Experimental investigation of trapped oil clusters in a water-wet bead pack using X-ray microtomography
Abstract
[1] Uncertainties in the quantification of transport properties associated with multiphase flow in porous systems often make the prediction of fluid residence and migration a difficult task. Movement and trapping of immiscible fluids in permeable formations depends upon a complex combination of fluid properties, rock properties, fluid-solid interactions, and forcing conditions. This work consists of using X-rays and visualization techniques to map the distribution of immiscible fluids, particularly trapped oil clusters, residing in a glass bead pack subject to different flow conditions. We analyze the effect of flowing conditions on the evolution of fluid microstructures using X-ray microtomography. Spherical glass beads (0.425–0.600 mm in diameter), a water-wet porous medium, were packed inside a specially designed core holder. High-resolution imaging provides detailed mapping of pore structures resulting from bead packing, and characterization of fluid microstructures formed during sequential water and oil injections. We present spatial distribution of trapped oil clusters for the entire bead pack, as well as mechanistic explanations leading to the fluid configurations observed. We also present simple statistical analyses of blob size, shape, and surface area at the end of different fluid injection cycles. Trapped oil clusters appear in sizes that range from 5.923 × 10−5 mm3 to 3.119 × 103 mm3, where 0.01–0.50 mm3 clusters are most common. About 98% of the total trapped oil at the end of drainage and imbibition cycles corresponds to blobs that are smaller than 1 mm3. It is also shown that most blobs are larger than the mean pore size (0.03 mm3). The mean oil blob size is about 5 times larger than the average pore. A typical blob extends through various interconnected pores, exhibiting elongated of ramified shapes that include multiple voids and constrictions at the same time. The mean aspect ratio of these clusters is less than 2, and the surface area to volume ratio is constant for those larger than 0.1 mm3. Experimental methods and findings presented in this paper are expected to lead to powerful calibration mechanisms for multiphase flow models.
1. Introduction
[2] The ability to predict the distribution and migration of fluids in subsurface environments is of great importance for earth sciences research and engineering applications. Understanding transport properties of porous materials and their dependence on structural features, fluid and rock properties, and boundary conditions, is essential for the design of effective hydrocarbon recovery and remediation strategies. Relative permeabilities, for instance, depend on the fluid properties, the pore space, wettability, and saturation history, which are in general poorly understood. This is mainly because the amount of good quality experimental data found in the literature is small and limited to few core samples. Careful benchmark experiments to quantify flow properties and transport mechanisms in well characterized samples are required not only to improve current understanding of physics of multiphase flow in porous media, but also to develop and validate physically based models that are capable of predicting fluid flow behavior and associated transport properties.
[3] Over the last 30 years, there has been a huge interest in development of different physically based pore-level models, e.g., network models [Øren et al., 1998; Piri and Blunt, 2005a; Piri and Blunt, 2005b; Valvatne et al., 2005; Ramstad and Hansen, 2006], Lattice-Boltzmann models [Gunstensen et al., 1991; Grunau et al., 1993; Chen and Doolen, 1998; Van Katz and Egberts, 1999] and Smoothed Particle Hydrodynamic (SPH) models [Morris et al., 1997; Zhu et al., 1999; Tartakovsky and Meakin, 2005, 2006], that can be used to predict various flow properties and are able to handle hysteresis and effect of wettability. The success of these models, however, has been dependent on four major components: (1) availability of accurate and realistic representations of pore space in the porous medium, (2) detailed understanding of multiphase displacement mechanisms at the pore level, (3) availability of inexpensive and powerful computational resources, and (4) availability of rigorous validation methodologies and relevant experimental data.
[4] Arrival of advanced technologies such as X-ray microtomography has made it possible to acquire accurate three-dimensional maps of the pore space in porous systems. This technique has been used to characterize the pore space at resolutions that were not possible before, revealing topologic features that are vital for predictive pore-level models. In other words, microCT imaging allows the extraction of a realistic depiction of the geometry of the pore space.
[5] Experimental studies involving multiphase micromodels have significantly improved our understanding of displacements mechanisms in porous media over the years. This trend has continued with application of microCT imaging and laser-induced fluorescence techniques to investigate details of displacement physics in porous media. They allow the extraction of accurate maps of resident fluids for the investigation of multiple displacement scenarios, entrapment mechanisms of fluids, and impact of gravity and viscous forces on fluid occupancy. For instance, we have used microCT imaging in the past to characterize structural features and trapping of two immiscible phases inside a rough fracture through pore-network modeling [Karpyn and Piri, 2007; Piri and Karpyn, 2007]. Also, Ovdat and Berkowitz [2006, 2007] have used laser-induced fluorescence technique to investigate flow patterns and pore-scale physics of drainage and imbibition displacements in two- and three-dimensional experiments.
[6] Furthermore, over the last 5–10 years computational resources have become relatively inexpensive making it possible to carry out large flow simulations that were prohibitively expensive in the past. Scalable parallel implementation of various pore-level models, however, is still an open area of research.
[7] Validation of the predicted flow behavior and properties, however, has received very little attention due to various reasons, e.g., scaling issues, difficulties in accurate characterization of solid surfaces, and experimental difficulties. One of the most rigorous ways of validating a pore-level model is to find out if the predicted fluid occupancies are consistent with their experimental counterparts. Fluid occupancy is a manifestation of the interplay between various forces in a porous system and their interactions with the solid surface and pore space geometry. Therefore, specially designed laboratory measurements using representative rock/fluid systems that can generate accurate three-dimensional maps of fluids' distribution under different flow conditions are very valuable. They can be used to validate and improve physically based pore-level models. Validated models can then be utilized to predict flow properties for similar systems. Therefore, the main goal of this work is to provide such data for glass bead packs using X-ray microtomography techniques.
[8] X-ray microtomography techniques have been used in the past to study multiphase flow in consolidated and unconsolidated porous media, but not necessarily with the goal of careful characterization of the fluid structures for the entire volume of the samples under study. For instance, relative permeability studies in which microCT scanning was used to image gel-water and gel-oil systems, show that relative permeability to oil tends to be higher than to water due to differences in the way oil and water move through the pore space in the presence of gel, thus revealing important pore-scale flow mechanisms in multiphase systems [Seright et al., 2006]. Also, an example of carbonate pore space reconstruction using a combination of microtomography (for macro pores) and multiple-point statistics from 2-D thin sections (for micro pores) is presented in the literature, and used as a reference for a Lattice Boltzmann model for the determination of permeabilities [Okabe and Blunt, 2007].
[9] Auzerais et al. [1996] used three-dimensional X-ray microtomography to image microstructures in Fontainebleau sandstone. Using a cylindrical core (approximately 37.5 mm long and 20 mm in diameter) they measured properties such as porosity, absolute permeability, pore volume to surface ratio (Vp/S), end point relative permeability, electrical resistivity and irreducible water saturation for oil primary drainage. They employed a variety of computational methods, e.g., random walk techniques, finite difference techniques, and Lattice-Boltzmann method, to calculate the same properties in the three-dimensional X-ray images that they had generated. The computed values of porosity, absolute permeability, Vp/S, and the end point relative permeability were in good agreement with their experimental counterparts, but this was not the case for electrical resistivity and irreducible water saturation. The samples that the authors had imaged for the theoretical calculations were much smaller (3.5 mm in diameter) than the sample they had used in the experiments, which may have contributed to the discrepancy between these two measurements and the associated model predictions.
[10] Culligan et al. [2004, 2006] used synchrotron-based X-ray microtomography techniques to study variations of water/air and water/oil interfacial area in glass bead packs during drainage and imbibition cycles. They used three-dimensional images in order to compute interfacial areas and saturation. More uniform saturation profiles were observed in the water/oil system than in the presence of air, also leading to higher residual oil saturations, which was primarily attributed to the differences in interfacial tension between the fluid pairs. They observed an increase in air/water interfacial area as water saturation decreased. The trend reached a maximum and then decreased as the saturation continued to zero. The bead pack used by the authors was 7.0 cm long and 7.0 mm in internal diameter and had a porosity about 34%. The authors determined a Representative Elementary Volume (REV) and then focused their study on imaging a small, i.e., 5 mm, vertical section of the cell to increase the resolution and accuracy of their results.
[11] In this work, however, we use a much larger bead pack (90.53 mm long and 25.4 mm in diameter) in order to study the displacement physics during drainage and imbibition processes, the resulting saturation distributions, and the size and shape of trapped oil clusters. We use similar imaging techniques, but we scan the entire bead pack to obtain comprehensive information about the microscopic displacement mechanisms and their macroscopic implications. We also discuss the variations in the interfacial areas computed from our X-ray microCT images. The data and findings resulting from this experimental work are anticipated to become a powerful source for the construction and validation of representative physically based pore-level models.
2. Experimental Design
2.1. Core Holder Design
[12] A low-pressure core holder was designed and built specially for this experimental study. This core holder allows the making of compact granular packs having 25.4 mm in diameter and up to 102 mm in length. Shorter samples require additional spacers also included in the design. Figure 1 shows a diagram of the core holder design (dimensions in inches). The core holder sleeve is made of polycarbonate, while inlet and outlet end plugs are made of stainless steel. Each of the two end plugs has two ports: a main flow port and a pressure port. A diagram of the face of the end plugs is shown in Figure 1 (top). A cylindrical ceramic filter is placed at both ends of the core to act as flow distributors and simultaneously straighten the flow lines directed into and from the pack. These distributors have multiple straight channels (2 mm × 2 mm openings) that run parallel to the main flow direction, thus promoting an even distribution of fluids into the face of the bead pack. Since the average bead diameter is significantly smaller than the filter opening, a fine perforated plate, or stainless steel screen is placed between the filter and the beads to prevent displacement of beads through the flow distributors and out through the end plugs.

