With the recognition that carbonate reservoir rocks commonly contain a significant microporosity component (pore sizes ∼1 μm), there has been an ongoing effort to understand how this affects hydrocarbon recovery. This work reports x-ray microtomography (XMT) and nuclear magnetic resonance (NMR) data on two characteristic rock types. One is micropore dominated, and the other exhibits mixed-pore sizes. Several new techniques are introduced to accommodate investigation of full-sized core-plug samples having preserved wettability and to perform such studies with native fluids. First, the uses of high-field NMR techniques are demonstrated to determine porosity, overall oil and water content, and how these fluids are distributed between micro- and macropores. It is found that microporosity values agree with those obtained by optical (total pore system) analysis. Second, the use of xenon gas to tag the native oil phase for XMT imaging is demonstrated, showing how this helps determine contributions from pores that are smaller than the instrument resolution. Finally, a new method that uses NMR measurements of oil and water saturations to constrain the image analysis is demonstrated. The analysis shows the extent to which oil recovery occurs from the different pore systems. In both rock types, oil in the macroporosity is preferentially swept. Nevertheless, in agreement with a recent theory, oil recovery from the microporosity is significant. For the 70% microporosity sample, approximately one-third of the total oil recovery comes from the micropores, a factor that agrees well with theory.
As is well recognized, oil recovery from a rock having a heterogeneous pore size distribution is typically poor when compared with that from one with a homogeneous pore size distribution (Lake, 1989). Conceptually, this observation fits the picture of how an immiscible sweep fluid, such as water, will be diverted into the connected pathways of larger pores (higher permeability) characteristic of the heterogeneous pore size distribution. The result is significant bypass of oil and low recovery efficiency. It would be desirable to understand the controls on this geometry-controlled sweep efficiency because it can be anticipated to be important in the many carbonates that contain micropores.
Pore size heterogeneity in carbonates is well known. An important class of such rocks exhibits abundant micropores in the same rock where macropores are present (Chatzis et al., 1983; Cantrell and Hagerty, 1999; Sok et al., 2002; Lambert et al., 2006; Clerke, 2009; Bultreys et al., 2015). The microporosity of such reservoir rocks has been an area of extensive study for many years. Recent work has summarized findings from that literature and complemented that with a substantial data set taken over a broad range of Phanerozoic carbonates (Fullmer et al., 2014; Kaczmarek et al., 2015; Hasiuk et al., 2016). This work has identified key structural characteristics and shown their impacts on permeability and recovery factors for water and gas floods. One key finding is that limestone microporosity is hosted in a matrix consisting of low-magnesium calcite microcrystals with diameters of 0.5 to 9 μm (Kaczmarek et al., 2015). These crystals are the result of diagenesis, that is, dissolution and recrystallization. Recently, Hasiuk et al. (2016) presented a large geochemical data set that is consistent with simple burial diagenesis. It is important for the present study that the flow characteristics are directly related to the textural characteristics and crystal size. Kaczmarek et al. (2015) identified three petrophysical types (I, II, III) consisting of progressively lower porosity, reduced crystal sizes, and smaller pore-throat radii. Using data from microporosity-dominated rocks, they find a systematic porosity–permeability trend, across the entire range, going from higher to lower permeability for types I to III. Therefore, for carbonate rocks in which the pore system is dominated by micropores, the flow characteristics are determined by the micropore size.
Focusing on type I microporous carbonates (typified by porosity of 22%–32% and permeability of 5–20 md, previous work (Fullmer et al., 2014) studied the oil recovery characteristics when macropores were also present. Using a typical petrographic technique, they measured the macropores, with a minimum size cutoff of approximately 10 μm in diameter. Supplemented by a bulk determination of porosity (i.e., helium porosimetry), microporosity is then calculated from the difference. This is total pore system analysis (Lucia, 2007). Fullmer et al. (2014) noted several key features in the type I carbonates. First, as microporosity increases, oil recovery increases (determined by the residual oil as measured at 1/99 oil-to-water flow for steady-state relative permeability, remaining oil saturation [ROS]). As the microporosity percentage approaches 100%, a small ROS value is observed. In another measurement, the minimum oil saturation, determined by primary imbibition measurements via water–oil centrifugal capillary pressure experiments, also decreases as microporosity increases. A third key observation is that overall permeability increases from 0.1 to 10 md as percentage of microporosity goes from 100% to 80%. They distinguish between the regimes of micropore and mixed-pore–dominated flow at a value of 80%.
In a recent publication (Xu et al., 2017), it was shown how oil recovery and permeability changes can be related to the underlying pore geometry for these carbonates. Although the jump in permeability can be related back to the percolation of intergrain void space, this factor alone does not explain the oil recovery. Accounting for the oil recovery requires accounting for oil sweep using an effective-medium model. In this model, oil is completely swept from all pores down to a characteristic size, reff, and oil in smaller pores is swept in proportion to their size, that is, (r/reff)2. This model accurately reproduces the overall ROS behavior. The recovery factors versus pore scale are also predicted, and results here compare favorably with those predictions.
