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Fractal characteristic has been considered as the essential parameter to determine transport properties of porous media. Fluid flow in the real porous media is more influenced by the narrow throat system than the relatively large pore system. In this work, the concept of throat fractal dimension is proposed and applied to predict permeability in porous media. First, pore system and throat system of six sandstone rock samples and three carbonate rock samples are divided from the pore network models extracted from rock CT images. Then, fractal dimensions based on the total pore space, pore system and throat system are calculated, respectively, based on the three-dimensional (3D) box-counting method. Three groups of permeabilities are estimated, respectively, using the fractal theory based on the pore space fractal parameter, pore system fractal parameter and the proposed throat system fractal parameter. The results indicate that permeabilities estimated by the proposed throat system fractal parameter are closer to the accurate permeabilities of rock samples compared with that estimated by the pore space fractal parameter and pore system fractal parameter. Our study results reveal that throat fractal dimension should be used to accurately predict fluid transport properties in porous media. [ABSTRACT FROM AUTHOR]

The multiphase flow behavior in shale porous media is known to be affected by multiscale pore size, dual surface wettability, and nanoscale transport mechanisms. However, it has not been fully understood so far. In this study, fractal model of gas–water relative permeabilities (RP) in dual-wettability shale porous media for both injected water spontaneous imbibition and the flow back process are proposed using fractal geometry. The shale pore structure is described as tortuous with different pore sizes and morphologies including slit pore, equilateral triangle, circular pore and square pore. The proportion of each pore morphology can be obtained from SEM/FIB-SEM pore structure characterization results. Injected water spontaneous imbibition after hydraulic fracturing is modeled as the capillary force dominated process and injected water flow back is modeled as a non-wetting gas phase drainage process in inorganic matter. The organic pores are deemed to be not accessible by injected water. The boundary slip of water and free gas flow in the inorganic matrix are considered while both free gas flow and adsorbed gas flow are modeled in organic matter. The proposed gas–water RP fractal model is verified via comparisons with the available experimental data and is discussed in detail. Study results reveal that gas phase RP increases with increasing pore fractal dimensions and tortuosity fractal dimensions, whereas it decreases with increasing Total Organic Carbon (TOC) volumes. Water phase RP decreases with increasing of pore fractal dimensions and tortuosity fractal dimensions, whereas it increases with increasing TOC volumes. [ABSTRACT FROM AUTHOR]

Abstract Many engineering technologies involve the moving boundary problems for the radial seepage flow with a threshold pressure gradient, such as the well testing in the development of low-permeability reservoirs, heavy oil reservoirs and groundwater resources. However, as a result of the strong nonlinearity, an exact analytical solution of the moving boundary problems for the radial seepage flow with a threshold pressure gradient has not been obtained yet. Here, a dimensionless moving boundary mathematical model for the radial fluid flow in an infinite low-permeability reservoir with a threshold pressure gradient is developed first. The setting of a variable well production rate for an inner boundary condition can make the mathematical model exhibit a full self-similarity property. Second, by introducing some similarity transformations, the nonlinear system of PDEs of the model can be equivalently transformed into a closed pseudo-linear system of ODEs, whose exact analytical solution can be easily obtained. What's more, the existence and the uniqueness of the exact analytical solution to the moving boundary model are also proved strictly through the mathematical analysis. Third, it is also strictly proved that the exact analytical solution can be degenerated to that of the model of the Darcy's radial fluid flow as the threshold pressure gradient approaches to zero. Finally, by a comparison of model analytical solutions, it is demonstrated that the moving boundary conditions must be incorporated in the modeling of the radial seepage flow with a threshold pressure gradient; otherwise, the effect of the threshold pressure gradient on the radial seepage flow can be overestimated largely. Highlights • A moving boundary model of radial flow with threshold pressure gradient is built. • Moving boundary must be incorporated in modeling this threshold problem. • Exact analytical solution of the model is obtained by similarity transformations. • Existence and uniqueness of the exact analytical solution are proved strictly. • It can be used for verifying the validity of two-dimensional flow simulation. [ABSTRACT FROM AUTHOR]

Gas flows in the forms of multiple transport mechanisms in shale nanoporous media with complex pore structure and different pore types. Laboratory pressure pulse decay technique is often applied to measure gas permeability but the current gas permeability interpretation model is mostly based on the homogeneous macro scale model while the influence of pore structure on real gas transport is neglected. In this study, a novel pore structure based real gas transport model is proposed to determine gas permeability in nanoporous shale combining laboratory pressure pulse decay technique with pore network simulation. The laboratory pressure pulse decay process is simulated in a virtual system based on the similarity principle which contains upstream vessel, downstream vessel, and core sample. The core sample is constructed by a series of connected pore networks and the sizes of pores and throats in each location of the pore network are randomly assigned according to laboratory measured pore size distribution. Gas transport mechanisms inside the core sample consider viscous flow, Knudsen diffusion, surface diffusion and real gas effect. At each time step, the upstream vessel pressure decreases and the downstream vessel pressure increases until the upstream vessel pressure and downstream vessel pressure become equal. The simulated pressure drop versus time curve is obtained and is applied to fit the laboratory measured pressure drop data by repeating core sample construction and pressure pulse decay process. The proposed model is applied to measure gas permeability of Sichuan basin, Longmaxi formation shale core sample. The results indicate that the predicted value based on the proposed model matches well with the experimental measured pressure drop data. The proposed model is used to study the influences of test gas type and pore size on gas permeability. When the average organic pore radius is less than 20 nm, helium tested permeability overestimates at least 40% of the methane permeability. [ABSTRACT FROM AUTHOR]

