Klinkenberg Permeability Research Articles

An improved Klinkenberg permeability model for tight reservoir cores: Effects of non-linear gas slippage to real gases

Absolute permeability is one of the most fundamental reservoir-rock properties required for reservoir simulation models. Most research studies are focused on the Klinkenberg gas slippage, considering the ideal behavior of the flowing gas under first- and second-order slippage conditions. This paper assesses the non-linear slippage of real gas through the low permeability reservoir rock samples. The cubic equation of state (van der Waals/Soave-Redlich-Kwong/Peng-Robinson), coupled with Taylor series-based non-linear slippage, predicts the apparent permeability for the non-Darcy gas flow in tight reservoir rock. The novelty of the present contribution is to develop a comprehensive mathematical model to describe the temperature- and pressure-dependent non-linear slippage effect accounting for the real gas behavior, which is based on the fundamental principle of momentum balance. The thirty-nine sets of experimental results of different authors using different core samples (e.g., coal seams, tight sandstones, tight carbonates, gas-shale reservoirs) and gases (Air, H2, He, N2, CH4, C2H6, and CO2) are used to authenticate the proposed non-linear slip model for real gases. Results show that (a) the proposed model correctly predicts infinite permeability and non-linear slippage coefficients of eight-tests non-ideal gases with an average absolute deviation of ≤9.69%, (b) non-linear slippage dominates for the core samples having permeability <1.5 mD, and (c) the first- and second-order slippage coefficients vary from 0.76 to 6.22 atm and 0.15–9.30 atm2, respectively. The proposed model is simple and may readily be applied for the reservoir simulation of coal seams, tight sandstones, tight carbonates, gas-shale reservoirs, etc., for reservoir characterization, forecasting future natural gas production, decision-making, and efficient reservoir management practices for enhanced production efficiency and sustainability.

Laboratory investigation on gas slippage phenomenon in coal sample and its research significance

The gas slippage effect (GSE) of coal is associated with the coalbed methane (CBM) wells' productivity. Through the helium permeability experiment of five coal samples with different vitrinite reflectance, characteristics of gas permeability variations in coal samples with different coalification degrees are analyzed, the influence of coalification degrees, coal pore structures, and different gases on GSE is revealed, and the impact of GSE on the CBM wells productivity is discussed. It indicatess that the gas permeability of coal varies with the pore pressure in a negative power function and a gas slippage coefficient of coals declines with the rise of Klinkenberg permeability by a negative power function. With the ascend of vitrinite reflectance of coal, there is an asymmetric “U-shaped” change trend in GSE. The GSE in coal with different vitrinite reflectance is mostly govern by the pore diameter distribution of coal. The slippage parameter of gas is consistent with the evolution law of coal pore structures during coal metamorphism. The slippage coefficient of different gases is obtained. On this basis, the prediction model of CBM well production considering GSE is established, and the impact degree of GSE on CBM well productivity is revealed.

Evaluating the accuracy of liquid permeability measurements in shale and tight rocks using transient flow method and comparison with gas permeability

The transient flow method for measuring permeability to liquid is a useful technique for shale and tight rocks; however, it is not as popular as the steady-state method in these rocks. One of the issues is the lack of clarity on a key term of compressibility of the fluid and rock system. Various forms of compressibility have been used in literature, which can lead to inconsistent results of liquid permeability. Using gas for the permeability measurement is more common in shale, and the Klinkenberg corrected permeability is often used to represent liquid permeability; however, how the Klinkenberg permeability is compared to liquid permeability in shale or tight rocks is not adequately addressed. This paper presents a study using the transient flow method for water and oil permeability measurement in three Eagle Ford Shale samples. Gas permeability was also measured for these samples. Different forms of the total compressibility of the fluid-rock system (Ct) are summarized from literature, and a new form of Ct is proposed. The accuracy of the calculations based on different forms of Ct is evaluated through the comparison between water and oil permeabilities and the comparison with gas permeability. The results are also compared with oil permeability obtained from the steady-state method. The new form of Ct provided the most accurate results, whereas the other forms of Ct led to errors. However, for samples with bulk compressibility of less than 1 × 10−7 psi−1, the error using those forms of Ct was negligible. The study also found that the Klinkenberg permeability obtained from the linear extrapolation is larger than the oil permeability for two samples by 12% and 37%, respectively, whereas it is smaller than the oil permeability for the other sample. This comparison suggests that a nonlinear gas slippage effect may exist in the high pressure range (>2000 psi) for shale or tight rock samples.

