Estimation Of Permeability Research Articles

Micromechanical schemes for Stokes to Darcy homogenization of permeability based on generalized Brinkman inhomogeneity problems

Mean field homogenization schemes are formulated for the Stokes to Darcy upscaling of the permeability on the basis of generalized inhomogeneity problems in which flow is described by Brinkman equations. The average velocity and drag force concentrations for flow in a potentially composite inclusion are characterized in terms of a permeability contribution tensor and an equivalent permeability, which allow for the direct transposition to Stokes to Darcy upscaling of most homogenization schemes available in elasticity (self-consistent, differential, Mori–Tanaka, Maxwell, …). The unified framework extends existing effective medium and cell model permeability estimates. Its flexibility is illustrated on a panel of microstructures of porous media: granular or fibrous materials, materials with spanning cylindrical or crack-like pores, double porosity materials with disconnected or connected meso-porosity and compared with existing or newly produced full field simulation results.

Prediction of permeability of five-harness satin fabric by a modified Kozeny constant determined from experiments

Permeability is a critical parameter not only in flow simulation analysis but also in liquid composite molding process. When a liquid resin is infused into a dry preform, the impregnation is mainly characterized by the permeability. The permeability of a dry preform can be obtained through theoretical and experimental methods. In the theoretical estimation of permeability, the effects of fiber arrangement as well as fabric type and form for various types of preforms are not sufficiently reflected in the calculation. Thus, there is a gap between the theoretical and experimental permeability. Recently, experimental determination has been gaining considerable attention as a mean to obtain accurate permeability values; however, it requires a number of trials. In this study, the permeability of the Hexforce G0926 5HS (five-harness satin) carbon fabric preform is estimated using representative theoretical prediction models, the Gebart and Kozeny–Carman equations. In addition to the Kozeny–Carman permeability (using the Kozeny constant values from literature), the Kozeny constant obtained through experiments was used to obtain a modified Kozeny–Carman permeability. All three calculated permeabilities were compared and verified with the fabric manufacturer’s reference value. The results showed that the modified Kozeny–Carman permeability using the experimentally determined Kozeny constant was closest to the reference value at 57% fiber volume fraction. Further, the predicted permeability was compared with other experimental permeability values from literature over the 40%–65% range of fiber volume fraction. We found that the modified Kozeny–Carman permeability once again came closest to the literature values. Finally, an optimized fitting equation was proposed to replace the Kozeny–Carman equation for predicting the permeability of Hexforce G0926 5HS carbon fabric over the 40%–65% fiber volume fraction range.

Coal permeability prediction method based on the microscopic pore-fracture dual-porosity structure

To better understand the effect of the pore-fracture dual-porosity structure on the coal permeability, the methods for calculating the pore size distribution as well as the fracture width distribution based on the Euclidean distance map function were given first. On this basis, a permeability estimation model considering pore-fracture structure was derived. Then, the pore-fracture structure and permeability of coal samples were quantitatively analyzed by scanning electron microscopy (SEM). By considering the pore size distribution and fracture width distribution characteristics separately, the complex pore structure of the coal sample can be more clearly defined. We found that both pores and fractures have their own distribution characteristics, but due to the effect of resolution, there is some influence in quantifying the minimum size distribution, especially in quantifying the pore size distribution. In predicting the permeability, the direct calculation using the pore and fracture size distribution is significantly larger than the experimental results (1.18✕10−14 m2 vs. 6.9✕10−16 m2 (measured) for the A1 and 1.22✕10−14 m2 vs. 8.1 ✕10−16 m2 (measured) for the A2 at ✕1000 magnification). However, by further considering the effect of tortuosity, more accurate prediction results can be obtained (1.14✕10−15 m2 for the A1 and 1.22✕10−15 m2 for the A2 at ✕1000 magnification). Fractures occupy less space, but they would cause higher permeability. The method proposed in the current study can be further applied to quantify the pore-fracture structure and permeability characteristics in microgeology.

