Imbibition Relative Permeability Research Articles

Hybrid Technique for Setting Initial Water Saturation on Core Samples

Relative permeability and capillary pressure are important parameters in reservoir simulations because it helps in understanding and anticipating oil and/or gas production scenarios over the years. They are both obtained in a laboratory after establishing the required initial conditions. As a matter of fact, before measuring imbibition relative permeability and capillary pressure, it is recommended to set initial rock reservoir conditions by establishing appropriate initial water saturation (Swi) and by aging the core to restore the reservoir wettability. There are several conventional techniques to establish Swi. Viscous flooding is a fast technique, but it may create a non-uniform saturation profile and, in some cases, be inefficient in reaching low Swi targets. Centrifugation is a capillary-driven technique that is also very fast; however, the possibility of not desaturating the outlet face is a significant constraint. In both cases, reversing flow direction is generally performed to flatten the saturation profile; however, this phenomenon is poorly controlled. The application of capillary pressure by porous plate allows targeting a specific value of Swi and generates a uniform saturation profile; however, it is a very time-consuming method. In this paper, we present the Hybrid Drainage Technique (HDT), which couples viscous flooding and porous plate approaches, significantly reducing the experimental duration when setting Swi. Another advantage of the method is the possibility of setting a uniform saturation profile at the targeted Swi. A specific core holder, adapted to nuclear magnetic resonance (NMR) imaging and capable of performing both viscous flooding and porous plate testing without unloading the rock, was designed. Using this core holder enables performing aging and imbibition coreflood testing with no further manipulation of the core sample. Monitoring saturation profiles was made possible by using an NMR imaging setup. The method has been tested and validated on two outcrop samples from Bentheimer (sandstone) and Richemont (limestone), drastically reducing the experimental time of the primary drainage step in comparison to classical porous plate drainage but also leading to uniform water saturation profiles. The experiment duration is reduced, and it enables the realization of coreflooding; therefore, this technique may be used for larger samples classically used in relative permeability experiments. This approach is preferred as it provides faster and more reliable measurements of saturation.

Forced imbibition and uncertainty modeling using the morphological method

The morphological approach is a computationally attractive method for calculating relative permeability and capillary pressure saturation functions. In the corresponding workflow, morphological operations are used to calculate the fluid phase distribution in the pore space of a digital twin. Once the pore space is occupied, the conductivity of the individual fluid phases and thus the relative permeability can be calculated by direct flow simulations. It therefore combines computationally favorable geometric operations with direct flow simulations. In contrast to pore network modeling, all calculations are directly performed on the digital twin without abstraction of the pore space. While the morphological operations conceptually correctly describe primary drainage processes and delivers good results, the method so far failed to describe imbibition processes and the influence of wettability. In this work, we implement contact angle distributions in a deterministic and stochastic way. In this manner, we extend the simulated saturation range from purely spontaneous to forced imbibition, resulting in a full-range imbibition relative permeability. Furthermore, by introducing stochastic contact angle distributions, different fluid phase distributions are obtained, which now allow for an uncertainty analysis. To verify the simulation results, we check (a) whether the simulation results agree with SCAL measurements and (b) compare morphologically and experimentally derived results on the pore scale. With the newly introduced concepts, the imbibition process behaves as physically expected, and shows a good agreement with experimentally derived relative permeability curves and microscopic fluid-phase distributions.

Water-Gas Imbibition Relative Permeability: Literature Review, Direct versus Indirect Methods and Experimental Recommendations

When an active aquifer encroaches into a gas bearing reservoir or when an oil rim sweeps gas during late depletion of the gas cap, gas displacement by liquid is important for estimating the gas recovery. In the water displacing gas condition, the viscosity ratio is extremely favorable, resulting in a sharp waterfront in the reservoir matrix: it results that changing the relative permeability Kr shape has negligible effect, while endpoints water relative permeability Krw Max and residual gas saturation Sgr are much more important to understand gas flow performance for estimation of gas recovery with active aquifer or productivity decline after water breakthrough. Three main methods are used to determine water/gas relative permeability curves: imbibition unsteady-state, imbibition steady-state or indirect approaches such as co-current spontaneous imbibition if transient data are available. One of the other popular indirect methods is called Brooks-Corey approach: by measuring the drainage Pc curve using centrifuge or porous plate methods, it is possible to calculate a pore size distribution index c. This coefficient is used in a Brooks-Corey model to determine the drainage Kr curve. It is also required to measure and determine the relationship between the residual gas saturation Sgr and the initial gas saturation Sgi relationship. Finally, it is accepted that there is no hysteresis on the water relative permeability Krw curve, as water is always the wetting phase in the gas/water couple. As non-wetting phase, gas exhibits strong hysteresis between drainage and imbibition curves: it is therefore necessary to apply a correction on the drainage Krg curve to build the imbibition one using correcting models. The aim of this paper is to compare gas/water relative permeability of clastic rocks using direct waterflooding information and indirect approach using Brooks-Corey model. It is shown that using the indirect approach leads to results like those experimentally obtained. Also, additional numerical simulations are proposed to discuss the relevance of measuring the entire water-gas imbibition relative permeability curve using the steady-state approach.

