Estimation Of Relative Permeability Research Articles

Relative permeability estimation using mercury injection capillary pressure measurements based on deep learning approaches

Relative permeability (RP) curves which provide fundamental insights into porous media flow behavior serve as critical parameters in reservoir engineering and numerical simulation studies. However, obtaining accurate RP curves remains a challenge due to expensive experimental costs, core contamination, measurement errors, and other factors. To address this issue, an innovative approach using deep learning strategy is proposed for the prediction of rock sample RP curves directly from mercury injection capillary pressure (MICP) measurements which include the mercury injection curve, mercury withdrawal curve, and pore size distribution. To capture the distinct characteristics of different rock samples' MICP curves effectively, the Gramian Angular Field (GAF) based graph transformation method is introduced for mapping the curves into richly informative image forms. Subsequently, these 2D images are combined into three-channel red, green, blue (RGB) images and fed into a Convolutional Long Short-Term Memory (ConvLSTM) model within our established self-supervised learning framework. Simultaneously the dependencies and evolutionary sequences among image samples are captured through the limited MICP-RP samples and self-supervised learning framework. After that, a highly generalized RP curve calculation proxy framework based on deep learning called RPCDL is constructed by the autonomously generated nearly infinite training samples. The remarkable performance of the proposed method is verified with the experimental data from rock samples in the X oilfield. When applied to 37 small-sample data spaces for the prediction of 10 test samples, the average relative error is 3.6%, which demonstrates the effectiveness of our approach in mapping MICP experimental results to corresponding RP curves. Moreover, the comparison study against traditional CNN and LSTM illustrated the great performance of the RPCDL method in the prediction of both So and Sw lines in oil–water RP curves. To this end, this method offers an intelligent and robust means for efficiently estimating RP curves in various reservoir engineering scenarios without costly experiments.

Sensitivity Analysis of Fluid–Fluid Interfacial Area, Phase Saturation and Phase Connectivity on Relative Permeability Estimation Using Machine Learning Algorithms

Recent studies have shown that relative permeability can be modeled as a state function which is independent of flow direction and dependent upon phase saturation (S), phase connectivity (X), and fluid–fluid interfacial area (A). This study evaluates the impact of each of the three state parameters (S, X, and A) in the estimation of relative permeability. The relative importance of the three state parameters in four separate quadrants of S-X-A space was evaluated using a machine learning algorithm (out-of-bag predictor importance method). The results show that relative permeability is sensitive to all the three parameters, S, X, and A, with varying magnitudes in each of the four quadrants at a constant value of wettability. We observe that the wetting-phase relative permeability is most sensitive to saturation, while the non-wetting phase is most sensitive to phase connectivity. Although the least important, fluid–fluid interfacial area is still important to make the relative permeability a more exact state function.

Using Nano-XRM and High-Contrast Imaging to Inform Micro-Porosity Permeability During Stokes–Brinkman Single and Two-Phase Flow Simulations on Micro-CT Images

Carbonate rocks have multiscale pore systems that are weakly understood. In this study, we use combined experimental, modeling, and pore space generation methods to tackle the impact of microporosity on the flow properties of Estaillades limestone. First, a nano-core from a microporous grain of Estaillades limestone was scanned using nanotomography (nano-XRM). The information from the nano-XRM scan was then used as input into an object-based pore network generator, on which permeability fields were simulated for a range of porosities, creating a synthetic Kozeny–Carman porosity–permeability relationship targeted for the specific microporous system present in Estaillades. We found a good match between the experimental and simulated Mercury Intrusion Capillary Pressure (MICP) range in the imaged geometry and a good match between the imaged and object-generated permeabilities and MICP. A micro-core of Estaillades was then scanned using X-ray microtomography (μCT), the differential pressure was measured during single-phase flow, and the rock was flooded with doped brine. The contrast between the images was used to assign a porosity to each voxel of connected microporosity. The flow through the pore space was solved using the Stokes–Brinkman (S–B) and Stokes-only solvers, and the differences between the measured permeability and computed permeabilities were evaluated. An agreement was seen between the computed permeability of the Stokes and S–B simulation with the measured permeability. However, the velocity fields with the S–B simulation captured stagnant regions of the pore space that were not present in the Stokes simulations. Additionally, we investigated the implications of including microporosity in the estimation of relative permeability. Nitrogen was experimentally co-injected through the core with doped brine at a 50% fractional flow and imaged to capture the two-phase effective permeability and was compared with the simulated numerical permeability. The Stokes simulation was not able to predict relative permeability with this method due to the major flow paths in the macroporosity being impeded by the injected non-wetting phase. The S–B simulations, however, allowed flow in the microporous regions around these blocked flow paths and were able to achieve a relative permeability prediction that was a reasonable match to the experimental measurement.