Fault and fracture study by incorporating borehole image logs and supervised neural network applied to the 3D seismic attributes: a case study of pre-salt carbonate reservoir, Santos Basin, Brazil

Fractures play a significant role in the development and production phases of carbonate reservoirs. Quantitative interpretation of fractures not only enhances reservoir models but also reduces the drilling risk and optimizes well design. In this study, we attempt to predict the fracture density map by integrating well and seismic data along with maximum horizontal stress identification. To this end, we propose a workflow with a set of machine learning approaches. First, 3D seismic data is conditioned after the migration processing sequence and the main faults and horizons are interpreted. Next, a number of curvature and coherence attributes are created for a supervised neural network technique to generate new seismic-based discontinuity attribute. Using a geostatistical method to incorporate the interpreted dip and azimuth attributes from well image logs and 3D seismic discontinuity attribute, the fracture density map is predicted and the results validated with a blind well. Finally, we evaluate the strike azimuth of possible open fractures based on the stress regime analysis, from which two distinctive zones are identified. There are, however, some limitations in this study. The predicted fracture density map can be employed to build a discrete fracture network, update dual porosity and permeability estimation, and identify sweet spots.

Reservoir permeability estimation from seismic amplitudes using variational mode decomposition

A new qualitative Reservoir Permeability estimation approach using variational mode decomposition named RPE-VMD is proposed which directly use seismic amplitude and frequency attributes. The method reveals amplitude anomalies that may reflect details about the heterogenous distribution of reservoir permeability. The main procedure is carried out in the time-frequency domain which generates by using a generalized S transform. Reflection coefficient information is used as seismic amplitude attribute and extracted by using variational mode decomposition combined with mutual information theory from seismic data using the logarithmic spectrum. The dominant frequency extracted in the time-frequency domain is used as seismic frequency attribute for estimating reservoir thickness information. The RPE-VMD approach uses dominant reflection coefficient information from the seismic data combined with reservoir thickness information for permeability estimation. Application of this approach to field data from a sandstone reservoir in China illustrates that it can provide permeability estimation with a high resolution and accuracy. The proposed method directly uses seismic data to measure the reservoir permeability avoiding the need of seismic velocity in the conventional estimation methods.

Estimating rock permeability and porosity using machine learning

Investigating the permeability and porosity of rocks is essential for petroleum production, CO2 geological storage and etc. The permeability is one of the most basic physical properties that evaluate the ease of flow of fluid in a porous object for understanding the behavior of fluids such as water, oil, and CO2 in rocks. Laboratory experiments using excavated rock for permeability estimation is very time and cost-consuming. In recent years, estimation of physical properties of rock using the deep learning technology has received a lot of attention. In this study, we have developed a method for efficiently predicting the physical properties of permeability using the convolutional neural networks (CNN). Four types of convolutional neural networks have been tested: basic CNN, VGG, GoogLeNet, and Resnet. These networks are trained using the dataset of directly calculated permeability values based on flow simulation and the corresponding raw CT images. By comparing the prediction accuracy of each network, we found that the Resnet model showed the best performance.

A NUMERICAL APPROACH FOR PERMEABILITY ESTIMATION IN RADIALLY HETEROGENEOUS RESERVOIRS

Analytical solutions are used extensively for pressure transient analysis in radially heterogeneous reservoirs. They are generally used for evaluating variation of reservoir properties along the reservoir radius. However, the available analytical solutions are not sufficiently accurate to determine boundaries of zones. As a result, the interior boundaries of heterogeneous zones are often estimated as a function of the average permeability of zones, which sometimes is a cause of nonunique solutions. As a matter of fact, the skin factor does not provide accurate information about the radius and permeability of an altered zone separately. A new numerical well test procedure is presented in this paper based on the finite element method and a special zonal discretization that utilizes nonlinear regression, which is able to detect the interior boundaries of heterogeneous zones. The results demonstrate that this numerical approach is able to capture the spatial variation of permeability in the radially heterogeneous reservoirs under various boundary conditions. A key advantage of this numerical procedure is quantifying heterogeneity in terms of the radius and permeability of the dissimilar zones, whereas analytical methods generally provide a combination of these parameters.