[13] The bead pack has a uniform diameter across its entire length. However, inlet and outlet ends have different diameters, forming what we call the static and dynamic ends (in Figure 1 (left) and 1 (right), respectively). The static end, or fixed ring, is larger in diameter and provides a fixed support against which beads are pushed to form a compact granular pack. The dynamic end, or push ring, is 25.4 mm in diameter and can slide inside the core holder sleeve to create the necessary compression to immobilize the bead pack, according to the sample length. The dynamic end is then tightened in place, maintaining a slight compression against the bead pack to ensure a compact and uniform packing. Inlet and outlet ends can be designated indistinctively, and the core holder can be used both in the vertical or horizontal orientations.
2.2. Experimental Installation
[14] The experimental installation comprises of four main entities: a core holder (described in section 2.1), a fluid reservoir, pumping and recirculation system, and X-ray microCT scanning unit. A schematic diagram of the experimental installation is presented in Figure 2. The cylindrical core holder is mounted on the X-ray microCT scanner so that its axial direction is aligned with the vertical axis. Oil and water phases are mixed vigorously and allowed to settle in a flat-bottom flask to establish an equilibrium between the two phases, minimizing mass exchange during the actual floods. Fluids drawn from the main flask are pumped into a rectangular, three-compartment glass tank with quarter valves installed at the bottom of each compartment. The displacing fluid (oil and water for drainage and imbibition, respectively) is pumped continuously to the first compartment. The liquid will overflow to the second and the third compartments with batch-wise recycling of unused fluid from the third compartment. An appropriate pumping rate into the first compartment is able to maintain a liquid level overflow in the first two. The displacing fluid is directed into the core inlet (bottom of the sample) by opening a valve under the second or middle compartment, and it is collected from the outlet at the top. A constant level in the second compartment maintains a constant pressure head during core flooding, which is essential in the monitoring of fluid displacement. The reservoir is mounted on a lever and pulley system that can be moved vertically to obtain different pressure heads. A graduated scale attached to the lever system then allows measurement of reservoir fluid, core inlet and outlet heights with respect to a suitable datum. The differences between these heights are used to calculate inlet pressure heads and pressure drops across the core. At the end of each flooding sequence, injection is stopped and the core holder moves vertically in steps and rotates along the vertical axis at each step during X-ray microCT scanning, providing a bottom-to-top three-dimensional view of fluid distribution inside the porous pack.