Owning to their differences in surface properties and pore geometry, pores of predominant submicron sizes in organic and inorganic matter of gas shale incur different gas flow and transport behaviours. Those differences can manifest at sample scales differently depending on the spatial distributions of shale organic and inorganic matter, and the pore-size distributions in these types of matter. Therefore, understanding the impacts of variable configurations of them on the gas flow is essential to guide progressive subsampling in multiscale shale characterisation that is required for modelling shale gas flow at the first place. This article reports a pore-scale numerical investigation into the impacts of combinations of three end-member spatial arrangements of the organic matter and two contrasting sets of organic and inorganic pore-size distributions at variable organic fractions on gas flow using pore-network modelling. A unified pore-network flow model for shale gas that captures a comprehensive set of gas flow and transport mechanisms is developed in this work to calculate the effective gas apparent permeability at reservoir conditions. In terms of the mean permeability at each selected organic fraction, the largest differences are found to appear at a high fraction above 25% across all the arrangements, and the upper bound can reach more than two orders of magnitude greater than the lower bound. The results suggest that subsampling ought to focus on subdomains where organic fractions are high, organic and inorganic pores differ in size, and distinct flow-enhancing or baffling arrangements of organic matter are present. [ABSTRACT FROM AUTHOR]

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

Accurate models of gas transport in shale gas reservoirs must consider complex gas transport mechanisms and phase behavior in nanopores, as well as different pore types. The gas transport mechanisms in shale gas reservoirs include viscous flow, Knudsen diffusion, surface diffusion, adsorption and desorption. In this study, a unified model of nanopore gas transport in shale gas reservoirs is presented. Gas storage patterns are different in organic pores and inorganic pores. Therefore, we develop two fully coupled apparent permeability models to describe gas transport in organic pores and inorganic pores separately. The apparent permeability model of organic pores considers the gas transport mechanisms of viscous flow, Knudsen diffusion, surface diffusion, adsorption and desorption. The apparent permeability model of inorganic pores considers the gas transport mechanisms of viscous flow and Knudsen diffusion. In both models, stress dependence, real gas effects and phase behavior are taken into account. Then, the influences of pore pressure, effective stress, real gas effects, pore radius, phase behaviors and transport properties on apparent gas permeabilities in organic pores and inorganic pores are analyzed based on the proposed models. [ABSTRACT FROM AUTHOR]

• A DAGP model is proposed based on shale geostatistical and petrophysical data. • A representative model is constructed by fractal organic matter particles. • DAGP exhibits different patterns, depending on a high or low matrix Young's modulus. • The impact of OM pores development degree on DAGP can be ignored at TOC < 5%. Current shale gas apparent permeability models often fail to integrate morphological properties of multiple storage spaces and various transport mechanisms. To deal with this, we propose a comprehensive model for estimating the dynamic apparent gas permeability (DAGP) during depressurization based on a representative model. First, dual fractal characteristics of organic matter (OM) particles and inorganic matter (IOM)/OM pores along with morphological information of OM particles from scanning electron microscope (SEM) images are considered to establish the representative model conditioned to a total organic carbon (TOC) content. Next, multiple transport mechanisms and a pore size change due to a poromechanical response and desorption-induced volumetric strain are incorporated in the DAGP calculation. Results reveal that the controlling factor of the DAGP comes from pore size shrinkage owing to a poromechanical response to gas transport mechanisms during depressurization at a high Young's modulus, while the DAGP is totally controlled by a poromechanical response at a low Young's modulus. The critical TOC content is determined to be about 5% at which the influence of the degree of OM pore development can be neglected. This work provides a practical method to estimate the DAGP from both geostatistical and petrophysical perspectives, which effectively decreases the uncertainty during productivity prediction in shale gas reservoirs and other unconventional reservoirs. [ABSTRACT FROM AUTHOR]

Conventional Darcy law cannot accurately describe the combined gas transport mechanisms in porous media with free gas only (such as tight gas reservoirs) and porous media with both free gas and adsorbed gas (such as shale gas reservoirs). The gas transport mechanisms in tight porous media including viscous flow, Knudsen diffusion, surface diffusion and molecular diffusion are investigated. Both the equivalent hydraulic radius and transport properties including intrinsic permeability, tortuosity and porosity, are used to build the coupled transport models describing the combined mechanisms of gas transport in ultra-tight porous media with free gas only and porous media with both free gas and adsorbed gas respectively. The effect of the pore-volume occupied by the adsorbed layer and surface diffusion through the adsorbed layer is considered in the transport model of porous media with adsorbed gas. The influences of equivalent hydraulic radius and transport properties on the gas transport mode in ultra-tight porous media are analyzed and the gas transport mode criteria in ultra-tight porous media are obtained. The result shows that viscous flow is the dominant mechanism, Knudsen diffusion can be ignored and Darcy law is applicable in porous media with equivalent hydraulic radius more than 100 nm. Surface diffusion can be ignored in the porous media with equivalent hydraulic radius less than 10 nm, while the effect of volume reduction by adsorption of porous media is less than 100 nm. The critical value of the transport function of intrinsic permeability, tortuosity and porosity also is given in this paper. [ABSTRACT FROM AUTHOR]