Guest Editorial: Want To Learn Something New About DFITs? Start With an Old Book

Early in the development of unconventional reservoirs, the industry had little choice but to rely on the toolsets handed down from decades of conventional engineering practices. Later, new tools would be crafted in the hopes of better fitting the unconventional paradigm. This presents a choice to the technical community—rely on a traditional and proven method, or one designed for the unconventional system but less tested? Recently, many hydraulic fracturing engineers have been asking themselves this question when it comes to the diagnostic fracture injection test (DFIT). That includes myself, and the journey I took to find an answer culminated in a technical paper (SPE 206239) that was presented at the 2021 SPE Annual Technical Conference and Exhibition. What follows are some of that paper’s key findings which are being shared with the intent to further the discussion on best practices for those challenged with interpreting unconventional diagnostics. The paper utilizes the concept of permeability to validate traditional minimum stress interpretations across multiple reservoir conditions by comparing DFIT fracture closure time permeability estimates with core, pressure buildup, after-closure pressure, and rate transient analysis. This author was able to further support the results by the integration of a wide range of diagnostic technologies such as fiber optics, microseismic, and, among others, DFIT numerical inversions shared through eight case histories. Diagnostic Injections, a Long History Made Short One of the few ways to begin a conversation with a reservoir is by pumping treated fluid at fracturing rates and analyzing how the pressure falls off with time after the injection is stopped. The language for such dialogue and information exchange is formed by the dimensionless time function called “G-function” and was introduced by Ken Nolte in 1979. Nolte’s innovative postulations allowed our industry to determine the expected frac geometry, its conductivity, the formation flow capacity, and the optimum hydraulic fracture design as well as the means necessary to place the treatment. Recently introduced into industry literature is the proposed fracture closure pressure interpretation based on the fracture compliance method, interpreting an earlier, higher-stress estimation than estimates from well‑established methodologies. The practitioner is now faced with the dilemma of finding out which fracture closure interpretation technique is correct since this has a profound impact on how fracture geometry is modeled and optimized. To answer this question, a multibasin analysis of pre-frac tests from the Russia, North Sea, Europe, North Africa, and South America regions was undertaken.

A simple method for estimation of permeability of concrete from the compressive strength and pore size distribution based on literature survey

ABSTRACT This study aims to investigate the impacts of compressive strength and curing conditions of concrete on pore size distribution and air permeability. An empirical correlation was developed by analyzing the results from existing studies that measured both pore size distribution and air permeability. Air permeability was calculated using an empirical correlation newly developed. However, the correlation was targeted only to dry concrete since the influence of water content is very large on air permeability of concrete. To calculate air permeability of concrete in various water content, another correlation was developed between the degree of pore saturation and air permeability. Using the measurement result of pore size distribution, this study examined the effect of compressive strength and curing conditions on changes in pore size distribution and air permeability. Pore size distribution was measured by mercury intrusion porosimetry (MIP) using samples taken from mortar fragments collected from concrete. The compressive strength of concrete ranged from 21 to 150 MPa. Curing conditions were either water curing or air curing or sealed curing.

Micro‐ and nanoscale pore‐throat structure, fractal characteristics, and permeability estimation models in deep sandstones: Palaeogene Shahejie Formation, Nanpu Sag, NE China

