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Digital rock physics: 3D imaging of core material and correlations to acoustic and fl ow properties

3D X-ray microtomographic imaging and visualization of core material at the pore scale and subsequent analysis

of petrophysical properties can give important insight to understanding properties of reservoir core material. 3D images allow one to map in detail the pore and grain structure and interconnectivity of core material. Numerical calculations on image data are in agreement with experimental data for fl ow and elastic properties on simple core material. Th is development forms the basis for developing more meaningful structure property correlations in rock.

In this paper we discuss the further development of this emerging technology to complex clastic and carbonate reser-voir core. In particular we describe the coupling of 3D im-aging data to more conventional petrographic analysis; this allows one to incorporate fabric and mineralogy information from thin section studies into 3D data and to probe the pore scale structure in reservoir core in 3D from nanometers to centimeter scales. Results of the analysis allow one to better understand reasons for scatter in elastic and other petrophysi-cal data in terms of rock type, pore structure, texture and in-terconnectivity. Examples for clastic and carbonate reservoir cores are discussed.

BackgroundTh e elastic and fl ow properties of porous sedimentary rocks are determined by the properties and microgeometry of constituents. Complete description of the microgeometry includes information about shapes, sizes, mutual positions, connectivity, etc., of the pore and granular phases. Relevant properties for elastic properties include information on the granular mineral phase composition and micromechanics of the grain contacts. Flow properties are primarily deter-mined by the size, shape and connectivity of the pore phase. Conventional methods for analyzing the pore and grain structure of rock material (e.g., mercury injection, sieving, petrographic thin section) have limitations in quantitatively describing the full 3D granular and porous microstructure. Recent developments in microtomographic imaging coupled with conventional petrographical analysis allow one to di-rectly measure rock fabric and texture, grain contacts and the pore structure of rocks in 3D. Th is ability, coupled with the numerical predictions of elastic and fl ow properties on the resultant digitized images, have shown that a range of petrophysical properties of porous rocks can be derived di-rectly from 3D images (Arns et al., 2005). Th is development allows a new numerical approach to the study of reservoir core which should allow one to better understand the cor-relations between microstructure and the physical properties of porous rocks.

Micro-CT imaging is capable of acquiring 3D images of

MARK A. KNACKSTEDT, SHANE LATHAM, MAHYAR MADADI, ADRIAN SHEPPARD, and TROND VARSLOT, Australian National UniversityCHRISTOPH ARNS, University of New South Wales

the pore structure of sedimentary rock with resolutions down to the micron scale. In Figure 1, we give an example of a slice through a 3D tomographic image of a sandstone sample of 5 mm in diameter. Th e sample was imaged at resolution of 2.8 microns per voxel to produce the resultant image composed of 20483 (> 8 billion) voxels. To illustrate the quality of the 3D image data, thin sections are prepared from within the volume imaged by micro-CT; the thin sections are then im-aged via SEM and optical microscopy. In Figure 1, we give the example of an SEM image of a thin section of the same slice of the tomogram shown in Figure 1 imaged at a scale of

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Figure 1. (a) Slice from tomographic image of a clean sandstone sample. Th is slice is identifi ed from within the 3D image as optimally matching the SEM image of the same rock shown in (b). (c) Shows the phase partitioning of the image in (a) into pore (black), solid grain (white) and clay (grey) regions. (d) Illustrates a colour map with the grain partitioning of the white phase in (c). Th e grain partitioning of the 3D image is visually similar to grain boundaries observed in the thin section in (b). (e) Gives a representation of the topology and geometry of a subset of sandstone pore structure in 3D based on a pore network representation. (f ) Shows the pore and throat size distributions measured directly from the image data.

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(~3500)2 with 1.3 micron pixels. Th e visual match of the SEM image to the tomographic slice is excellent. Th is illustrates the ability of micro-CT to accurately quantify the 3D pore-space structure of reservoir core at the 2–3 micron scale.

