel analytical solution for constant-head test in a patchy aquifer. International Journal for Numerical and Analytical Methods in Geomechanics 30: 1213–1230.
- Yang SY, Yeh HD, Chiu PY. 2006. A closed form solution for constant flux pumping in a well under partial penetration condition. Water Resources Research 42(5): W05502. DOI: 10.1029/2004WR003889.
- Yeh HD, Yang SY, Peng HY. 2003. A new closed-form solution for a radial two-layer hydraulic head equation for groundwater under constant-flux pumping in a finite-radius well. Advances in Water Research 26(7): 747–757.