Many previous x-ray microtomography (XMT) studies of core flooding have been reported (Wildenschild et al., 2005; Iglauer et al., 2011; Silin et al., 2011; Setiawan et al., 2012; Berg et al., 2013; Andrew et al., 2014). Unlike those studies, the present study makes use of native fluids and then labels the oil by infusing it with xenon. The xenon offers excellent x-ray contrast and is marginally soluble in water. A more typical approach is the addition of a soluble radio-opaque component to either oil or water. The new approach here is able to maintain the native wettability of the core plugs (the xenon concentration is low and does not affect fluid properties), an important consideration for such carbonates. A second major difference with previous XMT studies is the use of nuclear magnetic resonance (NMR)-guided image segmentation. Unlike segmentation that relies exclusively on gradients in x-ray attenuation to define pores, this method explicitly accounts for the fluid content of the pores. This results in porosity that matches that from the NMR, accounts for the micro- and macropore percentages, and is in agreement with the oil and water content of the sample.
EXPERIMENTAL PROCEDURES AND RESULTS
Samples came from a case study on rock cores from a large Cretaceous offshore oil reservoir (Fullmer et al., 2014). This study was designed to produce high-quality flow data (relative permeability dependence on water saturation as measured under steady-state flow conditions, i.e., special core analysis [SCAL]) aligned with pore-type data defining the rock types (Gao et al., 2015). Recognizing the heterogeneity of carbonate rocks, this study developed a unique plugging and companion rock sampling strategy to ensure consistency within a given sample category.
It is well known that a rock’s wettability will affect flow properties. Carbonate studies are particularly challenged because there is no recognized manner to restore reservoir-state wettability (Wang, 1988; Wang et al., 2008; Meissner et al., 2009). Consequently, a sampling strategy that included low-invasion coring and anaerobic sample preservation was pursued to ensure that all measurements were performed on core material in as close to native state as possible. Fluid contact was limited to native reservoir fluids. The capillary pressure data, shown in figure 4 of Gao et al. (2015), suggest that the overall sample suite is mixed-wet with an oil-wet bias. The primary selection criteria for the two samples used here was to exemplify micropore and a mixed-pore behavior. Properties from companion plugs are summarized in Table 1, and images of the actual samples are shown in Figure 1. Sample 1 is homogenous, reflecting its nearly uniform pore size because of the dominance of type 1 microporosity. It is a mud-dominated packstone, micropore-dominated rock, with a mean pore-throat radius of 0.7 μm. In contrast, the mixed-pore sample 2 has a heterogeneous structure. It is a micritized grainstone, mixed-pore rock, with a mean pore-throat radius of the microporous section of 0.7 μm. The interparticle pore component has a mean pore-throat radius of 5 μm. As detailed in previous publications (Fullmer et al., 2014; Gao et al., 2015), careful SCAL tests were conducted to establish measures of oil recovery. Experimental procedures for the steady-state relative permeability data are documented there (Gao et al., 2015). The primary measure of oil recovery is the value of ROS. For comparison, a secondary measure is calculated, recovery at water breakthrough. This value is from Johnson–Bossler–Naumann analysis of the steady-state relative permeability data (Johnson et al., 1959; Shafer et al., 1990; Gao et al., 2015).
Figure 1. Images of samples 1 and 2 from both x-ray microtomography, horizontal (1A, 2A) and vertical (1B, 2B) cross-section views of the core plugs from the three-dimensional volumes (top), and petrographic microscopy of thin sections (1C, 2C). The uniform pore structure of the micropore-dominated sample 1 is in contrast to the heterogeneity of the mixed-pore sample 2. In the photomicrographs, the abundant macropores for sample 2 are visible as blue-dyed epoxy, whereas the epoxy-filled micropores give sample 1 the familiar “blue haze” of unresolved porosity in such rocks.
Nuclear Magnetic Resonance
The T2 relaxation (spin–spin relaxation time) method of rock analysis using low-field NMR setup is commonly employed in industry to measure total fluid-filled porosity and provides guidance on volumes of mobile fluid and less mobile fluid based on the evolution of spin magnetization decay caused by collisions with pore walls (Kenyon et al., 1995; Fheed and Krzyżak, 2017). Accurate quantification of different fluids (e.g., brine versus oil) with low-field NMR is challenging as the T2 contrast detectable in the bulk phase (1–2 s for brine and 0.3–0.7 s for oil) diminishes in pores as the relaxation mechanism in pores is primarily affected by pore size, with the composition of fluid and pore walls also contributing to differences in T2.
