Skip to main content Accessibility help

Quantifying solute spreading and mixing in reservoir rocks using 3-D PET imaging

  • Ronny Pini (a1), Nicholas T. Vandehey (a2), Jennifer Druhan (a3), James P. O’Neil (a2) and Sally M. Benson (a4)...


We report results of an experimental investigation into the effects of small-scale (mm–cm) heterogeneities on solute spreading and mixing in a Berea sandstone core. Pulse-tracer tests have been carried out in the Péclet number regime $Pe=6{-}40$ and are supplemented by a unique combination of two imaging techniques. X-ray computed tomography (CT) is used to quantify subcore-scale heterogeneities in terms of permeability contrasts at a spatial resolution of approximately $10~\text{mm}^{3}$ , while [11C] positron emission tomography (PET) is applied to image the spatial and temporal evolution of the full tracer plume non-invasively. To account for both advective spreading and local (Fickian) mixing as driving mechanisms for solute transport, a streamtube model is applied that is based on the one-dimensional advection–dispersion equation. We refer to our modelling approach as semideterministic, because the spatial arrangement of the streamtubes and the corresponding solute travel times are known from the measured rock’s permeability map, which required only small adjustments to match the measured tracer breakthrough curve. The model reproduces the three-dimensional PET measurements accurately by capturing the larger-scale tracer plume deformation as well as subcore-scale mixing, while confirming negligible transverse dispersion over the scale of the experiment. We suggest that the obtained longitudinal dispersivity ( $0.10\pm 0.02$  cm) is rock rather than sample specific, because of the ability of the model to decouple subcore-scale permeability heterogeneity effects from those of local dispersion. As such, the approach presented here proves to be very valuable, if not necessary, in the context of reservoir core analyses, because rock samples can rarely be regarded as ‘uniformly heterogeneous’.


Corresponding author

Email address for correspondence:


Hide All

Present address: Department of Geology, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA.



