Mapping fluid distributions in 3D at the pore scale: Quantifying the influence of wettability and saturation history on rock resistivity

Mapping fluid distributions in 3D at the pore scale: Quantifying the influence of wettability and saturation history on rock resistivity Munish Kumar 1, Rob Sok 1, Mark A. Knackstedt 1, Shane Latham 1, Tim J. Senden 1, Adrian P. Sheppard 1, Trond Varslot 1, Christoph Arns 2 1 Applied Mathematics, Australian National University, Canberra, Australia 2 School of Petroleum Engineering, University of New South Wales, Sydney, Australia Copyright 2009, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 50 th Annual Logging Symposium held in The Woodlands, Texas, United States, June 21-24, 2009. ABSTRACT Complexities in pore scale structure, rock-fluid and fluid-fluid interactions have a profound effect on the estimation of reserves, reservoir recovery and productivity in reservoir core material. These complexities determine the pore scale distribution of fluids within the pore space, which, in turn, determine the petrophysical response of the rock. A very important example is the estimation of water saturation via resistivity measurements. Default saturation exponents (n=2) are often used in estimating saturations despite numerous measurements which have shown that n can depend strongly on the rock type, mineralogy, saturation history and wettability. Non- Archie behavior is reported frequently. Experimental laboratory results for the resistivity response of clastic and carbonate reservoir cores under varying wettability states have exhibited a range of saturation exponents; 1<n<6. Understanding the resistivity response of reservoir cores requires an ability to accurately map the pore scale structure and the fluid distributions in 3D within core material under variable wettability states and based on different saturation history. We use an image registration technique which allows voxel perfect overlays of 3D tomographic images of the same core sample at varying saturation states. The method allows one to explicitly visualize the experimental two-phase fluid distributions within reservoir core material at the pore scale. The ability to perform multiple experiments on the same core and to accurately compare their fluid distributions at the pore scale allows one to probe the (potentially competing) roles of complex rock structure, rock type, wettability and saturation history on the resistivity response. Reasons for non-archie behavior can be explained from the direct visualization of pore scale fluid distributions. This understanding can lead to 1 more accurate predictions of in-situ fluid saturations within reservoir core. The technique can also be applied to the prediction of other petrophysical and multiphase flow properties (e.g., recoveries, relative permeability). INTRODUCTION One of the most widely used techniques to evaluate hydrocarbon saturation in a petroleum reservoir is based on electrical logging. Standard methods in clay free reservoirs are based on the Archie saturation equation: RI = R t /R 0 =S w -n where RI is the resistivity index, R t is the resistivity of the sample at brine saturation S w and R 0 is the resistivity of the sample at 100% saturation. n, the Archie saturation exponent, is an empirical parameter which is best determined by experimental core analysis. One problem in petrophysics is how to carry out a meaningful evaluation of saturation when core analysis data is unavailable or is insufficient to ground truth the interpretation satisfactorily. Saturation exponent measurements are very time consuming, expensive and vulnerable to many factors. Default estimations of the saturation exponents (n=2) are often used despite numerous measurements which have shown that n can depend strongly on the rock type, pore morphology, mineralogy and wettability. A second problem is that the most common technique for measuring the saturation exponent is based on measurements of cleaned cores, often with air as the non-wetting phase and brine as the conducting phase. This air/brine system is only representative of drainage under strongly water wet conditions. Reservoir condition live-oil displacing brine may be a more acceptable (but expensive) standard as it most closely mimics conditions during original hydrocarbon charge; however issues whether to use native or restored state core lead to experimental variation in estimation of the saturation exponent on the same core material [Marzouk et al., 1995].

During production, when oil is displaced during waterflooding, a number of different distributions of fluid will exist at the pore scale due to hysteresis controlled by flooding rate, initial water saturation, pore structure, wettability and mineralogy. Wettability, a term describing which fluid amongst two or more immiscible fluids has a tendency to adhere to the mineral surface, is particularly important because the surface properties of the rock determine the ultimate fluid distribution in the pore space. Therefore electrical response, oil displacement and oil recovery are all affected by the wettability of the rock. Understanding the complex resistivity behaviour in reservoir core material requires an ability to map the pore structure and connectivity in three dimensions coupled with an accurate description of the fluid distributions in the pore space under varying production scenarios. 3D imaging and visualisation of core material at the pore scale and subsequent analysis of petrophysical properties, has given important insight to understanding properties of reservoir core material [Arns et al., 2005]. The methodology is schematically illustrated in Fig. 1. To date, this technology has focused on the description of the complex structure of different rock types [Knackstedt et al., 2008] and prediction of single phase and simple drainage properties compared with conventional core analysis. Results show that predictions of petrophysical properties from 3D image data (permeability tensor, formation factor and MICP drainage capillary pressure) are in good agreement with experimental core measurements. The use of 3D descriptions of pore structure to understand the more complex saturation-based resistive properties of reservoir core has also been undertaken recently. These studies [Toumelin and Torres-Verdin, 2005, Man and Jing, 2001] have focused on the use of realistic pore geometry and physically based descriptions of pore fluid configurations under varying wettability scenarios. These studies have illustrated the importance wettability, saturation history and pore structure can play on the resistivity response. However it remains unclear to what extent these 3D models are predictive for the multiphase flow properties of varying rock types. Comparative test studies [Caubit et al., 2008; Cense & Marcelis, 2008] of different 3D pore scale modeling methods have indicated that multiphase flow properties (resistivity, ultimate recoveries and relative permeability predictions) may be captured on more homogeneous samples for simple wettability conditions, but modeling techniques in 3D could not be considered as an accurate tool on the broad range of rocks and fluid saturation conditions encountered in the oil and gas industry. 2 Fig. 1 Illustration of digital core technology method. (Upper) X-ray microtomography is used to image core material in three dimensions. Lower left: The resultant 3D images are then used to calculate a range of petrophysical properties. The lower right image illustrates the porosity:permeability predictions from a homogeneous sandstone. Understanding the complex resistivity response of reservoir core under variable wetting and saturation conditions requires an ability to map both the complex pore structure of reservoir core in 3D and an ability to visualize the fluid distributions within these complex pore spaces under different experimental conditions. We illustrate this capability in this paper. We have recently developed 3D image registration techniques [Latham et al., 2008] which allow changes in individual pore occupancies to be imaged with changes in global fluid saturations and with changed wettability conditions. Alignment of images is undertaken regardless of the elapsed time or the nature of the intervening experiment. This provides a foundation for quantitative comparison of the pore scale distribution of fluids in core material and provides direct pore scale insight into complex experimental resistivity responses in reservoir core. The role of wettability and displacement rate on multiphase flow properties can now be studied using image registration to visualise pore-scale fluid distributions during saturation/desaturation experiments on the same core for any wettability state, displacement rate and oil/gas/brine system. In this paper the role of a subset of these parameters on the pore scale displacements and distributions of residual phases is directly visualized and quantified for drainage and imbibition displacements in clastic and carbonate cores. We subsequently use the results of this direct imaging of