From the X-ray image (attenuation map) one can separate the voxels into distinct pore and mineral phases. In Figure 1, we show a slice of the phase separation of the 3D image into grains, clay, and the pore phase. From the phase separated images descriptions of rock fabric and texture and pore scale structure and topology can be made. Textural descriptions, traditionally obtained via 2D petrographic analysis, are di-rectly measured on 3D digital images of core material (Saa-datfar et al., 2006). An example of the grain partitioning of the sandstone sample is given in Figure 1. Visual comparison of the digital grain partitioning to the thin section image is good. Moreover, one can obtain comprehensive grain shape data; over 100 000 grains are directly identifi ed in a typical 3D image and a number of petrological grain descriptors can be obtained (e.g., grain shape, contact areas, grain orienta-tion) in 3D.

Pore network descriptions can also be derived by parti-tioning of the pore space within the tomographic images. Th is partitioning allows one to quantify the complex geomet-rical and topological properties of the pore space; connectiv-ity, shape and sizes of pore bodies and pore interconnections can be derived directly. An example of the 3D pore network for the sandstone sample is illustrated in Figure 1. Th e pore body and pore throat or pore constriction size distribution for over 300,000 pore elements within the 3D image are given in Figure 1.

A number of papers (Adler et al., 1992; Fredrich et al.

1995; Auzerias et al. 1996; Arns et al., 2002, 2005) have illustrated the feasibility of combining digitized images with numerical calculations to predict petrophysical properties of porous rocks. From images of the pore space one can make pre-dictions of permeability, resistivity and drainage capillary pressure. As an example for the sample shown in Figure 1 the permeability derived from the image was 240mD; this data compares favor-ably to the experimentally derived value of 160 mD. From pore and grain phase information (in-cluding mineralogy) acoustic, NMR response and multiphase fl ow properties can also be probed.

Results to date have shown the feasibility of combining digitized images with numerical cal-culations to predict petrophysical properties of homogeneous core material. In this paper we dis-cuss the ongoing challenge to improve predictive capabilities of the method to more complex sam-ples and to extend the methodology to a wider range of properties. We fi rst discuss the use of a digital technique to predict the acoustic response of sandstones; we illustrate the ability to predict the elastic properties of simple (idealized) granu-lar materials and then show the need to integrate the digital rock physics methods with higher

resolution image data and petrographical information to es-timate acoustic properties of reservoir sands. We then discuss the prediction of acoustic response of carbonate samples. Th e heterogeneity of carbonates requires one to probe structure at scales from ten of nanometers to centimeters; methods to do this are described. Th e importance of incorporating pore level details at multiple scales are then illustrated for a set of oomoldic samples.

Acoustic properties of clasticsPrediction of elastic properties of idealized sintered granular

media. We fi rst illustrate the ability to predict elastic prop-erties directly from 3D image data by comparing numerical simulations on images of sintered glass sphere packs. Four images of a lightly sintered monodisperse sphere pack are obtained via microtomography. Th e porosity of the original packs varied from 36–41% (Figure 2). Sintering of this 3D packing of particles is then numerically simulated by growth of the solid phase at the grain/pore interface into the pore. A microstructure defi ned by a digital image is already discretized allowing one to directly perform numerical computation of any number of properties. A fi nite element method (FEM) is used to estimate the elastic properties (Arns et al., 2002). FEM uses a variational formulation of the linear elastic equa-tions and fi nds the solution by minimizing the elastic energy. Each voxel in the digital image is taken to be a trilinear fi nite element. A strain is applied, with the average stress or elastic energy giving the eff ective elastic modulus. Simulations are undertaken on grid sizes of up to (1200)3.

Th e structure of the bead pack is reminiscent of the syn-thetic sandstones described in Berge et al., 1995. Simulations

Figure 2. (a) 3D image of a lightly sintered monodisperse grain pack imaged via microtomography. (b–c) 2D slices of the 3D image with sintering via growth of the solid phase at the grain boundaries (φ =34% and 27% respectively). Th e images are similar to the SEM images of sintered monodisperse glass beads shown in Figure 2 of Berge et al., 1995. Th e comparison of the numerical simulation of (d) bulk (K) and (e) shear (G) modulus of the model sintered glass bead packs to data of Berge et al., 1995. Th e simulation data is in excellent agreement.