2.3. Imaging Technique
[15] X-ray microtomography was used to determine fluid structures in the porous system and map the distribution of oil and water during drainage and imbibition processes. X-ray microtomography is a nondestructive imaging technique that uses X-rays and mathematical reconstruction algorithms to view a cross-sectional slice of an object [Vinegar and Wellington, 1987]. The image reconstruction is based on multiple X-ray measurements made through the object along different paths. The microCT system consists of an ionized X-ray source, a detector, a translation system, and a computer system that controls motions and data acquisition. The X-ray source has a Tungsten target with a focal spot of 5 microns. It produces a cone beam that passes through the core and activates the detector. The detector surface releases electrons that are then focused on a screen that is photographed by a CCD camera forming an array of 1024 × 1024 pixels. The sample is rotated 360° in the X-ray beam while the detector is providing attenuation views to the data acquisition computer. After the sample is rotated a complete turn, the system reconstructs a slice, which is a cross-sectional image of the attenuation values that represent a combination of the density and the apparent atomic number of the sample at the imaged position. The imager operates in volume mode where several separate slices are collected in one rotation. A total of 41 slices were collected in each rotation, for a total of 77 rotations covering the entire sample length. After each rotation, the sample is translated axially to a new scanning position, thus allowing a continuous three-dimensional coverage of the sample. The voxel resolution in the experimental data presented in this paper was 0.026000 mm × 0.026000 mm × 0.029205 mm, where 0.029205 mm indicates the slice thickness. Additional details about the use of X-ray microtomography techniques to visualize multiphase flow and pore structure in porous materials can be found from Wildenschild et al. [2002, 2005].
2.4. Materials and Experimental Procedure
[16] An artificial cylindrical core of water-wet porous medium of length 90.53 mm and diameter 25.4 mm was prepared from glass beads of size range 0.425 to 0.600 mm, in diameter. Drainage and imbibition studies were carried out by injecting immiscible nonwetting and wetting phases, respectively. The wetting phase is an 8% by weight aqueous solution of NaI, while the nonwetting or oil phase is kerosene. This aqueous solution has a surface tension close to 71 mN/m, density of 1.060 gr/cm3, and viscosity of 1.05 cP, while kerosene has a surface tension of 26.69 mN/m, density of 0.797 gr/cm3, and viscosity of 2.43 cP. The experiment consists of four alternate stages each followed by X-ray microtomography imaging of the core. Scanning was carried out along the entire length, in the direction of fluid flow (bottom to top). Figure 3 presents a schematic sequence of the experimental procedure. Initially, the porous pack was scanned dry in order to obtain an accurate mapping of the pore structure. A vacuum of 250 microns was applied on the dry packed core prior to X-ray scanning of the dry beads. In stage II, the core was saturated with the water phase (presaturation) and scanned again, in order to obtain a comparison to use in image subtraction techniques to map fluid distributions during two-phase flow experiments. The NaI solution representing the wetting phase modifies the CT number registration of pure water to match that of the glass beads in order to facilitate segmentation and identification of the nonwetting oil phase residing in the pore space. Pressure heads of 2 to 13.9 cm of NaI solution were applied across the core, and flow rates measured were used to calculate absolute permeability of the porous medium. The core stood vertically at all times and injection took place from the bottom, i.e., the main flow direction was bottom to top, as indicated in Figure 2. Flow rates varied from 0.32 cm3/min at low-pressure heads to 5.1 cm3/min at high-pressure heads. The experimental procedure was then completed by consecutive cycles of oil and water injection, stages IV and V, respectively, which were expected to lead to irreducible (Swirr) and residual (Sor) saturation states at the end of drainage (oil injection, stage IV) and imbibition (water injection, stage V), respectively. The core was scanned at the end of each of these steps (see Figure 3).