the pore structure and fluid distributions within the core at the pore scale to study the complex resistivity response of reservoir core material. We first consider drainage displacements into clastic and carbonate core samples. We show that drainage displacements under strongly water wet conditions can be modeled accurately using pore scale techniques on image data. Results from experimental data and numerical analysis of a range of rocks show agreement. Correlation between rock type and resistivity response may therefore be possible with development of a comprehensive database of 3D pore scale structure. Studies of waterflooding are more complex. For example the pore scale distribution of the brine phase after waterflooding on core material is seen to be strongly dependent on wettability and initial water saturation. This study shows that the pore scale distribution of the trapped phase after waterflooding by spontaneous imbibition is reminiscent of a percolationbased model. Saturation exponents derived from image data for mixed wet samples exhibit significant hysteresis, variable values of n with S w and a range of values of 2<n<5. METHODS This section describes the analysis of air-water drainage and imbibition displacement experiments on cores. The cores were generally 5-6 mm in diameter and 15-20 mm in length. 3D Imaging 3D images of the cores in dry and a range of partially saturated states were obtained using the ANU micro-ct facility (see Fig. 1) at voxel sizes down to ~3 microns [Sakellariou et al., 2004]. Images were taken from the central 6 mm region of the core (away from the ends of the core to minimize end effects). All images were composed of 2048 3 voxels. Core preparation The preparation of cores to different saturation states is described below. The preparation of a drained core is based on cleaning to a water wet state followed by primary drainage with either oil or air. The specifics of the procedure follow: 1. Clean core using water plasma [Kumar et al., 2008]; 2. Heat shrink the core with a short carbon fibre tube at one end. 3. Overnight in vacuum oven at 60 / 85 o ± C. 4. Plasma clean core once more for 15 minutes. 5. Saturate under vacuum with CsI-water (0.25M for gas-water and 0.5M for oil-water). CsI is used to give better differentiation of the water phase within the core. 6. Centrifuge in air/oil to desired water saturation. 3 7. Seal off and allow core to equilibrate for 12-24 hrs. 8. Image on μ-ct facility. Waterflooding of cores via spontaneous imbibition was undertaken via the following procedure: 1. The drained sample was brought into hydraulic contact with a brine reservoir. 2. Spontaneous imbibition was carried out in a high humidity environment by suspending a sample from a balance. The water saturation is measured by the change in the mass of the sample. The imbibition was carried out until capillary intrusion ceased. 3. Seal off and image core on μ-ct facility. Waterflooding of cores via forced imbibition was undertaken via the following procedure: 1. The waterflooded sample is attached to a motor controlled syringe. The motor provides a constant driving force to drive brine into the sample. 2. ~7 pore volumes of brine, at different rates, is injected through the system. 3. Seal off and image core on μ-ct facility Spatial Identification of fluid phases in 3D A new image registration technique (Latham et al, 2008) has made it possible to superpose, at voxel resolution, images of the same core images at different saturation states. Alignment of images is undertaken regardless of the elapsed time or the nature of the intervening experiment. This allows direct imaging of the fluid distribution in the pore-spaces of the same core in 3D under a range of wettability and saturation states. Results of this method are illustrated in Fig. 2. The total 3D image volume is (2000) 3 voxels. Fig. 2 (a) shows on the left a (2000 x 2000) pixel slice through the 3D image of a clean sandstone in a dry state and on the right the same core after undertaking a spontaneous imbibition experiment under strongly water-wet conditions. Figs. 2(b) illustrates the pore structure of a small subset (500 x 500 x 60 voxels) in 3D and Fig. 2(c) shows the spatial distribution of the water and gas phase after imbibition. The non-wetting gas phase is seen to be trapped in the larger pores and displaced from many of the smaller pores/throats. Computational Methods We use a finite-element method (FEM) to estimate the electrical conductivity of the image data. FEM uses a variational formulation of the linear conductivity equations and solves Laplace equation by minimizing the energy using a fast conjugate-gradient method. Each voxel is taken to be a trilinear finite element. Nonperiodic boundary conditions are used and calculations carried out for voltage gradients applied along each of the major tomogram axes, giving three principal conductivities defined by the tomogram axes. The