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of the elastic properties are undertaken on the image data (Kglass=46.1 GPa, Gglass=29.1 GPa) across a range of porosities with the grains assumed to be perfectly cemented. We com-pare the predictions of the modulus-porosity relationships obtained from the image data and simulation to the Berge et al., 1995 experimental data set in Figure 2. Th e simula-tion results for the bead cementation model are in excellent agreement with experiment across the full range of porosity. Th is illustrates that numerical simulation of elastic proper-ties on image data where the elastic contact modulus is accu-rately estimated leads to a good match to experiment. Elastic simulation data from 3D images of Fontainebleau sandstone (well sorted and well cemented quartz sand) assuming well cemented grains has also previously been shown (Arns et al., 2002) to give reasonable agreement with experimental data.

Prediction of elastic properties of reservoir core. While the assumption of perfect cementation may be appropriate for sintered granular packs and ideal clay free sands, recent stud-ies by Kittridge et al. (2004, 2006) have shown that these idealized data sets are not appropriate geological analogs for many reservoir sandstone samples. Th ese studies, which sum-marize an extensive range of public domain laboratory-based elastic data sets, have shown that real sandstones tend to be much weaker than the idealized media. Th is behavior can be more appropriately modeled by incorporating realistic (weak-er) micromechanical properties at the grain contacts. To in-

corporate direct experimental measurement of grain contact stiff ness remains extremely diffi cult. However, the analysis of 3D image data coupled with detailed petrographical evalua-tion may allow a more robust evaluation of acoustic proper-ties of sandstones. Figure 3 shows an SEM slice of a more complex reservoir sandstone and the registered slice from the 3D tomographic data. Quantitative petrography allows one to incorporate fabric and mineralogical information from thin section; mineralogy, mineralogy of contact points as well as grain size and shape information and location of grain con-tacts are quantifi ed. Geometrical quantities can be directly compared to the grain partitioning of the 3D image data. Th e ability to directly couple 3D image and 2D SEM data will allow one to populate individual grain contacts in the 3D image with appropriate grain contact stiff nesses. Th e inclu-sion of realistic contact mineralogy and frequency can then be used to understand velocity variations in diff erent sands.

To illustrate the role of weaker micromechanical properties at grain contacts we simulate data for the modulus:porosity relationship for a simple Fontainebleau sandstone data assum-ing fi rstly perfect grain cementation and secondly a weaker grain contact stiff ness. Individual grains and grain:grain con-tacts throughout the 3D image are identifi ed (see examples in Figures 1 and 3). In the fi rst case, the perfect cementation model, the contacts are assumed to have the same modulus as the grains. In the second case the grain contacts are assigned a weaker stiff ness than the grains; we assign 60% of the grain modulus at the grain:grain contacts. Th e latter case gives a signifi cantly weaker modulus:porosity relationship; this is consistent with modulus:porosity characteristics for reservoir core (Kittridge et al., 2004).

Acoustic properties of carbonatesTh e heterogeneity of carbonate reservoirs at multiple scales makes it extremely diffi cult to characterize these reservoirs. Th is heterogeneity leads to complicated relations between porosity, acoustic properties and permeability. Anselmetti and Eberli (2003) illustrated that carbonates exhibit poorly defi ned velocity porosity trends with deviations from gen-eral correlation trends as high as 2500 m/s observed. Th e description of the pore and solid phases in carbonate rocks remains challenging; extreme variability in carbonate depo-sitional environments and susceptibility to a range of post-depositional processes results in complex pore and grain structures comprising length scales from tens of nanometers to several centimeters. Combining experimental techniques including micro-computed tomography, backscattered scan-ning electron microscopy (BSEM), and Focussed ion beam SEM (FIBSEM) allows one to directly probe the pore scale structure in carbonates in a continuous range across over six decades of length scales (from nm to cm scales).