Hide All
Baker, L. E. 1977 Effects of dispersion and dead-end pore volume in miscible flooding. SPE J. 17 (3), 219227.
Barry, D. A. & Sposito, G. 1989 Analytical solution of a convection-dispersion model with time-dependent transport coefficients. Water Resour. Res. 25 (12), 24072416.
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.
Benson, D. A., Wheatcraft, S. W. & Meerschaert, M. M. 2000 Application of a fractional advection-dispersion equation. Water Resour. Res. 36 (12), 14031412.
Berkowitz, B., Cortis, A., Dentz, M. & Scher, H. 2006 Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44, RG2003.
Berkowitz, B., Scher, H. & Silliman, S. E. 2000 Anomalous transport in laboratory-scale, heterogeneous porous media. Water Resour. Res. 36 (1), 149158.
Bijeljic, B. & Blunt, M. A. 2006 Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour. Res. 42, W01202.
Bijeljic, B. & Blunt, M. A. 2007 Pore-scale modeling of transverse dispersion in porous media. Water Resour. Res. 43, W12S11.
Bijeljic, B., Mostaghimi, P. & Blunt, M. J. 2011 Signature of non-Fickian solute transport in complex heterogeneous porous media. Phys. Rev. Lett. 107, 204502.
Boutchko, R., Rayz, V. L., Vandehey, N. T., O’Neil, J. P., Budinger, T. F., Nico, P. S., Druhan, J. L., Saloner, D. A., Gullberg, G. T. & Moses, W. W. 2012 Imaging and modeling of flow in porous media using clinical nuclear emission tomography systems and computational fluid dynamics. J. Appl. Geophys. 76, 7481.
Bretz, R. E. & Orr, F. M. Jr 1987 Interpretation of miscible displacements in laboratory cores. SPE Res. Engng 2 (4), 492500.
Brigham, W. E., Reed, P. W. & Dew, J. N. 1961 Experiments on mixing during miscible displacement in porous media. SPE J. 1 (1), 18.
Brooks, R. H. & Corey, A. T. 1964 Hydraulic properties of porous media. Hydrology Paper No. 3, Colorado State University 127.
Charlaix, E. & Gayvallet, H. 1991 Hydrodynamic dispersion in networks of capillaries of random permeability. Europhys. Lett. 16 (3), 259264.
Cirpka, O. A. & Kitanidis, P. K. 2000 An advective–dispersive stream tube approach for the transfer of conservative-tracer data to reactive transport. Water Resour. Res. 36 (5), 12091220.
Coats, K. H. & Smith, B. D. 1964 Dead-end pore volume and dispersion in porous media. SPE J. 4, 7384.
Cortis, A. & Berkowitz, B. 2005 Computing ‘anomalous’ contaminant transport in porous media: the CTRW MATLAB toolbox. Ground Water 43 (6), 947950.
Degueldre, C., Pleinert, H., Maguire, P., Lehman, E., Missimer, J., Hammer, J., Leenders, K., Böck, H. & Townsend, D. 1996 Porosity and pathway determination in crystalline rock by positron emission tomography and neutron radiography. Earth Planet. Sci. Lett. 140 (1), 213225.
Dentz, M., Le Borgne, T., Englert, A. & Bijeljic, B. 2011 Mixing, spreading and reaction in heterogeneous media: a brief review. J. Contam. Hydrol. 120, 117.
Donaldson, E. C., Kendall, R. F. & Manning, F. S. 1976 Dispersion and tortuosity in sandstones. In SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, October 3–6.
Dullien, F. A. L. 1992 Porous Media. Fluid Transport and Pore Structure. Academic.
Fernø, M. A., Gauteplass, J., Hauge, L. P., Abell, G. E., Adamsen, T. C. H. & Graue, A. 2015 Combined positron emission tomography and computed tomography to visualize and quantify fluid flow in sedimentary rocks. Water Resour. Res. 51, 78117819.
Fogler, H. S. 1999 Elements of Chemical Reaction Engineering, 3rd edn. Prentice Hall.
Fourar, M. & Radilla, G. 2009 Non-fickian description of tracer transport through heterogeneous porous media. Trans. Porous Med. 80 (3), 561579.
Ginn, T. R. 2001 Stochastic-convective transport with nonlinear reactions and mixing: finite streamtube ensemble formulation for multicomponent reaction systems with intrastreamtube dispersion. J. Contam. Hydrol. 47, 128.
Ginn, T. R., Simmons, C. S. & Wood, B. D. 1995 Stochastic-convective transport with nonlinear reaction: biodegradation with microbial growth. Wat. Resour. Res. 31 (11), 26892700.
Gist, G. A., Thompson, A. H., Katz, A. J. & Higgins, R. L. 1990 Hydrodynamic dispersion and pore geometry in consolidated rock. Phys. Fluids 2 (9), 15331544.
Gladden, L. F. & Mitchell, J. 2011 Measuring adsorption, diffusion and flow in chemical engineering: applications of magnetic resonance to porous media. New J. Phys. 13, 035001.
Goethals, P., Volkaert, A., Jacobs, P., Roels, S. & Carmeliet, J. 2009 Comparison of positron emission tomography and x-ray radiography for studies of physical processes in sandstone. Engng Geol. 103, 134138.
Grattoni, C. A., Rosen, M. R., Chertcoff, R. & Bidner, M. S. 1987 Use of radioisotopes to measure concentration distributions inside porous media during displacement tests. Chem. Engng Sci. 42 (8), 20552059.
Greiner, A., Schreiber, W., Brix, G. & Kinzelbach, W. 1997 Magnetic resonance imaging of paramagnetic tracers in porous media: quantification of flow and transport parameters. Water Resour. Res. 33 (6), 14611473.
Gründig, M., Richter, M., Seese, A. & Sabri, O. 2007 Tomographic radiotracer studies of the spatial distribution of heterogeneous geochemical transport processes. Appl. Geochem. 22 (11), 23342343.
Guillot, G., Kassab, G., Hulin, J. P. & Rigord, P. 1991 Monitoring of tracer dispersion in porous media by NMR imaging. J. Phys. D: Appl. Phys. 24 (5), 763773.
Haggerty, R., Mckenna, S. A. & Meigs, L. C. 2000 On the late time behavior of tracer test breakthrough curves. Water Resour. Res. 36 (12), 34673479.
