Permeability Prediction and the Relationship between Grain Size and Pore Size
One of the greatest challenges to a modern petrophysicist is to understand how the rock microstructure affects the physical properties of rocks. One of the greatest needs for the modern hydrocarbon industry is to be able to preduct the permeability of a given rock in a reliable manner. In a series of recent papers and presentations, we have developed methods for determining the permeability of reservoir rocks from common electrical parameters using a relationship that is based upon the electro-kinetic link, and then extended it to allow a transformation between the mean grain size of a rock and its mean pore throat size. This work has also led to a new interpretation of the cementation exponent, soon to be published in The Leading Edge, and work in progress on a generalised form of Archie's law for n-phases.
Permeability prediction using the RGPZ equation. The equation (see bibliography) is derived from the comparison of fluid and electrical flow in a porous medium. The predicted permeability as a function of porosity, cementation exponent and grain size is shown below, followed by a comparison of the predicted permeability with the measured permeability using the RGPZ equation and the Kozeny-Carmen equation for a range of sedimentary rocks.
Behaviour of the RGPZ model as a function of its major parameters. Predicted permeability as a function of (a) porosity for various values of cementation exponent, (b) porosity for various values of grain size.
Comparison of the measured and predicted permeabilities for 65 samples of sandstones and carbonates shown in Table 1. (a) RGPZ model, (c) Kozeny-Carman model.
The grain size-pore size transformation. The grain size pore size transformation arises from the comparison of two methods for calculating permeability that are based on the electro-kinetic properties of rocks. A comparison of the predicted effective pore radius with that obtained from mercury injection capillary pressure (MICP) measurements is show below (b) followed by the prediction of permeability that is then possible as part (c).
Comparison of the measured and predicted effective pore radii and measured permeability for a range of glass bead packs. (b) Predicted effective pore radius, reff as a function of the geometric mean pore radius from MICP measurements. (c) Predicted permeability using the predicted effective pore radius as a function of the measured Klinkenberg permeability.
A new interpretation of the cementation exponent. In addition we have been working with the conductive form of Archie's law. In 2000 we produced a modification of Archie's law that enables it to be used when the matrix is conductive. For example when the temperature is very high in the deep crust or around geothermal or volcanic areas. I am working on an generalised form of Archie's law for n-phases, but this is mathematically extremely difficult. In the meantime, I am about to publish a reinterpretation of the cementation exponent in terms of the connectedness of the pore space and its rate of change with porosity. This differential interpretation is fully consistent with the classical interpretation and gives further physical insight into the parameter. [pdf]
Bibliography
Glover, P.W.J., Hole, M.J. & Pous, J., A modified Archie's Law for two conducting phases, Earth Planet. Sci. Lett., 180(3-4), 369-383, 2000. [pdf]
Einaudi, F., Pezard, P.A., Iledefonse, B. & Glover, P.W.J., Electrical properties of slow spreading ridge gabbros from ODP Hole 1105A, SW Indian Ridge, in Petrophysical Properties of Crystalline Rocks, eds., P.K. Harvey, T.S. Brewer, P.A. Pezard & V.A. Petrov, Geological Society Special Publication 240, 179-193, 2005.
Glover, P.W.J., Zadjali, I. & Frew, K., Permeability prediction from MICP and NMR data using an electro-kinetic approach, Geophysics, 71, F49, 2006. [pdf]
Glover, P.W.J., What is the cementation exponent? A new interpretation, 2009, The Leading Edge, January 2009, 82-85. [pdf]
Glover, P.W.J. & Walker, E., A grain size to effective pore size transformation derived from an electro-kinetic theory, Geophysics, 74(1), E17-E29, 2009. [pdf]
Presentation
Glover, P.W.J., What is the cementation exponent? A new differential interpretation, Oral, EGU 2009, EGU2009-319, Vienna, 19-24 April 2009. [abstract] [presentation]
Glover, P.W.J., Ogilvie, S.R., Isakov, E., A new method for calculating the mean aperture of fractures in rocks: The dual mean, Poster, EGU 2009, EGU2009-325, Vienna, 19-24 April 2009. [abstract] [poster]
Glover, P.W.J., Measurements, modelling and applications of the electro-kinetic properties of rocks, Oral, Geodetic and Geophysical Research Institute, Hungarian Academy of Sciences, Sopron, Hungary, Invited Lecture as part of the GASTEM Lecture Tour 2009, 27 April 2009. [abstract] [presentation]
Glover, P.W.J., Measurements, modelling and applications of the electro-kinetic properties of rocks, Oral, University of Padua, Italy, Invited Lecture as part of the GASTEM Lecture Tour 2009, 29 April 2009. [abstract] [presentation]
Glover, P.W.J., Measurements, modelling and applications of the electro-kinetic properties of rocks, Oral, ETHZ, Zurich, Switzerland, Invited Lecture as part of the GASTEM Lecture Tour 2009, 12 or 13 May 2009. [abstract] [presentation]
Glover, P.W.J., Measurements, modelling and applications of the electro-kinetic properties of rocks, Oral, University of Strasbourg, France, Invited Lecture as part of the GASTEM Lecture Tour 2009, 11 May 2009. [abstract] [presentation]
Glover, P.W.J., Measurements, modelling and applications of the electro-kinetic properties of rocks, Oral, University of Paris II, France, Invited Lecture as part of the GASTEM Lecture Tour 2009, 19 May 2009. [abstract] [presentation]
Glover, P.W.J., Measurements, modelling and applications of the electro-kinetic properties of rocks, Oral, Imperial College of Science, Technology and Medicine, University of London, UK, Invited Lecture as part of the GASTEM Lecture Tour 2009, June/July 2009. [abstract] [presentation]
Glover, P.W.J., A differential interpretation of the cementation exponent, Oral, 2009 Joint Assembly, GA13, Toronto, 24-27 May 2009. [abstract] [presentation]
Glover, P.W.J. and Walker, E., How are grain size and pore size related? A transformation based on electro-kinetic theory, Poster, 2009 Joint Assembly, GA13, Toronto, 24-27 May 2009. [abstract] [poster]
© Copyright, Paul Glover 2008,2009: Last updated 03/03/2009