[17] Figure 4 shows horizontal cross sections of the bead packing obtained from X-ray microCT scans of the core after stages I, III, IV and V. The light gray regions represent high attenuation coefficient, characteristic of high-density material, whereas the dark gray zones represent regions of low-attenuation coefficient, characteristic of low-density material. In ‘A’, dark and light gray zones represent the empty pore space and the beads, respectively. ‘B’ is a core slice after presaturation with water. As mentioned previously, the NaI concentration is such that the water and solid bead structure have the same CT registration, thus no distinction can be made between water and beads. In ‘C’ and ‘D’ dark gray regions represent oil, whereas the light gray regions include beads and water. It can be seen in Figure 4 that slice ‘C’ (sample at Swirr, end of drainage) shows a larger amount of oil residing in the pore space when compared to slice ‘D’ (sample at Sor, end of imbibition).

3. Bead Packing and Pore Structure
[18] From the characterization of the pore structure obtained after packing, it is possible to construct a highly detailed three-dimensional replica to perform a series of flow simulations using pore-level modeling techniques. The scanning voxel resolutions determine the dimensions of each element in the synthetic structure. Pores have sizes and shapes that closely represent the principal geometric features of the three-dimensional void space. Although not the purpose of this work, it is possible to construct a model to validate against the data gathered in this investigation and use it to predict multiphase phase flow properties for a variety of flowing conditions relevant to hydrocarbon recovery processes, geologic sequestration, and remediation scenarios.
[19] Every substance has a CT registration number, corresponding to a combination of density and atomic number thus, segmentation of porous medium can be done by selecting a thresholding CT number to distinguish different substances/materials in the medium, namely the solid beads (high density–high CT number registration) and pore space (low density–low CT number registration), which can be further classified on the basis of fluid phases occupying the pores (oil or water).
[20] A statistical analysis of CT number distribution allows us to provide rough estimates of what could be the thresholding CT number. Figure 5 provides the CT number frequency distribution obtained from the dry bead packing CT images (Figure 3, part A). It shows two characteristic peaks, the lower peak, I, at low CT numbers (low density) and the higher peak, II, at high CT numbers (high density) corresponding to the empty pore space and the solid medium, respectively. The symmetric nature of the higher peak at high CT numbers is ascribed to the symmetry of spherical glass beads, with the highest point denoting the bead CT registration mode. The scattered band between peaks I and II are representative of the intensity interference pattern resulting in a smooth transition of CT registration numbers from the center of the pore volume (dark gray regions representing low CT numbers) to the beads' center (bright white regions representing high CT numbers). Image segmentation was accomplished by simple thresholding, i.e., all voxels that contain a CT registration number equal to or below a CT registration number threshold are segmented from the voxels with CT registration numbers above this threshold. Simple thresholding in this investigation is limited to segmentation only two phases at a time. To fully segment our three-phase (bead, kerosene, and brine) system using simple thresholding, a two-step approach is applied. First, the bead space is segmented from the pore space. The dry bead pack scan is used to segment bead space from pore space, as it is a two-phase system. Once the bead space is segmented from the pore space, the discretized 3-D grid of pore space and bead space is used to remove the bead space from all subsequent full core scans. After this subtraction, the resulting 3-D grids of the imbibition and drainage contain only two phases, the kerosene and brine residing in the pore space. The second step involves the segmentation of kerosene from brine. In both of these steps the CT registration number threshold is calculated in the same manner. The CT registration number threshold is calculated by assuming all segmented voxels have a CT registration number equal to the mean CT registration number of the phase occupying the voxel, and the mean CT registration number of this segmented image is equal to the overall mean CT registration number for the pore space.

[21] Figure 6 shows the local values of porosity at each horizontal cross-section, as we move along the bead pack (from bottom to top). The average porosity of the bead pack was found to be 41.63%, with local axial porosity values at different heights varying from 37.31% to 47.52%. This shows that the bead packing is fairly homogenous, with largest variations occurring at the top and bottom ends of the packing. As it can be seen in Figure 6, the bottom 15 mm and the top 10 mm of the bead pack show a slightly tighter pack, with lower porosity, than the rest of the sample. This is attributed to the packing methods, where vertical compressive stress alters the packing of the beads against the top and bottom boundaries. The average porosity value obtained lies between standard porosities of 47.64% and 25.96% characteristic of cubic and rhombohedral packing, respectively.

4. Determination of Absolute Permeability

5. Drainage and Capillary Transition Zone
[23] During stage IV of the experimental procedure (see Figure 3), continuous oil injection took place for 230 min at an average 0.94 cm3/min (equivalent to 11 pore volumes), thus displacing the water phase from the bead pack. After the first 90 min of injection, water production was negligible, which suggested reaching a stationary “irreducible” brine saturation state in the sample. To assure that the stationary “irreducible” brine saturation state had been achieved, injection was continued for another 140 min. At this point, oil injection was stopped and followed by full microCT scanning to monitor final fluid distribution. A vertical cross-section of the fluid distribution at the end of this drainage cycle is presented in Figure 7, as well as three individual slices showing segmentation of bead, oil, and water phases (yellow, red, and blue, respectively). It is evident, in Figure 7, that oil and water are not uniformly distributed along the core. In fact, irreducible brine saturation (Swirr) condition is only observed at the top of the core, and the profile corresponds to gravitational segregation of the oil and water phases. This segregation is mostly attributed to the high permeability of the porous medium and density difference between oil and water. Even though there was no significant water production at the end of this drainage cycle, leading to a fictitious “irreducible” water saturation state, it is now clear that large quantities of water either remained in, or migrated back into the core. In addition, it is possible that water remained in the neighboring flow distributors and flowlines, thus leading to gravitational flow back into the core after oil injection ceased. Scanning this 90.53 mm core took approximately 16 h, which allowed sufficient time for phase segregation given the high sample permeability, particularly if saturations are not at a true irreducible, immobile state. Throughout this manuscript, we refer to this state as “end of drainage.”

