Models for Tracer Test Analysis and Interpretation

  • Vyacheslav G. RumyninEmail author
Part of the Theory and Applications of Transport in Porous Media book series (TATP, volume 25)


A common approach to characterizing aquifer mass transfer properties is the use of tracer tests. Our focus is mostly on tracer tests that employ a forced flow field induced by injection and/or withdrawal wells. Such tests offer advantages for estimating transport properties in porous and fractured media over natural gradient tracer tests (Hydraulic and tracer testing…, 1996). We also will focus on the analysis of models describing the vertical movement of natural saltwater–freshwater interface in thick groundwater systems. The interpretation of the latter process also results in useful information about solute transport properties of systems featuring natural hydrogeochemical stratification. Those models are next modified to account for density difference between the fluids in contact (see Secs. 12.3 and 14.2).


Breakthrough Curve Flow Line Observation Well Injection Well Tracer Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abramowitz M, Stegun I (1970) Handbook of mathematical functions. Dover Publications, Inc, New YorkGoogle Scholar
  2. Alexeev VC, Communar GM, Sherzhukov BS (1989) Mass-transport in saturated rocks. VINITI, Moscow (In Russian)Google Scholar
  3. Bateman H, Erdelyi A (1954) Tables of integral transforms. Vol.1. McGraw-Hill Book Company, IncGoogle Scholar
  4. Becker MW, Charbeneau RJ (2000) First-passage-time functions for groundwater tracer tests conducted in radially convergent flow. J Contam Hydrol 40:299–310CrossRefGoogle Scholar
  5. Bochever FM, Oradovskaya AE (1969) Some problems of liquid waste flow in natural groundwater systems. Reports of the USSR Academy of Sciences. Series Mechanics of Fluid and Gas 6:196–202 (In Russian)Google Scholar
  6. Brouyère S, Carabin G, Dassargues A (2005) Influence of injection conditions on field tracer experiments. Ground Water 43:389–400CrossRefGoogle Scholar
  7. Chapuis RP, Chesnaux R (2006) Travel time to a well pumping an unconfined aquifer without recharge. Ground Water 44: 600–603CrossRefGoogle Scholar
  8. Charbeneau RJ (2000) Groundwater hydraulics and pollutant transport. Prentice Hall, Upper Saddle River, NYGoogle Scholar
  9. Chen C-S (1985) Analytical and approximate solutions to radial dispersion from an injection well to a geological unit with simultaneous diffusion into adjacent strata. Water Resour Res 21:1069–1079CrossRefGoogle Scholar
  10. Chen J-S, Liu C-W, Chen C-S et al (1996) A Laplace transformation solution for tracer tests in a radially convergent flow field with upstream dispersion. J Hydrol 183:263–275CrossRefGoogle Scholar
  11. Chen J-S, Liu C-W, Chen C-S et al (2002) A novel analytical power series solution for solute transport in a radially convergent flow field. J Hydrol 266:120–138CrossRefGoogle Scholar
  12. Chen J-S, Liu C-W, Liao C-M (2003) Two-dimensional Laplace-transformed power series solution for solute transport in radially convergent flow field. Adv Water Resour 26:1113–1124CrossRefGoogle Scholar
  13. Chen J-S, Chen C-S, Chen CY (2007) Analysis of solute transport in a divergent flow tracer test with scale-dependent dispersion. Hydrol Processes 21:2526–2536CrossRefGoogle Scholar
  14. Chen J-S, Ni C-F, Liang C-L (2008) Analytical power series solutions to the two-dimensional advection-dispersion equation with distance-dependent dispersivities. Hydrol Processes 22:4670–4678CrossRefGoogle Scholar
  15. Chen J-S, Jang C-S, Cheng C-T et al (2010) Conservative solute approximation to the transport of a remedial reagent1 in a vertical circulation flow field. J Hydrol 390:155–168CrossRefGoogle Scholar
  16. Communar GM (2000) Unsteady flow to wells partially penetrating in two-layered aquifer. Transp Porous Media 39:367–383CrossRefGoogle Scholar
  17. Communar GM, Sherzhukov BS, Muratova LN (1986) Advective dispersion and mass-exchenge in a radial flow. In: Forecast of submerging and protective measures. VODGEO, Moscow (In Russian)Google Scholar
  18. Dagan G (1971) Perturbation solution of the dispersion equation in porous medium. Water Resour Res 7:135–142CrossRefGoogle Scholar
  19. Gelhar LW, Collins MA (1971) General analysis of longitudinal dispersion in nonuniform flow. Water Resour Res 7:1511–1521CrossRefGoogle Scholar