Long‐term burial and strong diagenesis modification result in highly heterogeneous pore structures in deep clastic reservoirs; these heterogeneities exert a controlling influence over the development of these deep petroleum systems. A clear understanding of the pore structure simplifies the tasks of identifying and modelling reservoirs for the purposes of hydrocarbon exploration. This study characterizes the mineral compositions, physical properties, and pore systems of the first member of the Palaeogene Shahejie Formation (Es1) in the Nanpu Sag using thin section and scanning electron microscope observations, X‐ray diffraction measurements, mercury intrusion capillary pressure, and nuclear magnetic resonance data. Our results show that the Es1 sandstones typically fall into one of three different pore‐throat sizes: mainly 10 μm (type‐I), 1 μm (type‐II), and less than 1 μm (type‐III). Between type‐I and type‐III reservoirs, the pore system changes from residual intergranular pore (InterP) and secondary InterP to secondary intragranular pores (IntraP) and intercrystalline pores. The fractal theory is selected to quantify the heterogeneity of the pore‐throat structure, due to the existence of an irregular and complex pore system (IntraP and intercrystalline pores), the type‐III reservoir has the highest fractal dimension, which indicates that the complex pore‐throat structure is not conducive to the formation of high‐quality deep sandstone reservoirs. Using the fractal dimension and displacement pressure, a novel permeability prediction is proposed, compared with the previous method, the new model is simpler and more effective. Our research can deepen the geological understanding of deep‐burial sandstone reservoirs and further guide petroleum exploration.

Relationship between pore throat and permeability of porous carbonate reservoir in the Middle East

A significant behavior of carbonate reservoirs is poor correlation between porosity and permeability. With the same porosity, the permeability can vary by three orders of magnitude or more. An accurate estimation of permeability for carbonate reservoir has been a challenge for many years. The aim of this study was to establish relationships between pore throat, porosity, and permeability. This study indicates that pore throat radius corresponding to a mercury saturation of 20% (R20) is the best permeability predictor for carbonates with complex porous pore networks. Quantitative analysis was made to achieve three different patterns of pore throat for 417 carbonate samples which cover all pore types of carbonate rocks. Different relationships between porosity, pore throat radius, and permeability have been identified in different patterns, which are utilized to predict more accurate permeability by different pore throat patterns.

Study of the Influence of Change in the Sandstone and Aleurolite Collector Properties on the Geological Modeling Quality

The initial data when creating both geological and hydrodynamic reservoir models can lead to errors in the modeling results and the subsequent distortion of the economic assessment and prospects of an oil or gas field. In order to improve the predictive reliability of reservoir hydrodynamic models, a core material study for the Tula object of four fields at the Babkinskaya anticline was carried out. The ratio analysis of porosity (Kp), rock density () and permeability (Kperm) for sandstones and aleurolites was carried out. Using a statistical core sampling based on porosity, density and permeability parameters, a separation by sedimentation processes was carried out for all considered lithological differences. For aleurolite and sandstone, we could talk about the differentiation of characteristics in the process of reservoir properties formation. The values of the parameters Kp, and Kperm, determined from laboratory core studies, were combined into a single statistical sample for the possibility of developing a methodology that would be aimed at describing Kperm using the integrated laboratory studies, namely by adding rock to the analysis. As a result of statistical analysis, it was found that permeability in intervals with low reservoir properties was controlled with the same significance degree by both porosity and rock density for all lithological differences. At the same time, the presence of highly permeable reservoirs for sandstones and their practically absence for aleurolites were noted. For all lithological differences, relationships were established between the permeability coefficient not only with porosity, but also with rock density. The methodology for constructing statistical models for calculating permeability from the values of porosity and rock density was implemented separately for the fields of the eastern and western parts of the Babkinskaya anticline. The described approach to taking into account the influence of rock density on permeability made it possible to determine the differentiated influence of lithotypes on the filtration characteristics of the reservoir. When modeling a reservoir, it is necessary to move from linearity to nonlinearity and take into account that the problem of permeability distribution in the reservoir being solved is somewhat more complicated: in different areas, sometimes the permeability is not controlled by porosity in principle, but somewhere only this parameter prevails. The methodical approach was recommended for 3D modeling. Revealing the relationships between the parameters was most important when developing a methodology for tuning the model in the interwell space. The development of a reliable estimate of permeability for the vast majority of wells will significantly improve the efficiency of hydrodynamic modeling. At the same time, it is necessary to comprehensively take into account the identified relationships between the petrophysical characteristics of production layers. The use of the approach to the analysis of petrophysical characteristics will allow obtaining a more reliable and less subjective hydrodynamic model of the formation.

