Underestimation Of Permeability Research Articles

Gas mass transfer characteristics in shales: Insights from multiple flow mechanisms, effective viscosity, and poromechanics

Accurate characterization of gas transport behavior is indispensable for successful shale gas reservoir development. In this study, a fractal-theory-based apparent permeability (AP) model is developed to better characterize real gas mass transfer in shales. The proposed model involves multi-scale organic matter (OM) and inorganic matter (IOM) flow channels and incorporates poromechanics-related dynamic pore size, multiple gas transport mechanisms, and dynamic viscosity. The discrete integration method (DIM) is employed to address viscosity changes during fractal scaling up. Experimental data, molecular dynamics simulations, and published theoretical models were used to verify the proposed model and reasonable agreements have been achieved. Results indicate that as the pore pressure and size increase, dominant mechanisms for gas transport change from surface diffusion at low pressure (lower than switch pressure) to viscous flow at higher pressure and larger pore sizes. Furthermore, higher organic matter content makes the permeability curve more similar to OM type. Ignoring effective viscosity results in underestimation of permeability, which is more noticeable when pressure rises and pore shrinks. Poromechanical properties primarily affect pore size, larger elastic modulus and smaller Poisson's ratio leads to significantly lower permeability. The real gas effect on AP reduction cannot be ignored, especially at high pressure. This work provides insights into the gas transport characteristics in shales, which have practical implications for shale gas reservoir simulation and development.

Уточнение значений проницаемости при адаптации гидродинамической модели

Reservoir simulation models are used to design oil field developments, estimate efficiency of geological and engineering operations and perform prediction calculations of long-term development performances. A method has been developed to adjust the permeability cube values during reservoir model history-matching subject to the corederived dependence between rock petrophysical properties. The method was implemented using an example of the Bobrikovian formation (terrigenous reservoir) deposit of a field in the Solikamskian depression. A statistical analysis of the Bobrikovian formation porosity and permeability properties was conducted following the well logging results interpretation and reservoir modelling data. We analysed differences between the initial permeability obtained after upscaling the geological model and permeability obtained after the reservoir model history-matching. The analysis revealed divergences between the statistical characteristics of the permeability values based on the well logging data interpretation and the reservoir model, as well as substantial differences between the adjusted and initial permeability cubes. It was established that the initial permeability was significantly modified by manual adjustments in the process of history-matching. Extreme permeability values were defined and corrected based on the core-derived petrophysical dependence KPR = f(KP) , subject to ranges of porosity and permeability ratios. By using the modified permeability cube, calculations were performed to reproduce the formation production history. According to the calculation results, we achieved convergence with the actual data, while deviations were in line with the accuracy requirements to the model history-matching. Thus, this method of the permeability cube adjustment following the manual history-matching will save from the gross overestimation or underestimation of permeability in reservoir model cells.

Porosity\u2013permeability relationship derived from Upper Jurassic carbonate rock cores to assess the regional hydraulic matrix properties of the Malm reservoir in the South German Molasse Basin

For the successful realization and productivity prediction of new hydrothermal projects in the South German Molasse Basin, the hydraulic matrix properties of the Upper Jurassic Malm reservoir have to be determined as accurately as possible. To obtain specific information on the distribution of the petrophysical parameters (e.g., rock density, porosity, and permeability) 363 samples of rare drilling cores from the reservoir northeast of Munich (wells Moosburg SC4 and Dingolfing FB) were investigated using different experimental methods. Additionally, porosity was calculated by a downhole resistivity log of a nearby borehole close to Munich for comparison and the attempt of transferability of the data set to other locations within the Central Molasse Basin. Core data were divided into groups of different stratigraphic and petrographic units to cover the heterogeneity of the carbonate aquifer and provide data ranges to improve reservoir and prediction models. Data for effective porosity show a high variance from 0.3 to 19.2% throughout this heterogeneous aquifer. Permeability measured on core samples is scattered over several orders of magnitude (10−4–102 mD). Permeability models based on the porosity–permeability relationship were used to estimate permeability for the whole aquifer section and identify possible flow zones. A newly developed empirical model based on distinct lithofacies types allows a permeability estimation with a deviation < 10 mD. However, fractured, karstified, and vuggy zones occurring in this typically karstified, fractured, and porous reservoir cannot yet be taken into account by the model and result in an underestimation of permeability on reservoir scale. Overall, the dominant permeability trends can be mapped well using this model. For the regional transfer and the correlation of the results, a core-related porosity/permeability log for the reservoir was compiled for a well close to Munich showing similarities to the core investigations. The validation of the regional transferability of the parameter set to other locations in the Molasse Basin was carried out by correlation with the interpreted log data of a well near Munich.