Characterization of carbonate structure at multiple scales. In Figure 4 we show an SEM slice of a thin section of a limestone sample (1.25 microns per pixel); the registered tomographic slice is also shown (2.8 microns per voxel). Th e porosity re-solved directly in the images is <50% of the total porosity measured for the sample. Th e images match well, but it is clear

Figure 3. (a) Subsection of an SEM image of reservoir sand; quartz, feldspar, authigenic and detrital clays are evident in the small section. Th e image size shown is 940×768 and the pixel size is 1.25 microns. (b) shows the registered slice from the tomogram with a voxel size of 2.8 microns. Th e grain contacts obtained from the tomographic image are shown by the coloured lines in the image. (c) Illustrates the phase separation of the slice in (b) based on X-ray attenuation information alone for the granular (red), pore (black) and clay (green) phases. Th e mapping of mineralogy, clay distribution and grain contact information from quantitative petrographic studies of the thin section onto the tomographic data will assist in developing more realistic acoustic modeling studies. (d) Gives the bulk modulus: porosity relationship for a simple sandstone data assuming perfect cementation between grains (circles) and a weaker (60% of perfect) grain contact stiff ness (squares).

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from both the tomogram and the SEM that structure exists at length scales below image resolution. Mercury injection data for the core shows that a large fraction of the accessible poros-ity lies at scales below 1 micron. Th e role of the pores at these scales below image resolution cannot be ignored. Electron microscopy enables one to probe regions of the thin section at higher resolutions; from microns down to nanometres. In Figure 4 we show images of a small subset of the thin section imaged at 450x (110 nm per pixel); from mercury injection data this is suffi cient resolution to capture the pore structural parameters for this core. Th e presence of grains and pores at submicron scales are clear. Th e micropore structure measured in these high resolution images can be directly registered into the 3D image data. In Figure 4 we compare the high resolu-tion SEM data to the X-ray attenuation map on the tomo-gram; a direct mapping between the grey scale attenuation in the tomographic image and the amount of microporosity in the SEM image is observed. Based on this correlation one can assign microporosity to the individual voxel attenuation values (Knackstedt et al., 2008). After assignment of the mi-croporosity the image porosity is compared to the experimen-tally measured porosity; the agreement is good. Th is mapping enables one to incorporate submicron scale information from SEM into the 3D image data and to populate the eff ective properties of the 3D tomographic image. Th is incorporation of the microporosity has important implications to the nu-merical prediction of resultant petrophysical properties.

Multiscale modeling of oomoldic carbonates. A preliminary study illustrating the importance of incorporating pore level details of carbonate core across a range of length scales has been undertaken. A set of samples from a large ensemble of oomoldic samples which exhibited a large (>2000 m/s) scat-ter in the experimental velocity-porosity relationship (Baechle et al., 2007) were chosen; half the samples exhibited slower velocities while half were stiff er. Tomographic imaging and analysis was undertaken on the samples to attempt to com-prehend the scatter in the data. Initial data is given here.

In Figure 5, we show slices of two tomographic images; one fast and one slow velocity sample; both samples exhibit φ~20%. A clear visual diff erence in the images can be noted; the fast sample exhibits primarily resolved porosity within the image volume, while the slower sample exhibits a signifi cant proportion of porosity below image resolution. Modelling the acoustic properties of the two samples requires one to as-sign the eff ective elastic properties of the unresolved or mi-croporous regions. To investigate this, images were obtained of these regions via thin section (Figure 5). Th e microporous matrix in the slower sample consists primarily of cemented micrite crystals; a structure not unlike a cemented grain pack. Berge et al., 1995 show that the self consistent (SC) theory gives a good estimation of velocities of well cemented granu-lar media. Voxels in the microporous phase are therefore as-signed an eff ective elastic modulus based on SC theory and the overall elastic response of the two samples simulated. Nu-merical predictions for Vp correlate well with experiment and capture the observed scatter in the data: Fast sample; Vp

sim

=5834 m/s, Vpexp=5710 m/s; slow sample; Vp

sim =4641 m/s,

Figure 4. (a) SEM image of carbonate sample; image size is (~35002) and pixel resolution is 1.3 microns; (b) registered region of corresponding micro-CT 3D image (2.85 micron per voxel). (c) High-resolution 450× magnifi cation or 110 nm per pixel image from SEM of subset of thin section. (d) Registered region of micro-CT image. While microporosity is not directly resolvable via micro-CT, one does observe a strong correlation between porosity in the SEM image and X-ray attenuation in the tomogram image. Based on this one can assign microporosity values to individual voxels within the tomographic image volume.