An accelerated process-based method for the accurate computation of relative permeability from direct simulations of two-phase flow on micro-computed tomography images of porous media

Pore-scale forces have significant effects on the macroscopic behavior of multi-phase flow through porous media. We develop a robust and accurate accelerated process-based method for the computation of relative permeability from direct simulations of pore-scale two-phase flow on micro-computed tomography images. In the pressure drop calculation, we take advantage of an existing analysis that establishes a relationship between pore-scale forces and Darcy-scale pressure drops using an energy-conservation approach. We establish a thermodynamically consistent approximation of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each flowing phase for the first time within the context of a free-energy lattice Boltzmann method (LBM). In addition, we propose and test a new computationally efficient partial-mirror periodic boundary condition for a fully coupled visco-capillary pore-scale flow simulator based on a free-energy LBM. The new boundary condition is imposed only in the main flow direction and significantly reduces the computational cost of the process-based relative-permeability computation protocol at a small compromise on accuracy.We first compute primary-drainage and subsequent imbibition relative permeability curves for a reservoir sandstone rock sample. We use this real-reservoir dataset to validate the pressure drop computation method and the partial-mirror periodic boundary condition. We then simulate the entire drainage and imbibition cycle using an extensively studied Berea sandstone dataset. We quantitatively demonstrate that pore-scale direct numerical simulation-based relative permeability curves computed with our novel process-based method agree well with experimental steady-state relative permeability measurements. We also quantitatively demonstrate that the new partial-mirror periodic boundary condition accelerates the relative permeability computations 4 to 13 times.

Influence of capillary pressure boundary conditions and hysteresis on CO2-water relative permeability

This study examines the effect of capillary pressure boundary conditions and hysteresis on CO2-water relative permeability. We perform drainage and imbibition injections into a Berea sandstone core and a sintered glass core. The cores receive three injection stages: water, then water-saturated CO2 representing drainage, and finally CO2-saturated water representing imbibition. Pressure difference and fluid production are recorded. To generate relative permeability using these data, we propose that the conventional Johnson–Bossler–Naumann (JBN) method be modified to incorporate capillary pressure boundary conditions. We then compare the results yielded by the JBN and modified-JBN methods, which generate relative permeability for post-breakthrough water saturation. To generate relative permeability for all states of saturation, history matching is used, in which the relative permeability of a numerical model is tuned until the simulated data match the experimental data.For drainage, history-matched relative permeability curves are found to be significantly closer to modified-JBN estimates than to JBN estimates. This indicates that the proposed modified-JBN method can provide a more accurate initial guess for history matching. In addition, using the initial guess generated by modified-JBN is found to reduce the chance of non-unique history-matched relative permeability curves.For imbibition, the CO2-water relative permeability curve is generated directly from history matching because the experimental data are too sparse to apply the JBN or modified-JBN method. Both CO2 and water imbibition relative permeability are found to differ from the drainage relative permeabilities. This so-called relative permeability hysteresis is attributed to contact angle hysteresis. In addition, imbibition CO2-water relative permeability is found to be sensitive to imbibition capillary pressure boundary conditions.

A new approach to measure wettability by relative permeability measurements

Wettability is a key factor controlling the flow of fluids, solutes, heat and electrical current in porous media, and therefore it is important in studies of various processes including CO2 storage, secondary and tertiary oil recovery, as well as the displacement of water and nonaqueous phase liquid (NAPL). Although Amott-Harvey and USBM are conventional industry-standard techniques for measuring average wettability, they have some limitations. In this paper, we show that, in a plot of the relative permeability of a fluid, the area below the curve is closely related to the wettability. By using the areas below the water and oil relative permeability curves, we derive a new wettability index (called modified Lak). To demonstrate the applicability of this new index and testing other indices, we performed primary imbibition relative permeability, and primary imbibition and secondary drainage capillary pressure measurements on twenty carbonate reservoir samples. In general, all indices predicted oil-wet character of the tested rocks. USBM was associated with the broadest range of variation, whereas the new index corresponded to the smallest range of variation. Amott-Harvey and Lak, however, fell between USBM and the new index, with fairly similar ranges of variation. In addition, we report the correlations between different indices, and the change of wettability indices vs. reservoir depth. Advantages and limitations of different wettability indices are also discussed. Since each wettability index has some limitations in revealing the true state of wettability, none of these indices can be considered as an absolute measurement. Therefore, different indices should be regarded as complementary to each other, and determination of wettability should not be limited to only one method.