Integration of petrophysical and geochemical approaches for lower Miocene Euphrates and Jeribe Formations in selected wells in Tawke Oil Field, Northwestern Iraq, Zagros-fold belt

The Lower Miocene Euphrates and Jeribe Formations are among Iraq's potential reservoirs with significant proven reserves. Petrophysical and geochemical techniques were used to investigate these Formations in the recently discovered Tawke Oil Field. Investigation consisted of acquiring a considerable amount of data from eight wells including conventional core analysis, wireline logging data, gas chromatography data and formation water analysis. The Euphrates and Jeribe Formations are considered to have low to moderate porosity (avg. 2.7–20.5%) and low matrix permeability (avg. 0.87–15mD). Secondary porosity is more prevalent than primary depositional porosity and is a significant factor in optimal reservoir properties with an average of 3.7–5.4% Secondary Porosity Index (SPI) for Jeribe and Euphrates Formations respectively. Meanwhile, fractures increased matrix permeability by up to 33mD and 56mD in the Euphrates and Jeribe Formations respectively. Lithology and core analysis revealed that the Dhiban Formation is a non-reservoir rock with maximum 2% He-Porosity and 0.069mD Klinkenberg permeability confirming that the formation is insufficient as a hydrocarbon reservoir, and that the rock properties are primarily controlled by the depositional environment. The Jeribe Formation contains crude oil of intermediate gravity and high sulfur content. According to gas chromatograph analysis the liquid and oil extracted from the Jeribe Formation originated from a matured marine setting that was possibly algae rich (Type-II kerogen) and has been deposited in a reductive environment. It is believed that these hydrocarbons were sourced from the Middle Jurassic Sargelu and Upper Jurassic-Lower Cretaceous Chia Gara Formations. The chloride-calcium water class is determined from the produced water in the Jeribe Formation and the concentration of elements with dissolved salts confirmed that the Jeribe Formation is in contact throughout eight Tawke wells studied.

Development of a Supervised Learning Model to Predict Permeability of Porous Carbon Composites

Predicting the permeability of porous thermal protection system (TPS) materials is essential for understanding their performance during high-speed entry. High-fidelity formulation of Klinkenberg permeability for TPS materials is intractable because unique parameters are needed at each temperature, for various gaseous species, and at every stage of decomposition of resin in the porous material. A supervised learning model based on support vector machine is developed to predict the permeability of TPS materials and is found to be a robust technique to capture the complex relationship between temperature, average pressure, porosity, and permeability of the material. The ability of different gaseous species to permeate through the material is captured through the supervised learning model by constructing an input variable called species identifier, which relates the molecular weight and viscosity of the gaseous species. The model is also extended to capture the permeability of the full composite, which includes both the fibers and the resin. It is demonstrated that the new model captures the nonlinear relationship between permeability and degree of char during the decomposition of the resin in the porous material. The supervised learning model of the physical simulations offers a robust approach for predicting permeability of porous materials in both continuum and noncontinuum flow regimes.

Poro-perm evolution in Oligo-Miocene coastal sandstones: Constraining the relative influence of sedimentary facies, mineralogy, and diagenesis on analogue reservoir quality of the Nyalau Formation, Borneo

