Permeability Estimation Method Research Articles

Assimilating Seismic Data And Soil Basic Information to Predict Near-surface Permeability And Water Content

Soil permeability plays a key role in the study of earth sciences for agriculture and forestry. Because the traditional laboratory measurement is time-consuming and laborious, and only discrete profile data can be obtained. In this paper, a simple and efficient method using soil transfer function (PTFs), is proposed to estimate permeability and other parameters indirectly by seismic wave observation. Based on Biot’s theory establishing the relationship between shear-wave velocity and permeability, and the basic soil information in the study area, including land survey, logging and drilling data, using the PTFs constraint to estimate saturated hydraulic conductivity, soil components, saturated water content and residual water content may favor the physical corrections of the PTFs. The results show that there are three distinct layers of permeability in the study area, consistent with the velocity structure. The measured basic information further verifies the accuracy of the saturated permeability coefficient estimation, which shows the reliability of the improved PTFs. The established near surface permeability estimation method by integrating seismic wave observation and soil basic information may provide further assimilation for parameter estimation combining geophysical observation and hydrogeographic statistics.

Model-based cylinder radius and permeability estimation using eddy current testing

The material quality of metallic cylinders including microstructure is reflected in their physical properties. Eddy current testing techniques play an important role in the measurement of metallic cylinder measurement. In this paper, a cylinder radius and permeability estimation method is proposed based on the combined analytical and optimisation method. The Dodd and Deeds analytical model has been first simplified, which suggests an approximate linear relationship between the cylinder radius, permeability and coil inductance. Based on the proposed relation, the pre-estimated radius and permeability are used as the initial guess for the modified Newton–Raphson algorithm to solve the least squares problem between the measured and calculated coil inductance spectra. This method avoids the local minimum issue that occurs otherwise, to some extent. The effectiveness of the proposed method has been evaluated by numerical simulations and experiments, which indicates that fast estimation can be achieved with high accuracy.

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.

A new method for permeability estimation in carbonate reservoirs using NMR T2 distribution features and data clustering

A new method for permeability estimation in carbonate reservoirs using NMR T2 distribution features and data clustering

Quantitative analysis of pore structure and permeability characteristics of sandstone using SEM and CT images

Permeability determines the exploration and development efficiency of the oil and gas field, while the pore structure directly affects the permeability of sandstones. Therefore, in the current study, the pore structure and permeability of sandstones were quantitatively analyzed from macro and micro perspectives. With SEM images at different magnifications, pore size distributions (PSD) were obtained, and results were compared with values from the mercury intrusion method. Based on fractal theory, relationships between fractal dimension, magnifications, and porosity were analyzed, they showed apparent regularity. According to the results of PSD, permeability was further studied, while predicted values were more extensive than experiment results. With multislice CT images, the pore structure was obtained from the three-dimensional (3D) reconstruction. The connectivity of pores was discussed. In addition, an improved permeability estimation method based on multiple binary images was proposed, the permeability of A1 and A2 are 1.97 fm2 and 1.94 fm2 respectively, which are close to the experimental result (1.48 fm2 at the confining pressure of 1 MPa). Meanwhile, it can also eliminate the dispersion of the calculation based on the two-dimensional SEM image.

Improved ST-FZI method for permeability estimation to include the impact of porosity type and lithology

Permeability represents the flow conductivity of a porous media. Since permeability is one of the most vital as well as the complex properties of a hydrocarbon reservoir, it is necessary to measure/estimate accurately, rapidly and inexpensively. Routine methods of permeability calculation are through core analysis and well tests, but due to problems and weaknesses of the aforementioned methods such as excessive costs and time, these are not necessarily applied on neither in all wells of a field nor in all reservoir intervals. Therefore, log-based approaches have been recently developed. The goal of this research is to provide a flowchart to estimate permeability using well logs in one of Iranian south oil fields and finally to introduce a new algorithm to estimate the permeability more accurately. Permeability is firstly estimated using artificial neural network (ANN) employing routine well logs and core data. Subsequently, it is estimated using Stoneley-Flow Zone Index (ST-FZI) and is compared with the results of core analysis. Correlation coefficients in permeability estimation by artificial neural network and Stoneley-FZI are R2 = 0.75 and R2 = 0.85, respectively. On the next step, an improved algorithm for permeability prediction (improved ST-FZI) is presented that includes the impact of lithology and porosity type. To improve the permeability estimation by ST-FZI method, electro-facies clustering based on MRGC method is employed. For this purpose, rock pore typing utilizing VDL and NDS synthetic logs is employed that considers the porosity types and texture. The VDL log separates interparticle porosity from moldic and intra-fossil porosities and washes out and weak rock-type zones. Employing MRGC method, three main facies are considered: good-quality reservoir rock, medium-quality reservoir rock and bad-quality (non-reservoir) rocks. Permeability is then estimated for each group employing ST-FZI method. The estimated permeability log by improved ST-FZI method shows better match with the measured permeability (R2 = 0.93). The average error between estimated and measured permeability for ANN, ST-FZI method and improved ST-FZI method is 1.83, 1.18 and 0.796, respectively. The increased correlation is mainly due to involving the impact of porosity types on improved ST-FZI method. Therefore, it is recommended to apply this algorithm on variety of complicated reservoir to analyze its accuracy on different environments.