To overcome limitations of low-field NMR measurements, we developed two high-field NMR-based techniques to study fluids in the pore space of carbonate rocks. These techniques allow for the following: (1) the direct quantification of the amount of oil and water in the rock sample and from this total porosity and (2) the estimation of the micro- and macropore fractions and the fluid (water and oil) associated with each. Although less common than the use of low-field measurements, the superior signal-to-noise and access to spectroscopic analysis has made laboratory high-field investigations of petrophysical interest (Mitchell et al., 2009; Gladden and Mitchell, 2011; Fheed et al., 2018). These authors employ a variety of specialized methods to examine features such as wettability and spatial location of protons within the samples. To our knowledge, we are the first group to directly use chemically resolved signal to directly measure oil and water content.
High-Field In Situ Nuclear Magnetic Resonance/Magnetic Resonance Imaging
The experimental setup is based on a wide-bore Bruker Advance NMR spectrometer (9.4 T or 400 MHz for proton, 1H, precessional frequency) equipped with micro-2.5 probe and 30 mm (1.18 in.) 1H coil. Such a setup offers a spectroscopic separation and quantification of oil and water signals in the rock sample as well as one-dimensional and three-dimensional (3-D) imaging of either oil or water in a rock up to 25.4 mm (1 in.) in diameter (Figure 2). Tight space inside a probe of 30 mm (1.18 in.) restricts options to build a pressure cell for experiments above 0.5 MPa (>72.5 psi); thus, the investigations reported here were done under ambient conditions. The sample was encapsulated in a Teflon wrap to ensure no fluid loss during measurement, verified by measuring sample mass before and after NMR experiments.
Figure 2. Schematic of a high-field (magnetic field strength, Bo = 9.4 T) in situ nuclear magnetic resonance (NMR) spectrometer to study fluids in rocks. The magnet bore and pick-up coil have dimensions that can accommodate the 25.4-mm (1-in.) core plug. The sample is enclosed to prevent fluid loss. To the right, we indicate typical signals associated with aromatic and aliphatic hydrocarbon protons and those of water.
Core-Plug Scale Oil and Water with 1H Nuclear Magnetic Resonance Spectroscopy
The NMR technique is a direct and noninvasive way to quantitatively measure the amount of fluid in a rock. Additionally, high-field NMR differentiates 1H signals from different fluids such as oil and water based on different chemical environments of measured hydrogen nuclei (C-H versus O-H, respectively). Signal calibration ensures quantification of 1H NMR signal intensity. Combined volume of oil and water referenced against a core-plug bulk volume also gives a total fluid-filled porosity of the core plug.
High-field NMR spectroscopy was applied to measure oil and water content of carbonate samples under several conditions: (1) as received from the field, (2) after saturation with oil, and (3) after brine flood.
Figure 3A shows a typical 1H NMR spectrum from an oil-saturated core plug (gray) with broadened and scaled signal of a known amount of bulk oil (red) and brine (blue) dissolved in NMR invisible solvents, e.g., D2O and D8-toluene. This core-plug spectrum includes three peaks that reflect signals from three main proton ensembles—aromatic components of the oil –C(H)= at 7–8 ppm, aliphatic component of the oil –C(Hx)- at 1–2 ppm, and water H2O in the brine at 4–5 ppm. The core-plug line shapes are considerably broadened compared with the original bulk fluid lines because of confinement to pore volume (PV) and mineral-induced internal field heterogeneity. The bulk fluid line shape was manually broadened to achieve a fit to the observed spectra of the core plug, with the amplitude determining the amount of each fluid.
Figure 3. (A) The 1H nuclear magnetic resonance (NMR) spectrum of oil-saturated core plug (black) measured with a 30-mm NMR probe. Oil and brine peaks are fit with broadened and scaled line shapes from bulk oil (red) and brine (blue) to obtain the total fluid content. (B) Fluid-specific T2 relaxation (spin–spin relaxation time) decays for oil (black, green) and brine (blue) show two relaxation times; the shorter one is associated with microporosity. Amplitudes of the double exponential functions, indicated by the lines, give fractions of micro- and macroporosity for each fluid. Values are given in tables. chem. = chemical.
To quantify the 1H NMR signal from the core plug, it is best to directly fit the entire experimental spectrum from the core plug (such as Figure 3A) with broadened and weighted experimental spectra of a known amount of bulk oil and bulk brine measured on the same experimental setup under the same experimental conditions. Quantitative analysis is reported based on this approach with four reference samples: 0.992 g of crude oil dissolved in D8-toluene (invisible for 1H NMR), 1.022 and 2.032 g of brine in D2O, and 2.030 g of a seawater in D2O with total volumes of each reference sample similar to a core-plug volume (∼13.0 cm3). The best accuracy of fluid quantification was achieved by applying the simplest 1-pulse free induction decay sequence and subtraction of the probe background signal. Alternatively, a spin-echo sequence with short interpulse duration allows the probe background signal to be filtered out, but this requires extrapolation of the first echo signal to zero time to compensate a signal reduction because of T2 relaxation. This can introduce errors.