The application of enhanced recovery techniques to improve oil recovery requires a critical understanding of the depositional and post-depositional factors that impact fluid flow in sandstone reservoirs. This study combined facies, petrographic, mineralogical, and helium porosimetry analyses to examine the quality and producibility of the subsurface reservoir equivalents (Cycles I-III) of the Nyalau Formation in the underexplored Onshore Central Sarawak, Borneo. The Nyalau Formation consists of medium-to fine-grained, moderate-to well-sorted, and sub-rounded to sub-angular sublitharenite to lithic subarkose sandstones. Three facies associations and eight reservoir facies interpreted to have been deposited within a coast-to-coastal barrier depositional environment were delineated. The sandstones have undergone a wide range of diagenetic alterations, with the primary and secondary pore spaces predominantly occluded by authigenic quartz overgrowths and clay mineral cement. The helium porosity (ɸH) and Klinkenberg permeability (KK) in the reservoir facies widely vary, ranging from 3.0 to 22.14% and 0.003 to 8.283 mD, respectively. However, the weak correlation between ɸH and KK (R2 = 0.35) and petrographic datasets indicate limited diagenetic and mineralogical controls on the porosity-permeability (poro-perm) parameters, consistent with relatively high heterogeneous reservoirs. We inferred that the heterogeneous reservoir properties and fluid flow in the studied analogue reservoir sandstones are dominantly influenced by depositional processes, as shoreface sandstones typically yield better reservoir quality than those deposited within the intertidal reaches. Our data indicate that diagenetic modification and bioturbation exerted lesser control on fluid-flow quality. Nevertheless, the disparity of poro-perm values in samples of the same facies suggest that localised post-depositional modifications can disproportionately affect reservoir quality, regardless of uniformity or variations in depositional conditions.

A simulation experiment method for HTHP gas well productivity

In recent years, a series of major natural gas exploration discoveries and breakthroughs have been achieved in deep and ultra-deep carbonate gas reservoirs in the Sichuan Basin, and all discovered gas reservoirs are characterized by great burial depth, complex pore structures and high formation temperature and pore pressure. In order to accurately predict the gas flow rate of single well in high temperature and high pressure (HTHP) gas reservoirs and clarify the gas flow characteristics under formation conditions, this paper establishes a productivity simulation experimental device and method based on the formation temperature and pore pressure of carbonate gas reservoirs in the Middle Permian Qixia Formation of northwestern Sichuan Basin and the Upper Sinian Dengying Formation of central Sichuan Basin. Then, the cores of above mentioned gas reservoirs are selected to carry out the productivity simulation experiment under HTHP. Finally, the gas flow characteristics are studied. And the following research results are obtained. First, the newly established productivity simulation experimental device and method suitable for the conditions of 160 °C formation temperature and 100 MPa pore pressure is used to predict the natural gas AOF (absolute open flow) of Well S-1 in the Qixia Formation gas reservoir of northwestern Sichuan Basin. And the prediction result is better accordant with the calculation result of theoretical model, with a relative error of only 2.12%. Second, based on the Klinkenberg permeability under surface conditions, the single-well gas flow rate calculated from the productivity simulation experiment is better accordant with the gas flow rate from field completion testing; while based on the Klinkenberg permeability under formation conditions, the single-well gas flow rate calculated from the productivity simulation experiment is better accordant with the AOF. Third, the change of formation temperature and pore pressure has a significant influence on rock permeability, and the permeability is more sensitive to stress than to temperature. Fourth, to carry out the reservoir stress sensitivity experiment and the productivity simulation experiment, it is required that core samples be recovered to the formation conditions for aging, or the experimental results may have characteristics of strong stress sensitivity and cannot be used for reservoir engineering evaluation directly. In conclusion, the production rate and AOF of HTHP gas wells can be predicted accurately by means of productivity simulation experiment, based on drilling core samples. In addition, the Klinkenberg permeability under formation conditions can be evaluated by using the relational expression between surface or Klinkenberg permeability under formation conditions and single-well gas flow rate, combined with gas well testing data.

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

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

Influence of effective stress on gas slippage effect of different rank coals

Gas slippage effect is one of the key factors which would influence gas seepage in coal. The gas permeability of various rank coals under effective stresses are analyzed, and the influence of effective stresses on gas slippage effect of various rank coals and its control mechanism are revealed by the experiment of gas seepage in coal. The results indicate that with the decrease of pore pressure, the gas permeability and the gas slippage effect in coal increases, which follows the variation laws of Klinkenberg slippage equation. The gas slippage effect in various rank coals is controlled by the effective stress, which shows that with the increase of effective stress, the coal permeability decreases and the gas slippage coefficient increases. The relationship between Klinkenberg permeability of coal and its effective stress obeys negative exponential function. With the increase of effective stress, the gas slippage coefficient in coal varies by the positive exponential function. On this basis, a novel evaluation method of gas slippage effect is proposed. The permeability improvement degree of coal is used to quantitatively evaluate the influence degree of gas slippage effect on the coal permeability. With the increase of pore pressure, the permeability improvement degree of different rank coals dropped by the power function. And with the increase of effective stress, the value of permeability improvement degree of coal increases.