Comparative Permeability Estimation Method and Identification of Rock Types using Cluster Analysis from Well Logs and Core Analysis Data in Tertiary Carbonate Reservoir-Khabaz Oil Field

Characterization of the heterogonous reservoir is complex representation and evaluation of petrophysical properties and application of the relationships between porosity-permeability within the framework of hydraulic flow units is used to estimate permeability in un-cored wells. Techniques of flow unit or hydraulic flow unit (HFU) divided the reservoir into zones laterally and vertically which can be managed and control fluid flow within flow unit and considerably is entirely different with other flow units through reservoir. Each flow unit can be distinguished by applying the relationships of flow zone indicator (FZI) method. Supporting the relationship between porosity and permeability by using flow zone indictor is carried out for evaluating the reservoir quality and identification of flow unit used in reservoir zonation. In this study, flow zone indicator has been used to identify five layers belonging to Tertiary reservoirs. Consequently, the porosity-permeability cross plot has been done depending on FZI values as groups and for each group denoted to reservoir rock types. On the other hand, extending rock type identification in un-cored wells should apply a cluster analysis approach by using well logs data. Reservoir zonation has been achieved by cluster analysis approach and for each group known as cluster which variation and different with others. Five clusters generated in this study and permeability estimated depend on these groups in un-cored wells by using well log data that gives good results compared with different empirical methods.

Experimental Investigation on Sandstone Permeability under Plastic Flow: Permeability Evolution Law with Stress Increment

Permeability is an important physical property of rock. In rock and rock-like materials, permeability after yielding is closely related to plastic flow behavior. Theoretical analysis and experimental investigations are effective and reliable ways of studying the evolution of permeability. In this paper, fluid flow tests of sandstone samples under 11 stress states were conducted using the MTS 816.02 rock mechanics testing system and a self-designed permeation system. A new plastic flow rule was proposed based on the Mohr-Coulomb yield criterion and a nonassociated flow rule. The applicability of the flow rule was verified by comparing the estimated and experimental values of the equivalent shear strain of the Mohr–Coulomb criterion. Two new coefficients were defined to reflect the influence of the volume deformation and shear deformation on the permeability. A permeability model for plastic flow was established, which can be used to calculate both single-step and multistep permeability estimates of the sandstone samples during plastic flow. The errors of both estimation methods were analyzed. The experimental results showed that the plastic multiplier for the sandstone samples was positive during unloading conditions and negative during loading conditions. The experimental value error of the single-step permeability estimation was less than 16.5%. The experimental value errors of the multistep permeability estimations varied between 15.6% and 16.7%, indicating that the iterative format of the multistep permeability estimation method was generally stable and highly precise. A comparison of the permeability influence coefficients indicated that the influence of the equivalent shear strain on the permeability was smaller than that of the volumetric strain.

A new method for permeability estimation using integral transforms based on NMR echo data in tight sandstone

Permeability is a vital petrophysical parameter in reservoir evaluation and productivity prediction. In this study, a new method is presented to estimate permeability in tight sandstone using integral transforms of the NMR echo data. Different permeability indicators are directly computed from the NMR echo data using integral transforms without obtaining T2 distributions by inversion of the echo data which is usually an indispensable part in traditional NMR-based methods for permeability estimation. The forms of these permeability indicators are controlled by the parameter n. Furthermore, new empirical models are developed based on the permeability indicators to estimate the permeability of tight sandstone. Different from the fixed permeability characterization parameters used in traditional models, in the new models, more suitable parameters can be selected to characterize the rock permeability by optimizing the parameter n. The numerical simulation results show that the integral transform method is simpler, more stable, and more accurate than the traditional T2 inversion-based methods for permeability indicator computation and is still effective for low signal-to-noise ratio echo data. The core experiments and permeability estimation results indicate that the proposed method is superior to the traditional Schlumberger-Doll Research (SDR) method for permeability estimation in tight sandstone.

