Estimating pore volume compressibility by spheroidal pore modeling of digital rocks

The real pores in digital cores were simplified into three abstractive types,including prolate ellipsoids,oblate ellipsoids and spheroids.The three-dimensional spheroidal-pore model of digital core was established based on mesoscopic mechanical theory.The constitutive relationship of different types of pore microstructure deformation was studied with Eshelby equivalent medium theory,and the effects of pore microstructure on pore volume compressibility under elastic deformation conditions of single and multiple pores of a single type and mixed types of pores were investigated.The results showed that the pore volume compressibility coefficient of digital core is closely related with porosity,pore aspect ratio and volumetric proportions of different types of pores.(1)The compressibility coefficient of prolate ellipsoidal pore is positively correlated with the pore aspect ratio,while that of oblate ellipsoidal pore is negatively correlated with the pore aspect ratio.(2)At the same mean value of pore aspect ratio satisfying Gaussian distribution,the more concentrated the range of pore aspect ratio,the higher the compressibility coefficient of both prolate and oblate ellipsoidal pores will be,and the larger the deformation under the same stress condition.(3)The pore compressibility coefficient increases with porosity.(4)At a constant porosity value,the higher the proportion of oblate ellipsoidal and spherical pores in the rock,the more easier for the rock to deform,and the higher the compressibility coefficient of the rock is,while the higher the proportion of prolate ellipsoidal pores in the rock,the more difficult it is for rock to deform,and the lower the compressibility coefficient of the rock is.By calculating pore compressibility coefficient of ten classical digital rock samples,the presented analytical elliptical-pore model based on real pore structure of digital rocks can be applied to calculation of pore volume compressibility coefficient of digital rock sample.

Modeling of multiphase flow in low permeability porous media:Effect of wettability and pore structure properties

Multiphase flow in low permeability porous media is involved in numerous energy and environmental applications.However,a complete description of this process is challenging due to the limited modeling scale and the effects of complex pore structures and wettability.To address this issue,based on the digital rock of low permeability sandstone,a direct numerical simulation is performed considering the interphase drag and boundary slip to clarify the microscopic water-oil displacement process.In addition,a dual-porosity pore network model(PNM)is constructed to obtain the water-oil relative permeability of the sample.The displacement efficiency as a recovery process is assessed under different wetting and pore structure properties.Results show that microscopic displacement mechanisms explain the corresponding macroscopic relative permeability.The injected water breaks through the outlet earlier with a large mass flow,while thick oil films exist in rough hydrophobic surfaces and poorly connected pores.The variation of water-oil relative permeability is significant,and residual oil saturation is high in the oil-wet system.The flooding is extensive,and the residual oil is trapped in complex pore networks for hydrophilic pore surfaces;thus,water relative permeability is lower in the water-wet system.While the displacement efficiency is the worst in mixed-wetting systems for poor water connectivity.Microporosity negatively correlates with invading oil volume fraction due to strong capillary resistance,and a large microporosity corresponds to low residual oil saturation.This work provides insights into the water-oil flow from different modeling perspectives and helps to optimize the development plan for enhanced recovery.

“Rigid-elastic chimera” pore skeleton model and overpressure porosity measurement method for shale: A case study of the deep overpressure siliceous shale of Silurian Longmaxi Formation in southern Sichuan Basin, SW China

Based on analysis of pore features and pore skeleton composition of shale,a“rigid elastic chimeric”pore skeleton model of shale gas reservoir was built.Pore deformation mechanisms leading to increase of shale porosity due to the pore skeleton deformation under overpressure were sorted out through analysis of stress on the shale pore and skeleton.After reviewing the difficulties and defects of existent porosity measurement methods,a dynamic deformed porosity measurement method was worked out and used to measure the porosity of overpressure Silurian Longmaxi Formation shale under real formation conditions in southern Sichuan Basin.The results show:(1)The shale reservoir is a mixture of inorganic rock particles and organic matter,which contains inorganic pores supported by rigid skeleton particles and organic pores supported by elastic-plastic particles,and thus has a special“rigid elastic chimeric”pore structure.(2)Under the action of formation overpressure,the inorganic pores have tiny changes that can be assumed that they don’t change in porosity,while the organic pores may have large deformation due to skeleton compression,leading to the increase of radius,connectivity and ultimately porosity of these pores.(3)The“dynamic”deformation porosity measurement method combining high injection pressure helium porosity measurement and kerosene porosity measurement method under ultra-high variable pressure can accurately measure porosity of unconnected micro-pores under normal pressure conditions,and also the porosity increment caused by plastic skeleton compression deformation.(4)The pore deformation mechanism of shale may result in the"abnormal"phenomenon that the shale under formation conditions has higher porosity than that under normal pressure,so the overpressure shale reservoir is not necessarily“ultra-low in porosity”,and can have porosity over 10%.Application of this method in Well L210 in southern Sichuan has confirmed its practicality and reliability.