[24] Figure 8 shows a water saturation profile corresponding to the longitudinal view of the bead pack. The profile shows significant variations in water saturation from 13% to 90%, top to bottom, revealing an oil-water transition zone around the 70 mm level. The profile observed in Figure 8 (right) is comparable to a capillary pressure curve, showing the zonation of immiscible fluids typically found in porous media. It represents the balance of capillary and gravitational forces leading to a resting state, which is a valuable piece of information in the determination of characteristic capillary pressure curves. During the drainage process, oil displaces water from the pores mainly with an invasion percolation mechanism. Oil stays at the center of invaded elements leaving water in the crevices and small elements. Both phases are well connected under these conditions. But, as it was mentioned earlier, at the end of drainage we observed water migration back into the system. This took place during the scanning stage C, see Figure 3, when oil injection was ceased. It introduced a complete water flood (imbibition) at the bottom 60 mm of the bead pack, see Figure 8, reducing oil saturation to about 19%, which was completely trapped.

[25] Due to high permeability of the medium and also density difference between the fluids, the gravity segregation, along with capillary forces, plays an important role in determining fluid occupancies. This means that the displacements that occurred during water migration may have taken place in an order dictated by the interplay of these factors. Accessibility of water to the sites from which oil was displaced was not a major issue as the wetting phase is very well connected and present throughout the water-wet system. In other words, if threshold capillary pressure of the displacements were the only criterion, we would have seen relatively uniform distribution of oil saturation and trapped oil clusters, contrary to what is seen in Figure 8. Displacement of oil in the lower part of the bead pack was favorable to the displacement of oil sitting in the pores at the top of the bead pack, away from the inlet. This means the driving force created due to density difference was comparable to threshold capillary pressure of the displacements.
6. Imbibition
[26] Following the drainage cycle, the glass bead sample was placed under continuous water injection, as indicated in Figure 3, stage V (imbibition). Water injection took place for 130 min, at an average rate of 0.45 cm3/min (equivalent to 3 pore volumes). After the first 12 min of injection, and for the remaining 118 min of injection, the amount of oil collected at the outlet of the core was negligible, thus suggesting that the amount of oil remaining inside the bead pack was immobile and at residual saturation. Closer examination of the distribution of oil and water inside the bead pack was possible through X-ray microCT scanning, which confirmed a homogeneous distribution of disconnected, immobile oil clusters along the core. Figure 9 (left) shows a vertical cross-section of the scanned core sample, indicating oil blobs in dark gray. The remaining space corresponds to both beads and water, which have identical microCT registration. Figure 9 (right) presents a water saturation profile relative to height, with an average water saturation of 82.28%, thus leaving an average residual oil saturation of 17.72%. Fluid distribution along the height of the core is fairly homogeneous, as indicated in the profile shown in Figure 9, although the top and bottom of the sample show inverted saturation peaks. That is, low water saturation at the top and high water saturation at the bottom. This occurs at the top and bottom interfaces between the bead pack and the flow distributors, and can be explained by water accumulation in the lower flow distributor (inlet) and oil at the higher flow distributor (outlet), being the lighter liquid phase. As it is shown in Figures 8 and 9, water injection into the bead pack made very little (1–2%) difference in the saturation distribution at the bottom 60 mm of the bead pack as compared to drainage. This is mainly due to the fact that most of the oil in this part of the bead pack was trapped when water injection started, stage V (imbibition). The injected water channeled through water-filled pores and wetting water layers connecting to the top of the bead pack, where water displaced connected, i.e., not trapped, oil to reduce oil saturation to the same level as the lower part of the bead pack. This led to an average residual oil saturation of about 17.72%. The slight increase in water saturation in lower portion of the bead pack may be attributed to the entrainment of the smaller trapped oil clusters, formed during water migration before the main water flood. This may be the case due to the high permeability of the system.