Details of the comparison of low-field and high-field analyses are given in Supplement A (supplementary material available as AAPG Datashare 114A at www.aapg.org/datasharecaqravzardeqwb). For these carbonates containing both oil and water, there is no clear separation in signal between oil and water using low-field NMR. The spectroscopic resolution of high-field NMR makes differentiating oil from water possible.
Pore-Scale Oil and Water with Chemically Resolved T2 Relaxometry
The relative fraction of fluid-filled micro- and macropores can be estimated with NMR by monitoring the rate of an NMR signal decay (e.g., T2 relaxation), which is faster for a high rate of guest–host collisions (e.g., smaller pores or surface layer, larger surface-to-volume ratio) and slower for a low rate of guest–host collisions (e.g., larger pores, smaller surface-to-volume ratio). In addition to the standard Carr–Purcell–Meiboom–Gill pulse sequence for T2 relaxometry that measures combined relaxation of all protons, high-field NMR offers a chemically resolved T2 relaxometry measured by a spin-echo sequence with variable interpulse delays, which allows one to separately probe the confined environment for oil and water. Figure 3B shows an example of chemically resolved T2 relaxometry with individual proton relaxation rates associated with oil (black, green) and brine (blue). The fitting of each relaxation decay allows for the number of relaxation mechanisms to be estimated (reflecting various degree of pore confinements) and for the quantification of fractions of fluid affected by each mechanism. Combined with the total amount of oil determined by 1H NMR spectroscopy, this then allows one to quantify the amount of oil and brine in micro- and macropores.
For samples after flooding, the brine T2 values do not always reflect the pore occupancy. In particular, water occupying the macropores has a short relaxation time. A possible explanation is that there are paramagnetic ions in the brine that cause a rapid spin quenching, thus mitigating the effects of the pore walls. For the low-water, preflood samples, this would have a minimal impact on the calculated microporosity.
When analyzing fluid-filled porous media by XMT, a well-recognized problem is that water and oil have similar linear attenuation coefficients (Hubbell and Seltzer, 2004). This is commonly addressed by replacing the native fluid with a chemically altered brine or oil containing a high atomic number constituent, for example, potassium iodide or 1-bromo-hexadecane (Wildenschild et al., 2005; Dunsmuir et al., 2006). Here, it was important to preserve wettability, and this requires that the sample contacts only native fluids. Xenon shows a high solubility in crude oil but is sparingly soluble in water (Potter and Clynne, 1978; Kharaka and Specht, 1988). The high x-ray absorption coupled with high solubility results in a crude oil saturated with xenon at 1.030 MPa (150 psi) having a linear attenuation coefficient approximately three-quarters that of calcite, whereas the attenuation of water is approximately one-quarter that of calcite (see Supplement B, supplementary material available as AAPG Datashare 114B at www.aapg.org/datashare). Tests showed that diffusion into oil is relatively rapid as it is transported across a water barrier. Therefore, it is feasible to saturate the oil in a core plug over a period of a few days.
A modified Golden Ratio (GR) protocol (Köhler, 2004; Butler et al., 2011) is used to continuously monitor the xenon uptake during labeling and the oil distribution during water flood. The protocol details are discussed in Supplement C (supplementary material available as AAPG Datashare 114C at www.aapg.org/datashare). In contrast to the small angular steps between 0° and 360° used by conventional tomography, the modified GR protocol scans in irregular angular steps of approximately 10°, oscillating indefinitely between 0° and 360° rotation and improving the angular sampling with each oscillation. During each oscillation, an additional projection is acquired at a fixed KeyAngle that was preselected to give an easily interpreted two-dimensional (2-D) radiograph of the sample. These radiographs are used to determine saturation during labeling and residual oil saturation during water flooding.
The computerized tomography (CT) data were acquired using an X-Tek HMX-160 cone-beam microCT scanner equipped with a time delay integration (TDI) detector (Davis and Elliott, 1997). Although TDI is slower than conventional 2-D detectors, it offers a wide field of view, excellent signal-to-noise ratio, and significantly reduced reconstruction artifacts.
The microfocus x-ray source was operated at 160 kV and 50 μA with a 10-μm focal spot size on a tungsten target. The broad x-ray source spectrum was filtered to remove low-energy components using a 0.5-mm copper foil at the source and 0.3 mm at the TDI detector.
Pressure Cell and Fluid Manifold
A Hassler-type core holder Temco model FCH-1-MM (25.4-mm [1-in.] sample diameter, 34.5 MPa [5000 psi]) was used for the XMT flooding experiments. The fiberglass body of this holder is relatively transparent to x-rays. The holder was fitted at top and bottom with specially designed cassettes to accommodate 360° of CT scanner rotation. The cassettes contain four 1.59-mm coiled stainless steel lines, providing both hydrostatic confining stress and sample pore-volume fluids to each end of the sample.