Study of the permeability characteristics of porous media with methane hydrate by pore network model

The permeability in the methane hydrate reservoir is one of the key parameters in estimating the gas production performance and the flow behavior of gas and water during dissociation.In this paper,a three-dimensional cubic pore-network model based on invasion percolation is developed to study the effect of hydrate particle formation and growth habit on the permeability.The variation of permeability in porous media with different hydrate saturation is studied by solving the network problem.The simulation results are well consistent with the experimental data.The proposed model predicts that the permeability will reduce exponentially with the increase of hydrate saturation,which is crucial in developing a deeper understanding of the mechanism of hydrate formation and dissociation in porous media.

Probing deactivation by coking in catalyst pellets for dry reforming of methane using a pore network model

Dry reforming of methane(DRM) is an attractive technology for utilizing the greenhouse gases(CO_(2) and CH_(4)) to produce syngas. However, the catalyst pellets for DRM are heavily plagued by deactivation by coking, which prevents this technology from commercialization. In this work, a pore network model is developed to probe the catalyst deactivation by coking in a Ni/Al_(2)O_(3) catalyst pellet for DRM. The reaction conditions can significantly change the coking rate and then affect the catalyst deactivation. The catalyst lifetime is higher under lower temperature, pressure, and CH_(4)/CO_(2) molar ratio, but the maximum coke content in a catalyst pellet is independent of these reaction conditions. The catalyst pellet with larger pore diameter, narrower pore size distribution and higher pore connectivity is more robust against catalyst deactivation by coking, as the pores in this pellet are more difficult to be plugged or inaccessible.The maximum coke content is also higher for narrower pore size distribution and higher pore connectivity, as the number of inaccessible pores is lower. Besides, the catalyst pellet radius only slightly affects the coke content, although the diffusion limitation increases with the pellet radius. These results should serve to guide the rational design of robust DRM catalyst pellets against deactivation by coking.

Pore network modeling of water block in low permeability reservoirs

A pore network model was used in this paper to investigate the factors, in particular, throat radius, wettability and initial water saturation, causing water block in low permeability reservoirs. A new term - ＇relative permeability number＇ （RPN） was firstly defined, and then used to describe the degree of water block. Imbibition process simulations show that the RPN drops in accordance with the extension of the averaged pore throat radius from 0.05 to 1.5 μm, and yet once beyond that point of 1.5 μm, the RPN reaches a higher value, indicating the existence of a critical pore throat radius where water block is the maximum. When the wettability of the samples changes from water-wet to weakly water-wet, weakly gas-wet, or gas（oil）-wet, the gas RPN increases consistently, but this consistency is disturbed by the RPN dropping for weakly water-wet samples for water saturations less than 0.4, which means weakly waterwet media are more easily water blocked than water-wet systems. In the situation where the initial water saturation exceeds 0.05, water block escalates along with an increase in initial water saturation.

Constitutive model for methane desorption and diffusion based on pore structure differences between soft and hard coal

This paper aims to improve the accuracy and applicability of gas diffusion mathematical models from coal particles. Firstly, a new constitutive model for gas diffusion from coal particles with tri-disperse pore structure is constructed by considering the difference in characteristics between soft coal and hard coal.The analytical solution is then derived, that is, the quantitative relationship between gas diffusion rate(Qt/Q_∞) and diffusion time(t), The pore structure parameters of soft coal and hard coal from Juji coal mine are determined. Gas diffusion rules are numerically calculated and investigated by physical simulation methods. Lastly, the applicability of this model is verified. The results show that the homogeneous model only applies to the gas diffusion process of hard coal during the initial 10 min. The calculation results from this model and the physical experimental results of soft coal and hard coal are nearly identical during the initial 30 min.

