Modelling and Measurement of the Effect that Rough Rock Fractures have on Fluid Flow
I have been studying the effect of the roughness of fracture surfaces upon the flow and mechanical properties of rocks since 1997. The research began as a modelling project using supercomputers while I was at the Fluid Research Institute of Tohoku University in Japan. The initial results showed that only flow below a certain characteristic scale were effected by the fractal roughness of the fracture surfaces of a fracture, and this was confirmed using data from a field study at Hachimantai, Japan. The Hachimantai data is important because this site contains a single artificially created fracture (by hydrofracing) which has been intercepted by a second well. The physical characteristics of the fracture were recreated from core that contained the extracted fracture. The flow modelling results were compared with flow tests along the fracture using the two access wells. The work was continued on my arrival in Aberdeen University with the development of numerical and laboratory methods for studying rough rock fractures.
Two fracture surfaces in rocks (a) and (b) (here red granite), can be analysed to provide their surfaces (c) and (d). The method uses a dye thickness approach with a resolution of 15 microns. The two surfaces can be used to calculate the aperture (e). The measurement is done on an optical bench using the OptiProf software (written in-house). Both surfaces and aperture can be analysed for their full fractal physical characteristics using the ParaFrac software (written in-house). Any number of synthetic fractures that have the same physical properties can be calculated using the SynFrac software (written in-house).
This research was aided by many colleagues including Profs. Hayashi, Matsuki, Hashida in Japan, Drs. Ogilvie and Isakov, my post-doctoral researchers in Aberdeen and several others. Since then, the research has progressed significantly.
A screen shot of the SynFrac software using the improved Glover et al. method for creating partially correlated fracture surfaces using the physical parameters shown.
The measured surface of a fracture in pearly granite (left) compared with a synthesised fracture surface with the same physical parameters (right). Note the qualititative similarity even though the surface is obviously quite different.
Recent progress. In the most recent research synthetic fractures of various different scales from 0.2 m to 12.8 m were created using the Glover et al. spectral method. All the synthetic fractures were normalised such that the ratio of the power spectral density of the initial aperture (i.e., the aperture when the surfaces are in contact at a single point) to that of the surface height was the same as that determined for a tensile fracture of 1.0 m size. First, the size effect on the standard deviation of the initial aperture was analyzed for fractures with and without shearing. Next, by taking aperture data at constant intervals to establish a flow area, water flow was simulated for fractures during both normal closure and closure after shearing, by solving Reynolds equation to determine the hydraulic aperture. When the fracture is closed without shearing and has the same mean aperture, the effect of the fracture size on the hydraulic aperture disappears if the fracture is larger than about 0.2 m, since beyond this size the standard deviation of the initial aperture is almost independent of the fracture size. When the fracture is closed after shearing, the hydraulic conductivity shows remarkable anisotropy, which becomes more significant with both shear displacement and closure. However, the relation between the hydraulic aperture normalized by the mean aperture and the mean aperture normalized by the standard deviation of the initial aperture is almost independent of both the fracture size and shear displacement when the shear displacement is less than about 3.1% of the fracture size, at which point the standard deviation of the initial aperture of the sheared fracture is almost independent of the fracture size.
The synthesised fractures can be used in fluid flow modelling in 3D using a supercomputer or in 2D using a desktop computer running FemLab by Comsol Inc. Here the local flow rate is calculated for one section though the 3D model for a range of Reynold's numbers (from top: 0.1, 1, 3, 10, 15).
Full detail can be found in the papers in the bibliography and in the poster here.
Publications
Glover, P.W.J. & K. Hayashi, Modelling fluid flow in rough fractures: Application to the Hachimantai geothermal HDR test site, Phys.Chem.Earth, 22(1-2), 5-11, 1997. [pdf]
Glover, P.W.J., J.B. Gomez, P.G. Meredith, K. Hayashi, P.R. Sammonds & S.A.F. Murrell, Damage of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements: Experimental results, Phys.Chem.Earth, 22(1-2), 57-61, 1997. [pdf]
Glover, P.W.J., K. Matsuki, R. Hikima & K. Hayashi, Fluid flow in fractally rough synthetic fractures, Geophys.Res.Lett., 24(14), 1803-1806, 1997.
Glover, P.W.J., K. Matsuki, R. Hikima & K. Hayashi, Synthetic rough fractures in rocks, J.Geophys.Res., 103(B5), 9609-9620, 1998.
Glover, P.W.J., K. Matsuki, R. Hikima & K. Hayashi, Fluid flow in synthetic rough fractures and application to the Hachimantai geothermal HDR test site, J.Geophys.Res., 103(B5), 9621-9635, 1998. [pdf]
Glover, P.W.J., K. Matsuki, R. Hikima & K. Hayashi, Characterizing rock fractures using synthetic fractal analogues, Geothermal Sci. & Tech., 6, 83-112, 1999.