[27] The residual oil saturation (17.72%) is relatively low. However, the residual oil saturation in glass bead pack experiments (capillary dominated or not) is expected to be significantly lower than from those of capillary dominated flow in many consolidated porous systems, e.g., Berea sandstone. For instance, the experimental data by Morrow et al. [1988] show that the residual oil saturation in glass bead packs can vary between 0–16% with capillary numbers ranging between 10−2 to 10−6.
[28] Low residual oil saturations may have been caused by a combination of the following reasons: (1) hydraulic connectivity between the bulk oil and the wetting oil layer covering the internal surface of the core holder. The main body of the core holder is oil wet and therefore its internal surface is covered by a wetting oil layer. Since the oil layer stretches from the bottom to the top, it can maintain the hydraulic connectivity of the bulk oil, leading to lower residual oil saturations, (2) entrainment of the smaller trapped oil clusters by water, and (3) gravity segregation. The latter produces an effect that is similar to high capillary number flows where lower residual oil saturations are achieved, i.e., water into oil displacements that are closer to the inlet are favored over the displacements away from the inlet. The pressure drop, caused by density difference, from the inlet to a given element is greater than the threshold capillary pressure for displacement of oil by water in that element. This means that water will favor displacements closer to the inlet, which in turn reduces the possibility of trapping oil by bypassing large oil clusters and/or by snap off in elements away from the inlet. A similar effect is seen when water migrates back into the bead pack at the end of drainage.
[29] In the following text, we elaborate on the characteristics of the trapped clusters of oil found at the end of drainage and imbibition, as well as resulting interfacial areas.
7. Oil Trapping and Interfacial Areas
[30] Through careful data mining, we were able to identify each individual cluster of oil found in the pore space of the bead pack at the end of drainage and imbibition cycles. Keeping in mind that the lower portion of the bead pack at the end of drainage revealed a saturation state similar to that obtained at the end of imbibition, we present an in-depth comparison of trapped oil clusters found in both cases. In the following discussion, we show that trapped oil blobs formed through these cycles of drainage and imbibition present vast similarities in the size, shape and distribution, thus suggesting a predictable, deterministic path to their development.
[31] A total of 11,962 disconnected oil blobs were found at the end of drainage, and 17,129 at the end of imbibition. Blobs were identified through a search algorithm that evaluates the neighborhood of each blob element. Connectivity is defined when at least one neighboring voxel, in a six-point three-dimensional stencil, is also a blob element. Once the connectivity is broken, we have found an individual, disconnected blob. Surface areas and volumes are then computed for each blob using simple face counting and voxel counting, respectively. These blobs appear in sizes that range from 5.923 × 10−5 mm3 to 3.119 × 103 mm3, that is from 3 to 158,000,000 side-face connected microCT voxels. Figure 10 shows a histogram of oil blob volume at the end of drainage and imbibition cycles. In order to generate the above mentioned histogram for blobs with such a broad range of volumes, we created eight logarithmic blob volume groups and analyzed the blob volume frequency separately in each of these groups. We use the same blob volume groups in the rest of the analyses presented in section 7. The mean blob volume at the end of drainage and imbibition are 0.15306 mm3 and 0.16514 mm3, respectively. The mean pore size (i.e., volume), however, is 0.03351 mm3 which indicates that an average oil blob is about five times larger than the average pore. A typical blob extends through various interconnected pores, exhibiting ramified shapes that include multiple voids and constrictions at the same time. The similarities in blob volume frequency at the end of drainage and imbibition are evident in Figure 10. Although most blobs fall between 0.01 mm3 and 0.50 mm3 in volume, there is also a large amount of small blobs (0.0001 mm3, about 5–10 voxels). Nevertheless, the contribution of these small blobs to the total trapped oil in the pore space is not significant. Figure 11 shows the cumulative contribution of each blob group to the total trapped oil in the pore space. The steepest slopes are found in the 0.01 to 0.10 mm3 range, which confirms that oil blobs in this group account for an important portion, approximately 45%, of the total trapped oil in the pore space. The asymptotical trend observed for oil blobs with volume larger than 1 mm3 demonstrates that, even though there exist relatively large trapped oil clusters, these do not contribute significantly to the residual oil saturation. In fact, 98% of the total trapped oil at the end of our drainage and imbibition cycles corresponds to blobs that are smaller than 1 mm3; end of drainage and imbibition show nearly identical results in Figure 11.


[32] The spatial distribution of all disconnected oil blobs found at the end of drainage and imbibition is presented in Figures 12a and 12b. Each circle represents the vertical location of the centroid, or geometric center, of individual blobs. The upper portion of Figure 12a, end of drainage, appears rather sparse because most trapped oil clusters are found below the capillary transition zone. Above this transition zone, oil forms a continuous, interconnected phase, see correspondence with Figures 7 and 8. For the same reason, the largest continuous oil cluster found at the end of drainage is an order of magnitude larger than the largest trapped oil blob found at the end of imbibition. The population and distribution of trapped oil clusters according to blob volume is very similar at the end of both cycles, but notice that this analogy is only fair with the lower portion of Figure 12a, where residual oil saturation was obtained. The greatest density of blobs falls in the 0.01 to 0.10 mm3 range in both cases, consistent with the blob volume histogram in Figure 10. In Figure 12b, end of imbibition, there is no evidence of clustering of a characteristic blob size in certain locations in the sample, although top and bottom seem to have some preference for small-blob trapping, especially at the top of the sample. End effects and gravitational effects may be responsible for this observation. A magnification of the top and bottom blob distribution at the end of imbibition is presented in Figures 13. Approximately, the top 10 mm of the sample in Figure 13a shows greater density of oil clusters of various sizes, thus resulting in a local increase in oil saturation (decrease in water saturation). This observation is also consistent with the vertical saturation profile presented in Figure 9. At the very bottom of the core, the density of oil blobs is significantly reduced, which is also evident in the vertical saturation profile of Figure 9.