Analysis of the bounded and unbounded forms of USBM wettability index

Understanding wettability is important in many processes where porous media and fluids are in contact. The U.S. Bureau of Mines (USBM) is one of the industry standard techniques for measuring wettability. This index is calculated as USBM=lg(A1A2), where A1 and A2 are the areas under capillary pressure curves of oil-drive and water-drive processes, respectively. Usually, the USBM is mistakenly assumed to vary over the range of −1 to 1 and compared with other indices. In this study we indicate that the lower and upper bounds of this index are not fully known in practice. As a result, comparison between USBM and other indices may cause erroneous interpretations due to dissimilar ranges of variation. In addition, even during examining the USBM of a sample it may not be possible to accurately interpret its wettability. We highlight the bounded form of the USBM index (denoted as USBM∗=A1−A2A1+A2), which varies over the range of −1 to 1, and suggest that it should replace the traditional form of USBM index. Twenty limestone core-plugs were collected from Asmari and Fahlian formations in two Iranian fields. These samples were used for performing primary imbibition relative permeability measurements, as well as primary imbibition and secondary drainage capillary pressure tests. These experiments are used to show the differences between USBM and USBM∗ in comparative studies and compare them against other indices of Amott-Harvey, Lak and modified Lak.

Geometrical-Based Generative Adversarial Network to Enhance Digital Rock Image Quality

X-ray microcomputed tomography (micro-CT) is a common tool for the study of porous media structures and properties. High-quality micro-CT data are required to accurately capture pore structures. Acquiring high-quality micro-CT data, however, is not always possible, owing to application limitations and experimental constraints. Therefore, we propose a geometrical-based generative adversarial network (GAN) to rapidly restore noisy micro-CT images to their clean counterparts. The training data and related ground-truth (GT) data are scanned for 7 min and 9.5 h, respectively. To evaluate the performance of the geometrical-based GAN, a ${600}^{3}$ voxel image that has never been used for training is reconstructed and compared with the corresponding GT image. Histogram matching and linear normalization are implemented to adjust the histogram of the reconstructed image to that of the GT image. A watershed-based segmentation method is then applied to delineate pore and solid phases. Lastly, we measure the Minkowski functionals and petrophysical properties, including absolute permeability, pore size distribution, drainage capillary pressure-saturation curve, and imbibition relative permeability, to estimate the physical accuracy of the denoised image. The results show that the proposed geometrical-based GAN can accurately restore noisy micro-CT data. By reducing the scanning time from 9.5 h to 7 min, the expenditure of collecting micro-CT can be decreased significantly. This is particularly important for applications where time-lapse images of a dynamic process are required, high-throughput imaging is necessary for real-time data analysis, or where the quantification of large sample volumes is required.

Observations of the Impact of MM-Cm Scale Lamination on the Migration and Trapping of CO <sub>2</sub> in Reservoir Rocks

Small scale (mm-cm scale) capillary heterogeneity can result in capillary induced flows and trapping. This can have significant impact on the migration of the injected CO2. In this research, we have measured and characterized the impact of small scale lamination on multiphase-flow parameters and residual trapping of CO2 by combining experimental, numerical, and analytical methods. Experimental CO2/water core-flood tests were performed at reservoir conditions on a laminated reservoir rock core. A medical X-ray CT scanner was used for visualization. Effective drainage and imbibition relative permeability, effective drainage capillary pressure, and residually trapped CO2 were measured. The experimental results were used to obtain a model of the rock core using the method described in. The layers of the rock core are tilted and truncated at the inlet, outlet, and radial outer boundary of the core. To correct for this, the layers were shifted, such that the layers became parallel to the flow direction and extended in the lateral direction. The model of the rock core was used to simulate the drainage core-flood test for a range of flow-rates and flow-rate dependent effective relative permeability and capillary pressure were derived. In addition, simplified analytical models were used to obtain these drainage parameters, as well as capillary limit imbibition effective relative permeability and capillary pressure. The results indicate that simplified analytical models can give a good approximation of these effective multi-phase flow parameters. Furthermore, they show that to correctly derive effective multi-phase flow parameters for layered systems, the geology of the system has to be taken into account. Experimental measurements on rock cores with artificially truncated layers can lead to the incorrect inclusion of the impact small scale heterogeneity.