Ogilvie, S.R., J.M. Orribo & P.W.J. Glover, Novel and Conventional techniques for analyzing the petrophysical properties of deformation bands, Dialog, 8(3), October 2000. [pdf]
Ogilvie, S.R., Isakov, E., Glover, P.W.J. & Taylor, C.W., A New High Resolution Optical Method for Obtaining the Topography of Fracture Surfaces in Rocks, Proceedings of the 8th European Congress for Stereology and Image Analysis, Image Analysis and Stereology, 20 (2) SUPPL. 1, Sept, 386-391, 2001.
Isakov, E., Glover, P.W.J. & Ogilvie, S.R., Use of Synthetic Fractures in the Analysis of Natural Fracture Apertures, Proceedings of the 8th European Congress for Stereology and Image Analysis, Image Analysis and Stereology, 20 (2) SUPPL. 1, Sept, 366-371, 2001.[pdf]
Isakov, E., Ogilvie, S.R., Taylor, C.W. & Glover, P.W.J., Fluid flow through rough fractures in rocks I: High resolution aperture determinations, Earth Planet. Sci. Lett. 191 (3-4), 267-282, 2001. [pdf]
Ogilvie, S.R., Isakov, E., Glover, P.W.J. & Taylor, C.W., Use of Image Analysis and Finite Element Analysis to Characterise Fluid Flow in Rough Rock Fractures and their Synthetic Analogues. Proceedings of the 8th European Congress for Stereology and Image Analysis, Image Analysis and Stereology, 20 (2) SUPPL. 1, Sept, 504-509, 2001. [pdf]
Ogilvie, S.R. & Glover, P.W.J., High Resolution Petrophysical measurements of Deformation Bands in Sandstones, Phys. Chem. Earth, Part A, 26 (1-2), 27-32, 2001.
Ogilvie, S.R. Orribo, J.M. & Glover, P.W.J., The influence of deformation bands upon fluid flow using profile permeametry and positron emission tomography. Geophys. Res. Lett. 28 (1), 61-64, 2001. [pdf]
Ogilvie, S.R. & Glover, P.W.J., The petrophysical properties of deformation bands in relation to their microstructure, Earth Planet. Sci. Lett., 193 (1-2), 129-142, 2001. [pdf]
Ogilvie, S.R., Isakov, E. & Glover, P.W.J., Advances in the Characterization of Rough Fractures in Reservoir Rocks, First Break (Technical article), 20(4), 233-239, 2002.
Ogilvie, S., Isakov, E., Taylor, C. & Glover, P.W.J., A new high resolution optical method for obtaining the topography of fracture surfaces in rocks, Image Anal. Stereol., 21, 61-66, 2002. [pdf]
Ogilvie, S.R., Isakov, E., Taylor, C.W. & Glover, P.W.J., Characterisation of Rough-Walled Fractures in Crystalline Rocks, in Hydrocarbons in Crystalline Rocks, SP214, Eds. Petford N. & McCaffrey K.J.W., Geological Society of London Special Publication, 248 pp., ISBN: 162391378, 2003. 2005
Ogilvie, S.R., Isakov, E. & Glover, P.W.J., Fluid flow through rough fractures. II: A new matching model for rough rock fractures, Earth Planet. Sci. Lett., 241, 454-465, 2006. [pdf]
K. Matsuki, K., Chida, Y., Sakaguchi, K. & Glover, P.W.J., Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures, Int. J. Rock Mech. & Min. Abstr., 43, 726-755, 2006. [pdf]
Presentations
Glover, P.W.J., High Electrical Conductivity in the Earth`s Continental Crust, Symposium of the Assistant Professor`s Society of the University of Tohoku, University of Tohoku, Sendai, Japan, May 1996.
Glover, P.W.J., and K. Hayashi, Modelling fluid flow in rough fractures, 21st General Assembly of the European Geophysical Society, 1996.
Glover, P.W.J., J.B. Gómez, P.G. Meredith, & K. Hayashi, Damage of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements: Experimental results, 21st General Assembly of the European Geophysical Society, 1996.
Glover, P.W.J., K. Matsuki, R. Hikima & K. Hayashi, Synthetic rough fractures in rocks for flow modelling, 23rd General Assembly of the European Geophysical Society, 1998.
Glover, P.W.J., K. Matsuki, R. Hikima & K. Hayashi, Fluid flow in synthetic rough fractures and application to a field scale fracture, 23rd General Assembly of the European Geophysical Society, 1998.
Ogilvie, S.R., Orribo, J.M. & Glover, P.W.J., Experimental observation of fluid flow in single rough fractures using digital imaging and PET scanning, 25th General Assembly of the European Geophysical Society, Nice, France, 25-29th April, 2000.
Ogilvie, S.R., Orribo, J.M. & Glover, P.W.J., Novel and conventional techniques for analysing fracture fabrics, 25th General Assembly of the European Geophysical Society, Nice, France, 25-29th April, 2000.
Isakov, E., Ogilvie, S.R., Taylor, C.W. & Glover, P.W.J., High resolution aperture determination of rough fractures, Geology and Petroleum Geology Departmental Seminar, University of Aberdeen, october 2000.