parallel solver scales linearly to system sizes well above 1000 3 voxels (tested for 256 processors). For the resistivity calculations we assign zero conductivity (σ=0) to the solid and non-wetting phases and σ =1 to the wetting phase. (a) (b) (c) Fig. 2 Example of image registration of a Fontainebleau sandstone sample in a dry state and then after undertaking waterflooding by spontaneous imbibition. (a) shows 2 registered 2D slices (5mm x 5mm) from the 3D volume; left in the dry state and right after waterflooding. (b) and (c) show a registered subvolume of size (1.2mm x 1.2mm x 0.15 mm) in a dry state (c) and after waterflooding. The water phase and trapped non-wetting phase are clearly identified. RESULTS Mapping fluid distributions in 3D We first consider drainage displacements into clastic and carbonate core samples. We show that drainage displacements under strongly water wet conditions can be modeled accurately using pore scale techniques on image data. We start with the description of drainage into two simple cores; a set of sucrosic dolomite samples and a Fontainebleau sandstone core. We then consider drainage displacements in more complex carbonate cores including an oomoldic sample and a reservoir carbonate. We then discuss waterflooding (imbibition) into core material. Drainage Displacements into homogenous core In the first section of the results we will map the residual wetting phase saturation in homogeneous clastic and carbonate cores after drainage displacements. We will test for the robustness of the imaging technique including repeatability of the experimental data on the same core. This data also enables us to test for the predictivity of drainage simulation methods which have previously been undertaken on realistic 3D images [Hilpert & Miller, 2001, Toumelin & Torres-Verdin, 2005] for the regime where capillary forces control fluid motion and spatial distribution. Air:water drainage into Sucrosic Dolomite Core: The first sample considered was a sucrosic dolomite drained with air to an equivalent capillary radius of 18 and 9 microns (high and low S w ). Details of the plug from which the two samples were obtained and of measurements on the two subsamples are given in Table 1. Sample φ k (md) Plug 20% 870 φ image S w exp S w image Subsample A 21.5 86 88 Subsample B 21.5 32 23 Table 1 Information on the plug and two subsamples. Upper row is plug data. Last two rows gives wetting phase saturation data based on experimental (S exp w ) and image data (S image w ) of subsample A and B. The imaged pore-scale air-water distributions for the sucrosic dolomite cores at high and low water saturations are shown in Fig. 3. The core was first imaged dry and an equivalent pore network extracted from the imaged data. The network contained more than 50,000 pores and 120,000 throats. Information on the spatial distributions of pore body and throat sizes, aspect ratios and coordination numbers were obtained 4

from the networks. Images after drainage experiments were then obtained (Fig. 3(b,c)). Water saturations in individual pores and throats are determined by overlaying dry and partially saturated 3D images with voxel perfect registration. Fig 3(d) shows the distribution of the gas phase as a function of pore size on the resultant image at low S w. As expected the data shows a strong correlation between pore size and wetting phase saturation. The intermediate to large pores have low water saturations with the higher water saturations concentrated in the smallest pores. same slice for the two experiments. The distribution is spatially similar; both the global P c :S response and the local pore scale distribution of the wetting/non wetting fluids is repeatable at this scale. The remaining water saturations for the two experiments are summarized in Table 2. Fig. 4 Two experiments of oil-drainage into samples at an equivalent capillary radius of 9.5 μm. The pore scale distribution of the irreducible water phase is similar in both cases. (a) (b) (c) (d) Fig. 3 Slices of 3D micro-ct images: (a) dry sample; (b) registered slice of flooded sample at S w =88% (c) registered flooded sample at S w =23%. In (b) and (c) the water filled pores are now light grey while the air filled pores remain black. (d) shows the distribution of the wetting phase saturation in individual pores for the S w =23% sample. The blue points give a scatter plot of the local saturation within the pores and the red line gives a running average of the relationship between pore size and S w. Repeatability of Experiment - Oil:water drainage into Sucrosic Dolomite Core: Given the small sample size a concern is whether the water saturation observed in 3D can be duplicated across multiple experiments. To test this we undertake the same experiment twice on the same sample. A sample is first dried, rendered water wet, saturated with water and then oil drained in a centrifuge to an equivalent capillary radius of 9.5 microns. The sample is then oven dried and the experiment repeated. Fig. 4 shows that the pore-scale distribution of the remaining water saturation in the 5 Sample φ image exp S w image S w Subsample C 15.4 32 28 Subsample D 15.4 31 25 Table 2 Experimental (S exp w ) and image based (S image w ) water saturations obtained from repeated oil drainage imaging experiments. Comparing Model Data to Experiment: Centrifuge drainage experiments undertaken at capillary numbers (Ca) as high as 10-5 are assumed to be based on capillary dominated flow at the pore scale. Capillary dominated displacements are controlled by stable, equilibrium configurations of fluid/fluid interfaces in a pore system. At any given capillary pressure, the menisci separating bulk fluid phases will all have the same mean curvature if the system is truly in an equilibrium state. In the experimental regime which we are working (drainage or non-wetting invasion into a strongly water wet system), fluid-fluid boundaries can be represented by the envelope of the union of spherical cap segments with a radius greater than a common threshold. The threshold radius is related to a capillary pressure through the Laplace equation. Fluid advancement, in a quasi-static sense, is then governed by propagation of spherical menisci or the envelope of assemblages of spherical caps through the pore structure (the invasion percolation model [Wilkinson, 1984]). If true, drainage displacements can then be directly modelled on an image of the porous structure in 3D. In this subsection we compare experimental and numerical predictions of the drainage process in the sucrosic dolomite samples. First we compare the global capillary pressure function and secondly based on the local pore scale distribution of the fluids.

