• Development of a New Analytical Solution for Type Curves in Repeated Radial Tracer Tests Under Transient Flow Conditions
  • Heejun Suk1ㆍJize Piao1ㆍHongil Ahn2ㆍMinjune Yang3ㆍWeon Shik Han4*

  • 1Korea Institute of Geoscience and Mineral Resources, Daejeon 34132, Republic of Korea
    2Global Cooperation Center, Universal Environment Policy Institute, Heungandaero 427 gil, Anyang 14059, Republic of Koea
    3Department of Earth and Environmental Sciences, Pukyong National University, 45 Yongso-ro, Nam-gu,
    Busan 48513, South Korea
    4Yonsei University, Departiment of Earth System Science, 50, Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea

  • 부정류 흐름 하에서 반복적인 발산 추적자 시험을 위한 표준 곡선의 새로운 수학적 해석해 개발
  • 석희준1ㆍ박길택1ㆍ안홍일2ㆍ양민준3ㆍ한원식4*

  • 1한국지질자원연구원
    2국제환경정책연구원
    3부경대학교
    4연세대학교

  • This article is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

References
  • 1. Almeida, A.R. and Cotta, R.M., 1995, Integral transform methodology for convection-diffusion problems in petroleum reservoir engineering, Int. J. Heat Mass Transf., 38(18), 3359-3367.
  •  
  • 2. Chen, C.-S., 1987, Analytical solutions for radial dispersion with Cauchy boundary at injection well, Water Resour. Res., 23(7), 1217-1224.
  •  
  • 3. Chen, J.S., Chen, C.S., and Chen, C.Y., 2007, Analysis of solute transport in a divergent flow tracer test with scale-dependent dispersion, Hydrol. Process., 21(18), 2526-2536.
  •  
  • 4. Chen, Y. and Wang, Q., 2021, The effect of boundary conditions on the single-well push-pull test in a partially penetrated well, J. Hydrol., 603, 127035.
  •  
  • 5. Chen, Y., Lu, C., and Luo, J., 2012, Solute transport in divergent radial flow with multistep pumping, Water Resour. Res., 48, W02510.
  •  
  • 6. Chan, Y.K., Mullineux, N., and Reed, J.R., 1976, Analytic solutions for drawdowns in rectangular artesian aquifers, J. Hydrol., 31, 151-160.
  •  
  • 7. Cotta, R.M., 1993, Integral transforms in computational heat and fluid flow, CRC Press, Boca Raton, Fla.
  •  
  • 8. Doughty, C. and Tsang, C.-F., 2009, Analysis of three sets of SWIW tracer test data using a two-population complex fracture model for diffusion and sorption, Rep. LBNL-3006E, Lawrence Berkeley Natl. Lab., Berkeley, Calif.
  •  
  • 9. Field, J.A., Istok, J.D., Schroth, M.H., Sawyer, T.E., and Humphrey, M.D., 1999, Laboratory investigation of surfactant-enhanced trichloroethene solubilization using single-well, ¡°push-pull¡± tests, Groundwater, 37(4), 581-588.
  •  
  • 10. Field, M.S., 2011, Application of robust statistical methods to background tracer data characterized by outliers and left-censored data, Water Res., 45(10), 3107-3118.
  •  
  • 11. Gutierrez, A., Klinka, T., Thiéry, D., Buscarlet, E., and Binet, S., 2011, TRAC, a collaborative computer tool for tracer-test interpretation, 6th International Conference on Tracers and Tracing Methods, hal-00830238, Jun 2011, Oslo, Norway.
  •  
  • 12. Haddad, A.S., Hassanzadeh, H., Chen, Z., and Ware, A., 2015, Characterization of scale-dependent dispersivity in fractured formations through a divergent flow tracer test, Groundw., 53, 149-155.
  •  
  • 13. Hayek, S.I., 2001, Advanced mathematical methods in science and engineering, Marcel Dekker, Inc., N.Y., USA.
  •  
  • 14. Hsieh, P.-F. and Yeh, H.-D., 2014, Semi-analytical and approximate solutions for contaminant transport from an injection well in a two-zone confined aquifer system, J. Hydrol., 519, 1171-1176.
  •  
  • 15. Istok, J.D., Field, J.A., Schroth, M.H., Sawyer, T.E., and Humphrey, M.D., 1999, Laboratory and field investigation of surfactant sorption using single-well, ¡°push-pull¡± tests, Groundwater, 37(4), 589-598.
  •  
  • 16. Kinzelbach, W., 1986, Groundwater modelling, An introduction with sample programs in BASIC, Elsevier, New York, USA.
  •  
  • 17. Lee, J.-Y., Kim, H.-S., Choi, Y.-K., Kim, J.-W., Cheon, J.-Y., and Yi, M.-J., 2007, Sequential tracer tests for determining water seepage paths in a large rockfill dam, Nakdong River basin, Korea, Eng. Geol., 89, 300-315.
  •  
  • 18. Li, X., Wen, Z., Zhan, H., and Zhu, Q., 2019, Skin effect on single-well push-pull tests with the presence of regional groundwater flow, J. Hydrol., 577, 123931.
  •  
  • 19. Li, X., Wen, Z., Zhu, Q., and Jakada, H., 2020, A mobile-immobile model for reactive solute transport in a radial two-zone confined aquifer, J. Hydrol., 580, 124347.
  •  
  • 20. Liu, C., Ball, W.P., and Ellis, J.H., 1998, An analytical solution to one-dimensional solute advection-dispersion equation in multi-layer porous media, Transp. Porous Media, 30, 25-43.
  •  