A Novel Method for Permeability Estimation from Micro-tomographic Images

A methodology has been developed to create a pore network model (PNM) from the geometrical/topological information extracted from the micro-tomographic images of a polyurethane (PU) foam sample. By solving fluid-flow equations on this model, we could estimate the permeability of PU foams and validate with experimental findings. Previous literature suggested that the permeability of open-cell PU foams was overestimated using the traditional Carman–Kozeny and Duplessis–Masliyah models. Inter-cell connectivity was deemed as the potential cause of this difference. Thus, taking into consideration the effects of spatial arrangement of pores of different sizes, the throat constriction between pores, and the percentage open-cell content, a PNM was employed where the entire void space is treated as a network of pores and throats of varying dimensions. To simulate flow through the network, the mass conservation equations were solved at each pore, the Darcy’s equation was applied globally, and thus, the overall permeability of the foam was estimated. Using our PNM, we were able to estimate the permeability with very good agreement with experimentally observed results. This indicates that pore connectivity has a significant effect on permeability. Parametric studies with PNM also revealed that the permeability depends on the square of pore size while is quite sensitive to throat constrictions with cubic dependence.

A numerical study on the transient aspects of porous flows and the applicability of Darcy’s friction flow relation

In recent developments of shale reservoirs, it is important to estimate the permeabilities of hydraulic fractures accompanying the Non- Darcy effects and geometric changes. Accordingly, a new permeability estimation method that considers the varying geometric features under different flow regions is demanded. To this end, the present study introduces the generalized Darcy’s friction flow relation, especially for examining the friction factor-Reynolds number (f · Re) relationship of porous flow, which is originally used in general internal friction flow analyses. Moreover, simple hydraulic fractures comprising structured microbeads are simulated via computational fluid dynamics during fracture aperture variations under different flow conditions from laminar to turbulent. Frictional flow features, e.g., the preservation characteristics of f · Re values, are examined under different geometry and flow conditions, and the transient flow characteristics are investigated using streamline analyses. Consequently, it is verified that the f · Re values vary slightly in proportion to the geometric changes caused by aperture reduction in each medium. Even though the variations in the f · Re values are much smaller than the permeability variations, it seems to be contrary to our expectation. Otherwise, the almost linear-variation aspects of f · Re values were observed in both directional flow cases. The linear-variation aspect of f · Re values is expected to be useful in the permeability-variation estimations in porous media with changing basic geometric factors, such as hydraulic fracture closing. Moreover, it is demonstrated that regardless of aperture reduction in the same type of medium, each porous flow has a very similar power-law relation between f and Re values when the flow velocity changes from the laminar to the turbulent condition. This aspect can be effectively used for obtaining permeability estimations of the varied media, particularly under different flow conditions.

Permeability evaluation on oil-window shale based on hydraulic flow unit: A new approach

Permeability is one of the most important petrophysical properties of shale reservoirs, controlling the fluid flow from the shale matrix to artificial fracture networks, the production and ultimate recovery of shale oil/gas. Various methods have been used to measure this parameter in shales, but no method effectively estimates the permeability of all well intervals due to the complex and heterogeneous pore throat structure of shale. A hydraulic flow unit (HFU) is a correlatable and mappable zone within a reservoir, which is used to subdivide a reservoir into distinct layers based on hydraulic flow properties. From these units, correlations between permeability and porosity can be established. In this study, HFUs were identified and combined with a back propagation neural network to predict the permeability of shale reservoirs in the Dongying Depression, Bohai Bay Basin, China. Well data from three locations were used and subdivided into modeling and validation datasets. The modeling dataset was applied to identify HFUs in the study reservoirs and to train the back propagation neural network models to predict values of porosity and flow zone indicator. Next, a permeability prediction method was established, and its generalization capability was evaluated using the validation dataset. The results identified five HFUs in the shale reservoirs within the Dongying Depression. The correlation between porosity and permeability in each HFU is generally greater than the correlation between the two same variables in the overall core data. The permeability estimation method established in this study effectively and accurately predicts the permeability of shale reservoirs in both cored and un-cored wells. Predicted permeability curves effectively reveal favorable shale oil/gas seepage layers and thus are useful for the exploration and the development of hydrocarbon resources in the Dongying Depression. Cited as : Zhang, P., Lu, S., Li, J., Zhang, J., Xue, H., Chen, C. Permeability evaluation on oil-window shale based on hydraulic flow unit: A new approach. Advances in Geo-Energy Research, 2018, 2(1): 1-13, doi: 10.26804/ager.2018.01.01