In Fig. 5 we compare the numerical prediction of the modelled capillary pressure response of the core material based on two different boundary conditions: first, conditions equivalent to a mercury porosimetry (MICP) experiment, where all outside faces of the core are connected to the non-wetting phase, and second conditions equivalent to a centrifuge oil-brine drainage experiment, where the fluid invades at one inlet face and exits from the opposite face. The numerical predictions based on invasion from all faces for subsamples A-D are directly compared to an MICP experiment performed on a sister sample in Fig. 5(a). The data is in good agreement. The numerical prediction of the drainage capillary pressure based on invasion from a single face is shown in Fig. 5(b); it has a slightly smaller invasion radius. This numerical data is compared to the experimental data, with good agreement. Based on this data we conclude that simulations of drainage P c based on an assumption of capillary dominated flow are in good agreement with experiment. A more direct comparison is based on the pore occupancy of the system in 3D at a specific capillary pressure. This is illustrated in Fig. 6. Here we compare the fluid distribution obtained experimentally via centrifuge drainage at an equivalent entry radius of 9.5 microns for the subsample C with the numerical distribution of the two fluid phases based on invasion from a single face at an identical entry radius. The result is shown for a single slice from the 3D image. The individual pore scale distribution of drained and water wet pores is similar. This indicates that the numerical simulation of drainage based on the assumption of quasi-static capillary dominated flow does capture the physics of drainage in a strongly water wet rock at the local pore scale. (b) Fig. 5 Capillary pressure data from experiment on sucrosic dolomite sample versus numerical simulation on 3D image data. (a) MICP boundary condition (b) Centrifuge boundary condition. (a) 6 Fig. 6 (Upper) Slice of a drainage experiment at Sw=32%. The black pores are those drained during the displacement. The pores which remain grey are filled with residual water. (Lower) Simulation of drainage based on capillary dominated displacements to the

same entry radius as undertaken experimentally on the same core shown in upper figure; blue regions are simulated residual water phase. The local pore scale distribution of the water phase is visually very similar to the experimental data. Oil:water drainage into Fontainebleau sandstone: The second sample considered was oil:water drainage into a homogeneous Fontainebleau sandstone (φ=13.2%, k= 1800mD). Similar observations were made for this sample; the non-wetting phase is found primarily in the larger pores and the match between the experimental and the numerical prediction of the capillary pressure response of the core material was good (Fig. 7). accessible via throats of the order of >5 microns and half the pore space accessible via throats of the size <2 microns. Centrifuge drainage of the core was undertaken to an equivalent capillary radius of 3 microns and the displaced fluid visualized in 2D slices and 3D volumes (Fig. 9). The experimental and numerical distribution of the displaced fluid is compared. Good agreement is observed at the pore scale. This again illustrates the validity of the numerical simulation of drainage based on quasi-static capillary dominated flow. Fig. 7 (Upper) Slice of dry image of Fontainebleau sandstone (5mm diameter) and after oil drainage. (Lower) shows the capillary pressure data from experiment on the sample versus numerically based predictions. Drainage Displacements into more complex core Drainage into an oomoldic grainstone: An oolitic grainstone is considered as representing a more complex end member; a core with a bimodal pore structure. The moldic limestone sample (Fig. 8) we choose has two specific pore size populations; large partly leached round pores of scales >100 microns and small pores (<1-2 μm). Mercury porosimetry data (Fig. 8) for the sample shows a bimodal throat size distribution with approximately half of the pore space 7 Fig. 8 (Left): Slice through the tomographic image of the sample (5mm diameter and 3 micron resolution) and (middle) SEM image of a 1mm section at 250 nm resolution. The presence of submicron micropores throughout the matrix is evident. (Lower) curve shows the MICP drainage capillary pressure curve for the sample. Drainage into reservoir carbonate core: Images have been obtained of many reservoir carbonate cores. An example of a core with a mixture of interparticle and moldic porosity is given in Fig. 10. For this sample the porosity is 30%. The mercury drainage curve for the core is also shown; much of the accessible porosity exists at scales below the resolution of the current 3D tomographic techniques (~2 microns). Drainage experiments were undertaken on this core to equivalent pore diameter of 3 microns, but one could only observe non-wetting phase drainage into a small percentage of the total porosity S nw ~20%. Clearly in systems such as these one cannot directly image the distribution of the wetting and non-wetting phases across a broad range of saturations directly via 3D imaging.

the pores of scales 0.5-3 microns to the grey scale attenuation map. This will allow one to include multiscale (submicron scale) pore mapping into the 3D structure of the core. This will greatly impact on our ability to predict the resistivity response of these complex carbonate rocks. Fig. 9 (Upper): Left; Slice through the tomographic image of the sample (5mm diameter) after drainage to 3 micron equivalent capillary radius. Grey filled pores remain water filled. Right; numerical prediction of drained pores in same slice (green). Lower figure shows 3D visualization of the gas and water filled pores. Probing submicron pore sizes: To probe the resistivity response of many carbonates the saturation states at resolutions down to submicron scales need to be mapped. This necessitates an ability to probe the pore scale structure in carbonates across a broader range of length scales (from >100 nm) and to integrate information at these different scales. Registration techniques [Latham et al., 2008] can also be used to couple information at different length scales via different imaging techniques. For the carbonate systems considered here we couple Scanning Electron Microscopy (SEM) data at submicron resolutions to micro-ct data at ~2 micron resolution. This allows one to successfully map the sub-resolution porosity visible in the SEM image to gray scale levels in the 3D image (Fig. 11). From the attenuation histogram (Fig. 12) of the tomographic data of the sample we assign porosity to regions of intermediate attenuation [Knackstedt et al., 2008]; a mapping of the intermediate grey scale attenuation of the tomogram is also superimposed on the SEM data in Fig. 12. We observe a clear correlation between the porosity in the 2D SEM which can be calibrated to the grey scale in the 3D attenuation histogram. Further work has shown that one can map Fig. 10 (Upper): Left; Slice through the tomographic image of a reservoir carbonate sample (5mm diameter). Right shows the MICP data for the sample. The lower figures show the distribution of the non wetting phase in the sample after drainage to (left) 10 micron and (right) 3 micron equivalent diameters. The non-wetting phase saturation is 6% and 20% respectively in the two images. Waterflooding: Imbibition Displacements While the physics of drainage (non-wetting) displacements into water wet samples can be well characterized at the pore scale, waterflooding processes are more difficult to describe. Imbibition of a wetting fluid into a porous media is influenced by rate, heterogeneity of the pore space and local pore geometry, which can lead to a wide variety of wetting patterns including site invasion percolation, cluster growth and flat frontal advance [Lenormand et al., 1984; Blunt & Scher, 1995]. The complexity increases for spontaneous imbibition where the Ca is continually decreasing, and where the displacement front advances simultaneously at many locations - quasistatic rule based models do not generally apply. An added complication may be the mixed-wet nature of the core. All these factors impact on the electrical resistivity, oil displacement and hence oil recovery of the rock. 8