  • 21. Liu, C., Szecsody, J.E., Zachara, J.M., and Ball, W.P., 2000, Use of the generalized integral transform method for solving equations of solute transport in porous media, Adv. Water Resour., 23(5), 483-492.
  •  
  • 22. Moench, A.F., 1989, Convergent radial dispersion: a Laplace transform solution for aquifer tracer testing, Water Resour. Res., 25(3), 439-447.
  •  
  • 23. Moler, C. and van Loan, C., 1978, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev., 20(4), 801-837.
  •  
  • 24. Morales, T., Angulo, B., Uriarte, J.A., Olazar, M., Arandes, J.M., and Antiguedad, I., 2017, Solute transport characterization in karst aquifers by tracer injection tests for a sustainable water resource management, J. Hydrol., 547, 269-279.
  •  
  • 25. Nocedal, J. and Wright, S.J., 2006, Numerical Optimization, 2nd Edition, Springer.
  •  
  • 26. Pickens, J.F., Jackson, R.E., Inch, K.J., and Merritt, W.F., 1981, Measurement of distribution coefficients using a radial injection dual-tracer test, Water Resour. Res., 17(3), 529-544.
  •  
  • 27. Reimus, P.W. and Arnold, B.W., 2017, Evaluation of multiple tracer methods to estimate low groundwater flow velocities, J. Contam. Hydrol., 199, 1-13.
  •  
  • 28. Samani, N. and Sedghi, M.M., 2015, Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers, Adv. Water Resour., 77, 1-16.
  •  
  • 29. Sauty, J.P., Kinzelbach, W., and Voss, A., 1992, Computer aided tracer test interpretation (CATTI), program documentation, International Ground Water Modeling Center, Golden, Colorado.
  •  
  • 30. Sedghi, M.M. and Zhan, H., 2018, Flow to a well in an unconfined-fractured and leaky wedge-shaped aquifer system, J. Hydrol., 567, 605-625.
  •  
  • 31. Severino, G., De Bartolo, S., Toraldo, G., Srinivasan, G., and Viswanathan, H., 2012, Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations, Water Resour. Res., 48, W12527.
  •  
  • 32. Shi, W., Wang, Q., and Zhan, H., 2020, New simplified models of single‐well push‐pull tests with mixing effect, Water Resour. Res., 56, e2019WR026802.
  •  
  • 33. Shi, W., Wang, Q., Zhan, H., Zhou, R., and Yan, H., 2023, A general model of radial dispersion with wellbore mixing and skin effects, Hydrol. Earth Syst. Sci., 27, 1891-1908.
  •  
  • 34. Suk, H., 2013, Developing semianalytical solutions for multispecies transport coupled with a sequential first-order reaction network under variable flow velocities and dispersion coefficients, Water Resour. Res., 49, 3044-3048.
  •  
  • 35. Suk, H., 2016, Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients, Adv. Water Resour., 94, 412-423.
  •  
  • 36. Suk, H., 2017, Semi-analytical solution of land-derived solute transport under tidal fluctuation in a confined aquifer, J. Hydrol., 554, 517-531.
  •  
  • 37. Suk, H., Chen, J.-S., Han, W.S., and Park, E., 2022, New semi-analytical solutions to the radial advection-dispersion equation for solute transport in a transient divergent radial flow, Adv. Water Resour., 167, 104283.
  •  
  • 38. Toride, N., Leij, F.J., van Genuchten, and M. Th., 1995, The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments, Version 2.0, Research Report No. 137, U.S. Salinity Laboratory, USDA, ARS, Riverside, CA.
  •  
  • 39. Wang, Q., Wang, J., Zhan, H., and Shi, W., 2020, New model of reactive transport in a single-well push-pull test with aquitard effect and wellbore storage, Hydrol. Earth Syst. Sci., 24, 3983-4000.
  •  
  • 40. Wang, C., Huang, C.-S., Tong, C., and Lee, C.-H., 2023, Parameter correlation study on two new analytical solutions for radially divergent tracer tests in two-zone confined aquifers with vertical dispersion effect, Adv. Water Res., 179, 104506.
  •  
  • 41. Welty, C. and Gelhar, L.W., 1994, Evaluation of longitudinal dispersivity from nonuniform flow tracer tests, J. Hydrol., 153, 71-102.
  •  
  • 42. Yeh, H.-D. and Chang, Y.-C., 2006, New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions, Adv. Water Resour., 29(3), 471-480.
  •  
  • 43. Zhang, K., Huang, C.-S., Wang, C., Tong, C., and Wang, Z., 2023, A new analytical method for modeling radially divergent solute transport in two-zone confined aquifers with negative-skin effects, Adv. Earth Sci., 38(4), 429-440.
  •  

This Article

  • 2024; 29(5): 1-13

    Published on Oct 31, 2024

  • 10.7857/JSGE.2024.29.5.001
  • Received on Aug 2, 2024
  • Revised on Aug 12, 2024
  • Accepted on Aug 26, 2024

Correspondence to

  • Weon Shik Han
  • Yonsei University, Departiment of Earth System Science, 50, Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea

  • E-mail: hanw@yonsei.ac.kr