  20. Goldberg VM (1976) Groudwater quality forecasting at wellfields. Nedra, Moscow (In Russian)Google Scholar
  21. Grove DB, Beetem WA (1971) Porosity and dispersion constant calculations for a fractured carbonate aquifer using the two well tracer method. Water Resour Res 7:128–134CrossRefGoogle Scholar
  22. Hoopes JA, Harleman DRF (1967a) Dispersion in radial flow from a recharging well. J Geophys Res 72:3595–3607CrossRefGoogle Scholar
  23. Hoopes JA, Harleman DRF (1967b) Wastewater recharge and dispersion in porous media. J Hydraul Div 93(HY5):51–71Google Scholar
  24. Hsieh PA (1986) A new formula for the analytical solution of the radial dispersion problem. Water Resour Res 22:1597–1605CrossRefGoogle Scholar
  25. Hydraulic and tracer testing of fractured rock (1996) Rock Fractures and Fluid Flow. Contemporary Understanding and Applications. Committee on Fracture Characterization and Fluid Flow. National Academy Press. Washington, D.C.Google Scholar
  26. Indelman P, Dagan G (1999) Solute transport in divergent radial flow through heterogeneous porous media. J of Fluid Mechan 384:159–182.CrossRefGoogle Scholar
  27. Kabala ZJ (1993) The dipole flow test: a new single-borehole test for aquifer characterization. Water Resour Res 29:99–107CrossRefGoogle Scholar
  28. Kamke E (1977) Differentialgleichungen: Losungsmethoden und Losungen, I, Gewohnliche Differentialgleichungen, B.G. Teubner, LeipzigCrossRefGoogle Scholar
  29. Kisel VA, Abramov YS (1978) Exploitation of oil well-fields with bottom water. Nedra, Moscow (In Russian)Google Scholar
  30. Kocabas I, Islam MR (2000) Concentration and temperature transients in heterogeneous porous media. Part II: Radial transport. J Pet Sci Engin 26:221–233CrossRefGoogle Scholar
  31. Konosavsky PK, Mironenko VA, Rumynin VG (1993) Development of models for tracer tests in aquifers. Geoecology 3:104–124 (In Russian)Google Scholar
  32. Kreft A, Lenda A, Turek B et al (1974) Determination of effective porosities by the two-well pulse method. In: Isotope techniques in groundwater hydrology. International Atomic Energy Agency, Vienna, pp 295–312Google Scholar
  33. Kwok W, Hayes RE, Nasr-El-Din HA (1995) Dispersion in consolidated sandstone with radial flow. Transp Porous Media 19:37–66CrossRefGoogle Scholar
  34. Leij FJ, Torido N (1995) Discrete time- and length-average solutions of the advection-dispersion equation. Water Resour Res 31:1713–1724.CrossRefGoogle Scholar
  35. Maloszewski P, Zuber A (1990) Mathematical modeling of tracer behavior in short-term experiments in fractured rocks. Water Resour Res 26:1517–1528CrossRefGoogle Scholar
  36. McKnight D, Smalley AL, Banwart SA et al (2004) Development of a novel in situ aquifer assessment tool, the dipole flow and reactive tracer test. In: Young RN, Thomas HR (eds) Geoenvironmental engineering: integrated management of groundwater and contaminated land. Thomas Telford Ltd, Stratford-upon-Avon (UK)Google Scholar
  37. Mironenko VA, Rumynin VG (1979) Groundwater sampling during the study of mass transport in the subsurface environment. Prospecting and Protection of the Earth Interior 5:36–45 (In Russian)Google Scholar
  38. Mironenko VA, Rumynin VG (1986) Tracer tests in aquifers. Nedra, MoscowGoogle Scholar
  39. Mironenko VA, Rumynin VG (1998 a) Problems of environmental hydrogeology. Vol. 1: Theoretical analysis amd modeling of solute transport processes. MMSA, Moscow (In Russian)Google Scholar
  40. Mironenko VA, Rumynin VG (1998 b) Problems of environmental hydrogeology. Vol. 2: Experimental Studies. MMGA, Moscow (In Russian)Google Scholar
  41. Moench AF (1989) Convergent radial dispersion: A Laplace transform solution for aquifer tracer testing. Water Resour Res 25:439–447CrossRefGoogle Scholar
  42. Moench AF (1991) Convergent radial dispersion: a note on evaluation of the Laplace transform solution. Water Resour Res 27:3261–3264CrossRefGoogle Scholar
  43. Moench AF (1995) Convergent radial dispersion in a double-porosity aquifer with fracture skin: Analytical solution and application to a field experiment in fractured chalk. Water Resour Res 31:1823–1835CrossRefGoogle Scholar
  44. Moench AF, Ogata A (1981) A numerical inversion of the Laplace transform solution to radial dispersion in a porous medium. Water Resour Res 17:250–252CrossRefGoogle Scholar