Figure 5. Slices from tomographic image of (a) fast and (b) slower oomoldic core. Image sizes are 5mm in diameter. One observes in (b) a signifi cant amount of microporous matrix (grey regions). (c) and (d) show optical and SEM thin section data from the slower oomoldic sample. In (c) the resolution is 500 nm in plane, and the image size is 2000×1500. In (d) the resolution is 200 nm, and the image size is 2560×1920.

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Vpexp=4326 m/s. Incorporation of the cemented calcite crystal

microporous regions within the simulation was crucial in ac-curately predicting the elastic properties of the samples.

Correlating acoustic properties to structure. A range of fac-tors directly infl uence the elastic moduli of carbonates. Pore shape and the amount of microporosity have been used to cor-relate elastic moduli of carbonate core (Bächle et al., 2008). 3D imaging studies enable one to directly extract detailed 3D pore scale structure and quantify pore shape parameters di-rectly on pores > 2 micron in size (recall Figure 1). Th e role of micropores can also be integrated into pore scale descriptions in 3D. Th ese analyses, coupled with numerical simulation on 3D image data and experimental data, should improve our understanding of how the eff ective elastic properties of car-bonate rocks is infl uenced by pore structure.

ConclusionsTh e potential to estimate petrophysical properties from digi-tized tomographic images of small samples of reservoir core is an exciting development. Th is development allows for a new numerical approach to the study of reservoir core which should allow one to better understand the correlations be-tween microstructure and the physical properties of porous rocks. Unlike conventional analysis, digital analysis requires only small rock fragments, allowing data to be potentially obtained from side-wall cores, damaged, friable, thinly bed-ded and unconsolidated samples. In this paper we have dis-cussed the development of this technology to modeling the elastic properties of clastic and carbonate reservoir core. Th e coupling of 3D imaging data to more conventional petro-graphic analysis is shown to be crucial to advance the predic-tive nature of this emerging technology.

Suggested reading. “Th e formation factor of reconstructed po-rous media” by Adler et al., (Water Resources Research, 1992).

“Quantitative characterization of carbonate pore systems by digital image analysis”by Anselmetti et al. (AAPG Bulletin, 1998). “Computation of linear elastic properties from microto-mographic images: Methodology and agreement between theory and experiment” by Arns et al. (Geophysics, 2002). “Digital core laboratory: Petrophysical analysis from 3D images” by Arns et al. (Petrophysics, 2005). “Transport in sandstone: A study based on three dimensional microtomography” by Auzerias et al., (Geophysical Research Letters, 1996). “Oomoldic carbonates: pore structure and fl uid eff ects on sonic velocity” by Baechle et al. (SEG 2007 Extended Abstracts). “Eff ects of microporosity on sonic velocity in carbonate rocks” by Bächle et al., (TLE, 2008). “Ultrasonic velocity-porosity relationships for sandstone analogs made from fused glass beads” by Berge et al. (Geophys-ics, 1995). “Imaging the pore structure of geomaterials” by Fre-drich et al., (Science, 1995). “Geologically-consistent rock phys-ics modeling for sandstones: Modulus-based prediction of in situ elastic properties” by Kittridge et al. (EAGE 66th Conference & Exhibition, 2004). “Modulus-domain rock physics diagnostics: New Insights in Realistic granular media” by Kittridge (SEG 2006 Extended Abstracts). “Probing pore systems in carbon-ates: Correlations to petrophysical properties” by Knackstedt et al. (SPWLA 49th Annual Logging Symposium, 2008). “Rock fabric and texture from digital core analysis” by Saadatfar et al. (SPWLA 46th Annual Logging Symposium, 2005).

Acknowledgments: We acknowledge collaborations and discussions with Gregor Bächle, Gregor Eberli, Klaas Verwer, Mark Kittridge, and Lori Hathon on parts of this work. We thank the sponsors of the Digital Core Consortium (ADCO, Baker Hughes, BHP, BP, Chevron, ExxonMobil, JOGMEC, Maersk, Saudi Aramco, Schlumberger, Shell, Total) for their continued support of this research.

Corresponding author: mak110@rsphysse.anu.edu.au