Sustainable building material from CO2 mineralization slag: Aggregate for concretes and effect of CO2 curing

Carbonation curing for cement-based materials can be applied as a green concrete production technology, which provides a promising route to economic CO2 sequestration. The substitution of cement by industrial solid waste could further reduce the carbon footprint of concrete. This study proposed a sustainable building material of CO2 mineralization slag (CMS) from the wet process. Based on the accelerated carbonation experiment of Portland cementitious materials, the feasibility of blending CMS as enhanced addition is evaluated. This study discussed the effects of CMS aggregate on CO2 sequestration capacity and mechanical property during CO2 curing, and further investigated the related physicochemical mechanisms. It is revealed that the increase of CaCO3/SiO2 ratio would promote the nucleation and crystallization of CaCO3 microcrystal and result in higher CO2 uptake. With optimum CMS addition ratio of 30% and CaCO3/SiO2 ratio of 4:1, the carbonation degree can be increased by 74.2% in comparison with pure cement paste. Unlike natural curing (28d), a significant strength increment of 40% is observed after pure CO2 curing at 40℃ and 1.5 MPa with a 20% addition of CMS. It is considered that the strength gain is primarily contributed by the intensifying of the interfacial transition zone after CO2 curing. The Klinkenberg permeability tests verified the densification effect of carbonation. These findings provide a guidance for the industrial application of CO2 mineralization slag as the sustainable building material.

Fathoming the mechanics of shale gas production at the microscale

Unlocked by advanced technologies, such as hydraulic fracturing and horizontal drilling, gas shale reservoirs constitute one of the most promising hydrocarbon resources around the world. A combination of ultra-small complex pore throat geometries and an incomplete knowledge of the pertinent physics are partly behind underperforming wells. Further progress in terms of gas recovery hinges on a thorough understanding of the gas behaviour in the pores and between them (i.e., permeability). In this work, we propose a geometrically accurate model from a shale formation inspired from Scanning Electron Microscopy (SEM) imaging. The computational model implements the equations of flow, Klinkenberg permeability and gas compressibility. To compare the model results with experimental measurements, a non-dimensionalisation approach was developed which considers the real gas behaviour and shale permeability characteristics. Non-dimensional gas velocity and flow-rate findings demonstrated an intricate but more realistic flowrate-pressure relationship compared to conventional reservoirs. Owing to its versatility, the non-dimensionalisation methodology can be adapted and generalised to other complex geologies such as carbonate formations. Meanwhile, a flowrate sensitivity analysis was conducted in the context of the matrix and the fluid properties. The sensitivity analysis revealed that, although permeability is the most prominent parameter governing flowrate, reservoir pressure requires even more attention, since it changes considerably during gas production and it can be managed by a suitable development strategy.

Post-depositional controls on siliciclastic tight reservoirs: Implications from the Oligocene Nyalau Formation (Cycle 1), onshore Central Sarawak, Borneo

Abstract Subsurface tight reservoir sandstones of the Oligocene Nyalau Formation (Cycle I), NW Borneo were studied to understand the variability of its reservoir quality with depth, determine major controls responsible for porosity loss, identify reservoir facies and reconstruct paragenetic sequence. Core samples representing an estimated 125 Feet (38.1 m) interval from an onshore well in Central Sarawak were subjected to thin section, Helium porosimetry, inductively coupled plasma mass spectrometry, x-ray powder diffractometry, scanning electron microscopy and energy diffractive x-ray spectroscopy. The sandstones are fine-to-medium grained and comprise of sublithearenite and subarkose primarily sourced from recycled orogenic sources. Four lithofacies base on textural composition and diagenetic events were identified: (A) matrix dominated sandstone, (B) matrix-free sandstone, (C) quartz-cemented sandstone and (D) clay-coated sandstone. Obtained helium porosity, 0.90–11.52% (Average 4.27%) and Klinkenberg permeability,