[33] The maximum dimension of each of these oil blobs at the end of imbibition, measured over common orthogonal directions, is presented in Figure 14. In Figure 14, we notice that there is a well demarked zonation of oil clusters according to their length and relative volume. Although it may seem highly intuitive that the largest blobs (in volume) also have the largest dimension (in length), and vice versa, a less evident implication is that trapped clusters found in these experiments are not widely elongated. Long, worm-like blobs would be characterized by having a relatively small volume and large maximum blob length, which is not the case throughout our observations. Closer examination of some characteristic blobs of various sizes is presented in Figures 15 and 16. Figures 15 and 16 show three-dimensional visualization of oil blobs at the end of drainage and imbibition, and their corresponding volume and vertical location in the glass bead pack. Sample blobs, in red, were arbitrarily selected within specific size ranges to show typical structures found inside the bead pack. It is important to note that three-dimensional reconstruction and surface generation for these blobs was done without smoothing in order to have volumetric and area measurements that were least biased by postprocessing techniques. The pixelated surface appearance, which is more salient in smaller blobs, is explained by this lack of smoothing. Tables 1 and 2 report the coordinates, largest dimension, aspect ratio, volume and surface area of each selected blob, at the end of drainage and imbibition. The aspect ratio is a quantitative measure of how skewed these three-dimensional shapes are; it is the ratio of the maximum dimension length to the minimum one. The mean aspect ratio of all blobs found at the end of drainage and imbibition are 1.740640 and 1.577826, respectively. This confirms our earlier observation that the great majority of these clusters of oil are not widely elongated. Figures 17 and 18 present a closer look at blob aspect ratio, where blobs are grouped by volume. The aspect ratio of the smallest blobs, see Figure 17a, is the most dispersed among all the five volume groups. As blobs grow bigger, their shape becomes more equilibrated in terms of the length of each principal dimension. As we move from Figure 17a to 17e, the clouds of points become more consolidated and closer to 1. A similar trend is observed in 18, 18 to 18e, at the end of imbibition.









Blob | Centroid Coordinates (mm) | Largest Dimension (mm) | Aspect Ratio | Volume (mm3) | Surface Area (mm2) | ||
---|---|---|---|---|---|---|---|
X | Y | Z | |||||
A | 11.765 | 11.674 | 62.791 | 0.321255 | 1.123269 | 0.01001 | 0.27190 |
B | 14.807 | 18.096 | 49.269 | 0.806 | 1.623413 | 0.06701 | 1.22025 |
C | 19.279 | 7.670 | 35.791 | 3.302 | 1.175926 | 0.99593 | 17.1633 |
D | 10.452 | 5.031 | 19.465 | 10.86426 | 1.658159 | 8.53180 | 137.883 |
E | 20.137 | 5.096 | 63.900 | 9.491625 | 1.483994 | 19.4676 | 316.091 |
- a Blobs are at the end of drainage.
Blob | Centroid Coordinates (mm) | Largest Dimension (mm) | Aspect Ratio | Volume (mm3) | Surface Area (mm2) | ||
---|---|---|---|---|---|---|---|
X | Y | Z | |||||
A | 9.282 | 3.432 | 46.684 | 0.29205 | 1.02115 | 0.00979 | 0.26039 |
B | 15.327 | 23.309 | 56.249 | 1.61200 | 3.67974 | 0.09908 | 1.88306 |
C | 14.547 | 7.566 | 17.085 | 3.25000 | 1.48809 | 0.99756 | 15.5519 |
D | 15.756 | 5.213 | 39.690 | 10.71824 | 1.30456 | 9.46389 | 139.365 |
E | 15.951 | 7.267 | 74.969 | 11.12711 | 1.46564 | 19.6450 | 291.699 |
- a Information is from the end of imbibition.
[34] Larger oil blobs also have a larger surface area, and the relationship between these two properties can be observed in Figure 19. Although the shape of each individual blob reveals a complex structure through three-dimensional analysis, there is a consistent and strong relationship between blob volume and the associated surface area as seen in Figure 19. The blob surface area (Ab) is proportional to blob volume (Vb) through Ab ∝ Vb0.84.

[35] The surface area to volume ratio also changes as the blobs grow. These changes are captured in Figure 20. The smallest blobs have the largest surface area to volume ratio, and as blobs grow larger than 0.1 mm3, the ratio remains constant at about 15 mm−1. The trend of surface area to volume growth appears to reach a critical value at around 0.1 mm3, beyond which these blobs continue to grow tentacles through the pore space with proportional dimensional characteristics. It should be noted that results presented in Figures 19 and 20 are representative of oil clusters found at the end of drainage and imbibition cycles, as they were selected randomly from each volume group discussed earlier in section 7. In Figures 19 and 20, blobs from drainage and imbibition are shown using different markers. All blobs fall on the same trend regardless of the process they belong to. Namely, similar trends were observed using blobs from only drainage and only imbibition.

[36] Surface areas along the length of the core are presented in Figure 21 for oil/water, oil/bead, and water/bead interfaces obtained at the end of drainage and imbibition cycles. Surface areas presented in Figure 21 have been calculated over 5 mm thick volumes along the length of the core. Changes in fluid/fluid and fluid/solid interfacial areas were computed from microCT images using simple face counting.