A data mining approach for automatic classification of rock permeability

Reliable estimates of porosity can be obtained from different types of geophysical well logs. However, obtaining in situ permeability estimates is still a major challenge in the geosciences. This work aims to evaluate the application of data mining techniques to NMR logs for rock permeability classification, thus far tested only on laboratory data. For this study, we used a petrophysical database from two Brazilian Pre-salt wells located in the Santos Basin, a formation notoriously difficult to characterize, mainly due to its diversity and complexity. Six classification algorithms were evaluated (k-NN, NB, C4.5, RF, SMO, and MLP) according to their ability to estimate the permeability of rocks in four distinct classes (low: <1 mD, intermediate: 1–10 mD, high: 10–100 mD, and excellent: >100 mD). The predictive performance of the algorithms was compared to the behavior of two traditional permeability estimators. With an accuracy of 66%, the Naïve Bayes algorithm, combined with two preprocessing steps – unsupervised discretization and attribute selection – achieved the highest predictive performance. That mark surpassed the accuracy obtained by Kenyon and Timur-Coates estimators by 154% and 106%, respectively, providing evidence for the superiority of the data mining technique to recognize permeability classes based on NMR logs. Classification experiments employing NMR logs in conjunction with conventional logs were also conducted, but this log combination was not able to best the predictive result based solely on the NMR log data.

Comparison of Petrophysical Properties of Porous Rocks Using NMR, Micro-CT, and Fluid Flow Simulations

Micro-computed tomography (micro-CT) is increasingly utilized to image the pore network and to derive petrophysical properties in combination with modelling software. The effect of micro-CT image resolution and size on the accuracy of the derived petrophysical properties is addressed in this study using a relatively homogenous sandstone and a heterogenous, highly porous bioclastic limestone. Standard laboratory procedures including NMR (nuclear magnetic resonance) analysis, micro-CT analysis at different image resolutions and sizes and pore-scale flow simulations were used to determine and compare petrophysical properties. NMR-derived pore-size distribution (PSD) was comparable to the micro-CT-derived PSD at a resolution of 7 µm for both the rock types. Porosity was higher using the water saturation method as compared to the NMR method in both rocks. The resolution did not show a significant effect on the porosity of the homogeneous sandstone, but porosity in the heterogeneous limestone varies depending on the location of the sub-sample. The transport regime in the sandstone was derived by simulations and changed with the resolution of the micro-CT image. The transport regime in the sandstone was advection-dominated at higher image resolution and diffusion-dominated when using a lower image resolution. In contrast, advection was the dominant transport regime for the limestone based on simulations using higher and lower image resolutions. Simulation-derived permeability for a 400 Voxel3 image at 7 µm resolution in the Berea sandstone matched laboratory results, although local heterogeneity within the rock plays an integral role in the permeability estimation within the sub-sampled images. The simulation-derived permeability was highly variable in the Mount Gambier limestone depending on the image size and resolution with the closest value to a laboratory result simulated with an image resolution of 2.5 µm and a size of 300 Voxel3. Overall, the study demonstrates the need to decide on micro-CT parameters depending on the type of petrophysical property of interest and the degree of heterogeneity within the rock types.