Attenuation-type and failure-type curve models on accumulated pore water pressure in saturated normal consolidated clay

Based on dynamic triaxial test results of saturated soft clay, similarities of variations between accumulated pore water pressure and accumulated deformation were analyzed. The Parr＇s equation on accumulated deformation was modified to create an attenuation-type curve model on accumulated pore water pressure in saturated normal consolidation clay. In this model, dynamic strength was introduced and a new parameter called equivalent dynamic stress level was added. Besides, based on comparative analysis on variations between failure-type and attenuatiun-type curves, a failure-type curve model was created on accumulated pore water pressure in saturated normal consolidation clay. Two models can take cycle number, coupling of static and dynamic deviator stress, and consolidation way into consideration. The models are verified by test results. The correlation coefficients are more than 0.98 for optimization of test results based on the two models, and there is good agreement between the optimized and test curves, which shows that the two models are suitable to predict variations of accumulated pore water pressure under different loading cases and consolidation ways. In order to improve prediction accuracy, it is suggested that loading cases and consolidation ways should be consistent with in-situ conditions when dynamic triaxial tests are used to determine the constants in the models.

Modeling of the Relationship Between Pore Size Distribution and Thickness of Ceramic MF Membrane

The pore size distribution(PSD)measured by the gas bubble point(GBP)method ofceramic microfiltration(MF)membranes prepared by suspension technique was found to be signifi-cantly influenced by the membrane thickness.A culm-like model for pore structure was introduced tocharacterize the membrane pores instead of the conventional model which does not reflect the radiusvariation along the pore passages and is unable to explain the thickness effect on the membrane PSD.A laminate structure,taking the culm-like model for pore structure into consideration,was hypoth-esized for ceramic MF membranes.A mathematical model was then established to quantitativelydescribe the relationship between the membrane number PSD and the membrane thickness.Goodresults were obtained for the correlation of mean pore size and simulation of the PSD for ceramicMF membranes.

Model construction of micro-pores in shale: A case study of Silurian Longmaxi Formation shale in Dianqianbei area, SW China

Based on scanning electron microscopy and nitrogen adsorption experiment at low temperature, the pore types and structures of the Longmaxi Formation shale in the Dianqianbei area, SW China were analyzed, and a molecular model was built. According to mathematical statistics, the validation of the model was solved by converting it into a mathematical formula. It is found by SEM that the pores in clay mineral layers and organic pores occupy most of the pores in shale; the nitrogen adsorption experiment at low temperature reveals that groove pores formed by flaky particles and micro-pores are the main types of pores, and the results of the two are in good agreement. A molecular model was established by illite and graphene molecular structures. Moreover, based on the fractal theory and the Frenkel-Halsey-Hill formula, a modified Frenkel-Halsey-Hill formula was proposed. The reliability of the molecular model was verified to some extent by obtaining parameters such as the fractal dimension, replacement rate and fractal coefficients of correction, and mathematical calculation. This study provides the theoretical basis for quantitative study of shale reservoirs.

The effect of pore fluid on seismicity: a computer model

The influence of fluid on seismicity of a computerized system is analyzed in this paper. The diffusion equation of fluid in a crustal fault area is developed and used in the calculation of a spring slide damper model. With mirror imagin boundary condition and three initial conditions, the equation is solved for a dynamic model that consists of six seismic belts and eight seismogenous sources in each belt with both explicit algorithm and implicit algorithm. The analysis of the model with water sources shows that the implicit algorithm is better to be used to calculate the model. Taking a constant proportion of the pore pressure of a broken element to that of its neighboring elements, the seismicity of the model is calculated with mirror boundary condition and no water source initial condition. The results shows that the frequency and magnitude of shocks are both higher than those in the model with no water pore pressure, which provides more complexity to earthquake prediction.

Application of Pore Evolution and Fracture Development Coupled Models in the Prediction of Reservoir "Sweet Spots" in Tight Sandstones

The Chang-63 reservoir in the Huaqing area has widely developed tight sandstone ＂thick sand layers, but not reservoirs characterized by rich in oil＂, and it is thus necessary to further study its oil and gas enrichment law. This study builds porosity and fracture development and evolution models in different deposition environments, through core observation, casting thin section, SEM, porosity and permeability analysis, burial history analysis, and ＂four-property-relationships＂ analysis.