Verifying Pore Network Models of Imbibition in Rocks Using Time‐Resolved Synchrotron Imaging

AbstractAt the pore scale, slow invasion of a wetting fluid in porous materials is often modeled with quasi‐static approximations which only consider capillary forces in the form of simple pore‐filling rules. The appropriateness of this approximation, often applied in pore network models, is contested in the literature, reflecting the difficulty of predicting imbibition relative permeability with these models. However, validation by sole comparison to continuum‐scale experiments is prone to induce model overfitting. It has therefore remained unclear whether difficulties generalizing the model performance are caused by errors in the predicted filling sequence or by subsequent calculations. Here, we address this by examining whether such a model can predict the pore‐scale fluid distributions underlying the behavior at the continuum scale. To this end, we compare the fluid arrangement evolution measured in fast synchrotron micro‐CT experiments on two rock types to quasi‐static simulations which implement capillary‐dominated pore filling and snap‐off, including a sophisticated model for cooperative pore filling. The results indicate that such pore network models can, in principle, predict fluid distributions accurately enough to estimate upscaled flow properties of strongly wetted rocks at low capillary numbers.

Effect of Injection Pressure on the Imbibition Relative Permeability and Capillary Pressure Curves of Shale Gas Matrix

Effect of Injection Pressure on the Imbibition Relative Permeability and Capillary Pressure Curves of Shale Gas Matrix

Improved method for complete gas-brine imbibition relative permeability curves

Standard test methods for measuring imbibition gas-brine relative permeability on reservoir core samples often lead to non-uniform brine saturation. During co-current flow, the brine tends to bank up at the sample inlet and redistributes slowly, even with fractional flow of gas to brine of 400:1 or more. The first reliable Rel Perm point is often only attained after a brine saturation of around Sw=40% is achieved, leaving a data gap between Swirr and this point. The consequent poor definition of the shape of the Rel Perm function can lead to uncertainty in the performance of gas reservoirs undergoing depletion drive with an encroaching aquifer or subjected to a water flood. We have developed new procedures to pre-condition brine saturation outside of the test rig and progress it in small increments to fill in the data gap at low Sw, before continuing with a co-current flood to the gas permeability end-point. The method was applied to series of sandstone samples from gas reservoirs from the NW Shelf of Australia, and a Berea standard. We found that the complete imbibition relative permeability curve is typically ‘S’ shaped or has a rolling over, convex-up shape that is markedly different from the concave-up, Corey Rel Perm curve usually fitted to SCAL test data. This finding may have an economic upside if the reservoir produces gas at a high rate for longer than was originally predicted based on the old Rel Perm curves.

Complete gas-brine imbibition relative permeability curves increase confidence in gas field performance

The standard methods used for measuring gas relative permeability during brine imbibition have been found to be inadequate as the resulting curves are incomplete and may include invalid points. CSI...

Evolution of hysteresis relative permeability of wetting brine phase using contact angle hysteresis in a partially saturated CO2-brine system

ABSTRACT In sequestration of CO2 in deep saline aquifers, the relative permeability of the immiscible fluids plays a crucial role in governing dissolution and capillary trapping mechanisms. Relative permeability is solely dependent on capillary pressure and saturation at that instant of time, whereas the capillary pressure dynamically changes during flow reversal resulting in the hysteresis behavior of the relative permeability curves. However, the conventionally used models equate relative permeability as an explicit function of saturation, neglecting the inherent physics that govern the immiscible displacement of fluids. On the other hand, upscaling the pore scale mechanisms, such as contact angle hysteresis and wettability characteristics, to Darcy scale remains complicated. In the present investigation, an attempt has been made in formulating a methodology to compute relative permeability of the phase fluids based on contact angle hysteresis. The relative permeability curves calculated using the present model have been compared with that computed using existing methodology present in the literature. It has been observed that the present relative permeability model effectively calculates the drainage and imbibition relative permeability of both the wetting and non-wetting phases in the porous system.

