Klinkenberg-corrected Gas Permeability Research Articles

Investigation on gas permeability of compacted GMZ bentonite with consideration of variations in liquid saturation, dry density and confining pressure

During the long term operation of a disposal repository, gas will be inevitably generated. Determination of gas permeability of compacted bentonite is of great importance for the safety assessment of the engineered barrier system. In the present work, the steady-state and residual pressure methods were employed to determine the gas permeability of GaoMiaoZi (GMZ) bentonite with consideration of variations in liquid saturation, dry density and confining pressure. Results show that, gas migration in saturated GMZ bentonite was mainly controlled by diffusion with an effective gas permeability of 1E-23 m2 - 1E-25 m2. While in unsaturated GMZ bentonite, significant gas flow rates could be observed, which increased stably with the increase of gas injection pressure. Klinkenberg effect was significant when gas flow through GMZ bentonite. The Klinkenberg corrected gas permeability decreased by 3.5–5.5 orders of magnitude as the liquid saturation increased from 10% to 70%. A decreasing magnitude of 1–2 orders in Klinkenberg corrected gas permeability was presented with the dry density increased from 1.5 Mg/m3 and 1.7 Mg/m3. The Klinkenberg corrected gas permeability decreased by 0–1 orders of magnitude as the confining pressure increased from 3 MPa to 7 MPa. By using the accessible porosity, gas measured intrinsic permeability could be determined with values ranged between 1E-15 m2 to 4E-15 m2, which was higher than the water measured one by 5 orders of magnitude. Additionally, a generalized power law was successfully adopted in this study to describe the evolution of gas relative permeability with the liquid saturation. Overall, the effective gas permeability, Klinkenberg corrected gas permeability, intrinsic and relative permeability determined in this study provided a comprehensive perspective to assess the buffering property of GMZ bentonite in multi-physical field coupling environment. The parameters obtained can be adopted in further simulation works for long-term safety analysis of the disposal repository from the viewpoint of gas migration.

The influence of partial hydrocarbon saturation on porosity and permeability in a palaeogene lacustrine shale-hosted oil system of the Bohai Bay Basin, Eastern China

Palaeogene calcareous (>40% carbonate) mudstones (Ro from 0.56 to 0.88%) from the Bohai Bay Basin were studied by combined petrographical, geochemical and petrophysical analysis in order to assess and quantify the pore space, pore filling and its influence on gas transport capacity.TOC contents ranged from 1.44% to 5.12% and porosities (ΦHe) determined by helium pycnometry, from 1.3% to 6.4%. Bitumen-filled porosity (ΦS1) was estimated to range between 0.3 and 2.0% based on Rock-Eval S1 values and an assumed bitumen density of 0.90 g/cm3. The “true” total porosity (Φtotal = ΦHe + ΦS1) amounts to 1.9–8.5%. The in-situ oil saturation (So) was estimated to range between 25% and 52%, with two samples (L69-1B and L69-2) having relatively high oil saturation (71% and 91%).The conductivity of the remaining “open” pore space was measured on three samples with different orientations and oil saturations from 17 to 24%. The effective Klinkenberg-corrected gas permeability coefficients range between 63 and 2000 nDarcy, and permeability is highest parallel to bedding. Upon loading from 10 to 40 MPa confining pressure the intrinsic permeability coefficients decreased by one order of magnitude, revealing a relatively high exponential stress sensitivity coefficient (0.069 MPa−1) and much lower zero stress permeability (1.416 × 10−6 mD) than most gas shales. This could be due to pore plugging by ductile bitumen.

Gas permeability in unconventional tight sandstones: Scaling up from pore to core

Upscaling Klinkenberg-corrected gas permeability, k, in unconventional tight sandstones has numerous practical applications, particularly in gas exploration and production. In this study, we adapt the effective-medium approximation (EMA) model of Doyen – proposed first to estimate bulk electrical conductivity, σb, and permeability in sandstones from rock images – to scale up σb and k in tight-gas sandstones from pore to core. For this purpose, we calculate two characteristic pore sizes: an effective hydraulic and an effective electrical pore size from pore-throat size distributions – determined from mercury intrusion capillary pressure (MICP) curves – and pore-throat connectivity. The latter is estimated from critical volume fraction (or percolation threshold) for macroscopic flow. Electrical conductivity and permeability are then scaled up from the two characteristic pore sizes, tortuosity, and porosity by assuming two different pore geometries: cylindrical and slit-shaped. Comparison of results obtained for eighteen tight-gas sandstones indicates that the EMA estimates σb and k more accurately when pores are assumed to be cylindrical. We also estimate k from the pore-throat size distributions and the measured electrical conductivity using the EMA and critical path analysis (CPA), another upscaling technique borrowed from statistical physics. Theoretically, the former is valid in relatively heterogeneous porous media with narrow pore-throat size distribution, while the latter is valid in heterogeneous media with broad pore-throat size distribution. Results show that the EMA estimates k more accurately than CPA and arrives within a factor of two of the measurements on average.