(a) result matches data for Fontainebleau sandstone at similar porosity:permeability [Suzanne et al., 2003]. Tomography (a) (b) SEM (b) Solid 0-25% 25-50% 50-75% Fig. 11 (a) Concept of image registration across different imaging modes: Slice from tomographic data is coupled to an SEM image at much higher resolution. (b, left) Slice through a 3D tomogram at 2.1 micron voxel resolution. Image size is 700x400 microns. Although the sample porosity is >20%, only a small percentage of the image is clearly porous. Most of the image exhibits microporosity (intermediate attenuation). (b, Right) shows the same slice from a 2D SEM image at 250 nm per pixel. The micropores are now visible and equivalent pore sizes can be identified. Understanding the physics of pore scale displacement mechanisms during imbibition benefited greatly from experiments undertaken on 2D micromodels where the displacement mechanisms were directly observed [Lenormand et al., 1984]. Here we undertake waterflooding of reservoir core samples in 3D and map the resultant fluid distributions at the endpoints of spontaneous and forced imbibition. Spontaneous Imbibition (SI) into Simple Sandstone: A first experiment was undertaken on water imbibition into an air dried strongly water wet Fontainebleau sandstone. The sample came from a plug with φ=13.8% and k=1800md. The initial uptake of water during the spontaneous imbibition experiment was extremely rapid (< 1 minute). Images of the dry samples and the corresponding slice with the trapped gas saturation of the sample are shown in Fig. 13. The trapped gas saturation in this sample is measured as ~42%. This 9 (c) 75-100% Macro-pore Fig. 12 (a) Attenuation histogram of a carbonate sample exhibiting clear pore regions (lower attenuation < 18000), mineral phase regions (higher attenuation; >25000) and intermediate microporous regions. (b) We assign effective porosity to these voxels based on the attenuation value. (b) shows the visual comparison of the porosity derived from the same SEM to the grey scale attenuation of the registered slice. (c) shows the porosity mapping from the tomographic slice to the SEM image in Fig. 11(b). The mapping shows good correlation.

For strongly water wet conditions with extremely rapid water uptake across a small sample, one might expect that the effective Ca is very large and the imbibition mechanism would approach a frontal drive with little trapping of the gas phase [Lenormand et al., 1984; Blunt & Scher, 1995]. The imaged saturation distributions in Fig. 13 (b) show that the trapped gas phase is concentrated in the largest pores. This suggests that a simple percolation type mechanism may be relevant in describing the process [Wilkinson, 1984]. In a percolation-based model of an imbibition displacement the residual (trapped) gas saturation is formed when the displaced fluid (gas) stops percolating or becomes disconnected. This ordinary percolation threshold is easily determined on the 3D image data by incrementally removing spheres in the covering radius map from smallest to largest and tracking when the non-wetting phase first disconnects. The saturation associated with this threshold is 51% which is considerably higher than the experimentally measured residual gas saturation (S gr ) of 41%. However if a percolation argument is used and saturation is reduced to match the measured S gr by further incrementing the covering radius map (see Fig. 13(c-d)) the resulting distribution of residual gas is similar to that for the corresponding imaged experiment. experiments on the same sample. A sample is rendered water wet, water saturated under vacuum, drained to a S wi =30%, placed in contact with water and allowed to imbibe until equilibrated. The sample is then dried, rendered water wet and the experiment repeated. Fig. 14 (a-b) shows that the pore-scale distribution of the water phase is spatially similar in the two experiments. (a) (b) Fig. 14 Two separate SI experiments into the same water wet core. The pore scale distribution of the residual gas phase is similar in both cases. Spontaneous Imbibition into Reservoir Carbonate: A second experiment was undertaken on water imbibition into an air dried strongly water wet reservoir carbonate φ=30.8% and k=23 md. The initial uptake of water during the spontaneous imbibition experiment was extremely rapid (< 1 minute). Images of the dry samples and the corresponding slice with the trapped gas saturation of the sample are shown in Fig. 15. The trapped gas saturation in this sample is measured as S gr ~15%. (a) (b) (c) (d) Fig. 13 (a) Dry image of Fontainebleau sands and (b) residual gas saturation after spontaneous imbibition into air. (c) shows the water saturated (blue) and residual gas saturation (orange) pores from experiment and (d) (yellow) comparison to a percolation based model at similar saturation. Repeatability of Experiment: Given the small sample size and the fast imbibition rates (< 1 min) into the small samples we again test whether the water saturation observed in 3D can be duplicated across multiple experiments. To test this we undertake two SI 10 Scanning curves: In many reservoirs significant oil resides in transition zones. Residual hydrocarbon saturation is known to be dependent on the initial saturation and the details of the initial oil and brine in place. In addition to understanding the residual oil saturation/ initial oil saturation relationship, the multiphase characteristics of the rock (imbibition capillary pressure, resistivity index and relative permeability) starting at different initial oil/water saturations (see Fig. 16) are needed for accurate reservoir surveillance and modelling [Masalmeh et al., 2007]. Using 3D imaging and registration we can directly probe the role of initial water saturation on residual hydrocarbon saturation in core material. Spontaneous Imbibition into Simple Sandstone at variable S wi : A set of experiments were undertaken on the same Fontainebleau sandstone sample shown in Figs. 13 & 14 at four different initial water saturations (0%, 30%, 40% & 60%). The results in Fig. 13 illustrate the residual water saturation after SI at S wi =0% and in Fig. 14 we show the residual for two experiments with S wi =30%. The resultant residual gas saturations of these experiments are summarized in Table 3. The decrease in S gr with S wi is in agreement