Relative permeability estimation of oil−water two-phase flow in shale reservoir

Oil−water two-phase flow is ubiquitous in shale strata due to the existence of connate water and the injection of fracturing fluid. In this work, we propose a relative permeability model based on a modified Hagen−Poiseuille (HP) equation and shale reconstruction algorithm. The proposed model can consider the nanoconfined effects (slip length and spatially varying viscosity), oil−water distribution, pore size distribution (PSD), total organic matter content (TOC), and micro-fracture. The results show that the increasing contact angles of organic matters (OM) and inorganic minerals (iOM) increase the relative permeability of both oil and water. As the viscosity ratio increases, the relative permeability of oil phase increases while that of water phase decreases, due to the different water−oil distribution. The effective permeability of both oil and water decreases with the increasing TOC. However, the relative permeability of water phase increases while that of oil phase decreases. The increasing number and decreasing deviation angle of micro-fracture increase the effective permeability of oil and water. However, micro-fracture has a minor effect on relative permeability. Our model can help understand oil−water two-phase flow in shale reservoirs and provide parameter characterization for reservoir numerical simulation.

Modified Johnson–Bossler–Naumann method to incorporate capillary pressure boundary conditions in drainage relative permeability estimation

A proposed modification of the Johnson–Bossler–Naumann (JBN) method incorporates capillary pressure at the inlet and outlet of a rock sample. The experimental runs are performed on Berea and Obernkriechner sandstone rock samples. Fluid is injected into Berea rock at capillary to viscous ratios 0.05, 0.1, 0.5, and 1 and into Obernkriechner rock at capillary to viscous ratios 0.05 and 0.25. Rock samples are initially saturated with 20 g/l NaCl water. The experimental observations are analyzed using classical JBN and our modified JBN. The latter's relative permeability curves are found to closely match those derived by applying history matching to a numerical model. This indicates that modified JBN can be used to provide an initial guess for history matching. We also show that accurate estimates of threshold capillary pressure are crucial to obtaining accurate oil relative permeability estimates. In contrast to those derived from the JBN method, modified JBN relative permeabilities are independent of capillary to viscous ratio or injection rate. • The proposed model incorporates capillary pressure at the inlet and outlet boundary. • Experiments are performed to validate the model. • Derived relative permeability curves are less sensitive to capillary number compared to classical methods.

The carbonic acid-rock reaction in feldspar/dolomite-rich tightsand and its impact on CO2-water relative permeability during geological carbon storage

CO2 injection contributes to formation energy supplement to remedy the fast production decline in tight oil reservoir and CO2 storage at the same time.CO2 Here, we report CO2-water relative permeability with consideration of acid-rock reaction. The minerals of a tight rock sample were analyzed at first. CO2Then we established an experimental method to measure the relative permeability of CO2-water at reservoir conditions based on steady state method. After carbonic acid-rock reaction, the variation in rock mineralogy was compared. The pore size distribution in the rock sample was obtained by LF-NMR after dynamic corrosion at different pressure. Both small and large pore and throat were enlarged after corrosion. And the Klinkenberg permeability of tight sandstone was increased 7.4–18.8%. From the CO2-water relative permeability with corrosion, the irreducible water saturation was decreased for more than 15.1% in average, which indicates more flowing spaces for other fluids. In the two-phase flow regime, a good linear relationship was found between Krw/Krg and gas saturation in tight sand samples. It can be used for the estimation of relative permeability at different gas conditions.CO2CO2 Injection of CO2 in tight oil reservoir indicates improvement in EOR and GCS potential. Acid-rock reaction results in better fluid flow capacity for liquid and additional trapping of CO2.