IMBIBITION WATER-OIL RELATIVE PERMEABILITY: INTRODUCTION OF WETTABILITY STRENGTH FOR ENHANCING MODEL ROBUSTNESS

Water-oil relative permeabilty information of hydrocarbon reservoir rocks plays important roles in various modeling activities related to reservoir modeling and production forecast. The imbibition relative permeability scheme - the process of concern in this study affects many dynamic processes in reservoir. Water flooding and water encroachment form aquifer to oil zone in the reservoir are two two examples which representation in reservoir model requires the data. This study uses the standard Corey relative permeability model as a tool to study and model imbibition relative permeability behaviour of some reservoir rocks in Indonesia. Laboratory data from as many as 340 rock samples - sandstones and limestones - of various permeability and wettability from various oil fi elds in Indonesia is used. Activities in the modeling has pointed out the need to introduce two new empirical factors that relate to rock wettability and non- wetting fl ow hindrance to the model. The two factors appear to have signifi cantly improved the ability of the model to agree and match to the measured data. The modeling also produces suggested values of the factors for rock groups based on rock wettability type and strength, as well as on permeability categories. Comparison between modeling results before and after modifi cation has shown signifi cant improvement in validity of output.

Characterization of Hysteretic Multiphase Flow from the MM to M Scale in Heterogeneous Rocks

Incorporating mm-m scale capillary pressure heterogeneity into upscaled numerical models is key to the successful prediction of low flow potential plume migration and trapping at the field scale. Under such conditions, the upscaled, equivalent relative permeability incorporating capillary pressure heterogeneity is far from that derived conventionally at the viscous limit, dependent on the heterogeneity structure and flow rate, i.e. dependent on the capillary number. Recent work at the SCA 2017 symposium (SCA2017-022) demonstrated how equivalent functions can be obtained on heterogeneous rock cores from the subsurface under drainage conditions; going beyond traditional SCAL. Experimental observations using medical CT scanning can be combined with numerical modelling so that heterogeneous subsurface rock cores can be directly characterized and used to populate field scale reservoir models. In this work, we extend this characterization approach by incorporating imbibition cycles into the methodology. We use a Bunter sandstone core with several experimental CO2 – Brine core flood datasets at different flow rates (2x drainage, 1x imbibition and 2x trapping) to demonstrate the characterization of hysteretic multiphase flow functions in water-wet rocks. We show that mm-m scale experimental saturations and equivalent, low flow potential relative permeabilities can be predicted during drainage and imbibition, along with trapping characteristics. Equivalent imbibition relative permeabilities appear as a function of capillary number, as in the drainage cases. We also find that the form of capillary pressure function during imbibition has a large impact on the trapping characteristics, with local heterogeneity trapping reduced (or removed), if the capillary pressure drops to zero, or below at the residual saturation.

Cyclic Steam Stimulation Results in High Water Retention for Kuwaiti Heavy-Oil Field

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 184154, “High Water Retention in Cyclic-Steam-Stimulation Wells of Kuwait Heavy-Oil Field,” by Anil Kumar Jain, Amal Al-Sane, and Fatma Ahmad, Kuwait Oil Company, prepared for the 2016 SPE International Heavy Oil Conference and Exhibition, Mangaf, Kuwait, 6–8 December. The paper has not been peer reviewed. Cyclic steam stimulation (CSS) is one of the principal enhanced-oil-recovery methods for heavy oil. CSS was performed in some of the wells of a heavy-oil field in Kuwait. Multiple cycles were applied in these wells. However, the total water produced in each cycle was much less than expected. This paper presents experiments that were conducted to find possible reasons for the high water retention. Hysteresis in CSS Hysteresis in drainage and imbibition nonwetting-phase capillary pressure and relative permeability curves is an established phenomenon. Hysteresis of capillary pressure and relative permeability to water has a great effect on heavy-oil recovery and producing water/oil ratios (WORs) during cyclic steam stimulation. Produced WOR calculated without considering hysteresis will be unrealistically high relative to that observed in the fields. Water Retention During water injection, relative permeability to water increases, and, during the production phase, it decreases; however, it does not follow the same path. Relative permeability to water during the production phase is always less than that during the injection phase at the same water saturation. Irreducible water saturation during the production phase is more than the initial water saturation before injection. The difference between these two water saturations is water retention. The same phenomenon occurs when CSS is applied. As a result of hysteresis and temperature, irreducible water saturation does not reach the initial water saturation. When steam is injected into a formation, the formation becomes increasingly water-wet. In subsequent cycles, steam injection reduces the oil saturation and increases the water saturation around the wellbore. Relative permeability to oil at high water saturation is also reduced. In later cycles, increasingly more water is produced than oil, and, therefore, the WOR increases. The produced water consists of both the condensed steam and the formation water. After steam is injected, fresh water is produced first, and slowly the salinity of the produced water increases. Initially, some of the condensed steam returns, but, later, formation water is produced with the condensed steam. If the well produces for long enough, eventually only formation water will be produced.