with data reported by Suzanne et al., 2003 and is adequately described by the empirical correlation of Land, 1968. Spontaneous Imbibition into Carbonate at variable S wi : A set of experiments were undertaken on a strongly water wet carbonate sample at three different initial water saturations; S wi =0%, 40% and 50%. A comparison of the S gr within a 3D slice for low S wi and S wi =40% is illustrated in Fig 17. In both images we observe most of the water has come into the rock via the tighter microporous regions and the larger (connected) macropores remain unswept and trapped. Again the percolation based model seems to characterize the distribution of the trapped non-wetting phase. The primary difference in the two images is the presence of water in the tightly accessed moldic porosity for the higher initial water saturation experiment. This sample (similar to the oomoldic rock in Fig. 8) exhibits a dual pore system. We assume that this water present in the tighter pores was present after primary drainage (S wi ~50%). The resultant residual gas saturations of all experiments is summarized in Table 4. Fig. 15 (a) Dry image of reservoir carbonate (5mm diameter) and (b) residual gas saturation after spontaneous imbibition into air. (c) shows a more detailed inset of a slice in 3D (400 microns x 1 mm) in the dry condition and (d) after spontaneous imbibition. Fig. 16 Illustration of bounding and scanning curves for primary drainage and spontaneous and forced imbibition. Sample S wi S gr S gr (Suzanne) FB-Dry 0 42 50 FB_30_1 30 46 50 FB_30_2 30 50 50 FB_40 40 33 35 FB_60 60 15 25 Table 3 Initial water saturations (S wi ) and residual gas saturations (S gr ) obtained from imaging experiments. Data in the rightmost column comes from Suzanne et al., 2003 11 Sample S wi (%) S gr (%) Carb WW 0 50 Carb WW 40 37 Carb WW 50 37 Table 4 Initial water saturations (S wi ) and residual gas saturations (S gr ) obtained from imaging experiments on bimodal carbonate. Resistivity Index: Model and image based results Despite the heterogeneous nature of the rock samples considered and the complexities associated with multiphase displacement, one can make some important conclusions from the experimental results mapping the pore scale fluid distributions. A first conclusion is that the pore scale distribution of wetting and non-wetting fluids during drainage into a water wet rock can be numerically simulated assuming quasi-static capillary dominated flow. This wettability condition (drainage into a water wet rock) is often thought to be relevant to a reservoir during oil accumulation assuming the reservoir is originally water wet. This enables us to investigate the resistivity response of different rock types under these conditions of accumulation. A second conclusion is that the fluid distributions after spontaneous imbibition, exhibit trapped non-wetting oil or gas phase predominantly concentrated in the largest pores. This suggests that a simple percolation type mechanism may be relevant in describing the results of imbibition into a strongly water wet core [Wilkinson, 1984]. The case of waterflooding into a strongly oil wet system or mixed wet system where the largest pores in contact with the oil become uniformly oil wet [Marzouk et al., 1995, Skauge et al., 2006] can also be considered. Waterflooding into an oil wet rock is simply a drainage displacement and can therefore be

modelled assuming quasi-static capillary dominated flow. of n in the drainage simulations increases; this is not observed experimentally. In fact, experimental results show a strong negative deviation from n=2 at low saturations [Han et al., 2008]. It is argued that this deviation is due to the existence of a liquid film of water on the pore surface of the sandstone. This film of water cannot be directly observed via microtomography, but incorporation of some film conductance allows reproduction of the experimental behaviour at low water saturations [Han et al., 2008]. Imbibition RI is also simulated on the image data based on the assumption that a percolation based model of imbibition is relevant (the trapped non-wetting phase is concentrated in the largest pores). Using this model we observe a little hysteresis in the RI behaviour during the imbibition cycle. The value of n decreases with increasing water saturation and reaches a value of n=1 for S w >60%. This result is consistent with previous work on simple sands for primary imbibition via film thickening [Toumelin & Torres-Verdin, 2005]. Waterflooding under oil wet conditions is also simulated on the image data. In this case the water invades the largest pores first and wets the surface of the grains. For this scenario we observe very large n >5 values (data not shown). This result is again consistent with results reported by [Toumelin & Torres-Verdin, 2005] for mixed oil wet cycle and [Sharma, 1993] for drainage into oil wet bead packs. Fig. 17 (Top) 2D slice from dry 3D image of reservoir carbonate (2mm x 1mm field of view). (Middle) shows the result after water imbibition at low S wi ; (bottom) shows the water saturation into the same sample at S wi =50%. Fractionally wet and mixed wet systems particularly where the mixed wet characteristics are patchy remain problematic and are not easily simulated. We believe that understanding the multiphase displacement properties in these systems will benefit greatly from 3D mapping of fluid distributions under different wettability conditions. Homogeneous Samples: The full RI curve can be derived by simulation of capillary dominated displacement. Data for water wet drainage into the Fontainebleau sandstone samples is given in Fig. 18. Experimental porous plate RI measurements have also been undertaken in our laboratories on sister plugs of the sample for comparison. Data for Fontainebleau for similar poro:perm is also plotted [Durand, 2003]. We observe a good match between simulation and experiment for drainage with classic Archie behaviour, n=2 for all S w > 0.25%. At lower saturations the value 12 Fig. 18 Simulation of drainage into Fontainebleau sandstone (filled squares) compared with experimental data on the same core and sample with similar poro:perm. Imbibition RI data is shown by the blue points. Complex Carbonates: The value of n derived directly from the water saturated image data of reservoir carbonate core (see Fig. 10 for example) is limited to high S w (>75%). To probe the RI behaviour of carbonates at lower saturations requires use of our ability to directly correlate SEM data at submicron

