Parameter Estimation in a Model for Tracer Transport in One-Dimensional Fractals

  • E. C. Herrera-HernándezEmail author
  • M. Coronado
Conference paper
Part of the Environmental Science and Engineering book series (ESE)


The problem of parameter estimation in a model for one-dimensional fractals is analysed and solved. The model describes advection and dispersion of a tracer pulse in a one-dimensional fractal continuum with uniform flow. It involves three parameters: fractal dimension of length, connectivity index associated to dispersion and dispersion coefficient. By using synthetic tracer breakthrough data the effect of data noise level, amount of data points and number of fitting parameters on the results have been analysed. It has been found that the developed estimation methodology is in general robust to the standard data noise level, and to the amount of data points between the typical cases of around 10 and 40. It has been also found that the curve fitting procedure is consistently more sensitive to the fractal dimension of length than to the other two parameters: the connectivity and the dispersion coefficient.


Synthetic Data Dispersion Coefficient Fractal Continuum Connectivity Index Tracer Breakthrough 
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.



This work has been suported by Sener-Conacyt-Hidrocarburos Fund through the project No. 143935. ECHH acknowledges financial support from Conacyt for the postdoctoral fellowship at the Instituto Mexicano del Petróleo and the Cátedra Conacyt at CIDESI.


  1. Balankin AS, Elizarraraz EB (2012) Map of fluid flow in fractal porous medium into fractal continuum flow. Phys Rev E 85:056314CrossRefGoogle Scholar
  2. Bear J (1972) Dynamics of fluid in porous media. Dover Publications, New YorkGoogle Scholar
  3. Bogatkov D, Babadagli T (2010) Fracture network modelling conditioned to pressure transient and tracer test dynamic data. JPSE 75:154CrossRefGoogle Scholar
  4. Chaberneau RJ (2000) Groundwater hydraulics and pollutant transport. Prentice Hall, New JerseyGoogle Scholar
  5. Chakraborty P, Meerschaert MM, Lim CY (2009) Parameter estimation for fractional transport: a particle-tracking approach. Water Resour Res 45:W10415CrossRefGoogle Scholar
  6. Coronado M, Ramírez-Sabag J, Valdiviezo-Mijangos O (2011) Double-porosity model for tracer transport in reservoirs having open conductive geological faults: determination of the fault orientation. JPSE 78:65CrossRefGoogle Scholar
  7. Danckwerts PV (1953) Continuous flow systems: distribution of resident times. Chem Eng Sci 2:3857CrossRefGoogle Scholar
  8. Fourar M, Radilla G (2009) Non-Fickian description of tracer transport through heterogeneous porous media. Transp Porous Media 80:561CrossRefGoogle Scholar
  9. Gefen Y, Aharony A, Alexander S (1983) Anomalous diffusion on percolating clusters. Phys Rev Lett 50:77CrossRefGoogle Scholar
  10. Hernandez-Coronado H, Coronado M, Herrera-Hernández EC (2012) Transport in fractal media: an effective conformal group approach. Phys Rev E 85:066316CrossRefGoogle Scholar
  11. Herrera-Hernández EC, Coronado M, Hernández-Coronado H (2013) Fractal continuum model for tracer transport in a porous medium. Phys Rev E 88:063004CrossRefGoogle Scholar
  12. Illiassov PA, Datta-Gupta A (2002) Field-scale characterization of permeability and saturation distribution using partitioning tracer tests: the ranger field. Texas, SPE, Annual Technical Conference and Exhibition, New Orleans, 71320Google Scholar
  13. Orbach R (1986) Dynamics of fractal networks. Science 231:814CrossRefGoogle Scholar
  14. Ostoja-Starzewski O (2009) Continuum mechanics models of fractal porous media: integral relations and extremum principles. J Mech Mater Struct 4:901CrossRefGoogle Scholar
  15. Ramírez-Sabag J, Valdiviezo-Mijangos, Coronado M (2005) Inter-well tracer test in oil reservoir using different optimization methods: a field case Geofís Int 44Google Scholar
  16. Sahimi M (1993) Fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media. Transp Porous Media 13:3CrossRefGoogle Scholar
  17. Suzuki A, Makita H, Niibori Y, Fomin SA, Chugunov VA, Hashida T (2012) Characterization of tracer response using fractional derivative-based mathematical model and its application to prediction of mass transport in fractured reservoirs. GRC Trans 36:1391Google Scholar
  18. Tarasov VE (2005) Fractional hydrodynamic equations for fractal media. Ann Phys 318:286CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Centro de Ingeniería y Desarrollo IndustrialQuerétaro, Qro.Mexico
  2. 2.Instituto Mexicano del Petróleo (IMP)MéxicoMexico

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