Relative permeability of tight hydrocarbon systems: An experimental study

Relative permeability is notoriously difficult to measure in the laboratory for low-permeability rocks with permeability values in the nanodarcy/microdarcy range. The objectives of this work are to 1) implement a series of laboratory methods for relative permeability estimation in tight hydrocarbon formations and 2) examine the impact of fluid saturation and operational (e.g. pore pressure, differential pressure) controls on relative permeability. Seven tight siltstone/sandstone and organic/clay-rich core plugs, covering a broad range of helium porosity (2.9–13.8%) and slip-corrected gas (N2, CH4) permeability values (1.5·10−5–1.6·10−1 md), were analyzed in this study. Two direct methods for measuring gas/liquid (CH4,N2/oil) relative permeability data are investigated including a modified version of the Dacy method and the “gas breakthrough” technique, tailored to high- (˃0.001 md) and low-permeability rocks (<0.001 md), respectively. The non-steady-state method under constant flow rate is used for evaluating liquid/liquid (oil/water) relative permeability for a Montney core plug sample. Using a unipore diffusion model, the gas/liquid (CH4/oil) effective diffusion/dispersion coefficient is evaluated for a Duvernay core plug sample. The relative permeability values measured on fully/partially oil-saturated core plug samples vary between 0.006 and 0.9, depending on methodology, oil saturation (30–75%), pore pressure (1.3–6.4 MPa), effective stress (3.3–19.4 MPa), differential pressure (0.5–3.1 MPa) and hysteresis path. The systematic experiments conducted herein extend the available experimental dataset and are of significant importance for constraining rate-transient analysis (RTA) models and numerical simulations used to evaluate primary and enhanced oil recovery in tight hydrocarbon systems.

Technology Focus: EOR Modeling (January 2021)

The enhanced-oil-recovery (EOR) literature produced in the past several months was dominated by reservoir modeling and characterization; flood enhancements; machine learning; and, more notably, relative permeability estimation. This last one needs to be under-stood further. Relative permeability characterizes flow in porous media, the understanding and manipulating of which is key to the success of EOR. Our fascination with the topic during the last 75 years, therefore, is understandable. Starting with a seminal paper from W.R. Purcell in 1949, we have more than 12,000 articles in the SPE collection alone on relative permeability estimation, of which more than 400 were published in the last year. Mechanics of motion is also important to mankind, but we do not have literature piling up on Newton’s laws of motion. Is it that we haven’t understood flow in porous media yet, or is it because the subject matter is so complex? The truth, perhaps, lies somewhere in between. Flow in pores that are randomly sized, randomly connected, and have variable chemical makeup is, by nature, complex and mathematically unmanageable. Relative permeability has been our attempt to lend its aggregate behavior some sense of manageability. This has always been done in a fit-for-purpose manner. What is fit for one context, however, may not be so for the others, and this uncertainty continues to churn out theses, antitheses, and syntheses. Expectedly, even more such activity arises with every improvement in computing capabilities, as is once again evident with advances in machine learning—new tools to handle old problems. That is where my first pick is for you, with some additional suggested readings in references that follow. Data analytics does much more than estimate relative permeability, and the second paper abridged here uses it to predict a flood performance. To allow a break from data science, the third paper chosen deals with the important topic of electromagnetics as applied to reservoir characterization and heating. I hope you find these to be useful and interesting reads.

Radiotherapy target volume definition in newly diagnosed high grade glioma using 18F-FET PET imaging and multiparametric perfusion MRI: A prospective study (IMAGG)