Applicability Analysis of Klinkenberg Slip Theory in the Measurement of Tight Core Permeability

The Klinkenberg slippage theory has widely been used to obtain gas permeability in low-permeability porous media. However, recent research shows that there is a deviation from the Klinkenberg slippage theory for tight reservoir cores under low-pressure conditions. In this research, a new experimental device was designed to carry out the steady-state gas permeability test with high pressure and low flowrate. The results show that, unlike regular low-permeability cores, the permeability of tight cores is not a constant value, but a variate related to a fluid-dynamic parameter (flowrate). Under high-pressure conditions, the relationship between flowrate and apparent permeability of cores with low permeability is consistent with Klinkenberg slippage theory, while the relationship between flowrate and apparent permeability of tight cores is contrary to Klinkenberg slip theory. The apparent permeability of tight core increases with increasing flowrate under high-pressure conditions, and it is significantly lower than the Klinkenberg permeability predicted by Klinkenberg slippage theory. The difference gets larger when the flowrate becomes lower (back pressure increases and pressure difference decreases). Therefore, the Klinkenberg permeability which is obtained by the Klinkenberg slippage theory by using low-pressure experimental data will cause significant overestimation of the actual gas seepage capacity in the tight reservoir. In order to evaluate the gas seepage capacity in a tight reservoir precisely, it is necessary to test the permeability of the tight cores directly at high pressure and low flowrate.

Investigating Permeability of Coal Samples of Various Porosities under Stress Conditions

Among the numerous factors that have an impact on coal permeability, coal porosity is one of the main parameters. A change in the mechanical stress applied to coal results in a change of porosity. The main objective of the conducted research was to answer the following question: is a decline in coal permeability a direct effect of a decrease in coal porosity, and does mechanical stress result solely in a porosity change? A study of coal porosity under mechanical stress conditions was conducted using a uniquely constructed measurement stand. The coal samples used were briquettes prepared from a granular coal material (middle-rank coal of type B—meta bituminous, upper carboniferous formation) from the “Zofiówka” coal mine, in Poland. In order to describe coal permeability, the Klinkenberg equation was used, as it takes into consideration the slippage effect, typical of porous media characterized by low permeability. On the basis of the obtained results, it was established that the values of the Klinkenberg permeability coefficient decrease as the mechanical stress and the corresponding reduction in porosity become greater. As the briquette porosity increased, the Klinkenberg slippage effect: (i) disappeared in the case of nitrogen, (ii) and was minor for methane. The briquettes used were characterized by various porosities and showed that mechanical stress results mainly in a change in coal porosity, which, in turn, reduces coal permeability.

New insights from shale gas production at the microscopic scale

Until recently, natural gas encountered in tight shales, which provided the source and seal of the gas, was considered uneconomical to produce. Although unconventional formations may be as porous as other reservoir rocks, their exceedingly small pore sizes and low permeability render them resistant to gas movement. Considering their importance to gas transport, we outline the characteristics of shale rocks, the mechanisms of Fickian and Knudsen diffusion as well as Klinkenberg's permeability. Given the challenges in unlocking natural gas from tight formations, various techniques such as the generation of artificial fractures and the introduction of pressurised fluids are detailed. To identify the parameters which govern natural gas production, we propose a computational porous rock model inspired from an actual image of a shale formation. The solution of the conservation of mass, momentum and energy equations appear to adequately capture the physics of gas transport at the microscopic level. Permitting the comparison between numerical and analytical gas velocity results, the validation framework we developed, demonstrates good agreement of numerical with theoretical findings. Gas pressure and velocity results point to the importance of pore throats, shale permeability and pressure maintenance in dislodging gas from the shale formations.

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.

Scaling law for slip flow of gases in nanoporous media from nanofluidics, rocks, and pore-scale simulations

In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport in porous media begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK), a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation.Due to difficulties in fabrication and experimentation, previous study on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels with a controlled channel size on a sillicon wafer. A core-based permeability measurement apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Methane was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions are handled by directly integrating the BGK equation along each molecules trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable.The slippage factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the slippage factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.