Xenon gas is supplied to the top of the sample through a gas manifold. Reservoir brine is supplied to the bottom of the sample through a liquid manifold connected to the output of an isolator. The isolator input is connected to an Isco Model 500D syringe pump with a D-series pump controller filled with deionized and degassed water. Pressure transducers are located in the gas and brine manifolds. Brine flow is computer controlled, operating at either constant pressure or constant flow rate. Gas and brine pressures and brine flow rate and volume are recorded during each experiment. All experiments were performed at a room temperature of approximately 25°C. A schematic of the cell configuration is shown in Figure 4.
Figure 4. Schematic of computerized tomography pressure cell and sample fluid supply. The core plug is capped top and bottom by porous glass frits, placed in a Viton boot, and sealed with polyether ether ketone end caps. This sealed assembly is placed in a fiberglass-epoxy sleeve that is transparent to x-rays. The core holder is connected to two fluid sources (confining pressure and pore pressure) through a set of rotary cassettes, which allow sample rotation. The x-ray attenuation is measured on a charge-coupled device (CCD). On the right is shown a schematic of core-plug flooding with xenon saturation. Xenon saturation is performed prior to brine flooding by subjecting the sample to a pressure (P1) of xenon gas, which diffuses into the sample from the top. The brine source is isolated from the sample through valve 1 (V1), which prevents fluid movement within the core plug during xenon filling. Upon saturation, the pressures at P2 and P3 are set equal and valve V1 is opened. The P3 is then increased to maintain a constant flow rate, and typical flood rates are 0.1 to 0.05 cm3/min (0.00026 to 0.00013 gal/min).
Samples were competent 25.4-mm (1-in.)-diameter right cylinders with flat top and bottom faces initially saturated with native reservoir oil to a low residual water content.
The sample holder is assembled by placing a porous glass frit into the bottom of the Viton rubber boot and filling the frit and tubing with reservoir brine. The sample is inserted above the frit, and a second frit is placed on top. The porous frits ensure uniform distribution of fluids in contact with the core-plug faces. They also minimize capillary end effects within the core plug and suppress cone-beam attenuation errors at the top and bottom of the sample. Both frits are highly permeable compared with the sample.
The starting point for each flow experiment is an oil-saturated core plug (with residual water saturation) at 6.9 MPa (1000 psi) confining stress. Samples were scanned at a 30-μm pixel pitch. This resolution is set by our need to analyze relatively large-volume core plugs of a size comparable with standard SCAL flow experiments.
An initial low-noise tomographic image is acquired. The 3-D image is evaluated, and a KeyAngle view is selected. The sample is rotated to the KeyAngle, and an initial low-noise radiograph is acquired. Referring to Figure 4, the brine valve 1 (V1) is closed. A GR sequence is initiated, V2 is opened, and xenon gas is introduced to the top of the sample.
Xenon uptake is monitored using the KeyAngle images. Using the prexenon image as a reference, differential absorbance images are direct measures of xenon content. For a sample with uniform porosity, the objective is to obtain uniform xenon distribution from top to bottom of the core plug. Variable xenon pressures are applied to accelerate that process (see Supplement A, supplementary material available as AAPG Datashare 114A at www.aapg.org/datashare). The equilibrium part of the GR sequence is reconstructed to obtain a xenon-saturated 3-D image. An image of the oil and water distribution is obtained by subtracting the initial image.
The flow experiment begins with a core plug in which the oil is fully xenon saturated. The brine pressure is set equal to the xenon (sample pore) pressure, and V1 is opened. Sample flooding is started by initiating a constant flow rate from the syringe pump. Because all of the lines were degassed before liquid filling, there is little compliance in this fluid column, and the recorded pump volume accurately measures the fluid in the sample. The typical flood rates are 0.1 to 0.05 cm3/min (0.00026 to 0.00013 gal/min) (similar to that used for SCAL experiments).
Initial recording of the flow front is made through a series of KeyAngle radiographs. Contrast between the xenon-saturated oil and the injected brine highlights the advancing brine. After injection of a preselected number of PVs, the flow is halted and data are obtained for approximately 12 hr for a 3-D reconstruction. Afterward, the flow is restarted and additional brine is injected (several PVs). Details for each sample are given in the Results section below.
Beam Hardening and Image Reconstruction
The x-ray source used by conventional CT scanners produces a broad spectrum of x-ray energies. Low energies are readily absorbed by short paths through the sample, whereas higher energies are needed to penetrate longer paths. The average energy of the x-ray beam increases or “hardens” as it passes through the specimen. Thus, a thick part of a homogeneous material appears less attenuating per unit length than a thin part. This energy filtration by the sample is referred to as beam hardening and results in a “cupping” artifact in reconstructed slices where the linear attenuation coefficients near the thin outside edge of a sample are higher than the interior. Prefiltering the x-ray source to attenuate the low-energy x-rays reduces, but does not eliminate, the artifact.