PurposeThe aim of this study was to prospectively investigate tumor volume delineation by amino acid PET and multiparametric perfusion magnetic resonance imaging (MRI) in patients with newly diagnosed, untreated high grade glioma (HGG). Materials and methodsThirty patients with histologically confirmed HGG underwent O-(2-[18F]-fluoroethyl)-l-tyrosine (18F-FET) positron emission tomography (PET), conventional Magnetic Resonance Imaging (MRI) as contrast-enhanced (CE) and fluid-attenuated inversion recovery (FLAIR) and multiparametric MRI as relative cerebral blood volume (rCBV) and permeability estimation map (K2). Areas of MRI volumes were semi-automatically segmented. The percentage overlap volumes, Dice and Jaccard spatial similarity coefficients (OV, DSC, JSC) were calculated. ResultsThe 18F-FET tumor volume was significantly larger than the CE volume (median 43.5 mL (2.5–124.9) vs. 23.8 mL (1.4–80.3), p = 0.005). The OV between 18F-FET uptake and CE volume was low (median OV 0.59 (0.10–1)), as well as spatial similarity (median DSC 0.52 (0.07–0.78); median JSC 0.35 (0.03–0.64)). Twenty-five patients demonstrated both rCBV and CE on MRI: The median rCBV tumor volume was significantly smaller than the median CE volume (p < 0.001). The OV was high (median 0.83 (0.54–1)), but the spatial similarity was low (median DSC 0.45 (0.04–0.83); median JSC 0.29 (0.07–0.71)). Twenty-eight patients demonstrated both K2 and CE on MRI. The median K2 tumor volume was not significantly larger than the median CE volume. The OV was high (median OV 0.90 (0.61–1)), and the spatial similarity was moderate (median DSC 0.75 (0.01–0.83); median JSC 0.60 (0.11–0.89)). ConclusionWe demonstrated that multiparametric perfusion MRI volumes (rCBV, K2) were highly correlated with CE T1 gadolinium volumes whereas 18F-FET PET provided complementary information, suggesting that the metabolically active tumor volume in patients with newly diagnosed untreated HGG is critically underestimated by contrast enhanced MRI. 18F-FET PET imaging may help to improve target volume delineation accuracy for radiotherapy planning.

Rapid estimation of permeability from digital rock using 3D convolutional neural network

Permeability and its anisotropy are of central importance for groundwater and hydrocarbon migration. Existing fluid dynamics methods for computing permeability have common shortcomings, i.e., high computational complexity and long computational time, reducing the potential of these methods in practical applications. In view of this, a 3D CNN-based approach for rapidly estimating permeability in anisotropic rock is proposed. Using high-resolution X-ray microtomographic images of a sandstone sample, numerous samples of the size of 100-cube voxels were generated firstly by a series of image manipulation techniques. The shrinking and expanding algorithms are employed as the data augmentation methods to strengthen the role of porosity and specific surface area (SSA) since these two parameters are critical to estimate permeability. Afterwards, direct pore-scale modeling with Lattice-Boltzmann method (LBM) was utilized to compute the permeabilities in the direction of three coordinate axes and mean permeability as the ground truth. A dataset including 3158 samples for training and 57 samples for testing were obtained. Four 3D CNN models with the same network structure, corresponding to permeabilities in 3 directions and in average, were built and trained. Based on those trained models, the satisfactory predictions of the permeabilities in x-, y-, and z-axis directions and the mean permeability were achieved with R2 scores of 0.8972, 0.8821, 0.8201, and 0.9155, respectively. Furthermore, those proposed 3D CNN models achieved good generalization ability in predicting the permeability of other samples. The trained model takes only tens of milliseconds on average to predict the permeability of one sample in one axial direction, about 10,000 times faster than LBM. The promising performance clearly demonstrates the effectiveness of 3D CNN-based approach in rapidly estimating permeability in anisotropic rock. This new approach provides an alternative way to calculate permeability with low computing cost, and it has the potential to be extended to the estimation of relative permeability and other properties of rocks.