The transport problem in a three-layer channel consisting of a noticeable transition layer sandwiched by a free-fluid region and a homogeneous porous medium is investigated analytically. The heterogeneous transition layer is characterized by the continuous variation of porosity and permeability, which are specifically described by applying two sets of functions. The Brinkman model is employed in the transition layer, and the analytical velocity profile is obtained in terms of the Airy function. Consistency is found between the computation results and the PIV data measured by Goharzadeh et al. (Phys. Fluids 17:057102, ). After comparing the estimated permeability variations with the calculated variation, we find the former predicted permeability values are two orders of magnitude larger than the latter ones. The velocity discrepancy in the transition layer is ascribed to the effectiveness of the empirical permeability function: although the well-known Kozeny- Carman formula can precisely predict the permeability of the monodisperse spherical packing bed with constant porosity, it will overestimate the permeability in the transition layer. Then, the exact permeability variation is expressed by an exponential function, and a more general formula is needed to model the gradual change of permeability along the transition layer region. [ABSTRACT FROM AUTHOR]

The multiphase flow processes during water injection and flowback in shales are largely affected by its multiscale pore structure, different pore types and complex fluid transport mechanisms. At present, it is difficult to measure shale multiphase flow properties in laboratory. This study presents an upscaling model to derive core-scale relative permeability from pore-scale multiphase simulation using organic matter (OM)/inorganic matter (IOM) pore network models. Gas and water absolute permeabilities on OM/IOM pore network models are determined, and gas-water two-phase imbibition (during water injection) and drainage (during flowback) processes in the IOM pore network model are conducted using the invasion percolation theory. A core-scale model is generated with stochastically distributed IOM/OM patches. The upscaled relative permeabilities are derived by assembling gas-water transport properties in the IOM/OM based on the corresponding pore network simulation results. The upscaling method is validated by comparison with an analytical model during water injection and flowback processes. Furthermore, the impacts of total organic carbon (TOC) content and intrinsic permeability ratio of OM to IOM on the upscaled relative permeabilities are analyzed. The critical TOC content and intrinsic permeability ratio at which OM influences the upscaled relative permeabilities are determined. This study provides an effective upscaling workflow to obtain core-scale gas-water relative permeabilities based on pore-scale modeling considering multiple gas/water transport mechanisms in different pore systems. • Relative permeabilities upscaling model is built with multiple transport mechanisms. • Upscaled relative permeabilities largely rely on multiphase flow properties in IOM. • The impact of OM on upscaled relative permeabilities can be ignored at TOC <4%. • Intrinsic permeability ratio (γ) of OM to IOM is in effect at γ < 0.3. [ABSTRACT FROM AUTHOR]

In this work, a series of microscopic simulations are conducted to investigate the effect of wettability, flow rate and surface tension in porous system by using pairwise force smoothed particle hydrodynamics (PF-SPH) method. Firstly, a novel inflow and outflow boundary is introduced in the SPH framework. The overall proposed model is verified by two benchmarks. The test cases are run in the two dimensional heterogeneous porous media. The effect of wettability, flow rate and surface tension to the macroscopic parameters such as relative permeability and residual oil saturation are thoroughly examined. Through our simulations, we conclude that (i) the type of residual oil changes with contact angle; water wetting porous media has a higher level of waterless oil recovery period and the discrepancies of ultimate oil recovery efficiencies happen before water phase breaks through the outlet of porous media; the residual oil saturations present excellent linear correlations with contact angles; (ii) it's better to increase the flow rate at the high water cut stage (eg f w = 90 %) in hydrophilic porous media and rise the flow rate at early water cut stage (eg f w = 0 %) in lipophilic porous media; increasing the flow rate dramatically shortens the effective production time in strong oil wetting porous media; (iii) decreasing the surface tension could change the type of residual oil, which leads to the further extraction of oil film and cluster residual oil. • A robust PF-SPH model is adopted considering the advantages of different SPH models. • A novel inflow and outflow boundary model is introduced in the SPH framework. • The effects of wettability, flow rate and surface tension to macro parameters are thoroughly analyzed in SPH field. [ABSTRACT FROM AUTHOR]