Novel liquid-gas corrected permeability correlation for dolomite formation

Standard practice for determining permeability is to perform gas permeability measurement and apply correlations to receive corrected permeability as the value of absolute permeability. However, these correlation are dedicated for the specific reservoirs or unconsolidated porous media and cannot be applicable for other rock formations. The objective of this study is to establish correlation between liquid and gas permeability for the pure dolomite. A series of liquid and gas permeability measurements were performed on cylindrical rock samples from formation located in Poland. To determine Klinkenberg-corrected gas permeability, measurements of gas permeability at three (randomly selected) different inverse mean pressure were extrapolated to infinity. Then values of water and corrected-gas permeability were contrasted against each other. The results showed that Klinkenberg permeability overestimates water permeability and the observed difference is in range of 11–24%. This fact can be caused by water polar nature. Hydrogen bonds are formed with neighboring molecules and cause high surface tension and capillary forces. Later, the effect of overburden pressure on water permeability was studied and results showed reduction in permeability as a function of increasing stress. In the last part of the research, the permeability values obtained by using novel equation has been compared with values using other mathematical formulas designed for sandstone and limestone. We learned that our correlation provides results with higher accuracy than the previous equations.

Comparison of Klinkenberg-Corrected Gas and Liquid Permeability in Kirthar Fold Belt Tight Gas Sands

Comparison of Klinkenberg-Corrected Gas and Liquid Permeability in Kirthar Fold Belt Tight Gas Sands

Effect of low-velocity non-Darcy flow on well production performance in shale and tight oil reservoirs

There are many core flooding studies showing that the liquid-measured permeability is lower than the Klinkenberg-corrected gas permeability. The flow velocity in a low pressure gradient regime is lower than what is estimated from Darcy’s law. This phenomenon is considered as low-velocity non-Darcy flow in the literature. Besides, many researchers believe that there is a threshold pressure gradient (TPG) that needs to be overcome before the fluid flow can occur. The related results in the literature are critically reviewed in this paper. By analyzing the flow mechanism, considering boundary effect, and presenting counter examples, we conclude that the low-velocity non-Darcy flow regime consists of a nonlinear flow part and a linear flow part. The nonlinear flow part starts from the zero pressure gradient instead of TPG. Based on this observation, a non-Darcy model is introduced and the corresponding correlation parameters are derived by fitting the available experimental data. This model is used to estimate the well performance of a vertical well and a multi-fractured horizontal well. For a vertical well, the production rate of non-Darcy flow is much smaller than that of Darcy flow, and the ultimate oil recovery of non-Darcy flow is approximately 48% of the Darcy flow. The production rate of a multi-fractured horizontal well if non-Darcy flow is considered is smaller in the beginning but greater than the corresponding Darcy flow rate after about some time (in our example model, 2700days). The ultimate recovery factor of non-Darcy flow is 80% of Darcy flow, which indicates that multi-fractured wells are less affected by the low-velocity non-Darcy phenomenon compared with the vertical wells. Multi-fractured horizontal wells exhibit a significant advantage in developing shale and tight reservoirs, and low velocity non-Darcy flow plays a significant impact on the well production performance in tight and shale reservoirs.

Klinkenberg-corrected gas permeability correlation for Shuaiba carbonate formation

Abstract Standard industry practice to correct absolute gas permeability for what is known as the Klinkenberg effect is to perform single point gas permeability measurement and use assumptions or existing correlations. Available correlations for Klinkenberg-correction of gas permeability are based on measurements of sandstone samples. However, correlations developed for specific fields/formations may not be applicable for other reservoirs of different lithology due to the difference in the pore geometry. The present experimental investigation was conducted for the purpose of establishing one or several correlations for correcting single point gas permeability measurements (standard conventional core analysis) for the Klinkenberg effect for the Shuaiba Formation (carbonate) as well as to learn whether there is any significant difference between the sandstone-based correlation and the new results for the Shuaiba limestones. Measurements were made on 175 core-plug samples from the Shuaiba Formation. This limestone unit (Shuaiba) was chosen for study as it is an important oil reservoir in Oman and in the Middle East. Multi-point gas permeability ( K g ) was measured for each sample at four different mean pressures and extrapolated to infinite pressure to obtain the Klinkenberg-corrected gas permeability ( K L ). Correlation between K L and K g was then established. The robustness of the derived correlation has been validated using existing data (95 additional samples) from another study conducted in parallel to this study on core samples from similar formation (Shuaiba). The results can be useful for directly applying Klinkenberg-correction to other gas permeability data measured at only a single pressure.