For relatively homogeneous samples, such as the ones here, the cupping artifact can be corrected by weighting the projection attenuations with a function that produces a uniform reconstructed attenuation profile at an averaged or effective x-ray energy. The beam-hardening corrections for each sample are determined from the xenon-free initial image and are used consistently for all time slices, that is, the uptake of xenon does not significantly alter the effective x-ray energy.
Using the KeyAngle sequence for guidance, GR projections were time-sliced using a custom ImageJ (US National Institutes of Health, Bethesda, Maryland) plugin. The software CT-Pro (Nikon Metrology, Brighton, Michigan) was used to apply beam-hardening corrections and for tomographic reconstruction. Although samples were scanned at a 30-μm pixel pitch, these data were binned to a 60-μm resolution using the ImageJ macro Image/Scale to improve signal-to-noise ratio.
Image Analysis Using Nuclear Magnetic Resonance–Guided Segmentation
Using XMT techniques to image pores in rocks is a common operation in the field of digital rock physics. However, when the pores are below the instrument resolution, there is a problem using conventional methods that rely on edge-finding routines to segment pore from rock (Dunsmuir et al., 2006; Leu et al., 2014). Commonly, this is addressed by subsampling and producing high-resolution images of the subsample. This has the significant disadvantage of reducing the sampled volume significantly below that used in traditional core flood experiments. Because core-plug–sized samples have been subjected to a long-established set of protocols that have proven robust in defining flow characteristics for reservoir rocks, their use is preferred. Also, subsampling can miss important structural heterogeneity that affects flow. Such is the case for our samples where both micro- and macropores are important.
Ideas discussed in previous publications (Dunsmuir et al., 2006; Xu et al., 2017) are used here to segment the rocks into three components: rock, macropores, and micropores. The procedures make use of the analysis of voxel-scale linear attenuation values throughout the sample combined with the attenuation change that is caused by xenon gas infusion into the pores. Guided by NMR data taken on the same core plug, which provide the values of porosity, oil, water, and fraction of microporosity, this new method determines the voxel-scale distribution of rock, oil, and water consistent with those NMR values. The outcome is an excellent map of interpore connectivity, but with an incomplete resolution of pore shape. It emphasizes the importance of connectivity to fluid flow. For example, it is shown in the images below how oil distribution is affected by percent microporosity, and also shown is that connected pathways, explored by invasion percolation, closely align with experimental sweep.
The image segmentation method is detailed in Supplement D (supplementary material available as AAPG Datashare 114D at www.aapg.org/datashare
). Briefly, voxels are segmented into three populations: rock, micropore, and macropore using two thresholds denoted as
, the linear attenuation threshold between micropores and macropores, and
, that between micropores and rock (calcite). Unique values for a given core plug are obtained by solving two simultaneous equations, using as inputs the linear attenuation values for the 3-D volume and the NMR values of porosity and percent microporosity. Having defined the pore space, a “difference image” is created by subtracting the base 3-D XMT volume from that same volume after xenon saturation. Because xenon is strongly partitioned into the oil, this “difference image” is proportional to the oil content of each voxel. The threshold linear attenuation,
, is then calculated based on the NMR values for oil and water. The resulting segmentation is true to both the XMT and NMR quantities, producing a porosity map of the sample and the fluid filling of those pores, achieved with modest XMT resolution, for a full core-plug sample.
Of course, macropores are well resolved, and the size distributions have been previously reported for these two samples (Xu et al., 2017). The pores in sample 1 and sample 2 are described by a log-normal distribution, with parameters, respectively, a0 = 56.5 μm, s0 = 0.68 and a0 = 148.1 μm, and s0 = 0.69, where a0 and s0, respectively, are the mean and standard deviation of the log-normal distribution.
Nuclear Magnetic Resonance Results
As explained earlier, the primary measurement is total mass of each fluid. Using the measured fluid densities, one then calculates the fluid-filled porosity. From the fluid-specific relaxation times, one obtains the relative proportion of fluids in macro- and micropores. The volumes for water and oil in small pores relative to that fluid’s total volume are reported as microporosity water and microporosity oil, respectively. The total volume of fluid in small pores relative to the fluid-filled porosity is the microporosity total. The results for sample 1 are summarized in Table 2 and for sample 2 in Table 3. The microporosity total values compare favorably with petrographic analyses in Table 1.