• Shale permeability upscaling is proposed considering multiple transport mechanisms. • A REV size is determined as 420 μm with experimental data of Sichuan basin. • Bulk gas in inorganic matter contributes roughly 70% to core-scale permeability. • Water film effect can be neglected at mean pore size larger than 40 nm. This paper presents a new upscaling method to derive the core-scale apparent gas permeability from an improved pore-scale permeability model and experimental data, with more rigorous incorporation of varying gas storage/transport mechanisms in nano/micro pores. First, in use of SEM images of a gas-rich shale field example in Sichuan Basin from our lab, pore network models of inorganic-matter (IOM) and organic-matter (OM) are characterized by using a digital-core technique. Next, an improved pore-scale real gas apparent permeability is modeled rigorously for both IOM/OM, respectively, with 1) bulk gas transport, gas adsorption, surface diffusion, pore-size confined phase behavior, and stress-dependent rock properties and 2) an additional reduction in inorganic pore sizes by water film adhered on pore surfaces. Core-scale permeability is then derived by assembling the permeabilities of stochastically distributed IOM/OM patches with different pore network models properties using the Monte Carlo sampling method. The new core-scale permeability model is validated by pulse-decay permeability experiment. Moreover, the representative elementary volume (REV) size is determined by analyzing the relative standard deviation of apparent gas permeability in cases with different sample sizes. The contributions of different gas transport mechanisms are discussed, and the impacts of stress-dependence for several field examples (i.e., Sichuan, Pierre and Barnett Basins) and water film with varying relative humidity (RH) on core-scale apparent permeability are analyzed. This work provides an effective approach to determine the core-scale shale permeability by directly using pore-scale experimental data, which is a common challenge in the unconventional resources. [ABSTRACT FROM AUTHOR]

Highlights • Multiscale image-based shale pore structure fractal characteristic is studied. • The real gas permeability fractal model considering second order slip is derived. • Image resolution for accurate permeability prediction should be less than 50 nm. Abstract The heterogeneities of shale are manifested in the complex pore spatial configurations and the wide distribution of pore sizes. The recent advances of high-resolution imaging techniques such as Scanning Electron Microscope (SEM) and Focussed Ion Beam Scanning Electron Microscopes (FIB-SEM) enable accurate characterization of shale pore structure in the limited imaging area. Due to the nature of multiscale pore size, image-based petrophysical properties are highly dependent on the selection of image resolution. Fractal theory proves to be an effective approach to characterize pore structure as well as calculate fluid transport properties. In this study, the image-based fractal characteristic of shale pore structure at multiscale resolutions is investigated and its impact on the accurate prediction of gas permeability is analyzed. The fractal dimensions of pore phase in 100 SEM images at resolutions ranging from 15.5 nm to 420 nm are calculated by the box counting method and Sierpinski carpets analytical solution. The real gas permeability model in consideration of second order slip is derived based on the fractal theory. Two groups of gas permeabilities at different resolutions are estimated respectively based on the fractal dimensions obtained from the box counting method and Sierpinski carpets analytical solution. The results found that fractal dimensions obtained from the box counting method at different resolutions are more close to the exact fractal dimension compared with that obtained from the Sierpinski carpets analytical solution at low resolutions and gas permeabilities calculated at different resolutions based on the box counting estimated fractal dimensions are more close to the exact gas permeability. The image resolution for accurate calculation of shale pore structure properties and gas permeability should be less than 50 nm based on our analysis results. [ABSTRACT FROM AUTHOR]

Duo to different transport mechanisms and gas storage in organic and inorganic systems, a new triple-continuum model coupling Discrete Fracture Model (DFM) was established to investigate gas flow in shale gas reservoir. Considering the multi-scale and heterogeneity of shale matrix, fractal theory was used to calculate the apparent permeability of organic and inorganic systems while multiple gas transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, gas absorption/desorption effect and real gas effect were incorporated. This coupled mathematical model was solved by Finite Element Method (FEM) and the presented fractal apparent permeability model was validated with the experimental data. The results show that fractal characteristics of shale matrix have great impact on gas reservoir performance. The model without considering the influence of fractal characteristics could lead to underestimate gas production by approximately 17%. Viscous flow is the dominate transport mechanisms of shale gas and Knudsen diffusion has an impact on gas flow when the pressure declines. Surface diffusion should be only considered in organic systems and can be ignored. Then the results of sensitivity analysis show that the characteristic parameters of inorganic matter have a greater impact than those of organic matter and establishing a triple-continuum model with considering comprehensive effect of organic and inorganic matter is necessary. In addition, gas production would decrease as the pore fractal dimension and tortuosity fractal dimension increase, which results from the increasing number of small pores and more tortuous path for gas flow. [ABSTRACT FROM AUTHOR]

At present, researchers predict permeability through core experiments that require specific experimental conditions and methods, which are difficult and time-consuming. Conventional simulation methods for predicting permeability require considerable computational resources. Therefore, deep learning can be used as a pore-scale simulation prediction method. In this study, we established a workflow for directly predicting permeability from images. Considering that the mineral properties of the nanopore wall of shale oil have a large influence on the flow, a core dataset with organic distribution was constructed with random circles, and the slip influence of organic pores was considered. From our dataset, we found that the average permeability with organic distribution was 32.3% higher than that without organic distribution. Therefore, to simulate the microscopic flow and predict the permeability of shale oil, considering the differences in the pore flow mechanisms of different minerals is necessary. We designed a convolutional network for the dataset, adopted the structure of SE-ResNet, added the squeeze-and-excitation (SE) module to the double-layer residual module of ResNet18, and combined the characteristics of the SE block with the attention mechanism and ResNet to effectively obtain the information between channels and avoid the problem of gradient disappearance or explosion. Using SE-ResNet for directly predicting the apparent permeability from images, the accuracy of the test set reached 88.5%. The model had strong generalization ability, and the SE-ResNet could map the image of the core to the apparent permeability, which was approximately 100 times faster than the direct flow simulation. [ABSTRACT FROM AUTHOR]