Совершенствование метода оценки проницаемости горных пород-коллекторов природных резервуаров нефти и газа

Совершенствование метода оценки проницаемости горных пород-коллекторов природных резервуаров нефти и газа

Permeability estimations and frictional flow features passing through porous media comprised of structured microbeads

Permeability estimation has been extensively researched in diverse fields; however, methods that suitably consider varying geometries and changes within the flow region, for example, hydraulic fracture closing for several years, are yet to be developed. Therefore, in the present study a new permeability estimation method is presented based on the generalized Darcy’s friction flow relation, in particular, by examining frictional flow parameters and characteristics of their variations. For this examination, computational fluid dynamics (CFD) simulations of simple hydraulic fractures filled with five layers of structured microbeads and accompanied by geometry changes and flow transitions are performed. Consequently, it was checked whether the main structures and shapes of each flow path are preserved, even for geometry variations within porous media. However, the scarcity and discontinuity of streamlines increase dramatically in the transient- and turbulent-flow regions. The quantitative and analytic examinations of the frictional flow features were also performed. Accordingly, the modified frictional flow parameters were successfully presented as similarity parameters of porous flows. In conclusion, the generalized Darcy’s friction flow relation and friction equivalent permeability (FEP) equation were both modified using the similarity parameters. For verification, the FEP values of the other aperture models were estimated and then it was checked whether they agreed well with the original permeability values. Ultimately, the proposed and verified method is expected to efficiently estimate permeability variations in porous media with changing geometric factors and flow regions, including such instances as hydraulic fracture closings.

A new method for permeability estimation from conventional well logs in glutenite reservoirs

Permeability is one of the most important petrophysical parameters in formation evaluation. In glutenite reservoirs, the traditional permeability estimation method from conventional well logs cannot provide satisfactory results due to the characteristic of strong heterogeneity resulting from the wide variety of clastic grains and the extremely complex percolation network. In this paper, a new method for estimating permeability from conventional well logs is developed. On the basis of previous research, a simple method for estimating the flowing porosity of the Maxwell conductive model via well logs is proposed and then a ‘flowing permeability’ equation is established by using the equivalent parameters of geometry and flowing porosity. The form is similar to that of the Kozeny–Carman model for characterizing permeability. Based on the Maxwell conductive model, threshold theory, conductive efficiency theory and core analysis data, a new method to calculate the permeability of glutenite reservoirs by using float porosity is built up through deduction and analysis of the Kozeny–Carman equation, and field application to a glutenite reservoir shows that the result of the proposed method in this paper is accurate and reasonable.

An improved method for permeability estimation of the bioclastic limestone reservoir based on NMR data

Permeability is an important parameter in formation evaluation since it controls the fluid transportation of porous rocks. However, it is challengeable to compute the permeability of bioclastic limestone reservoirs by conventional methods linking petrophysical and geophysical data, due to the complex pore distributions. A new method is presented to estimate the permeability based on laboratory and downhole nuclear magnetic resonance (NMR) measurements. We divide the pore space into four intervals by the inflection points between the pore radius and the transversal relaxation time. Relationships between permeability and percentages of different pore intervals are investigated to investigate influential factors on the fluid transportation. Furthermore, an empirical model, which takes into account of the pore size distributions, is presented to compute the permeability. 212 core samples in our case show that the accuracy of permeability calculation is improved from 0.542 (SDR model), 0.507 (TIM model), 0.455 (conventional porosity-permeability regressions) to 0.803. To enhance the precision of downhole application of the new model, we developed a fluid correction algorithm to construct the water spectrum of in-situ NMR data, aiming to eliminate the influence of oil on the magnetization. The result reveals that permeability is positively correlated with percentages of mega-pores and macro-pores, but negatively correlated with the percentage of micro-pores. Poor correlation is observed between permeability and the percentage of meso-pores. NMR magnetizations and T2 spectrums after the fluid correction agree well with laboratory results for samples saturated with water. Field application indicates that the improved method provides better performance than conventional models such as Schlumberger-Doll Research equation, Timur-Coates equation, and porosity-permeability regressions.