Modeling and petrophysical properties of digital rock models with various pore structure types: An improved workflow

Pore structure is a crucial factor affecting the physical properties of porous materials,and understanding the mechanisms and laws of these effects is of great significance in the fields of geosciences and petroleum engineering.However,it remains a challenge to accurately understand and quantify the relationship between pore structures and effective properties.This paper improves a workflow to focus on investigating the effect of pore structure on physical properties.First,a hybrid modeling approach combining process-based and morphology-based methods is proposed to reconstruct 3D models with diverse pore structure types.Then,the characteristics and differences in pore structure in these models are compared.Finally,the varia-tion laws and pore-scale mechanisms of the influence of pore structure on physical properties(permeability and elasticity)are discussed based on the reconstructed models.The relationship models between pore structure parameters and perme-ability/elastic parameters in the grain packing model are established.The effect of pore structure evolution on permeability/elasticity and the microscopic mechanism in three types of morphology-based reconstruction models are explored.The influence degree of pore structure on elastic parameters(bulk modulus,shear modulus,P-wave velocity,and S-wave veloc-ity)is quantified,reaching 29.54%,51.40%,18.94%,and 23.18%,respectively.This work forms a workflow for exploring the relationship between pore structures and petrophysical properties at the microscopic scale,providing more ideas and references for understanding the complex physical properties in porous media.

3D pore-scale modeling of nanofluids-enhanced oil recovery

The numerical modeling of oil displacement by nanofluid based on three-dimensional micromodel of cores with different permeability was carried out by the volume of fluid(VOF)method with experimentally measured values of interfacial tension,contact angle and viscosity.Water-based suspensions of SiO_(2) nanoparticles with a concentration of 0–1%and different particle sizes were considered to study the effect of concentration and size of nanoparticles,displacement fluid flow rate,oil viscosity and core permeability on the efficiency of oil displacement by nanofluid.The oil recovery factor(ORF)increases with the increase of mass fraction of nanoparticles.An increase in nanoparticles’concentration to 0.5% allows an increase in ORF by about 19% compared to water flooding.The ORF increases with the decrease of nanoparticle size,and declines with the increase of displacing rate.It has been shown that the use of nanosuspensions for enhanced oil recovery is most effective for low-permeable reservoirs with highly viscous oil in injection modes with capillary number close to the immobilization threshold,and the magnitude of oil recovery enhancement decreases with the increase of displacement speed.The higher the oil viscosity,the lower the reservoir rock permeability,the higher the ORF improved by nanofluids will be.

Three-dimensional modeling and porosity calculation of coal rock pore structure

Coal rock is a type of dual-porosity medium,which is composed of matrix pores and fracture-cutting matrix.They play different roles in the seepage and storage capacity of coal rock.Therefore,constructing the micropore structure of coal rock is very important in the exploration and development of coalbed methane.In this study,we use a coal rock digital core and three-dimensional modeling to study the pore structure of coal rock.First,the micropore structure of coal rock is quantitatively analyzed using a two-dimensional thin-section image,and the quantitative information of the pore and fracture(cleat)structure in the coal rock is extracted.The mean value and standard deviation of the face porosity and pore radius are obtained using statistical analysis.The number of pores is determined using dichotomy and spherical random-packing methods based on compression.By combining with the results of the petrophysical analysis,the single-porosity structure model of the coal rock is obtained using a nonequal-diameter sphere to represent the pores of the coal rock.Then,an ellipsoid with an aspect ratio that is very much lesser than one is used to represent the fracture(cleat)in the coal rock,and a dual-pore structure model of the coal rock is obtained.On this basis,the relationship between the different pore aspect ratios and porosity is explored,and a fitting relationship is obtained.The results show that a nonlinear relationship exists between them.The relationship model can provide a basis for the prediction of coal rock pore structure and the pore structure parameters and provide a reference for understanding the internal structure of coalbed methane reservoirs.

The impact of heterogeneity and pore network characteristics on single and multi-phase fluid propagation in complex porous media:An X-ray computed tomography study

This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media,providing insights into the factors affecting fluid propagation in such systems.Specifically,high-resolution or micro X-ray computed tomography(CT)imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada,considered flow analogous to the Brazilian Pre-salt carbonate reservoirs.The petrophysical results comprised two distinct stromatolite depositional facies,the columnar and the fine-grained facies.By generating pore network model(PNM),the study quantified the relationship between key features of the porous system,including pore and throat radius,throat length,coordination number,shape factor,and pore volume.The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores.Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length.Additionally,a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields.The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation.Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others.The relation between saturation profiles,porosity profiles,and the number of fluid flow patterns for the samples was evident.Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection(SB)observed.