The volumetric lattice Boltzmann method (VLBM) has been recently developed and validated for dealing with flows in complex geometries. To reveal the intricate and arbitrary porous media skeleton, VLBM categorizes the computational domain into fluid, solid, and boundary cells by introducing a volumetric parameter P ( x → ) , through which the lattice Boltzmann equations are self-regularized. As a result, the no-slip bounce-back boundary condition at the inter walls is integrated in the streaming term. Since its data structure is aligned and kernel pattern is clear, VLBM is ideally suited for GPU parallelization. Using the P ( x → ) in the streaming operation, branch diverse can be effectively decreased. In this paper, we use several optimization methods, such as memory arrangement and kernel design, to maximize the performance of parallelization for VLBM. As an application, we simulated petroleum flow in a digital sandstone with two resolutions, 256 3 and 256 2 × 512 , and evaluated its permeability. The best parallel performance reaches 808.7 MLUPS (Million Lattice Updates Per Second), which is 1421.3-times speedup compared with the serial computation with allocated memory. [ABSTRACT FROM AUTHOR]

Various numerical models exist for numerical simulation of fluid flow in fractured porous media, such as dual-porosity model, discrete fracture model and equivalent continuum model. As a promising model, the embedded discrete fracture model is a powerful tool for fractured porous media with complex fracture distribution, because it incorporates the effect of each fracture explicitly without requiring the simulation mesh to conform to the fracture geometry. Moreover, it does not need mesh refinement near fractures and offers computationally-efficient simulations compared to other discrete fracture models. In this paper, the Mimetic Finite Difference method and Finite Volume Method are used to improve the numerical solution of the embedded discrete fracture model, the improved method can deal with permeability tensor and can be used to simulate fractured reservoir with complex geometrical shape, which fails to be solved by the primal method based on the finite difference method. Several numerical simulations and physical experiment demonstrate the applicability of the proposed method for studying flow processes in fractured porous media. [ABSTRACT FROM AUTHOR]

• The region of heterogeneous formation first touched by downward CO 2 fingers plays a dominant role in convective mixing. • For heterogeneous porous media, the relationship between Sh and Ra is not power-law. • High permeability reverse rhythm reservoir which have higher density-driven CO 2 convection rate is suitable for CO 2 storage. Underground storage of CO 2 in saline aquifers has emerged as a promising strategy for mitigating global warming. The dissolution of CO 2 in saline aquifers induces the descent of high-density CO 2 -saturated brine to the reservoir bottom, driven by gravity-induced natural convection. The manifestation of this convection is linked to the heterogeneity of the reservoir. We thus analyzed the impact of heterogeneous permeability distribution, which represent various geological structures, on the CO 2 plume morphology and CO 2 storage efficiency. In a homogeneous high-permeability core, high convection rate resulting in wider CO 2 fingers. For heterogeneous cores, the convective mixing rate depends on average permeability, while the morphology of fingers is determined by local permeability. Abrupt permeability changes (from low permeability to high permeability) led to CO 2 finger channeling, resulting in reduced sweep efficiency. In heterogeneous layered core, the permeability of the upper layer dominated convection, while vertically decreasing permeability (reversed-rhythm) was more conducive to the dissolution capture of CO 2. However, increasing the number of rhythm layer, the larger permeability distribution range and the number of vertical bedding layers enhanced the convective instability, which was unconducive to efficient CO 2 sequestration. Besides, a power relationship between the Rayleigh number and the Sherwood number was identified. The power-law exponent b = 1.07 was higher than the value (b ≈0.984) obtained by two-dimensional plate experiments. In conclusion, reversed-rhythm reservoirs with high permeability exhibit a preference for CO 2 dissolution trapping. Our study provides detailed insights into the processes of CO 2 dissolution for heterogenous reservoir. The results should further facilitate the extensive implementation of Carbon Capture and Storage projects. [ABSTRACT FROM AUTHOR]

Non-marine sandstones in the Upper Triassic Xujiahe Formation form an important reservoir unit in the Sichuan Basin, western China. Widespread authigenic chlorite cement is present in the second and fourth members of the formation, referred to as the Xu II and IV members. This study, based on data from 12 wells from three gasfields, focusses on chlorite development and evolution and attempts to evaluate its influence on reservoir quality. Data included results of X-ray diffraction (XRD) and electron microprobe analyses (EMPA), scanning electron microscopy (SEM), and stable carbon and oxygen isotope analyses. The results showed that chlorite coatings preserve primary pore spaces in the sandstones by inhibiting the nucleation of quartz cements on grain surfaces. Iron for chlorite growth came from the dissolution of Fe-rich magmatic rocks derived from the palaeo-Longmenshan fold-belt, from dissolved and colloidal iron which had been precipitated in the Xujiahe Formation in a fluvio-deltaic environment, and from compacting mudstones in other pars of the formation. The chlorite initially precipitated from pore waters during eodiagenesis (< 70 °C; < 2 km burial depth). During mesodiagenesis (>70 °C, > 2 km), the chlorite was modified due to exposure to Mg-rich fluids derived from the underlying carbonate-dominated Leikoupo Formation. Thus the Mg content of chlorite in the Xu II member increases with depth. However this phenomenon was not observed in the Xu IV member. The effects of authigenic chlorite on the sandstones' petrophysical properties were evaluated from correlations between chlorite content and porosity. Optimum thicknesses for chlorite coatings range from 5 to 10 microns. Thicker or thinner coatings appear to be less capable of preserving primary porosity and permeability. [ABSTRACT FROM AUTHOR]

A new analytical model has been developed for determiningthe wettingphase relative permeabilities in a multiple gas–liquid drainageprocess. The multistep drainage process consists of a series of drainageprocesses with a tiered pressure-difference profile. With this model,the wetting phase relative permeabilities can be readily obtainedthrough regression of the wetting phase recovery history. The assumptionsused in deriving the analytical model are examined by numerical simulations.The agreement between the analytical and the numerical results indicatesthat these assumptions are reasonable and valid. Numerical simulationsand laboratory results demonstrate that this model is effective fordirect estimation of the wetting phase relative permeabilities inthe multistep drainage process. [ABSTRACT FROM AUTHOR]

The stress-dependent flow and transport behaviors of porous media are ubiquitous in various scientific and engineering applications. It has been shown that the change of effective stress has important effects on the permeability and porosity of porous media. In this paper, a new stress sensitivity model for porous media is developed based on the fractal theory and the elasto-plastic thick-walled cylinder model. The proposed model is able to predict the elasto-plastic deformation of the fractal porous media under loading–unloading stress cycles, which plays a crucial role on the permanent variations of the permeability and porosity. It is found that the permeability of stress-sensitivity porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, minimum and maximum capillary diameters, Young's modulus and Poisson's ratio of capillary. Each parameter has a clear physical meaning. The validity of the developed fractal model is verified by comparing the model predictions with the available experimental data. [ABSTRACT FROM AUTHOR]

Because of the complex pore structure and multiple types of gas storage, the traditional Darcy permeability model is not valid for describing shale gas flow. In this paper, an upscaled transport model is established based on homogenization theory to consider multiple transport mechanisms and the heterogeneity of shale samples. This new transport model is employed to successfully explain pressure decay experimental data. The results show that absorbed gas cannot be ignored in pressure decay experiment and the pressure difference decreases rapidly when the absorbed gas is not considered. Then several critical conclusions have been drawn as follows. The permeability anisotropy for stochastic distribution model can be ignored and the effective permeability will be underestimated by double porosity model if surface diffusion dominates gas flow in shale reservoir. In addition, shale gas transport is dominated by Knudsen diffusion when the pore pressure is below 2 MPa and the contribution of surface diffusion increases as the pore pressure increases. The macroscopic effective permeability of the whole domain is dominated by the permeability of the connected phase; meanwhile, it can be influenced by the permeability of the disconnected phase. When the pore pressure is below 3.52 MPa, the effective permeability increases as the organic matter content (TOC) decreases. However, the effective permeability increases as the TOC increases when the pore pressure is above 3.52 MPa, which is different from traditionally believed when the relationship between the TOC and gas absorption capacity of the shale matrix is not considered. The effective permeability particularly increases at a high pore pressure as the Langmuir volume increases. In addition, the effective permeability increases as the Langmuir pressure decreases; however, this becomes apparent when the pore pressure is smaller. • An upscaled transport model is established based on homogenization theory by considering multiple transport mechanisms and heterogeneity of shale gas reservoir. • This new transport model is employed to successfully explain the pressure decay experiment data successfully and the absorption phenomenon is also considered. • The permeability anisotropy for stochastic distribution model can be ignored and the effective permeability will be underestimated by double porosity model if surface diffusion dominates gas flow in shale reservoir. • The macroscopic effective permeability of whole domain is dominated by the permeability of connected phase meanwhile it can be influenced by the permeability of disconnected phase. [ABSTRACT FROM AUTHOR]

The incompatibility between workover fluid and reservoir rock is one of the causes of formation damage. Fines migration and clay swelling are considered as the major mechanisms responsible for formation damage, which results in declining productivity. However, there has been limited visualized evidence of pore structural changes during formation damage. This paper establishes a formation damage evaluation method for sandstone reservoirs based on X-ray micro-computed tomography (CT) analysis. We presented conclusive evidence for clay swelling and fines migration during workover fluid flooding and formation liquid flooding. Water sensitivity and flow rate sensitivity tests were performed on a Dongying sandstone (heterogeneous argillaceous sandstone) plug. In addition, the plug was micro-CT imaged before and after flooding with workover fluid and formation liquid at medium resolution (24 μm voxel size); the changes in core permeability and the associated changes in 2D and 3D pore space were analyzed. We found that the sandstone pore space was partially blocked by clay minerals and moving particles, leading to significantly decreased porosity (5.17%–4.19% for sample 1, 5.38%–2.76% for sample 2) and permeability (3.38 × 10−3 μm2 to 1.28 × 10−3 μm2 for sample 1, 13.30 × 10−3 μm2 to 3.15 × 10−3 μm2 for sample 2). This permeability decrease was caused by a decrease in the average pore radius and coordination number. Moreover, increased micro-CT intensity was measured by comparison of initial and final tomogram images, representing clay swelling & blockage of pores during the displacement and a generally lower porosity. This work visualized microscale formation damage, which reminds that incompatibility between workover fluid and reservoir rock damages formation seriously and the fluid injection rate should be lower than the critical flow rate when developing a reservoir with a strong water sensitivity and flow rate sensitivity. Image 1 • A formation damage evaluation method for sandstone reservoir based on X-ray micro-computed tomography is established. • Conclusive evidence for clay swelling and fines migration during workover fluid and formation water flooding is provided. • Pore radius distribution, coordination number and Micro-CT intensity are analyzed with respect to formation damage. [ABSTRACT FROM AUTHOR]

Microfractures have great significance in the study of reservoir development because they are an effective reserving space and main contributor to permeability in a large amount of reservoirs. Usually, microfractures are divided into natural microfractures and induced microfractures. Artificially induced rough microfractures are our research objects, the existence of which will affect the fluid-flow system (expand the production radius of production wells), and act as a flow path for the leakage of fluids injected to the wells, and even facilitate depletion in tight reservoirs. Therefore, the characteristic of the flow in artificially induced fractures is of great significance. The Lattice Boltzmann Method (LBM) was used to calculate the equivalent permeability of artificially induced three-dimensional (3D) fractures. The 3D box fractal dimensions and porosity of artificially induced fractures in Berea sandstone were calculated based on the fractal theory and image-segmentation method, respectively. The geometrical parameters (surface roughness, minimum fracture aperture, and mean fracture aperture), were also calculated on the base of digital cores of fractures. According to the results, the permeability lies between 0.071–3.759 (dimensionless LB units) in artificially induced fractures. The wide range of permeability indicates that artificially induced fractures have complex structures and connectivity. It was also found that 3D fractal dimensions of artificially induced fractures in Berea sandstone are between 2.247 and 2.367, which shows that the artificially induced fractures have the characteristics of self-similarity. Finally, the following relations were studied: (a) exponentially increasing permeability with increasing 3D box fractal dimension, (b) linearly increasing permeability with increasing square of mean fracture aperture, (c) indistinct relationship between permeability and surface roughness, and (d) linearly increasing 3D box fractal dimension with increasing porosity. [ABSTRACT FROM AUTHOR]

• Coupled porous media and free flow model of fluid flow in fractured karst reservoirs. • Analytical expression of connectivity for discrete fracture-cave networks. • Flow channeling dominated by network connectivity. • Permeability scaling with connectivity in a power law for connected systems. Fractured karst reservoirs play a significant role in hydrocarbon reserves and groundwater storage. They often exhibit complex multiscale heterogeneities involving pores, fractures and caves, whose length scales range from microns to tens or hundreds of meters. Thus, the study of fractured karst reservoirs is faced with a significant unresolved challenge in quantitatively characterizing the geometrical connectivity and hydraulic conductivity as well as their interrelationships in such strongly heterogeneous, multicomponent systems. In this paper, we propose an analytical formulation to characterize the connectivity of discrete fracture-cave networks building upon the excluded area concept of the percolation theory. By implementing a state-of-the-art computational model solving coupled Navier-Stokes (free flow) and Darcy (porous media flow) equations, we numerically derive the permeability of a fractured and karstified porous media, such that the relationship between the connectivity and permeability is further explored. The high-fidelity numerical model also permits us to elucidate the process of flow channelization within the fracture-cave network. The results show that the fracture-cave network connectivity correlates to the permeability via a power law scaling for connected systems. Significant flow channeling occurs around the percolation threshold where the flow is dominated by a limited number of preferential pathways. Caves play a crucial role in the flow due to the fact that caves could globally enhance the network connectivity and locally serve as hotspots for high fluid velocity. Finally, a semi-analytical permeability model for fractured karst reservoirs is developed. The results of our research and insights obtained have important implications for understanding the subsurface fluid flow in fractured karst reservoirs. [ABSTRACT FROM AUTHOR]

Reservoir modeling data could be divided into two categories: spatial data (i.e. permeability, effective grids, crack, irregular boundaries) and vector data (fluid properties i.e. relative permeability, density, viscosity). This paper is mainly interested in considering the permeability and relative permeability, which are the representatives of the two data types, to construct a proxy model for forecasting saturation and pressure maps in heterogeneous reservoirs during water flooding. The proxy model is built on the dense encoder-decoder network, to learn the reservoir dynamic states at different time steps. Results indicate that the trained proxy model could predict fluid saturation and pressure fields accurately. This paper presents a calibration method, which is adding a constraint to well-blocks. After calibration, the trained proxy model is utilized to calculate reservoir production. The comparison results illustrate that the proxy model can forecast well rates with relatively high accuracy. Compared with traditional reservoir numerical simulators, the proxy model could predict fluid saturation, pressure and well rates with similar accuracy and less time-cost. • This paper constructs a proxy model for forecasting saturation and pressure maps in heterogeneous reservoirs. • The paper considers permeability and relative permeability, which are the representatives of spatial data and vector data. • This paper presents a calibration method, which is adding a constraint to well-blocks. [ABSTRACT FROM AUTHOR]

An effective stress calculation formula was proposed for coal containing gas with considering the swelling stress of gas adsorption based on the effective stress principles for porous media. Referring to dynamic model of porosity and permeability in coal containing gas, solid-gas coupling model which could describe the skeleton deformability of coal containing gas and the compressibility of gas under the solid-gas interaction condition was built. First we made excavation on the three-dimensional model based on the physical parameters of Pingdingshan tenth coal mine to obtain the stress distribution of coal seam after excavated instead of easy uniform loading. Then we simulated the gas drainage from boreholes based on constructed mathematical model. From the results we got: (1) Negative pressure didn't have a great influence on gas drainage. (2) The porosity of coal seam decreased gradually over time. (3) The effective radius increased gradually to a fixed value over time. [ABSTRACT FROM AUTHOR]

Water flooding is the most widely used method to enhance oil recovery. Simulating the influence of particle content on fluid flow in water flooding process can provide instructive significance for oilfield development. In this paper, a pore network model was established to simulate the transport process of particles in injected water and fallen particles from the reservoir. It was used to study the influence of particle blockage, deposition and migration on the clogged throats and changes of oil-water relative permeability curves. In the model, four parameters were set, fallen particle diameter, injected particle diameter, fallen particle number and injected particle number. Other parameters were fixed and only a variable was changed to explore the changeable rule of relative permeability curves. It can be generally noted that fallen particle changes have great influence on the relative permeability curves of oil phase and injected particle changes mainly affect the relative permeability curves of water phase. It is of great significance for oilfield development to study the influence of particle transportation on fluid seepage processes. • A pore network model containing particles was established. • A transport process of injected particles and fallen particles from the reservoir during water flooding was simulated. • The influence of particle blockage, deposition and migration on the clogged throats and oil-water relative permeability curves was studied. [ABSTRACT FROM AUTHOR]

This study proposed an advection-diffusion-mechanical deformation integral model to predict coal matrix methane permeability combining digital rock physics with laboratory measurements. The coal matrix pore network was first extracted from the segmented 3D digital coal image. Organic pore-controlled methane transport pathways and mineral-associated pore methane transport pathways were identified from the coal matrix pore network. Advection and Knudsen diffusion processes were considered for methane transport in the mineral associate pores and bulk methane transport in organic pores. To determine the adsorbed methane surface diffusion ability in organic pores, laboratory adsorption and desorption experiments were conducted to determine the desorption curve and critical desorption pressure. Pore shrinkage was considered for organic pores and mineral-associated pores whereas sorption-induced volumetric strain was also modeled for the organic pore system. The coal matrix methane permeability was calculated over a wide range of production pressures and the influences of reservoir and methane transport properties on coal matrix methane permeability were analyzed in detail. Results revealed that gas slippage and initial formation pressure dominate the coal matrix methane permeability more than other influencing factors. Coal matrix methane permeability was underestimated by at least 40% by using Darcy flow to describe methane flow in the coal matrix and the influence of organic matter bulk modulus variation on coal matrix methane permeability can be neglected at initial formation pressures less than 10 MPa. • An advection-diffusion-deformation coal matrix methane permeability model is proposed. • Pore size change caused by stress and sorption-induced volume are modeled. • Methane transport mechanisms in different pore types are considered. • Influences of geochemical properties on coal matrix methane permeability are studied. [ABSTRACT FROM AUTHOR]

Digital core simulation technology, as an emerging numerical simulation method, has gradually come to play a significant role in the study of petrophysical properties. By using this numerical simulation method, the influence of micro factors on seepage properties of reservoir rock is taken into consideration, making up the shortcomings of the traditional physical experiment. Three-dimensional core images are reconstructed by a computed tomography scanning technique. Different sizes of the sub-region were simulated by three methods including the direct computation of Navier-Stokes equations, the simulation of the pore network model, and the lattice Boltzmann method. The permeability computed by each simulation was compared. After comparison between these three methods, the results of the direct computation method based on Navier-Stokes equations were found to be higher than the other two methods. The pore network model simulation has an obvious advantage on the computation speed and the simulation area. The lattice Boltzmann method shows the low efficiency due to the time-consuming process. At last, the permeability calculated by the three methods is matched by the Kozeny-Carman equation. A more accurate formula can be obtained by a series of numerical simulations, which can be applied to marco-scale simulation. [ABSTRACT FROM AUTHOR]