[37] In a water-wet system like the bead pack used in this work, the oil/water interfacial area is the area formed between the bulk oil sitting at the center of the pores and (1) water in the crevices and (2) bulk water in the neighboring water-filled elements. As it can be seen in Figure 21, the oil/water contact area at the end of imbibition is similar to that of drainage below the 60 mm line, or below the capillary transition zone. The oil/water contact area stays almost constant throughout the pack at the end of imbibition as the entire pack is at the water flood residual oil saturation, i.e., contact area is between the trapped oil clusters and connected water in the above mentioned forms. This is consistent with what is seen in Figure 9. The oil/water contact area increases within the top 60–90 mm of the pack at the end of drainage due to presence of large, connected clusters of oil. Presence of large quantities of oil increases the contact area between oil at the center of the elements and water in the crevices, while it reduces the bulk-bulk contact areas. One should note that at the top 5–10 mm of the pack, most of the water is in the crevices instead of the center of small pores.
[38] Injection of water leads to displacement of oil from the pores reducing the contact area between the bulk oil and water in the crevices, as those pores become fully saturated with water. But, oil trapping phenomena that takes place during water-flooding works in the opposite direction, i.e., it increases the interfacial area between the trapped bulk oil and the bulk water. Each trapped oil cluster, that sits at the center of one or more elements, is surrounded by bulk water in the neighboring water-filled elements. This is in addition to the oil/water contact area between the trapped oil in the center and water in the crevices of elements hosting the trapped oil. The combined effect of these two phenomena is responsible for the observed reduction in contact area between oil and water below the transition zone at the end of drainage and throughout the pack at the end of imbibition.
[39] The oil/bead contact area is significantly lower at the end of imbibition in comparison to the end of drainage at the top of the bead pack. This is mainly because there are fewer elements occupied by oil at the end of imbibition. In other words, oil saturation is much lower at the top 60–90 mm of the core. When there is oil in the center of a pore, it is assumed to be in direct contact with the beads forming that pore. One should note that in these elements, a thin film of water could still be present, separating the oil from the beads, i.e., the oil pressure may not have been high enough to rupture the films. Theses thin films, however, could not be visualized by the imaging technique and hence the oil is considered to be in direct contact with the beads. These thin films are different (negligible hydraulic conductivity) from the wetting layers occupying the crevices. Similar to oil/water interfacial area, oil/bead contact area at the bottom 60 mm of the pack is similar for both drainage and imbibition processes, as both are at residual oil saturation in this region of the bead pack.
[40] Furthermore, the water/bead contact area at the end of the drainage and imbibition is similar in the bottom 60 mm of the pack. The significant decrease in the top 60–90 mm of the pack, at the end of drainage, is due to the presence of large, connected oil clusters, i.e., oil-filled elements. But, one should note that, the beads are water-wet and hence all the crevices are filled by water during all stages of the experiment, and are mainly responsible for the formation of water/bead areas. Occupation of the center of the elements by the nonwetting phase (oil) reduces the water/bead contact area only by 50% at very high oil saturations at the top of the core (So = 0.85).
[41] These results also confirm the similarities between end of drainage and end of imbibition states below the 60 mm line, or below the capillary transition zone. Large, connected clusters of oil at the top of the sample, at the end of drainage, are evident through a sharp increase in bead/oil and water/oil surface areas, while removal of water from the pore space is reflected in a reduction of bead/water interfaces.
8. Conclusions
[42] Findings from this investigation shed light on pore-scale flow phenomena responsible for important macro-scale flow behavior. The distribution and retention of trapped oil clusters observed through microCT scanning in a glass bead pack demonstrate the relevance of structural and wetting characteristics of the medium, and the balance of gravitational, viscous, and capillary forces in the physics of flow.
[43] At the end of drainage, the high permeability of the medium allowed partial segregation of phases, and the appearance of an oil-water transition zone attributed to capillary retention in the pore space. Migration of water back into the bead pack (during the long X-ray imaging stage), coupled with the above mentioned phenomena, led to the formation of a residual oil saturation region at the bottom 60 mm of the pack. This allowed us to perform a rigorous comparison of the trapped oil clusters with those formed during the main imbibition.
[44] Relatively low residual oil saturations observed at the end of imbibition (17.72%) were attributed to the high permeability and unconsolidated nature of the glass bead pack. In addition, the potential entrainment of small oil clusters by water, hydraulic connectivity of bulk oil to the wetting oil layer covering the internal surface of the core holder, and gravity segregation, may have contributed to further decrease in residual oil saturation.
[45] Trapped oil clusters formed after drainage and imbibition are similar in size, shape and distribution. The majority of oil clusters found in the glass bead pack have volumes ranging between 0.01 mm3 and 0.50 mm3, extending through various interconnected pores. The size of these clusters may vary in orders of magnitude, but 98% of the total trapped oil comes from clusters that are smaller than 1 mm3. The smallest clusters have the largest surface to volume ratio, but as they grow, this ratio decreases to a critical value where volume growth becomes proportional to the added surface area. Finally, quantification of fluid/fluid and fluid/solid surface areas along the core allowed us to discuss mechanistic explanations responsible for the fluid distributions observed.
[46] The ability to reconstruct not only a three-dimensional representation of grains, pores, and fluids in this system, but also the physical mechanisms responsible for such configurations are powerful scientific tools to improve pore-scale models of flow in porous media and other tortuous channels.
Acknowledgments
[47] The School of Energy Resources and the Office of Research and Economic Development at the University of Wyoming, the Center for Quantitative Imaging at Pennsylvania State University and the American Chemical Society (PFR 45799-G9) are gratefully thanked for their support. We also thank Phillip M. Halleck and Christopher J. Landry (Pennsylvania State University), Brian Berkowitz (Weizmann Institute of Science), Markus Hilpert (Johns Hopkins University) and anonymous reviewers for their scientific insight and the valuable comments and discussions.