Spatio-temporal evolution of pore and fracture structures in coal induced by initial damage and creep behavior:A real-time NMR-based approach

Understanding the impact of mining disturbances and creep deformation on the macroscopic deformation and the microscopic pore and fracture structures(MPFS)of coal is paramount for ensuring the secure extraction of coal resources.This study conducts cyclic loading-unloading and creep experiments on coal using a low-field nuclear magnetic resonance(NMR)experimental apparatus which is equipped with mechanical loading units,enabling real-time monitoring the T2spectrum.The experiments indicated that cyclic loading-unloading stress paths initiate internal damage within coal samples.Under identical creep stress conditions,coal samples with more initial damages had more substantial instantaneous deformation and creep deformation during the creep process.After undergoing nearly 35 h of staged creep,the total strains for coal samples CC01,CC02,and CC03 reach 2.160%,2.261%,and 2.282%,respectively.In the creep stage,the peak area ratio of seepage pores and microfractures(SPM)gradually diminishes.A higher degree of initial damage leads to a more pronounced compaction trend in the SPM of coal samples.Considering the porosity evolution of SPM during the creep process,this study proposes a novel fractional derivative model for the porosity evolution of SPM.The efficacy of the proposed model in predicting porosity evolution of SPM is substantiated through experimental validation.Furthermore,an analysis of the impact mechanisms on key parameters in the model was carried out.

煤体注水渗流模型构建及微观主控影响规律

煤层注水技术是目前矿井除尘的主要技术手段之一,起到润湿煤体、源头减尘的作用.但随着开采深度的增加,煤体孔隙率相对较低,极大影响煤层注水的润湿效果.因此,为了提高煤层注水的效果,结合煤体固有属性、孔隙尺度等影响因素,首先,引入连通孔隙率,建立了包含孔喉、等效孔径、有效孔隙率、毛细管束、迂曲度、流动路径在内的渗流模型;其次,采用高精度射线显微镜(μ-CT)对内蒙古煤矿、同富新煤矿、梅花井煤矿、大黄山煤矿以及磁窖沟煤矿5个煤矿的不同变质程度煤进行扫描,三维重建可视化煤体微观有效孔隙结构,运用分形理论,提取煤体有效连通孔隙结构参数进行计算;再次,通过实验对5个煤矿不同变质程度的煤进行渗透率实测;最后,引入“敏感度”来表征每种影响因素对渗流量的影响程度,运用Morris筛选法,将数值分析法与渗流模型相耦合,定量筛选了煤体坚固性系数、迂曲度分形维数、有效孔隙率、体积分形维数、孔喉半径等主控因素,并分析了各主控因素对注水能力的影响规律.本研究建立了一个综合煤体坚固性系数、迂曲度分形维数、有效孔隙率、体积分形维数和孔喉半径的渗流模型.分析表明,影响注水能力的主控因素依次为煤体坚固性系数、迂曲度分形维数、有效孔隙率、体积分形维数和孔喉半径.注水能力与煤体坚固性系数呈正弦函数关系,随着有效孔隙率的增加,迂曲度分形维数和体积分形维数的减小,注水能力增强.研究结果可为进一步完善煤层注水渗流理论、增强煤层注水润湿效果,防治矿井粉尘灾害提供理论依据.

Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data

The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.

Pore-scale study of the pressure-sensitive effect of sandstone and its influence on multiphase flows

The pressure-sensitive effect on the pore structure of sandstone was investigated using X-ray computed micro-tomography and QEMSCAN quantitative mineral analysis. In a physical simulation study, we extracted the pore network model from digital cores at different confining pressures and evaluated the effect of pressure sensitivity on the multiphase displacement process. In both the pore network model and QEMSCAN scanning, the pore structure was observed to be damaged under a high confining pressure. Due to their different scales, the pores and throats exhibited inhomogeneous changes; further, the throats exhibited a significant variation compared to that exhibited by the pores. Meanwhile, the heterogeneity of the pore structure under the two aforementioned activities was aggravated by the elastic-plastic deformation of the pore structure.The pressure-sensitive effect increased the proportion of mineral particles, such as quartz(the main component of the core skeleton), and reduced the proportion of clay minerals. The clay minerals were originally attached to the pore walls or interspersed in the pores; however, as the pressure increased, the clay minerals accumulated in the pores resulting in blockage of the pores. While simulating the multiphase displacement process, increasing the confining pressure was observed to severely restrict the flowability of oil and water. This study promises to improve the efficiency of reservoir development in terms of oil and gas exploitation.