  45. Novakowski KS (1992) Analysis of tracer experiments conducted in divergent radial flow fields. Water Resour Res 28:3215–3225CrossRefGoogle Scholar
  46. Novakowski KS, Lapcevic PA (1994) Field measurement of radial solute transport in fractured rock. Water Resour Res 30:37–44CrossRefGoogle Scholar
  47. Novakowski KS, Evans G, Lever DA (1985) A field example of measuring hydrodynamic dispersion in a single fracture. Water Resour Res 21:1165–1174CrossRefGoogle Scholar
  48. Ogata A (1970) Theory of dispersion in a granular medium. Fluid movement in Earth materials. US GS Professional Paper, N 411-I, Washington, DCGoogle Scholar
  49. Raimondi P, Gardner GHG, Petrick CB (1959) Effect of pore structure and molecular diffusion on the mixing of miscible liquids flowing in porous media. Amer. Inst. Chem. Eng. Society of petroleum Eng. Confer., Preprint 43Google Scholar
  50. Reimus P, Pohll G, Mihevc T (2003) Testing and parameterizing a conceptual model for solute transport in fractured granite using multiple tracers in a forced-gradient test. Water Resour Res. doi:1029/2002WR001597Google Scholar
  51. Roshal AA (1981) Field methods for assessment of migration properties of aquifers. In: Hydrogeology and Engineering Geology. VIEMS, Moscow (In Russian)Google Scholar
  52. Rumynin VG (1981) Study of mass transfer in fractured-porous reservoirs. PhD Thesis. Leningrad Mining Institute (In Russian)Google Scholar
  53. Rumynin VG, Mironenko VA (1996) Development of theoretical and technical basis for tracer tests in aquifer. In: Aral MM (ad) Advances in Groundwater Pollution Control and Remediation. NATO ASI Series, Kluwer Academic Publ, pp 173–199Google Scholar
  54. Sauty JP (1978) Identification des parametres du transport hidrodispersif dans les aquiferes par interpretation de tracages en ecoulement cylindriqoe convergent on divergent. J Hydrol 49:69–103CrossRefGoogle Scholar
  55. Sauty J-P (1980) An analysis of hydrodispersive transfer in aquifer.Water Resour Res 16:145–158Google Scholar
  56. Shestakov VM (1963) On theory of solution migration in soils. In: Problems of groundwater quality formation. VODGEO, Moscow (In Russian)Google Scholar
  57. Shestakov VM (1995) Hydrogeodynamics. MGU, Moscow (In Russian)Google Scholar
  58. Sutton DJ, Kabala ZJ, Schaad DE et al (2000) The dipole-flow test with a tracer: a new single-borehole tracer test for aquifer characterization. J Contam Hydrol 44:71–101CrossRefGoogle Scholar
  59. Tang DH, Babu DK (1979) Analytical solution of a velocity dependent dispersion problem. Water Resour Res 15:1471–1478CrossRefGoogle Scholar
  60. Veling Ed JM (2001) Analytical solution and numerical evaluation of the radial symmetric convection – diffusion equation with arbitary initial and boundary data. In: Gehrels H, Peters NE, Hoehn E (ed) Impact of Human Activity on Ground Water Dynamics. Proceedings of a symposium held during the Sixth IAHS Scientific Assembly at Maastricht. IAHS Publ. 269:271–276Google Scholar
  61. Wang HQ, Crampon N (1995) Method for interpreting tracer experiments in radial flow using modified analytical solutions. J Hydrol 165:11–31CrossRefGoogle Scholar
  62. Welty C, Gelhar LW (1994) Evaluation of longitudinal dispersivity from nonuniform flow tracer tests. J Hydrol 153:71–102CrossRefGoogle Scholar
  63. Zhou Q, Liu H-H, Molz FJ et al (2007) Field-scale effective matrix diffusion coefficient for fractured rock: Results from literature survey. J Contam Hydrol 93:161–187CrossRefGoogle Scholar
  64. Zlotnik VA, Ledder G (1996) Theory of dipol flow in uniform anisotropic aquifers. Water Resour Res 32:1119–1128CrossRefGoogle Scholar
  65. Zlotnik VA, Logan JD (1996) Boundary conditions for convergent radial tracer tests and effect of well bore mixing volume. Water Resour Res 32:2323–2328CrossRefGoogle Scholar
  66. Zuber A (1974) Theoretical possibilities of the two-well pulse method. Isotope Techniques in Groundwater Hydrology. In: International Atomic Energy Agency. Vienna, pp 277–294Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Geological DepartmentThe Russian Academy of Sciences Institute of Environmental Geology Saint Petersburg Division Saint Petersburg State UniversitySt. PetersburgRussian Federation

Personalised recommendations