Honari, M., Bijeljic, B., Johns, M. L. & May, E. F. 2015 Enhanced gas recovery with CO2 sequestration: the effect of medium heterogeneity on the dispersion of supercritical CO2/CH4 . Intl J. Greenh. Gas Control 39, 3950.
Hulin, J. P. & Plona, T. J. 1989 ‘Echo’ tracer dispersion in porous media. Phys. Fluids 1 (8), 13411347.
Illangasekare, T. H., Frippiat, C. C. & Fucik, R. 2011 Dispersion and mass transfer coefficients in groundwater of near-surface geologic formations. In Chemical Mass Transport in the Environment (ed. Thibodeaux, L. J. & Mackay, D.), chap. 15, 413–452. CRC Press.
Josendal, V. A., Sandiford, B. B. & Wilson, J. W. 1952 Improved multiphase flow studies employing radioactive tracers. Petrol. Trans. AIME 195, 6576.
Khalili, A, Basu, A. J. & Pietrzyk, U. 1998 Flow visualization in porous media via positron emission tomography. Phys. Fluids 10 (4), 10311033.
Kitanidis, P. K. 1994 The concept of the dilution index. Water Resour. Res. 30 (7), 20112026.
Krause, M., Krevor, S. & Benson, S. 2013 A procedure for the accurate determination of sub-core scale permeability distributions with error quantification. Trans. Porous Med. 98 (3), 565588.
Krause, M., Perrin, J.-C. & Benson, S. 2011 Modeling permeability distributions in a sandstone core for history matching coreflood experiments. SPE J. 16 (4), 768777.
Le Borgne, T. L., Dentz, M., Bolster, D., Carrera, J., de Dreuzy, J.-R. & Davy, P. 2010 Non-Fickian mixing: temporal evolution of the scalar dissipation rate in heterogeneous porous media. Adv. Water Resour. 33, 14681475.
Levy, M. & Berkowitz, B. 2003 Masurement and analysis of non-Fickian dispersion in heterogeneous porous media. J. Contam. Hydrol. 64, 203226.
Levin, C. S. & Hoffman, E. J. 1999 Calculation of positron range and its effect on the fundamental limit of positron emission tomography system spatial resolution. Phys. Med. Biol. 44 (3), 781799.
Maguire, R. P., Missimer, J. H., Emert, F., Townsend, D. W., Dollinger, H. & Leenders, K. L. 1997 Positron emission tomography of large rock samples using a multiring pet instrument. IEEE Trans. Nucl. Sci. 44 (1), 2630.
Meyer, D. W. & Tchelepi, H. A. 2010 Particle-based transport model with Markovian velocity processes for tracer dispersion in highly heterogeneous porous media. Water Resour. Res. 46, W11552.
Motulsky, H. J. & Christopoulos, A. 2003 Fitting Models to Biological Data Using Linear and Nonlinear Regression. A Practical Guide to Curve Fitting. Oxford University Press.
Murphy, W. F., Roberts, J. N., Yale, D. & Winkler, K. W. 1984 Centimeter scale heterogeneities and microstratifaction in sedimentary rocks. Geophys. Res. Lett. 11 (8), 697700.
Ogilvie, S. R., Orribo, J. M. & Glover, P. W. J. 2001 The influence of deformation bands upon fluid flow using profile permeametry and positron emission tomography. Geophys. Res. Lett. 28 (1), 6164.
Perkins, T. K. & Johnston, O. C. 1963 A review of diffusion and dispersion in porous media. SPE J. 3 (1), 7084.
Perrin, J.-C. & Benson, S. 2010 An experimental study on the influence of sub-core scale heterogeneities on CO2 distribution in reservoir rocks. Trans. Porous Med. 82 (1), 93109.
Pini, R. & Benson, S. M. 2013a Characterization and scaling of mesoscale heterogeneities in sandstones. Geophys. Res. Lett. 40 (15), 39033908.
Ringrose, P. S., Sorbie, K. S., Corbett, P. W. M. & Jensen, J. L. 1993 Immiscible flow behaviour in laminated and cross-bedded sandstones. J. Petrol. Sci. Engng 9 (2), 103124.
Sahimi, M., Hughes, B. D., Scriven, L. E. & Davis, H. T. 1986 Dispersion in flow through porous media: I. One-phase flow. Chem. Engng Sci. 41 (8), 21032122.
Sarma, D. D. 2009 Geostatistics with Applications in Earth Sciences, 2nd edn. Capital Publishing Company.
Scheidegger, A. E. 1974 The Physics of Flow Through Porous Media, 3rd edn. University of Toronto Press.
Simmons, C. S., Ginn, T. R. & Wood, B. D. 1995 Stochastic-convective transport with nonlinear reaction: mathematical framework. Water Resour. Res. 31 (11), 26752688.
Steefel, C. I. & Maher, K. 2009 Fluid-rock interaction: a reactive transport approach. Rev. Mineral. Geochem. 70 (1), 485532.
Thiele, M. R., Rao, S. E. & Blunt, M. J. 1996 Quantifying uncertainty in reservoir performance using streamtubes. Math. Geol. 28 (7), 843856.
Vandehey, N. T. & O’Neil, J. P. 2014 Capturing [11 C]CO2 for use in aqueous applications. Appl. Radiat. Isot. 90, 7478.
Walsh, M. P. & Withjack, E. M. 1994 On some remarkable observations of laboratory dispersion using computed tomography (CT). J. Can. Petrol. Technol. 33 (9), 3644.
Wellington, S. L. & Vinegar, H. J. 1987 X-ray computerized tomography. J. Petrol. Tech. 39, 885898.
Withjack, E. M. 1988 Computed tomography for rock-property determination and fluid-flow visualization. SPE Formation Eval. 3 (4), 696704.
Yabusaki, S. B., Steefel, C. I. & Wood, B. D. 1998 Multidimensional, multicomponent, subsurface reactive transport in nonunifom velocity fields: code verification using an advective reactive streamtube approach. J. Contam. Hydrol. 30, 299331.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Quantifying solute spreading and mixing in reservoir rocks using 3-D PET imaging

  • Ronny Pini (a1), Nicholas T. Vandehey (a2), Jennifer Druhan (a3), James P. O’Neil (a2) and Sally M. Benson (a4)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed