Gas Slippage Effect Research Articles

Productivity Model Study of Water-Bearing Tight Gas Reservoirs Considering Micro- to Nano-Scale Effects

Tight sandstone is rich in micron- and nano-scale pores, making the two-phase flow of gas and water complex. Establishing reliable relative permeability and productivity models is an urgent issue. In this study, we first used a slip model to correct the gas phase’s no-slip Hagen–Poiseuille equation for nano- and micropores. Then, combined with the fractal theory of porous media and the tortuous capillary bundle model, we established two-phase relative permeability models for nanopores and micropores. These relative permeability models comprehensively consider the gas slippage effect, the initiation pressure gradient, the pores’ fractal characteristics, and water film mechanisms. Based on these models, we developed a three-region coupling productivity model for water-bearing tight gas reservoirs with multi-stage fractured horizontal wells. This productivity model considered the micro- and nano-scale effects and the heterogeneity of fracture networks. Then, the model was solved and validated with a field case. The results indicated that the three-region composite unsteady productivity model for water-bearing tight gas reservoirs, which incorporated micro- and nano-scale effects (with consideration of micro-scale and nano-scale phenomena in the fluid flow), could accurately predict a gas well’s productivity. An analysis of the factors influencing productivity showed that ignoring the micro- and nano-scale effects in water-bearing tight gas reservoirs will underestimate the reservoir’s productivity. The initial water saturation, the two-phase flow’s initiation pressure gradient, and capillary force are all negatively correlated with the productivity of gas wells, while the conductivity of the fractures is positively correlated with gas well productivity.

Experimental study on gas slippage effect in coal at different temperatures based on nuclear magnetic resonance

Coalbed methane (CBM) can be recovered more effectively through heat injection mining. The slippage effect in coal becomes more significant as CBM is exploited, essential for maintaining consistent production of CBM wells. By “slippage effect,” we mean that gas molecules exhibiting non–zero velocity near the wall surface of coal pores, leading to higher gas permeability than liquid permeability. To explore the slippage effect and its control mechanism during heat injection mining, methane seepage experiments with constant effective stress were conducted under five different temperatures and seven pore pressures. An analysis was conducted on the mechanisms by which pore pressure and temperature affect gas slippage effect. Furthermore, the correlation between coal pore structure and the gas slippage effect was revealed using the nuclear magnetic resonance (NMR) technique. The results appear that, first, as pore pressure increases, the slippage effect is suppressed due to the influence of the average molecular free path, despite the positive impact of adsorption–induced matrix expansion. Second, as temperature rises, the average molecular free path and thermal expansion have a positive impact on gas slippage, while matrix shrinkage caused by desorption has a negative impact. The positive impact is stronger, resulting in a continuous enhancement of the slippage effect. Finally, a new slippage factor calculation based on NMR T2 distribution of micropores and transitional pores (<100 nm, T2 < 8.33 ms) was provided, and the method was verified by slippage factor fitted by permeability experimental data. The heat injection mining of CBM can be theoretically guided by the research results.

Experimental study on the Klinkenberg effect for gas permeability in carboniferous shales, Eastern Qaidam Basin, China

It is crucial to understand the conditions and influencing mechanisms of shale gas slip effect for predicting the productivity of shale gas reservoirs. This study focuses on the Carboniferous Hurleg Formation shales in the eastern Qaidam Basin and conducts gas permeability tests using different gases (He/N2), as well as geochemical and pore-structure tests. The slip behavior of different gases in micro- and nanopores as well as the anisotropy of gas permeability were analyzed and discussed. The results show that helium permeability is 1.81–3.56 times higher than nitrogen permeability, with a greater difference at lower pore pressures. These permeability differences are attributed to variations in gas molecule size and slip effects. Specifically, the slip effect of helium gas has a greater contribution to permeability at lower pore pressures, with a helium slip factor averaging 2.79 times that of nitrogen. The effective pore size of shale, calculated based on the helium slip factor, is 0.74 to 1.51 times larger than when nitrogen is used, with an average of 1.67 times. Helium molecules have smaller diameters and longer average molecular free paths, resulting in a more pronounced slip effect compared to nitrogen. While helium does not adsorb, nitrogen exhibits some adsorption, causing radial expansion during gas penetration. Furthermore, when testing with different gases, the horizontal permeability (S043∥; S052∥) is higher than the vertical permeability (S043⊥; S052⊥). The anisotropy of permeability is controlled by the pore system formed by the arrangement and combination of minerals. Calcium-rich samples (S052) tend to exhibit higher anisotropy compared to calcite-rich samples (S043). The effective pore size in the vertical sample is larger than that in the parallel sample, and the gas slip effect is significantly greater in the vertical sample. These findings provide valuable data for future studies on shale gas slip effects and productivity prediction.

Experimental Study on Permeability and Gas Production Characteristics of Montmorillonite Hydrate Sediments Considering the Effective Stress and Gas Slippage Effect

Summary Gas permeability in hydrate reservoirs is the decisive parameter in determining the gas production efficiency and gas production of hydrate. In the South China Sea (SCS), the gas flow in tight natural gas hydrate (NGH) silty clay reservoirs is significantly affected by the gas slippage effect and the effective stress (ES) of overlying rock. To improve the effectiveness of hydrate exploitation, it is necessary to understand the influence of gas slippage in hydrate reservoirs on the permeability evolution law. For this paper, the gas permeability characteristics and methane production of hydrate montmorillonite sediments were studied at different pore pressures and ESs. Experimental data revealed that the gas permeability of montmorillonite samples before methane hydrate (MH) formation is seriously affected by the Klinkenberg effect. The gas permeability of montmorillonite sediments before hydrate formation is generally smaller than that after hydrate formation, and the gas slippage effect in the sediments after hydrate formation is weaker than that before hydrate formation. With the change in ES, the intrinsic permeability of sediment has a power law relationship with the simple ES. The ES law coefficient n was determined using the response surface method to eliminate the influence of gas slip on gas permeability. As pore pressure decreases and MH decomposes, montmorillonite swelling seriously affects gas permeability. However, the gas slippage effect has a good compensation effect on the permeability of montmorillonite sediments after MH decomposition under low pore pressure. The multistage depressurization-producing process of MH in montmorillonite sediments is mainly 3 MPa depressurization-producing stage and 2 MPa depressurization-producing stage. In this paper, the influence mechanism of gas slippage effect of hydrate reservoir is studied, which is conducive to improving the prediction accuracy of gas content in the process of hydrate exploitation and exploring the best pressure reduction method to increase the gas production of hydrate in the process of exploitation.

RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES

Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective gas permeability of the adjacent finger seals annulus considering the gas slip effect and the temperature change is established, and a finite element calculation method of the two-way thermo-mechanical coupling for the finger seal is proposed. The results show that the solid-phase thermal conductance decreases with the increase of the scale coefficient. When the axial pressure difference is greater than 0.4[Formula: see text]MPa, the rotor speed is greater than 11,000[Formula: see text]r/min, the radial displacement excitation is [0.03[Formula: see text]mm, 0.09[Formula: see text]mm], and the temperature is less than 600[Formula: see text]K, the gas-phase thermal conductance between the finger seal and the rotor shows an increasing trend. The gas-phase thermal conductance of the finger seal and the rotor is always the main position under different working conditions. Under different fractal dimensions, the solid-phase thermal conductance gradually occupies the dominant position. Temperature has a certain effect on the effective gas permeability, and fractal dimension, scale coefficient, and axial pressure difference have less effect on the effective gas permeability. At an axial pressure difference of 0.08[Formula: see text]MPa, the numerical calculation results of the two-way thermo-mechanical coupling calculation method for finger seal are closer to the experimental results, with a maximum error rate of 1.96%. The above results further improve the theoretical research system of the heat transfer characteristics of the finger seal.

Permeability Evolution of Bituminous Coal and Its Dynamic Control, a Case Study from the Southeastern Ordos Basin, China

Coalbed methane (CBM) reservoirs’ permeability is the result of dynamic variations influenced by tectonics, hydrology and the CBM production process. Taking samples from the southeastern Ordos Basin, China, the permeability evolution of bituminous coal and its control were analyzed in three steps: (1) the coal fracture permeability evolution was acquired via X-ray CT scanning and permeability evolution experiments; (2) the permeability variation was determined while considering the coupling characteristics effective stress, gas slippage, and matrix shrinkage effect and its influencing factors; and (3) a dynamic permeability model was built while considering those effects. For samples in which neither fractures nor bedding developed, the permeability decreased first and then increased as the gas pressure increased. For samples with fractures that developed parallel to the axial direction, with a gradual increase in gas pressure, the permeability also increased. As the gas pressure decreased, the matrix shrinkage effect became positive, resulting in a permeability increase. The gas slippage effect was positive in the low-pressure stage, which also resulted in a permeability increase.

Effect of temperature on gas breakthrough and permeability of compacted loess in landfill cover

In China, municipal solid waste containing large amounts of kitchen waste possesses the characteristics of lower cellulose content (15% on a dry basis) and a faster CH4 generation rate. This promotes the emission of hazardous gases and the increase in gas pressure in landfill cover systems. The higher temperature further aggravates the aforesaid phenomena. The present work investigated the temperature effect on the gas breakthrough pressure (GBP) and permeability of compacted loess. The water permeability kw increases with increasing temperature. The intrinsic water permeability KW independent of pore fluid properties behaves just in an opposite manner. KW would have been increased with increasing temperature if the rigid wall of the permeameter had not been intervened in the permeability tests. The intrinsic permeability KG also decreases with the increase in temperature. Although the higher KG neglects the gas slippage effect, the combination of the thermal expansion of minerals, the transformation of bound water to free water, and the thermal expansion of free water causes pore water to migrate into macropores. Such a pore water migration is accompanied by the water-gas boundary moving to the vadose zone. On the other hand, the capillary pressure shows a correspondence with the GBP value. The higher temperature reduces the difficulty for gas molecules to overcome the surface tension at the water-gas boundary, corresponding to the lower GBP value. The findings provide critical guideposts concerning the design of the gas breakthrough and permeability of compacted loess in landfill covers under the temperature effect.

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.

Crucial Development Technologies for Volcanic Hydrocarbon Reservoirs: Lessons Learned from Asian Operations

Oil and gas reservoirs in volcanic rocks are a particular type of unconventional reservoir and present unique challenges for exploration and production engineers. To help the oil industry understand volcanic reservoirs and solutions to complex development problems, we reviewed their key engineering technologies as well as their geological characteristics. The distinctive geological characteristics of volcanic hydrocarbon reservoirs are strong heterogeneity, low porosity and permeability, complex fracture systems, etc. The volcanic reservoir rock types in order of hydrocarbon abundance are basalt (38.5%), andesite (15.9%), volcaniclastic (12.1%), and rhyolite (11.5%). The porosity ranges from 0.1 to 70%, and permeability ranges from 0.0007 to 762 md. In some commercially developed volcanic reservoirs of China, the average porosity is 7.7–13%; the average permeability is 0.41–3.4 md. Engineers have applied a variety of adapted technologies to produce volcanic reservoir economically. Horizontal wells can increase production and reserves by 4–6 times those of vertical wells, and longer wells are preferred. Specialized hydraulic fracturing techniques are suggested, including small or mixed proppant size, second HF treatment after proppant slugging, high-viscosity frac fluid with high-temperature resistance, special fluid loss reducer, high pump pressure, Extreme Overbalance Perforating, limited-entry fracturing, matrix acidizing, etc. Water control measures include producing below critical rates, partial perforation or penetration, controlling hydraulic fracture height, using horizontal wells, implementing complete cementing job, etc. Well productivity evaluation should be conducted to understand well performance and appropriately allocate production rates among wells, using the modified AOF method and other productivity prediction models considering breakdown fracture gradient, gas slippage effect, non-Darcy effect, etc. Well sites need to be selected based on recognizing profitable lithologies, lithofacies, high porosity and permeability, relatively developed fracture systems, thick net pay zones, etc. The critical questions for the industry are how to enhance volcanic reservoir recovery with more efficient and economic hydraulic fracturing and water control techniques. This is one of the first papers systematically summarizing the engineering technologies and unique solutions to develop volcanic reservoirs. Further and more complete reviews can be carried out in the future, and more novel and effective techniques can be explored and tested in the field.

Pore-Scale Simulation of Fracture Propagation by CO2 Flow Induced in Deep Shale Based on Hydro-Mechanical Coupled Model

Summary The depletion of conventional reservoirs has led to increased interest in deep shale gas. Hydraulic fracturing addresses the challenge of developing low-permeability shale, involving hydro-mechanical coupling fracture propagation mechanics. Supercritical CO2 (SC-CO2) has become a promising alternative to fracturing fluids due to its ability to be buried underground after use. The high temperature, pressure, and stress of deep shale lead to the flow of fracturing fluid to plastic deformation of rock, resulting in microfractures. In this paper, we simulate the fracture propagation process of deep shale fractured by SC-CO2 based on the coupling of the Darcy-Brinkman-Biot method, which adopts the Navier-Stokes-like equation to solve the free flow region, and the Darcy equation with Biot’s theory to solve flow in the matrix. To clearly probe the mechanism of deep fracturing from a microscopic perspective, the plastic rock property is taken into consideration. We investigate the effects of injection velocity, rock plastic yield stress, formation pressure, and gas slippage effect on fluid saturation and fracture morphology, and find that increasing the injection rate of fracturing fluid can form better extended fractures and complex fracture networks, improving the fracturing effect. Furthermore, we find that it is more appropriate to adopt SC-CO2 as a fracturing fluid alternative in deep shale with higher plastic yield stress due to higher CO2 saturation in the matrix, indicating greater carbon sequestration potential. High confining pressure promotes the growth of shear fractures, which are capable of more complex fracture profiles. The gas slip effect has a significant impact on the stress field while ignoring the flow field. This study sheds light on which deep shale gas reservoirs are appropriate for the use of SC-CO2 as a fracturing fluid and offers recommendations for how to enhance the fracturing effect at the pore scale.

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.

Experimental study on dynamic pore-fracture evolution and multiphase flow in oil-saturated coal considering the influence of in-situ stress

The methane drainage in liquid-saturated coal is directly related to the multiphase flow in complex geological structures. In this study, the pore-fracture dynamic evolution induced by in-situ stress and the corresponding gas-liquid migration and morphology characteristics were investigated by a self-developed online LF-NMR triaxial stress system. The dynamic variation, obvious change, and slight response were occurred at the migration pore (MP＞3ms), percolation pore (0.3ms < PP < 3ms), and adsorption pore (AP<0.3ms) with the increased stress, and development of gas channel was contributed by MP (15%–20%), AP (5%–10%), and PP(0–5%) responding to the gas flooding. The pore-fracture successively experienced compression, dilation, expansion, and coalescence, and PP and MP dominated the fracture initialization and connection. The permeability is negatively correlated with the fractal dimension of the pore-fracture structure and is exponentially related to the porosity and MP porosity. The longitudinal shear fracture is beneficial for the gas-liquid migration, and the horizontal tension crack connects the scattered pore and branch fracture. The gas channel was influenced by the liquid capillary pressure and gas jiamin effect in poor pore-fracture and mainly influenced by the gas slippage effect, immiscible behavior, and fracture surface tension force in mature pore-fracture. The optimal gas channel occurred at the crack-propagation period, which was located at around 70% peak strength with 1.5md permeability, high liquid relative permeability and lower gas relative permeability. The findings provide significant insight into methane extraction.

Productivity Formula of Horizontal Well in Low-Permeability Gas Reservoir considering Multiple Factors

For horizontal well in low-permeability gas reservoir, the effects of threshold pressure gradient, stress sensitivity, and gas slippage have significant impacts on the well productivity. At present, there are few productivity formulas for horizontal gas well considering all these factors. In this paper, based on the flow analysis of horizontal well in low-permeability gas reservoir, the whole flow field was divided into two parts, namely, far wellbore region and near wellbore region, among which the far wellbore region is composed of plane linear flow region and plane radial flow region and the near wellbore region is composed of vertical plane radial flow region and spherical plane central flow region. Then, a new productivity formula is established based on the steady-state seepage theory and the equivalent seepage resistance method, with the consideration of threshold pressure gradient, stress sensitivity, and gas slippage effect. The accuracy of the formula in this paper is verified through comparing with other classical models, and the influence of various factors on the well productivity is analyzed. The analysis results show that stress sensitivity has the most significant effect on horizontal gas well production, followed by threshold pressure gradient, and the gas slippage has the least effect. With the consideration of all influencing factors, the higher the formation pressure and reservoir thickness, the higher the productivity, and the increase of productivity increases with the increase of flow pressure difference. The increasing trend of gas productivity index per meter with the increase of reservoir permeability is first fast and then slow. When the reservoir permeability is greater than 1.2 mD, the increment of gas productivity index per meter (MGPI) decreases. When the length of horizontal well is greater than 1400 m, the increment of gas productivity index per meter decreases with the increase of gas reservoir thickness. Therefore, it is recommended to control the horizontal well length within 1400 m in low-permeability gas reservoir. In addition, the absolute open flow charts corresponding to reservoir thickness and horizontal well length under different reservoir permeability conditions were also given, which can provide theoretical guidance for the selection of horizontal well length during the development of low-permeability gas reservoirs.

A discrete unified gas kinetic scheme for simulating transient hydrodynamics in porous media with fractures

Tight gas reservoirs have typical characteristics of well-developed natural fractures, extremely low permeability, and low porosity. The flow in such media can be described by a dual-porosity dual-permeability (DPDP) model with the consideration of gas slippage and real gas effects. Based on this model, in this study, a discrete unified gas kinetic scheme is developed to describe the transient hydrodynamic behaviors in porous media with fractures. With an interporosity term, two kinetic equations are employed to capture the pressure propagation in matrix and fracture sub-systems, respectively. The proposed DUGKS can correctly recover the DPDP model through the Chapman–Enskog analysis. Unlike the traditional numerical methods, the velocity in DUGKS can be calculated locally by the non-equilibrium distribution functions. The presented method is verified by three typical problems, including the flow in a fractured porous medium, the flow around a vertical production well, and the flow around a fractured horizontal production well. The numerical results are in good agreement with the reference data. In the test, the global relative errors in pressures are on the order of 10−3. Moreover, the transient hydrodynamics in porous media with fractures are evaluated. The simulation results show that the slippage mainly occurs in the matrix, and this effect may result in a 20% increase in permeability. With the consideration of slippage and real gas effects, the predicted production is higher than that predicted by Darcy’s law. In addition, the results indicate that hydraulic fractures have a great impact on production.

Pressure- and temperature-dependent klinkenberg slippage effect in porous media to non-ideal gases

The present paper evaluates the effect of non-ideal gas behavior on the Klinkenberg gas slippage effect for measuring the permeability of porous media. The generic cubic equation of state, particularly van der Waals (vdW-), Soave-Redlich-Kwong (SRK-), and Peng-Robinson (PR-) equation of state, are used to consider the non-ideal behavior of the gases, including nonhydrocarbons and hydrocarbons. The above cubic equation of state is expressed in terms of the gas compressibility factor involving the temperature-dependent second and third virial coefficients. A comprehensive mathematical model leading to a generalized analytical solution for the pressure- and temperature-dependent apparent permeability of porous media to non-ideal gas is proposed after combining the first-order Klinkenberg slippage effect and virial equation of state. Experimental data of Klinkenberg (1941) and Calhoun (1976) [Klinkenberg, L. J., The permeability of porous media to liquids and gases. Drill Prod Prac. API, 200–213, 1941; Calhoun, J. C., 1976. Fundamentals of Reservoir Engineering, University of Oklahoma Press, Oklahoma] are used to validate the proposed apparent permeability models. The proposed methodology accurately predicts the liquid permeability using the 18-test core samples and 7-test gases, accounting for the non-ideal behavior. The temperature-dependency of the apparent permeability of porous media to non-ideal gases with varying mean pressure is also established.

Coal permeability behaviors and non-uniform deformations under various boundary conditions: Part 1 – Experimental observations

Permeability is a key parameter to evaluate the ability of coal reservoir for transmitting coalbed methane (CBM). Deformations of internal components of coal caused by the variations of physical fields control the evolution of coal permeability. And there is obvious non-uniform in the deformations of coal bulk and fracture due to the heterogeneity of coal. However, at present, the evolution of non-uniform deformation and its relationship with coal permeability are unclear. In this study, first of a two-part series, we completed a series of experiments to measure the permeability, axial strain, radial strain, overall strain and fracture strain of a coal sample under different boundary conditions (constant confining pressure, constant effective stress and uniaxial strain) at different injection pressures of carbon dioxide (0.2 MPa, 1.0 MPa, 2.0 MPa, 3.0 MPa, 4.0 MPa and 5.0 MPa). And we defined the comprehensive non-uniform deformation index (CNDI) as the ratio of the fracture strain to the overall strain to quantify the degree of the non-uniform deformation between coal bulk and fracture. The experimental results show that the deformation of the coal sample in the longitudinal joint direction is smaller than that in the transverse joint direction, which indicates that the mechanical properties of the coal sample is anisotropic in different directions. And there are obvious differences between the deformations of coal bulk and fractures. When the gas pressure is in the range of 0.2 ∼ 5.0 MPa, the non-uniform deformations are vaguely related to the change of gas pressure, but closely related to the type of boundary conditions. The influence of gas pressure under displacement-controlled boundary condition (uniaxial strain) on the CNDI is greater than that under stress-controlled boundary conditions (constant confining pressure, constant effective stress). In addition, we also observed the phenomenon by the experimental results of the constant effective stress group: the permeability decreases gradually with the gas pressure even after removing the influence of gas slip effect, which is inconsistent with the traditional theoretical solution under the constant effective stress condition. Based on the fact that coal sample is a heterogeneous body, we tentatively believe that one of the reasons for this inconsistency may be that the traditional definition of effective stress does not include the effect of gas adsorption.

Self-similar analysis of gas dynamics for van der Waals gas in slipping flow after normal shock wave

A self-similar model of gas dynamics and heat transfer behind the shock wave was developed with allowance for the effects of slippage and dissipation. The model takes into account the impact of the following factors: shock wave intensity (U∞/Us), physical properties (Prandtl number Pr), thermodynamic gas properties (van der Waals numbers Waa, Wab), slippage effects (Knundsen number Kn), and dissipation (Brinkman number Br), as well as the relation of the temperatures of the flow and the wall (T0/Tw). The numerical solution was performed with the help of MATLAB software, as well as an in-house code written using the programming language C++ to verify the accuracy of calculations. The study demonstrated that for the case at hand, the Reynolds analogy holds under the influence of all mentioned factors provided that Pr = 1, except for the conditions when the effects of mechanical energy dissipation become significant. The paper presents the results of calculations of the velocity and temperature profiles, friction, and heat transfer coefficients (Nusselt numbers).

Simulation of Gas-Water Two-Phase Flow in Tight Gas Reservoirs Considering the Gas Slip Effect

A mathematical model for the gas-water two-phase flow in tight gas reservoirs is elaborated. The model can account for the gas slip effect, stress sensitivity, and high-speed non-Darcy factors. The related equations are solved in the framework of a finite element method. The results are validated against those obtained by using the commercial software CMG (Computer Modeling Group software for advanced recovery process simulation). It is shown that the proposed method is reliable. It can capture the fracture rejection characteristics of tight gas reservoirs better than the CMG. A sensitivity analysis of various control factors (initial water saturation, reservoir parameters, and fracturing parameters) affecting the production in tight gas wells is conducted accordingly. Finally, a series of theoretical arguments are provided for a rational and effective development/exploitation of tight sandstone gas reservoirs.

Tight gas fracturing productivity calculation model based on gas-water permeability curve

Measuring well production per well can not only simplify the process flow, improve economic efficiency, but also reduce the development cost of the oil field. In this paper, a single-well measurement of oil well production is carried out by establishing a capacity calculation model for fracturing straight wells in tight gas reservoirs by means of gas-water phase infiltration curve. According to different permeability and porosity, several representative relative permeability curves are selected for normalization treatment, and then the angle-preserving transformation principle is used, considering the formation stress sensitivity effect and gas slip effect, as well as the stress sensitivity effect in the fracture and the effect of high-speed non-Daxi effect on gas seepage, the quasi-pressure function is introduced, and the capacity calculation model of the fracturing straight well of the tight gas reservoir is established, so as to achieve the calculation of the yield.