Glover, P.W.J., 4D Image Analysis of Geomaterials, University of Aberdeen Symposium on Image Analysis Opportunities, University of Aberdeen, UK, 2000.
Glover, P.W.J., Isakov, E. & Ogilvie, S.R., Measurement and modelling of fluid flow through rough fractures in rocks, Annual Industrial Symposium for the Department of Geology and Petroleum Geology, University of Aberdeen, UK, 2000.
Ogilvie, S.R. & Glover, P.W.J., The Influence of deformation bands on fluid flow in reservoirs using high resolution permeability mapping and porosity analysis, "Advances in Reservoir Characterisation: The Key to 21st Century Reservoir Management", Annual Symposium of the Aberdeen Formation Evaluation Society, S.P.W.L.A. Aberdeen Chapter, 2000.
Glover, P.W.J., Ogilvie, S.R., & Taylor, C.W., The scaling behaviour of fluid flow in rock fractures, Geoscience 2000 "Understanding the Micro-to-Macro Behaviour of Rock Fluid Systems", University of Manchester, 20th April, 2000. [pdf]
Ogilvie, S.R., Isakov, E. & Glover, P.W.J., Advances in the Characterisation of Rough Fractures in Hydrocarbon Reservoirs, Annual Symposium of the Aberdeen Formation Evaluation Society "Unlocking Reserves with Unconventional Formation Evaluation Methods", Nov. 28th, 2001.
Glover, P.W.J., Isakov, E., Ogilvie, S.R. & Taylor, C., Fluid Flows Through Rough Fractures in Rocks, International Conference "Stability of Homogenous and Heterogenous Fluid Flows" Novosibirsk, Russia, 2001.
Ogilvie, S.R., Isakov, E., Glover, P.W.J. & Taylor, C.W., Use of Image Analysis and Finite Element Analysis to Characterise Fluid Flow in Rough Rock Fractures and their Synthetic Analogues, 8th European Congress for Stereology & Image Analysis, Bordeaux, France, Sept 4-7th, 2001.
Isakov, E., Glover, P.W.J. & Ogilvie, S.R., Use of Synthetic Fractures in the Analysis of Natural Fracture Apertures, 8th European Congress for Stereology & Image Analysis, Bordeaux, France, Sept 4-7th, 2001.
Ogilvie, S.R., Isakov, E., Glover, P.W.J. & Taylor, C.W., A New High Resolution Optical Method for Obtaining the Topography of Fracture Surfaces in Rocks, 8th European Congress for Stereology & Image Analysis, Bordeaux, France, Sept 4-7th, 2001.
Ogilvie, S.R., Isakov, E. & Glover, P.W.J., Modelling Fluid Flow Through Rough Fractures in Rocks, SPWLA Topical Conference on Well Planning and Formation Evaluation Using 3-D Visualization and Modelling: What is Net Pay?, Bergen, Norway, April 1-4, 2001.
Ogilvie, S.R., Isakov, E., Taylor, C.W. & Glover, P.W.J., High Resolution Aperture Determinations of Rough Fractures in Rocks, 26th General Assembly of the European Geophysical Society, Nice, France, 26-30th March, 2001. [pdf]
Ogilvie, S.R., Isakov, E., Taylor, C.W. & Glover, P.W.J., A New Optical Method for Mapping Surface Roughness of Fractures and Determining Fracture Aperture, 26th General Assembly of the European Geophysical Society, Nice, France, 26-30th March, 2001.
Isakov, E., Glover, P.W.J. & Ogilvie, S.R., Use of synthetic fractures in the analysis of natural fracture apertures, 26th General Assembly of the European Geophysical Society, Nice, France, 26-30th March, 2001. [pdf]
Isakov, E., Glover, P.W.J. & Ogilvie, S.R., Modelling rough fractures in rocks, 26th General Assembly of the European Geophysical Society, Nice, France, 26-30th March, 2001.
Isakov, E., Ogilvie, S.R. & Glover, P.W.J., High-resolution aperture determinations of rough fractures in crystalline rocks, "Hydrocarbons in Crystalline Rocks", Geol. Soc. Lond. Meeting, Burlington House, London, 13-14th Feb., 2001.
Glover, P.W.J., Isakov, E. & Ogilvie, S.R., Fluid flow through rough fractures in crystalline rocks (présentation), Franco-Canadian International Meeting, Québec, Canada, 13-14th June, 2002. [pdf]
Glover, P.W.J., Ogilvie, S.R., Isakov, E. & Taylor, C.W., The scaling behaviour of fluid flow in rock fractures, Micro-to-Macro finale: Understanding the micro-to-macro behaviour of rock-fluid systems, The Geological Society, Burlington House, Piccadilly, London, 4-5 November 2003.
Matsuki, K., Chida, Y., Sakaguchi, K. & Glover, P.W.J., The variation of fracture aperture and permeability during normal closure and shearing and with scale in large synthetic fractures, Poster, EGU 2008, EGU2008-A-11740, 13-18 April 2008. [pdf]
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]
© Copyright, Paul Glover 2008, 2009: Last updated 03/03/2009