Integration of 3D Volumetric Computed Tomography Scan Image Data with Conventional Well Logs for Detection of Petrophysical Rock Classes

Summary Core measurements are used for rock classification and improved formation evaluation in both cored and noncored wells. However, the acquisition of such measurements is time-consuming, delaying rock classification efforts for weeks or months after core retrieval. On the other hand, well-log-based rock classification fails to account for rapid spatial variation of rock fabric encountered in heterogeneous and anisotropic formations due to the vertical resolution of conventional well logs. Interpretation of computed tomography (CT) scan data has been identified as an attractive and high-resolution alternative for enhancing rock texture detection, classification, and formation evaluation. Acquisition of CT scan data is accomplished shortly after core retrieval, providing high-resolution data for use in petrophysical workflows in relatively short periods of time. Typically, CT scan data are used as two-dimensional (2D) cross-sectional images, which is not suitable for quantification of three-dimensional (3D) rock fabric variation, which can increase the uncertainty in rock classification using image-based rock-fabric-related features. The methods documented in this paper aim to quantify rock-fabric-related features from whole-core 3D CT scan image stacks and slabbed whole-core photos using image analysis techniques. These quantitative features are integrated with conventional well logs and routine core analysis (RCA) data for fast and accurate detection of petrophysical rock classes. The detected rock classes are then used for improved formation evaluation. To achieve the objectives, we conducted a conventional formation evaluation. Then, we developed a workflow for preprocessing of whole-core 3D CT-scan image stacks and slabbed whole-core photos. Subsequently, we used image analysis techniques and tailor-made algorithms for the extraction of image-based rock-fabric-related features. Then, we used the image-based rock-fabric-related features for image-based rock classification. We used the detected rock classes for the development of class-based rock physics models to improve permeability estimates. Finally, we compared the detected image-based rock classes against other rock classification techniques and against image-based rock classes derived using 2D CT scan images. We applied the proposed workflow to a data set from a siliciclastic sequence with rapid spatial variations in rock fabric and pore structure. We compared the results against expert-derived lithofacies, conventional rock classification techniques, and rock classes derived using 2D CT scan images. The use of whole-core 3D CT scan image-stacks-based rock-fabric-related features accurately captured changes in the rock properties within the evaluated depth interval. Image-based rock classes derived by integration of whole-core 3D CT scan image-stacks-based and slabbed whole-core photos-based rock-fabric-related features agreed with expert-derived lithofacies. Furthermore, the use of the image-based rock classes in the formation evaluation of the evaluated depth intervals improved estimates of petrophysical properties such as permeability compared to conventional formation-based permeability estimates. A unique contribution of the proposed workflow compared to the previously documented rock classification methods is the derivation of quantitative features from whole-core 3D CT scan image stacks, which are conventionally used qualitatively. Furthermore, image-based rock-fabric-related features extracted from whole-core 3D CT scan image stacks can be used as a tool for quick assessment of recovered whole core for tasks such as locating best zones for extraction of core plugs for core analysis and flagging depth intervals showing abnormal well-log responses.

Minimising the impact of sub-resolution features on fluid flow simulation in porous media

Resolution of micro-computed tomography (micro-CT) images of rocks affects flow simulation results, especially on low resolution images where the pore-grain boundary is not well resolved. However, there are two occasions where conducting flow simulations on low resolution images may be beneficial. The first case is when computation costs need to be reduced, and second is when high-resolution scanned images are unavailable and segmentation on available low-resolution images is difficult due to uncertainty at the pore boundary. A novel analytical formulation, the concentric pipes method, is introduced in this paper to include the effect of sub-resolution features in flow simulation. For the first case, we compare porosity, permeability, pore connectivity, and the velocity field obtained from applying different approaches to solve for flow on images with sub-resolution features. We find that the permeabilities obtained from downsampled images using the concentric pipes method have 13.2% errors on average compared to results from high-resolution images, while computation time decreases by at least 80%. For the second case, three phase segmentation can be applied to low resolution images and the concentric pipes method can be applied to the uncertain region which allows flow in the system to be solved. Permeability estimations in this case are within 0.5% error for a sandstone image and 11% error for carbonate images. We also simulate transport of particles on downsampled images and compare the transport properties with the high-resolution images.