Experimental study of fluid transport processes in the matrix system of the European organic-rich shales: II. Posidonia Shale (Lower Toarcian, northern Germany)

A laboratory study has been conducted to investigate the transport of gases (He, Ar, CH4) and water in the matrix of Lower Toarcian Posidonia Shale samples from three shallow boreholes in northern Germany. The maturity of the organic matter of the shale samples ranged between 0.53 and 1.45% vitrinite reflectance (VRr). The measurements were performed at effective stresses ranging between 6 and 37MPa and a temperature of 45°C. The effects of different controlling factors including permeating fluid, maturity, anisotropy, moisture content and effective stress on the fluid conductivity were analyzed and discussed.Permeability coefficients measured perpendicular and parallel to bedding (3·10−22 to 9.7·10−17m2) were within the range previously reported for other shales and mudstones. They exhibited a strong dependence on permeating fluid, maturity, anisotropy, moisture content and effective stress. The permeability coefficients measured with helium as permeate were consistently higher (up to two times) than those measured with argon and methane. Permeability coefficients measured with water were up to three orders of magnitude lower than Klinkenberg-corrected gas permeability coefficients measured with helium and methane under similar experimental conditions. Among the samples studied, the lowest porosity and permeability coefficients were measured on samples of intermediate thermal maturity (0.88% VRr, oil-window). Permeability coefficients (He, CH4) measured parallel to bedding were up to more than one order of magnitude higher than those measured perpendicular to bedding. Permeability coefficients measured with He and CH4 on a dry sample were up to two times higher than those measured on a sample with the “as-received” moisture content. All samples showed a nonlinear reduction in permeability parallel to bedding with increasing effective stress (6–37MPa). The permeability anisotropy and stress dependence of permeability were controlled by the mineralogy.

Brine versus Klinkenberg corrected gas permeability correlation for Shuaiba carbonate formation

Reservoir studies that are based on simulation techniques require data of absolute liquid permeability for static initialization of the dynamic model. Standard industry practice for determining permeability is to perform single point gas permeability measurements and use assumptions or correlations to get Klinkenberg-corrected gas permeability to be used in the dynamic model as the value for absolute liquid permeability or use values of liquid permeability based on a limited number of measured brine permeability. Corrected gas permeability is always higher than the absolute liquid permeability. A series of brine permeability measurements has been carried out on core samples from the Shuaiba formation with the objective of establishing a correlation between these data and previously measured Klinkenberg-corrected gas permeability data on the same core samples. This correlation is potentially useful for converting Klinkenberg-corrected gas permeability data from the Shuaiba formation to liquid permeability for input to the dynamic model.

Correction to “comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks”

Correction to “comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks”

Comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks

We measured intrinsic permeability of sedimentary rocks from the western foothills of Taiwan by using nitrogen gas and distilled water as pore fluids in effective-pressure cycling tests at room temperature. The observed difference in gas and water permeabilities was analyzed in view of the Klinkenberg effect. This effect is due to the slip flow of gases at pore walls, which enhances gas flow when pore sizes are very small. Our experimental results showed that (1) gas permeability was larger than water permeability by several times to one order of magnitude, (2) gas permeability increased with increasing pore pressure, and (3) water permeability increased slightly as the pore-pressure gradient across the specimen increased. Results (1) and (2) can be explained quantitatively by an empirical power law in relation to the Klinkenberg constant b that is applicable in low permeable range. This correlation enables us to estimate water permeability from gas permeability. The Klinkenberg effect is important when permeability is lower than 10 −18 m 2 and at low pore-pressure differentials, and correction for the effect is essential to estimate water permeability from gas permeability measurement data. A simplified Bingham flow model for water can partially explain the trend of result (3), although non-Darcy flow behavior or inertial forces of water–rock interaction are needed to account for the observed deviation from Darcy's law.