Scaling of two-phase water-steam relative permeability and thermal fluxes in porous media

Two-phase water-steam flow conditions are frequently encountered in many engineering applications, including geothermal reservoirs. Although routine calculations are based on the multiphase Darcy’s law, the role of the topology of the flowing phases at the pore-scale is usually neglected in the estimation of relative permeabilities. Instead, the latter are frequently computed using empirical models like the Corey correlation. In this work, we first apply the model for relative permeabilities based on pore-scale flow regimes developed by Picchi and Battiato (2019), Relative permeability scaling from pore-scale flow regimes, Water Resour. Res. 55, 3215–3233, to scenarios typical of geothermal reservoirs and then extend it by deriving the scaling laws for the transmissibilities and the thermal properties as a function of temperature. First, we discuss the scaling behavior of normalized relative permeabilities in terms of viscosity ratio and capillary number of water-steam systems and, then, we provide a validation of the model against experimental data available in the literature. The model captures well the data trends collected in real 3D porous media. These results suggest that water-steam relative permeabilities follow the same scaling behavior of gas-liquid systems where the non-wetting phase is much less viscous than the wetting phase. Finally, we investigate the impact that relative permeabilities have on heat transfer rates at two-phase flow conditions and the scaling of mass and energy transmissibility and thermal properties of the mixture. An estimation of the exergy carried by the two-phase water-steam mixture is also included.

A Hybrid Approach for the Prediction of Relative Permeability Using Machine Learning of Experimental and Numerical Proxy SCAL Data

Summary Accurate estimation of relative permeability is one of the key parameters for decision making in upstream applications from project appraisal to field development and evaluation of various field development options. In this study, we identify Euler number (Arns et al. 2001) (a quantitative measure of fluid connectivity/distribution) and saturation as being the first-order predictors of relative permeability and develop a reliable correlation between them using machine learning of experimental special core analysis (SCAL) data and pore network simulation results. In order to achieve our objective, first, we developed a machine-learning model based on the random forest algorithm (Breiman 2001) to analyze specific SCAL data that indicates a key missing feature in the traditional saturation-based relative permeability prediction. We identified this missing feature and proposed the Euler characteristic as a potential first-order predictor of relative permeability in combination with in-situ fluid saturations. We generated “artificial” relative permeability data using pore network simulation (Valvatne and Blunt 2004) by systematically varying a set of key parameters such as pore geometry, wettability, and saturation history. Subsequently, we used machine learning to rank the importance of each parameter and identify possible correlative responses to those selected variables. At a fixed saturation (zero-dimensional volumetric abundance) and Euler number coordinates, the relative permeability is very consistent and varies insignificantly across different cases, suggesting these two parameters as first-order predictors. Euler number characterizes the fluid connectivity/distribution, while saturation represents the net volumetric fluid quantity. We believe that Euler number could be the missing first-order predictor in traditional saturation-based predictive relative permeability models, especially for connected pathway dominated flow regime. Finally, we identified the quantitative relationship between relative permeability and Euler characteristic, and present a reliable correlation to determine the relative permeability on the basis of Euler number and saturation.

A NEW RELATIVE PERMEABILITY MODEL OF UNSATURATED POROUS MEDIA BASED ON FRACTAL THEORY

The multiphase flow through unsaturated porous media and accurate estimation of relative permeability are significant for oil and gas reservoir, grounder water resource and chemical engineering, etc. A new fractal model is developed for the multiphase flow through unsaturated porous media, where multiscale pore structure is characterized by fractal scaling law and the trapped water in the pores is taken into account. And the analytical expression for relative permeability is derived accordingly. The relationships between the relative permeability and capillary head as well as saturation are determined. The proposed model is validated by comparison with 14 sets of experimental data, which indicates that the fractal model agrees well with experimental data. It has been found that the proposed fractal model shows evident advantages compared with BC-B model and VG-M model, especially for the porous media with fine content and texture. Further calculations show that water permeability decreases as the fractal dimension increases under fixed saturation because the cumulative volume fraction of small pores increases with the increment of the fractal dimension. The present fractal model for the relative permeability may be helpful to understand the multiphase flow through unsaturated porous media.

Applications of critical path analysis to uniform grain packings with narrow conductance distributions: II. Water relative permeability

Accurate estimation of water relative permeability has been of great interest in various research areas because of its broad applications in soil physics and hydrology as well as oil and gas production and recovery. Critical path analysis (CPA), a promising technique from statistical physics, is well known to be applicable to heterogeneous media with broad conductance or pore size distribution (PSD). By heterogeneity, we mean variations in the geometrical properties of pore space. In this study, we demonstrate that CPA is also applicable to packings of spheres of the same size, known as relatively homogeneous porous media. More specifically, we apply CPA to model water relative permeability (krw) in mono-sized sphere packs whose PSDs are fairly narrow. We estimate the krw from (1) the PSD and (2) the PSD and saturation-dependent electrical conductivity (σr) for both drainage and imbibition processes. We show that the PSD of mono-sized sphere packs approximately follows the log-normal probability density function. Comparison with numerical simulations indicate that both the imbibition and drainage krw are estimated from the PSD and σr data more accurately than those from the PSD. We show that CPA can estimate krw in mono-sized sphere packs precisely.