Boundary retention layer influence on permeability of tight reservoir

The permeability of typical tight oil reservoir cores is measured using difference fluid medium (nitrogen, formation water, kerosene), and a capillary permeability model considering boundary retention layers is build. The computed values of the model are compared with experimental values of cores. The difference of permeability using different fluid medium is discussed concerning boundary retention layer thickness, movable fluid pore space and clay contents. The experiment results showed that targeted reservoir cores klinkenberg permeability K∞ was 66.86% of conventional gas permeability Kg, and water permeability KW was 11.66% of Kg, and oil permeability KO was 2.46% of Kg. KW and KO could characterize reservoir water injection and development difficulty better than Kg. Kh/K (ratio between permeability of capillary model considering and not considering boundary retention layer), is perfectly consistent with K∞/Kg, which indicates that capillary permeability model considering boundary retention layer has good consistency with seepage characteristics of actual reservoir. The tight cores have smaller effective pore-throat space for flowing, and get larger effect of boundary retention layers. The smaller the permeability core have, the closer between Kh/K and K∞/Kg. Boundary layer thickness are increased by Clay swelling, and flow channel are blocked by clay off and migration, that the main reason of KW smaller than K∞. The lower Kg cores have, the more KW/K∞ decrease magnitude. KO is much lower than K∞ and KW because of increased oil seepage resistance by two-phase seepage and boundary retention layer.

Experimental Determination of Gas Relative Permeability Considering Slippage Effect in a Tight Formation

In this paper, the gas relative permeability considering slippage effect has been experimentally examined under various experimental conditions (i.e., ambient, high confining pressure, and high temperature). Experimentally, Klinkenberg permeabilities of 12 core samples have been measured by using steady-state flow experiment. It has been found that the Klinkenberg permeability is independent of the experimental temperature and dramatically decreases as confining pressure is increasing. Furthermore, linear correlations have been newly developed between the Klinkenberg permeability and the gas-measured permeability under various conditions. Subsequently, the developed correlations are correspondingly applied to calibrate the gas relative permeability. It has been found that the gas relative permeability can be overestimated without consideration of the slippage effect, i.e., Klinkenberg effect. In addition, the newly developed correlations have been applied to analyze the sensitivity of gas–water relative permeability to gas-measured permeability, confining pressure, and temperature. It is demonstrated that mobile water greatly alleviates the gas relative permeability in comparison to irreducible water. Although an increased confining pressure simultaneously reduces the effective water phase and gas phase permeability, the gas relative permeability increases and the water relative permeability decreases as the confining pressure increases. It is attributed to the fact that the effective water phase permeability is more sensitive to the confining pressure. Given an elevated experimental temperature, the gas relative permeability is reduced while the water relative permeability is enhanced, implying the significance of temperature effect on gas–water relative permeability measurements.

Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations

This paper has developed a pragmatic technique to efficiently and accurately determine the Klinkenberg permeability for tight formations with different pore-throat structures. Firstly, the authors use steady-state experiments to measure the Klinkenberg permeability of 56 tight core samples under different mean pore pressures and confining pressures. Secondly, pressure-controlled mercury injection (PMI) experiments and thin-section analyses are conducted to differentiate pore-throat structures. After considering capillary pressure curve, pore types, throat size, particle composition, and grain size, the pore-throat structure in the target tight formation was classified into three types: a good sorting and micro-fine throat (GSMFT) type, a moderate sorting and micro-fine throat (MSMFT) type, and a bad sorting and micro throat (BSMT) type. This study found that a linear relationship exists between the Klinkenberg permeability and measured gas permeability for all three types of pore-throat structures. Subsequently, three empirical equations are proposed, based on 50 core samples of data, to estimate the Klinkenberg permeability by using the measured gas permeability and mean pore pressure for each type of pore-throat structure. In addition, the proposed empirical equations can generate accurate estimates of the Klinkenberg permeability with a relative error of less than 5% in comparison to its measured value. The application of the proposed empirical equations to the remaining six core samples has demonstrated that it is necessary to use an appropriate equation to determine the Klinkenberg permeability of a specific type of pore-throat structure. Consequently, the newly developed technique is proven to be qualified for accurately determining the Klinkenberg permeability of tight formations in a timely manner.