Relative permeability prediction considering complex pore geometry and wetting characteristics in carbonate reservoirs

The measurement of relative permeability in carbonate rocks is very uncertain because of the complex pore system. Several equations for the relative permeability have been previously developed. However, most equations assume a single pore system that cannot be applied accurately. This study presents a relative permeability estimation method that considers capillary pressure, contact angle, pore size distribution, and residual oil saturation with respect to the heterogeneous pore network. As results, the capillary pressure was observed to have different tendencies for macropore and micropore. Also, the pore size distribution index of the macropore system was greater than the micropore system. For the macropore, water has a higher relative permeability than oil; a small reduction in oil saturation can easily flow water. In contrast, the micropore tends to follow the conventional relative permeability curve. Therefore, stable water displacement was not assured, leading to an early breakthrough for the hetero...

Characterization of gas transport behaviors in shale gas and tight gas reservoirs by digital rock analysis

Due to the extremely tiny pore size of tight gas and shale gas reservoir, the modified Darcy’s law in which the intrinsic permeability is replaced by the apparent permeability that can be obtained by a function of three transport parameters (intrinsic permeability, porosity and tortuosity), is used to describe the combined mechanisms of viscous flow, Knudsen diffusion, the effect of the adsorbed layer thickness and surface diffusion through the adsorbed layer. A new apparent permeability estimation method based on digital rock was proposed in this paper. The digital rock with nanopores could be constructed by 3D pore structure images obtained from micro/nano CT and FIB-SEM images directly or reconstructed with Markov Chain Monte Carlo (MCMC) method from the 2D SEM images of pore structure; then Lattice Boltzmann method can be applied to calculate the intrinsic permeability, porosity and tortuosity of 3D digital rock. These parameters are used to calculate the apparent permeability under consideration of different combined gas transport mechanisms. This method is applied to samples from the shale gas reservoir in Silurian Longmaxi Formation of Sichuan Basin and from the tight gas reservoir in the Wenchang Formation of Huizhou Sag. The results show that all considered transport mechanisms greatly impact the shale apparent permeability and cannot be ignored in shale samples. In tight gas reservoirs, Knudsen diffusion is an important mechanism at low pressures of less than 1MPa. However, Knudsen diffusion could be ignored when pressure is greater than 1MPa due to its smaller impact.

Permeability estimation based on thin-section image analysis and 2D flow modeling in grain-dominated carbonates

Permeability estimation based on image analysis is a good alternative when an intact core-plug is not available for laboratory measurement. While there is much research on permeability estimation from 2D and 3D images or models, accurately estimating permeability for carbonates, a type of rock with substantial heterogeneity, is still challenging. In this study, a method for permeability estimation based on thin-section image analysis and 2D permeability simulation is developed for grain-dominated carbonates based on semi-theoretical analysis of 2D and 3D permeability (K2D and K3D) relationship. The mathematical expression of the K2D/K3D is examined and validated with a grainstone carbonate sample, for which both K2D and K3D were obtained through permeability simulation based on micro-CT images. The method was applied to 24 grain-dominated carbonate samples collected from different locations with a large variation in rock textures and fabrics and a broad range of permeability from 0.1 mD to 3200 mD. Representativeness of the thin section and the correct determination of the effective pores are the key for accurate estimation. The estimated permeability was compared to the measured value, and 92% of the results are within a factor of ±5, and 46% are with a factor of ±2. Potential sources of systematic error are discussed both qualitatively and quantitatively.

Permeability estimation of porous media by using an improved capillary bundle model based on micro-CT derived pore geometries

The purpose of this work is to develop a permeability estimation method for porous media. This method is based on an improved capillary bundle model by introducing some pore geometries. We firstly carried out micro-CT scans to extract the 3D digital model of porous media. Then we applied a maximum ball extraction method to the digital model to obtain the topological and geometrical pore parameters such as the pore radius, the throat radius and length and the average coordination number. We also applied a random walker method to calculate the tortuosity factors of porous media. We improved the capillary bundle model by introducing the pore geometries and tortuosity factors. Finally, we calculated the absolute permeabilities of four kinds of porous media formed of glass beads and compared the results with experiments and several other models to verify the improved model. We found that the calculated permeabilities using this improved capillary bundle model show better agreement with the measured permeabilities than the other methods.