Modeling relative permeability of gas condensate reservoirs: Advanced computational frameworks

In the last years, an appreciable effort has been directed toward developing empirical models to link the relative permeability of gas condensate reservoirs to the interfacial tension and velocity as well as saturation. However, these models suffer from non-universality and uncertainties in setting the tuning parameters. In order to alleviate the aforesaid infirmities in this study, comprehensive modeling was carried out by employing numerous smart computer-aided algorithms including Support Vector Regression (SVR), Least Square Support Vector Machine (LSSVM), Extreme Learning Machine (ELM), Multilayer Perceptron (MLP), Group Method of Data Handling (GMDH), and Gene Expression Programming (GEP) as predictors and Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Levenberg-Marquardt Algorithm (LMA), Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG) and Randomized Polynomial Time (RP) as optimizers. To this end, a wide variety of reliable databanks encompasses more than 1000 data points from eights sets of experimental data was utilized in the training and testing steps of the modeling process. The predictors were integrated with optimization algorithms to assign the optimum tuning parameters of each model. The modeling was implemented in two different manners from the standpoint of models inputs: (1) 2-input (saturation and capillary number); (2) 3-input (saturation, interfacial tension, and capillary number). The results of the comparison between these strategies demonstrate more accuracy of the models when employing three independent parameters as the input (3-input). Among the developed models, the MLP-LMA modeling algorithm outperformed all other models with root mean square errors (RMSEs) of 0.035 and 0.019 for gas and condensate phases, respectively. At the end, in a comparison between both 2-input and 3-input MLP-LMA models and five traditional literature models, both smart modeling approaches were established themselves as the most accurate techniques for estimation of relative permeability in gas condensate reservoirs.

Capillary pressure and relative permeability estimation for low salinity waterflooding processes using pore network models

In this work, the effect of low salinity waterflooding (LSWF) on capillary pressure and relative permeability is studied at pore scale. For this purpose, a pore-scale model implemented on OpenPNM is developed to describe fluid flow, salinity transport and wettability change in a pore network. The effect is studied by considering high salinity waterflooding followed by low salinity waterflooding. The system wettability change is introduced as modifications of the local contact angle that are induced by the water salinity reduction. These modifications are evaluated by calculating the contact angle change in each pore and throat of the network, and then integrating it. From this analysis, a methodology has been developed to study the LSWF impact on capillary pressure and relative permeability. This methodology has been successfully applied to two pore network cases available in an open rock data base; one network correspond to a sandstone and the other to a carbonate sample. The methodology developed here can be seen as a tool to complement laboratory tests needed to determine the efficiency of LSWF processes.

Dos and Don’ts When Developing a System to Investigate Spontaneous Imbibition in Unconsolicdated Porous Media

This paper describes the development of a consistent model system to measure spontaneous imbibition and determine saturation functions in unconsolidated porous media. Sand grains or glass beads were packed in up to 0.5 m long, transparent glass tubes with optical access to local saturation development during spontaneous imbibition processes. The Two Ends Open-Free spontaneous imbibition (TEOFSI) boundary condition was used, where one end face is exposed to the wetting fluid and the other end to the non-wetting fluid. Dynamic measurement of the advancing displacement front and volumetric production from each open end-face enabled estimation of capillary pressure and relative permeability for the system. A range of wetting- and non-wetting phase viscosities and viscosity ratios was used during spontaneous imbibition in unconsolidated sand or glass packs. Wetting phase (water) viscosity was increased using water soluble glycerol or polymers. Air or mineral oil of varying composition provided a wide range of non-wetting phase viscosities. High permeable systems are extremely sensitive to laboratory properties, which may dominate the viscous resistance and determine flow behaviour. Systematic discrepancies observed in early testing indicated that end effects were present, even in long systems, in the filters at each end of the glass tube to maintain the grains or beads in place. Different filters were tested (no filter, glass, paper and micro-porous discs) to determine the impact of the filter on spontaneous imbibition. In addition to slower oil recovery than anticipated, developmentof a non-uniform displacement front was observed, demonstrating the large influence from minute heterogeneities within the packs, and at the end faces. A standard sand grain packing procedure, using a custom-designed packing device, was therefore developed to ensure homogeneous properties throughout theporous media, and limited the spread in porosity and permeability values. Homogeneous sand packs with reproducible properties are necessary, to systematically investigate flow parameters and changes in wettability in unconsolidated porous media.