A Site-specific Comparison of Permeability Prediction Models in Alluvial Sediments from Physical and Geoelectrical Measurements

An evaluation of five petrophysical models for hydraulic permeability predication was completed for a site-specific set of alluvial sediments. The models considered were the Kozeny-Carmen (1927–1937), Börner (1996), Revil-Cathles (1999), and two Revil-Florsch (2010) models. The river deposited sediments represent a relatively narrow grain-size distribution, and were acquired adjacent to the Kansas River, in Olathe, Kansas. Using measured physical, electrical, and hydraulic data from Slater and Glaser (2003) , a comparison of the performance of these five petrophysical models for hydraulic permeability estimation of soils was completed. For models where the key parameter is effective grain-size, three model variations were considered using d10, d50, and d90, resulting in an evaluation of a total of eleven individual models. Parameters included in the models can be classified as three different types: a) physical parameters only, b) electrical parameters only, and c) physical and electrical parameters together. The performance of each model was rated in terms of linear regression R squared, slope, and y-intercept values when plotted against the measured hydraulic conductivities. The top three models were the Kozeny-Carmen, a modified Revil-Cathles, and the Börner model. The Kozeny-Carmen model performed with the highest rating, followed by the modified Revil-Cathles model, and the Börner model rounding out the top three. There was a significant disparity between the rating associated with the top three and the fourth best performing model suggested by Revil and Florsch. However, it should be noted that the Börner model and Revil-Florsch model are based entirely on electrical measurements. The Revil-Cathles model was greatly improved when d10 was substituted for d50 for this limited sediment grain-size range.

Fuzzy support vector regression for permeability estimation of petroleum reservoir using well logs

Fuzzy support vector regression for permeability estimation of petroleum reservoir using well logs

Fracture permeability estimation utilizing conventional well logs and flow zone indicator

Characteristics of the natural open fractures on the oil and gas reservoirs is crucial in drilling and production planning. Direct methods of fractures studies such as core analysis and image log interpretation are usually not performed in all drilled wells in a field. Therefore, in absence of these data, the indirect methods can play an important role. In this study, an integrated algorithm is introduced to identify the fractures and estimate its permeability employing conventional well logs. First, open fractures were identified and their properties including density, aperture, porosity and permeability were estimated using FMI log. Subsequently, the fracture index log (FR_Index) was estimated utilizing conventional logs including density, micro-resistivity, sonic (compressional, shear and stoneley slownesses), and caliper logs. After that, the fracture index permeability was estimated by improving the FZI permeability equation. The coherence coefficient between two estimated fracture permeability logs is 0.66. A good correlation is observed on the high permeability zones, but the lower correlation on the low permeability zones. It is notified that, in the high fracture permeability zones, the conventional logs are heavily impacted by fracture permeability. However, due to lower vertical resolution of conventional logs compared with the image logs, the conventional logs are less influenced by less dense fracture zones. However, this algorithm can be used with acceptable accuracy in all uncored and image log wells.

A Permeability Estimation Method Based on Elliptical Pore Approximation

Digital rock images may capture more detailed pore structure than the traditional laboratory methods. No explicit function can correlate permeability accurately for flow within the pore space. This has motivated researchers to predict permeability through the application of numerical techniques, e.g., using the finite difference method (FDM). However, in order to get better permeability calculation results, the grid refinement was needed for the traditional FDM and the accuracy of the traditional method decreased in pores with elongated cross sections. The goal of this study is to develop an improved FDM (IFDM) to calculate the permeabilities of digital rock images with complex pore space. An elliptical pore approximation method is invoked to describe the complex pore space. The permeabilities of four types of idealized porous media are calculated by IFDM. The calculated results are in sound agreement with the analytical solutions or semi-empirical solutions. What’s more, the permeabilities of the digital rock images after grid coarsening are calculated by IFDM in three orthogonal directions. These results are compared with the previously validated lattice-Boltzmann method (LBM), which indicates that the predicted permeabilities calculated by IFDM usually agree with permeabilities calculated by LBM. We conclude that the presented IFDM is suitable for complex pore space.