Focusing on the macropore oil content, these data uphold a concept, suggested by intuition and confirmed by theory (Xu et al., 2017), that oil recovery in mixed-pore systems is biased toward the larger pores. For sample 1, the macropores are nearly fully swept, leaving the remaining oil mostly in microporosity. For sample 2, oil saturation in macropores is 38% before brine flooding 15% after. To compare with theory, we calculate the experimental ratio of micropore recovered oil to total recovered. For samples 1 and 2, respectively, the volume ratios from the NMR data are 0.92 and 0.33. The effective-medium theory values for this ratio are calculated using (see equation 13 in Xu et al., 2017, function Sm and definition of terms), giving 0.94 and 0.30, respectively, in good agreement with those from the experiment.
X-Ray Microtomography Results
Flow Conditions: Mobility Ratio and Capillary Number
Extensive work to define the characteristic behavior of immiscible fluid-flow behavior in porous media has been conducted (Lenormand et al., 1988; Hughes and Blunt, 2000; Al-Gharbi and Blunt, 2005). With the carbonates being mixed-wet with an oil-wet bias, the relevant studies are those where the nonwetting fluid invades the grain pack, so called drainage. These previous studies have emphasized the importance of key hydrodynamic controls described by two dimensionless numbers. The mobility ratio is M = μ2/μ1, where the flooding fluid (brine) viscosity is μ2 and the oil viscosity is μ1. The capillary number is Ca = Vμ2/IFT, where V is the fluid velocity and IFT is the water-to-oil interfacial tension. The room-temperature parameters for the fluids are as follows: oil: density = 0.85 g/cm3 (53.1 lb/ft3); viscosity = 57.3 mPa s (57.3 cP) and brine: density = 1.1 g/cm3 (68.7 lb/ft3); viscosity = 1.544 mPa s (1.544 cP). The IFT = 19 mN/m (0.00011 lb/in.). The resulting calculated value of the mobility ratio is M = 0.027. Using the flow rates of sample 1 = 0.1 cm3/min (0.00026 gal/min) and sample 2 = 0.05 cm3/min (0.00013 gal/min), the calculated Ca of the nonwetting fluid are Ca = 1.3 × 10−6 and Ca = 5.2 × 10−7, respectively. Using these, along with such studies (e.g., Lenormand et al., 1988), allows one to classify the expected flow behavior (see their figure 8). The M values correspond to zone II, the transition zone where the viscous pressure drops in both fluids, and they are a significant factor. The Ca values are in the range where viscous forces are small compared with capillary forces. This places the results close to the boundary marking the transition from compact flow to capillary fingering but still in the regime where flows will be compact for a uniform grain pack. Recent visualizations (Datta et al., 2014) of drainage at a comparable Ca value confirm that compact flow is expected.
The present experiments were designed to examine how this flow pattern is distorted when there is a mixed-pore system. It was anticipated that sample 2 would exhibit fewer compact flow patterns.
Compare Flooding Behavior
In the discussion of xenon filling (Supplement B, supplementary material available as AAPG Datashare 114B at www.aapg.org/datashare), it is discussed how the use of DiffTau imaging (radiographs) allows one to take snapshots of fluid content. Here, similar data are used to demonstrate how brine flooding displaces that xenon-saturated oil. These data are utilized in two ways. The first is to generate real-time movies of displacement, useful for a qualitative impression of sample differences. However, a quantitative measure of oil content can be obtained from the average attenuation for each DiffTau image. These values decline with brine flooding as oil content decreases. The one correction necessary is that for a constant background attenuation coming from the xenon-saturated Viton rubber boot. This correction is calculated from the NMR data and is simply the ratio of NMR oil volume before and after brine flood. The correction is equal for both samples and is approximately one-third of the total attenuation.
Figure 5. Plotted data are the normalized average DiffTau attenuation values for all KeyAngle images taken during brine flooding. The plotted values are corrected for the attenuation of the xenon-saturated rubber boot surrounding the sample. In the insets are displayed panels at selected pore-volume values, showing the progression of oil (red) exiting the top of the sample. Note the strong gradient in sample 1 compared with the more diffuse pattern for sample 2. The slight rise at the beginning of the scan is caused by some extra xenon entering the field of view, likely from the bottom porous frit.
A clear difference in fluid displacement can be observed between samples 1 and 2. In the first PV of the flood, uniform sweep in sample 1 produces a higher oil recovery than for sample 2. This is also reflected in the more compact flow shown in the comparison radiographs (Figure 5) and in the 3-D distributions (Figure 6). After eight PVs, the recovery factor for sample 2 is still less, consistent with what has been found for SCAL data (Table 1). As shown in the next section, this is caused by bypassed oil remaining in the core plug.
Figure 6. The three-dimensional oil volumes showing the effects of progressive brine flood from the bottom of the image. The gray scale is adjusted to show the oil as white. As expected, the mixed-pore sample 2 shows a much less compact oil distribution. Flow in that system is governed by the higher permeability of larger pore pathways. The samples are presented on a common grayscale level. A minor amount of oil in the lower part of sample 1 is present, but barely visible, at this gray scale. PV = pore volume.