length scales to the tomographic image data [Latham et al., 2008]. For the carbonate systems considered here we consider couple Scanning Electron Microscopy (SEM) data at submicron resolutions to micro-ct data at ~2 micron resolution. As shown in Fig. 12 this allows one to successfully map the sub-resolution porosity visible in the SEM image to gray scale (porosity) values in the 3D image. In addition to this correlation, we observe that a correlation exists between the pore size in the 2D SEM and the grey scale at that voxel in the 3D tomogram (Fig. 19). This allows one to assign both porosity and an effective pore size to regions of intermediate attenuation. This ability to map the pore size distribution enables one to model drainage at water saturations down to S w ~20% in many carbonate samples and therefore probe the region of interest for RI measurements. measured electrical conductivity in carbonate rocks; particularly those rocks containing microporosity. In many carbonate systems dry oil is produced from zones where borehole logs indicate water [Sen, 1993, Fleury, 2002]. A common explanation for this behaviour is the possibility that oil and water zones form parallel conductive pathways which respond like water zones to resistivity measurements but flow dry or nearly dry when put on production. In other carbonate systems the resisitivity can become anomalously large when the conducting water phase is trapped in isolated regions; this often occurs when the mineral surfaces become oil wet. The techniques described in this paper could provide the foundations for understanding this vexed and complex behaviour often noted in carbonate formations. Based on this mapping the resistivity index is simulated for drainage down to an equivalent pore size of ~1/2 micron (S w ~20%); Fig. 20(a). The RI prediction is shown by the open blue triangles in Fig. 21. For the drainage we observe a consistent value of n=2 across the broad saturation range. When imbibition waterflooding is modeled based on a water wet scenario (percolation based model), where water displaces the oil in smallest oil saturated pores first and gradually invade larger pores (Fig. 20(b)), little or no hysteresis is observed in the RI curve. If we assume that pores in contact with oil after accumulation become oil wet, the subsequent waterflooding will be again a drainage displacement. Water, the non-wetting fluid in the oil wet pores will invade the oil filled pores via the largest accessible pores first and then gradually into smaller pores (Fig. 20(c)). This waterflooding scenario into the oil wet pores is modeled by quasi-static capillary drainage of the oil. We undertake this waterflood modelling based on three saturation history scenarios; drainage into pores accessible via throats > 3 microns (S wi =50%); drainage into pores > 1 microns (S wi =30%) and drainage into all pores >.5 microns (S wi =15%). In all three cases we assume that after oil accumulation, the migrated oil has changed the wettability of the pores from water wet to oil wet. For these scenario we observe significant hysteresis in the RI curve, variable saturation exponents and n values varying from 2 to >4. DISCUSSION Evaluating carbonate reservoirs using borehole logging presents a special challenge due to the ongoing difficulty in estimating hydrocarbon saturation from Fig. 19 Regions identified by attenuation from Fig. 11. Upper left (640x480 microns field of view) shows the regions identified as solid in the micro-ct data in white superimposed on the SEM at 250 nm resolution. The upper right shows the regions identified as 50-75% porous. One observes a good correlation with porosity. (Lower left) one can identify individual pores and pore sizes at the submicron scale of the SEM. (Lower right) (130x100 microns) shows a magnified view of the 50-75% porous region. A correlation is made between the x-ray attenuation and the pore size. This allows one to probe the drainage into the samples at much lower water saturations. 13