A comparative study of predictive models for imbibition relative permeability and trapped non-wetting phase saturation

The hysteresis in two phase relative permeability occurs when the saturation history of the flow changes from drainage to imbibition or vice versa. The imbibition relative permeability is a strong function of initial non-wetting phase saturation from which the imbibition process starts. Hence, it is very time-consuming to conduct many experiments for measuring all possible imbibition relative permeability (kr) data. An alternative approach is to predict the imbibition relative permeability using the measured Land trapping coefficient and primary drainage relative permeability. Some predictive models, found in the literature, such as that of Land, Carlson and Killough are available in commercial simulators. For prediction of imbibition data, these models require the primary drainage kr data and one set of imbibition kr data to calculate the corrected Land trapping coefficient. However, the imbibition relative permeability is not always available and the inappropriate use of these models can introduce significant errors in the calculations. In this study, the limitations of the available models are discussed and a modified method is suggested, which only requires the primary drainage kr data and the measured Land trapping coefficient.The available models for prediction of imbibition kr data are based on the calculations of trapped non-wetting saturation (Snwt). Therefore, in this study, a modified method was introduced which improved the estimations of trapped non-wetting phase saturation. The predicted values of imbibition relative permeability using this improved method were in good agreement with the experimental data. It was shown that this method can be used for both gas and oil as non-wetting phases in a water-wet medium. However, the trapped non-wetting phase is a function of capillary number and the Land trapping coefficient changes as the capillary number changes. Hence, the measured Land trapping coefficient cannot be assumed as constant in cases where severe changes in pressure result in changing interfacial tension (IFT) and fluid viscosity.

Effect of Network Topology on Relative Permeability; Network Model and Experimental Approaches

The effect of topological properties on imbibition relative permeabilities and residual saturations was previously studied by utilizing quasi-static network model topologies extracted from actual sandstones 3D micro-tomographic images. Non-wetting fluid in imbibition displacements can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. The findings showed that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. The findings were valid for random networks and for networks displaying short-range pore-throat and longer-range spatial correlations. The aim of this study is to validate network model findings by comparing them with laboratory measurements of relative permeabilities. Laboratory measured data include imbibition relative permeability for sandstones of similar petrophysical properties to Fontainebleau sandstone used to extract 3D micro-tomographic images. Laboratory measurements were made at ambient conditions on core samples of different diameters and different porosities and permeabilities. Experimental measurements were in good qualitative agreement with stochastic networks that match the full coordination number distribution and geometric properties of networks obtained from 3D micro-CT images. Experimental measurements were also in good agreement with networks displaying both short-range pore-throat correlations and longer-range spatial correlations.

Connected pathway relative permeability from pore-scale imaging of imbibition

Pore-scale images obtained from a synchrotron-based X-ray computed micro-tomography (µCT) imbibition experiment in sandstone rock were used to conduct Navier–Stokes flow simulations on the connected pathways of water and oil phases. The resulting relative permeability was compared with steady-state Darcy-scale imbibition experiments on 5cm large twin samples from the same outcrop sandstone material. While the relative permeability curves display a large degree of similarity, the endpoint saturations for the µCT data are 10% in saturation units higher than the experimental data. However, the two datasets match well when normalizing to the mobile saturation range. The agreement is particularly good at low water saturations, where the oil is predominantly connected. Apart from different saturation endpoints, in this particular experiment where connected pathway flow dominates, the discrepancies between pore-scale connected pathway flow simulations and Darcy-scale steady-state data are minor overall and have very little impact on fractional flow. The results also indicate that if the pore-scale fluid distributions are available and the amount of disconnected non-wetting phase is low, quasi-static flow simulations may be sufficient to compute relative permeability. When pore-scale fluid distributions are not available, fluid distributions can be obtained from a morphological approach, which approximates capillary-dominated displacement. The relative permeability obtained from the morphological approach compare well to drainage steady state whereas major discrepancies to the imbibition steady-state experimental data are observed. The morphological approach does not represent the imbibition process very well and experimental data for the spatial arrangement of the phases are required. Presumably for modeling imbibition relative permeability an approach is needed that captures moving liquid-liquid interfaces, which requires viscous and capillary forces simultaneously.