Golden Ratio Imaging
Now compare the 3-D images taken during progressive brine flooding. The quantification from NMR-guided segmentation is summarized for sample 1 in Table 4 and for sample 2 in Table 5. However, the power of the XMT imaging is best displayed with 3-D images, and the sample image is segmented into rock, water, and oil using values in Tables 4 and 5 to produce images of each component. The displayed images in Figure 6 are those of the oil component. Brine floods in these images originate from the bottom of the sample. Examining Figure 6, the bypassed oil in sample 2 at 8.6 PV is readily apparent, and a significantly different pattern is seen for sample 1 at essentially the same PV sweep condition.
Comparison with Simulation
As was discussed above, for the flow conditions, compact sweep of a uniform porous media is the norm. How then can one account for the heterogeneous flow paths of the mixed-pore rock? Use of invasion percolation for a nonwetting fluid provides a quantitative means to describe how fluid flow is affected by interpore connectivity. Using a simulation method described in Xu et al. (2017), a comparison between experiment and simulation is shown in Figure 7. This simulation uses the interpore connectivity to define the invasion pathway. Pores are progressively invaded from the bottom of the digital volume. At each step, invasion stops when the pathway for further invasion reaches a selected critical lower limit of pore size. One progressively decreases that limit and thus digitally samples more and more of the interconnected pores. Here, that simulation has been run to invade approximately 20% of the pore space for the digital volume for sample 2 (Figure 7B). Figure 7A shows the actual oil displacement measured for sample 2 after 2.4 PV flood, corresponding to the same 20% total volume of oil displaced. Similar to the NMR, this work shows that larger pores are preferentially swept of their oil. In addition, the comparison demonstrates that digital flooding can well describe how the displacement pattern is governed by the pore space and that modest-resolution XMT can adequately describe the pore geometry that controls fluid flow in such rocks. When a wetting fluid invades a porous media, greater complexity is found because wetting films are notoriously sensitive to small details of the pore geometry, such as roughness. However, the carbonates are mixed-wet or oil-wet and brine is a nonwetting fluid.
Figure 7. Oil distribution after experimental 2.4 pore-volume flood (A) compared with that simulated by invasion percolation (B). The digital flooding is accomplished through operation of an invasion percolation algorithm on the digital volume. Progressing from largest interconnected pores toward smaller ones, the fluid invasion mimics the pore-size–dependent oil sweep efficiency. The swept volumes for both experimental and simulated images are comparable, approximately 20% of the total pore volume.
A new method for tagging in-place oil has been developed, one that allows use of native fluids. Together with a new segmentation procedure that brings the fluid content as measured by NMR into alignment with the XMT data, these new procedures allow the investigation of fluid displacement in core-plug scale samples. This affords direct comparison with conventional SCAL results that are obtained from similar plug-scale samples. The effects of heterogeneities are imaged and can be related to the overall SCAL behavior. These benefits have been demonstrated through the analysis of two characteristic microporous carbonate samples, one micropore dominated and one having mixed pores. The mixed-pore sample exhibits greater dispersion in the oil movement during brine sweep, and increased residual, bypassed oil. As has been show previously, such samples exhibit lower oil recovery. It was recently demonstrated that this can be modeled through the use of an effective-medium model (Xu et al., 2017). Results here quantify the oil sweep efficiency for each pore type and one finds quantitative agreement with that model.
An advantage of this new approach is the use of XMT resolutions that are less than the individual pore sizes. This approach succeeds because the mineralogy of carbonates is simple, making the linear attenuation of an individual voxel a simple linear combination of calcite, oil, and water. The additional NMR data on the fluids allows one to solve this equation. This approach should work equally well in other rocks. Certainly, it can be used for all varieties of carbonates, providing the pore space is fluid accessible. Also, as noted above, high-field NMR works best when used for carbonates, where paramagnet ions are typically low (Mitchell et al., 2010). The XMT method will work well for any rock where the mineralogy is not too complex, for example, diatomites like the Monterey Formation (California). For accurate segmentation, the x-ray absorption must be a linear combination of mineral, oil, and water. A final consideration is whether the rock contains significant solid organics. If so, these will dissolve xenon, causing an increase in apparent porosity. For such rocks, xenon uptake is not a good proxy for fluid-filled porosity.
The recognition of subvoxel resolution afforded by imaging before and after infusion with xenon (or another x-ray absorber) is an important tool for examination of porous rocks. Combined with digital flooding, it provides a way to characterize how pore spaces in rocks are interconnected. For example, with some digital manipulation of the analyses presented here, local values of tortuosity can be obtained (Dunsmuir et al., 2006).
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Conversations with Shawn Fullmer, ExxonMobil Upstream Research Company were greatly appreciated.
Supplements A–D are available in an electronic version on the AAPG website (www.aapg.org/datashare) as Datashare 114.