Three Statistical Pitfalls of Phi-K Transforms

Summary Phi-k transforms are used widely to predict permeability. Some of the difficulties of this exercise are well identified, such as the homogeneity of the population (rock typing), the matching of cores and logs (especially depth matching), and the problem of permeability upscaling. Not so well-known, however, are the pitfalls of a statistical and geostatistical nature that may create significant biases—always in the same direction—an underestimation of permeability. The passage from Phi to k is performed in three steps: (1) in cored wells, an exponential regression equation is established between core porosity and core permeability k; (2) in uncored wells, log porosity is used instead as input to predict permeability; and (3) the same equation is sometimes used again to populate the cells of a dynamic reservoir model in 3D, where input porosity values are obtained by interpolation. The core-scale regression equation generally underestimates permeability by at least a factor of 2. The origin of the bias lies in the reverse transformation from logarithmic to arithmetic scale. To avoid this pitfall, a new permeability estimator is proposed, based on the quantile curves of the Phi-k crossplot. This estimator is data driven and does not assume a priori any particular functional relationship between Phi and k, such as an exponential-regression function. One of the simplest diagnostic tools to check the agreement between log and core porosity is a crossplot of one against the other. In the absence of bias, the points are expected to be distributed along the y = x line. In reality, they either are or they are not, according to which variable is plotted along the x-axis. This apparent paradox is elucidated by bivariate regression theory and related to the difference of investigated volume between core and log data. Direct input of upscaled cell porosity into an exponential core-scale permeability transform amounts to forcing geometric permeability averaging, which may again lead to serious underestimation of the true upscaled permeability when heterogeneity is significant.

Capillary Permeability in Skeletal Muscle

AbstractCapillary permeability in skeletal muscle was investigated by applying the single injection, external registration method to the autoperfused cat gastrocnemius preparation. 51Cr‐EDTA (MW: 341.2) and 57Co‐B12 (MW: 1353.5) served as simultaneously injected indicators. At a plasma flow of 7 ml/100 g×min and an assumed capillary surface area, S, of 70 cma/g the permeability coefficients Pd(51Cr‐EDTA) and Pd(57Co‐B12) were 0.74 × 10‐5 cm/s and 0.45×10‐6 cm/s, respectively. However, correction for the recruitment of perfused capillaries yields Pd(51C‐EDTA)‐ 1.5 × 10‐5 cm/s and Pd(57Co‐B12) = 0.9 × 10‐5 cm/s. The results indicate that the permeability of a muscle capillary for hydrophilic solutes is similar to that of continuous capillaries in other tissues. The Pappenheimer pore radius estimate of 30 Å, the Karnovsky 40 Å interendothelial slit width, and pinocytotic transport are defective in accounting for the results as 51Cr‐EDTA and 57Co‐B12 diffuse across the capillary membrane at rates proportional to their free diffusion coefficients in water (CDC(51Cr‐EDTA)/CDC(57Co‐B12) = D(51Cr‐EDTA)/D(57Co‐B12)= 1.79). The intraendothelial patent channel system of fused vesicles might be the pathway for transcapillary exchange of hydrophilic molecules as this system alone could account for the experimental results. Only 1–2 open channels per μm capillary length are necessary to account for the observed permeabilities. For both indicators CDC was a linear function of plasma flow and CDC increased 3‐3.5 fold when plasma flow increased from 4 to 52 ml/100 g× min. Assuming constant permeability coefficients, the CDC increase with plasma flow reflects an increase in capillary surface area indicating a 3‐3.5 fold recruitment of capillaries. A constant ratio of CDC(51Cr‐EDTA)/CDC(57Co‐B12) within the perfusion range indicates that 51Cr‐EDTA and 57Co‐B12 can be employed at plasma flow &gt; 4 ml/100 g× min without risk of early back‐diffusion resulting in underestimation of permeability.