(a) radius <0.3 microns are well connected and remain water saturated one would expect a decrease in n due to the concentration of these microporous-rich regions. However some rocks may exhibit a large proportion of microporosity yet these pores do not connect effectively in 3D. 3D microtomography studies coupled with higher resolution 2D (SEM) and 3D (FIBSEM) techniques [Tomutsa et al., 2003; Ghous et al., 2009] will allow one to directly measure the connectivity of these microporous rich regions using the micropore mapping methods described in Figs. 11, 12 & 19. Both the proportion and connectivity may be strongly correlated to the resultant resistivity. 3D imaging coupled with FEM modelling of the conductivity should give further insight into this observed behaviour. (b) (c) Fig. 20 (a) Illustration of the MICP curve for sample shown in Figs. 10 & 15 and the saturation history assuming (a) oil drainage into a water wet rock and (b) waterflooding under water wet conditions. (c) Saturation history assuming the oil filled pores become oil wet and the waterflooding proceeds from large to small pores. Firstly, consider the cases where a rock exhibits anomalously small values of n under water wet conditions. The reason given for this behaviour is that a network of interconnected (water saturated) micropores exists within the rock. The hypothesis can be directly tested via 3D imaging studies. Dixon and Marek, 1990 showed that rocks with a significant fractional volume of microporosity (defined in that paper as pores with an equivalent entry radii of <0.3 microns) had a strong correlation with the measured n (<2). If all the pores of 14 Fig. 21: RI simulations under different saturation history and wettability conditions. Water wet conditions gives n=2, as observed experimentally. Imbibition under water wet conditions leads to little hysteresis in the RI curve. Mixed wet conditions with large pores assumed oil wet and small pores assumed water wet leads to a strongly hysteresis in RI curve. Mixed wet scenarios are considered for three different saturation histories/depths: the green curve is for S wi =15%, the red for S wi =30% and black points for S wi =50%. The nature of the mineral surface (wettability) is also a key variable to consider when attempting to understand the resistivity response of a core. As noted by Dixon and Marek, 1990, in one sample the grain surfaces were coated with a thin organic residue which rendered much of the surface oil wet and led to anomalously large values of n (>4). If, as modelled simply in Fig. 20, the wettability of core material is based on pore occupancy after initial drainage assuming that the oil rich regions become oil wet one can observe quite complex behaviour in the saturation exponent (Fig. 21). Unfortunately studies of brine/crude/rock interactions have shown that this simple picture may be naïve. The depositional tendencies of asphaltenes and resins in crude oil may allow finer pores to be invaded and

rendered oil wet [Fogden, 2009]. The extent of this may depend on the brine composition. Understanding this complex system will benefit greatly from the ability to both image structure and multiple fluid phases at the pore scale in 3D. Use of this new capability, coupled with quality experimental data on sister core material may allow one to better explain non-archie behaviour observed in carbonates. It is hoped that the development of a significant database of 3D images of core, coupled with geological facies descriptions and characterization of mineral/fluid effects will lead to a more robust understanding. CONCLUSIONS We utilize an image registration technique [Latham et al, 2008] to superpose, at voxel resolution, images of the same core images at different saturation states. This allows direct imaging of the fluid distribution in the pore-spaces of the same core in 3D under a range of wettability and saturation states. Experiments of drainage are undertaken on simple outcrop and reservoir samples and on complex multimodal reservoir material. The results show that the numerical simulation of drainage based on the assumption of quasi-static capillary dominated flow does capture the physics of drainage in a strongly water wet rock at the local pore scale. Experiments of residual hydrocarbon saturations after waterflooding a water wet rock (imbibition) are in agreement with available experiment. The pore scale distribution of the trapped phase after waterflooding by spontaneous imbibition is reminiscent of a percolation-based model. Saturation exponents for drainage and water wet imbibition in simple samples exhibit values of n between 1 and 2. Saturation exponents for mixed wet samples exhibit significant hysteresis, variable values of n with Sw, and n values ranging from 2 4. REFERENCES Abu-Shiekah, I., Masalmeh, S. K., and Jing, X. D., 2008, Shuaiba Transition Zone Fields: From Laboratory SCAL Experiments to Field Development Challenges, Society of Core Analysts, Paper No. 2, 1 12. Arns, C. H., Bauget, F., Ghous, A., Sakellariou, A., Senden, T. J., Sheppard, A. P., Sok, R. M., Pinczewski, W. V., Kelly, J. C., and Knackstedt, M. A., 2005, Digital Core Laboratory: Petrophysical Analysis from 3D Imaging of Reservoir Core Fragments, Petrophysics, 46, 260 277. Blunt, M. J. and Scher, H., 1995, Pore level modeling of wetting, Physical Review E, 52, 6387 6403. Caubit, C., Hamon, G., Sheppard, A. P., and Øren, P. E., 2008, Evaluation of the Reliability of Prediction of Petrophysical Data through Imagery and Pore Network Modelling, Society of Core Analysts, Paper No. 33, 1 12. Cense, A. and Marcelis, F., 2008, A comparative study of Three Pore-Scale Reconstruction and Pore-Network Extraction Techniques, Society of Core Analysts, Paper No. 36, 1 12. Cerepi, A., Durand, C., and Brosse, E., 2002, Pore microgeometry analysis in low-resistivity sandstone reservoirs, Journal of Petroleum Science and Engineering, 35, 205 232. Dixon, J.R. and Marek, B.F., 1990, The effect of bimodal pore size distribution on electrical properties of some Middle-Eastern limestones, Society of Petroleum Engineers, Paper No. 20601, 743 750. Fleury, M., 2002, Resistivity in Carbonates: New Insights, Society of Petroleum Engineers, Paper No. 77719, 1 9 Fogden, A., 2009, Experimental investigation of deposition of crude oil components in brine-filled pores, Society of Core Analysts, Paper No. A16, 1 12 Ghous, A., 2009, 3D Imaging of Reservoir Core at Multiple Scales, PhD Thesis, University of New South Wales Hilpert, M. and Miller, C. T., 2001, Pore-morphologybased simulation of drainage in totally wetting porous media, Advances in Water Resources, 24, 243 255. Knackstedt, M. A., Sok, R. M., Sheppard, A. P., Latham, S., Madadi, M., Varslot, T., Arns, C. H., Bachle, G, Eberli, G., 2008, Probing Pore Systems in Carbonates: Correlations to Petrophysical Properties, Society of Petrophysicists and Well Log Analysts 49 th Annual Logging Symposium, Paper No. A, 1-16 Kumar, M., Senden, T. J., Latham S., Sheppard, A. P., Knackstedt, M.A., Cinar, Y., and Pinczewski V.W., 2008, Designing for Mixed Wettability, Society of Petroleum Engineers, Paper No. 113862, 1-12 Land, C. S., 1968, Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow from 15