Co-history Matching: A Way Forward for Estimating Representative Saturation Functions

Core-scale experiments and analyses would often lead to estimation of saturation functions (relative permeability and capillary pressure). However, despite previous attempts on developing analytical and numerical methods, the estimated flow functions may not be representative of coreflood experiments when it comes to predicting similar experiments due to non-uniqueness issues of inverse problems. In this work, a novel approach was developed for estimation of relative permeability and capillary pressure simultaneously using the results of “multiple” corefloods together, which is called “co-history matching.” To examine this methodology, a synthetic (numerical) model was considered using core properties obtained from pore network model. The outcome was satisfactorily similar to original saturation functions. Also, two real coreflood experiments were performed where water at high and low rates were injected under reservoir conditions (live fluid systems) using a carbonate reservoir core. The results indicated that the profiles of oil recovery and differential pressure (dP) would be significantly affected by injection rate scenarios in non-water wet systems. The outcome of co-history matching could indicate that, one set of relative permeability and capillary pressure curves can reproduce the experimental data for all corefloods.

A Feature-Based Stochastic Permeability of Shale: Part 1—Validation and Two-Phase Permeability in a Utica Shale Sample

Estimate of permeability plays a crucial role in flow-based studies of fractured tight-rocks. It is well known that most of the flow through tight-rocks (e.g., shales) is controlled by permeable features (e.g., fractures, laminations, etc.), and there is negligible flow through the matrix. However, current approaches in the literature to model permeability of tight-rocks do not account for such features present within the rock ranging from micro-scale to field-scale. Current permeability modeling approach assumes a single continuum without considering the presence of permeable features within the matrix (e.g., micro-fractures) or outside the matrix (e.g., natural fractures). Although the laboratory-measured permeability implicitly captures discrete features present in that sample (e.g., fractures, laminations, micro-fractures), most of the permeability models proposed for shale do not account for these features. Fracture permeability in the literature is typically modeled using an ideal slit assumption; however, this highly overestimates its permeability because fractures in real medium are non-ideal in terms of their porosity and tortuosity, which affect their permeability. Additionally, the transition zone between fracture and matrix also affects the permeability of fracture. In this study, part of a two-part series, a new method to predict permeability of fractured shale by discretizing the medium into matrix (inorganic and organic) and fractures is presented. New analytical expressions of permeability are derived to account for non-ideal nature of porous medium and two-phase flow in fractures. Rock feature in each cell of the grid is identified as one of the three elements (organic matter, inorganic matter, or fracture), and permeability of that cell is estimated using a suitable analytical expression. This method allows estimating permeability at any scale of interest and more robustly than by a pure analytical approach. The proposed method is validated against local and global-scale measurements on three fractured samples from laboratory. Finally, the method is used to predict two-phase flow permeability of supercritical CO2 displacing water within a fracture in a Utica shale sample. The proposed two-phase flow permeability equations can be used as a quick analytical tool to predict relative permeability estimates of two-phase flow in fractured shale samples. In Part 2, the proposed method is used to estimate field-scale permeability through an optimization process that uses field-scale production and other readily available information.

Downhole Estimation of Relative Permeability With Integration of Formation-Tester Measurements and Advanced Well Logs

Downhole Estimation of Relative Permeability With Integration of Formation-Tester Measurements and Advanced Well Logs