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.

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.

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.

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.

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.

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.

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.

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.

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 attenuation-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.

Study on water saturation computation models in complex pore volcanic reservoir

Determination of water saturation is important for reservoir evaluation.When complex pore structures such as fracture and cavity are present in reservoir,Archie equation is no longer suitable.According to different models of pore structure division,the authors studied water saturation computation models.The results show that dual porosity system is divided into four models.The first model is based on dual laterolog,the second is Dual Porosity Ⅰ,the third is Dual Porosity Ⅱ,and the last one is based on the conductive pore.Besides,the triple porosity system is triple porosity model.Compute water saturation was using all the above five models in volcanic reservoir in Songnan gas field.The triple porosity system is the most suitable model for water saturation computation in complex pore structure volcanic reservoir.

A Potential Model for Cylindrical Pores

An analytical potential for cylindrical pores has been derived by introducing a variational method into the integration for the calculation of the interaction energy between the wall molecules and a test molecule, all of which are represented by Lennard-Jones potential. The model proposed gives good fit to the results from the cylindrical surface model and the pseudoatom model. To test the potential proposed rigorously, we have carried out grand canonical ensemble Monte Carlo(GCMC) simulation of nitrogen in the MCM-41 pore at 77 K, and compared the simulated adsorption isotherm with the experimental data reported in the literature. The simulated isotherm from our model is in almost qualitative agreement with experiment. Consequently, the model proposed provides an explicit and accurate description of cylindrical pores represented by the Lennard-Jones potential. Moreover, the model can be easily applied to a variety of cylindrical pores, ranging from cylindrical surface to finite thickness walls, in both theoretical studies and computer simulations.

Flow-Induced Clogging in Microfiltration Membranes: Numerical Modeling and Parametric Study

Microfiltration membrane technology has been widely used in various industries for solid-liquid separation. However, pore clogging remains a persistent challenge. This study employs (CFD) and discrete element method (DEM) models to enhance our understanding of microfiltration membrane clogging. The models were validated by comparing them to experimental data, demonstrating reasonable consistency. Subsequently, a parametric study was conducted on a cross-flow model, exploring the influence of key parameters on clogging. Findings show that clogging is a complex phenomenon affected by various factors. The mean inlet velocity and transmembrane flux were found to directly impact clogging, while the confinement ratio and cosine of the membrane pore entrance angle had an inverse relationship with it. Two clog types were identified: internal (inside the pore) and external (arching at the pore entrance), with the confinement ratio determining the type. This study introduced a dimensionless number as a quantitative clogging indicator based on transmembrane flux, Reynolds number, filtration time, entrance angle cosine, and confinement ratio. While this hypothesis held true in simulations, future studies should explore variations in clogging indicators, and improved modeling of clogging characteristics. Calibration between numerical and physical times and consideration of particle volume fraction will enhance understanding.

喷射混杂纤维混凝土抗冻性及损伤模型

目的为提高高寒地区喷射混凝土耐久性,改善冻融环境下普通喷射混凝土易开裂、抗冻性能差等问题。方法在喷射混凝土中掺入混合纤维,通过冻融循环试验、超声波检测、压拉性能试验以及气孔结构测试等方法,研究不同冻融循环次数下喷射混杂纤维混凝土的相对纵波波速、相对压拉强度以及试件内部气孔结构变化规律。通过压拉性能损伤量对试件冻融损伤进行多项评价,分析钢纤维和聚丙烯纤维贡献率与喷射混凝土抗压强度之间的关系,并根据钢纤维和聚丙烯纤维贡献率公式建立喷射混凝土冻融损伤模型。结果与单掺钢纤维和聚丙烯纤维试件相比,混合掺入1%钢纤维、0.1%聚丙烯纤维喷射混凝土试件的抗压强度损失分别降低了7.5%、33.3%,劈裂抗拉强度损失分别降低了15.6%、35.0%。在弦长尺寸0.1mm<d<1mm处,混合掺入0.1%聚丙烯和1%钢纤维喷射混凝土气泡弦长频率比单掺1%钢纤维喷射混凝土和单掺0.1%聚丙烯喷射混凝土分别降低了24.9%和27.3%。钢纤维和聚丙烯纤维对抗压强度的贡献率呈现先增长后下降趋势。基于冻融损伤与钢纤维和聚丙烯纤维贡献率建立冻融损伤模型。结论喷射混杂纤维混凝土力学性能损伤量低,不易开裂,抗冻性能好,可为高寒地区喷射混凝土结构提供理论参考。

有机物料还田对草甸土孔隙结构及玉米产量的影响

为了研究有机物料还田对草甸土孔隙结构及玉米产量的影响,优化草甸土耕作层结构、提高作物产量,2019年以吉林省公主岭市的草甸土为试验地,在玉米播种前设置了秸秆浅混还田(CT,0~15cm)、秸秆深混还田(STS,0~35cm)、秸秆和有机肥深混还田(STSM,0~35 cm)、无秸秆还田常规耕作(CK)4个处理。对玉米收获后的土壤进行取样分析,测定0~35 cm土层土壤物理性质和孔隙结构,并采用结构方程模式、Mantel test和随机森林方法分析土壤孔隙结构调控玉米产量的途径。结果表明,经CT、STS和STSM处理后的0~15 cm土层土壤容重与CK处理相比显著下降了5.2%~7.8%(P<0.05),而田间持水量和饱和导水率均呈现上升趋势,分别显著增加了7.8%~16.6%和77.5%~325%(P<0.05);STS和STSM处理进一步显著改变了>15~35 cm土层上述3个土壤物理性质。CT扫描结果显示,有机物料还田显著改善了相应土层土壤结构。与CK处理相比,CT、STS和STSM处理显著增加了0~15 cm土层>1000µm孔隙数量和孔隙度;与CT处理相比,STS和STSM处理>15~35 cm土层>1000µm孔隙数量和孔隙度分别显著增加了1.2倍~1.3倍和47.5%~58.9%(P<0.05)。有机物料还田增加了土壤孔隙的复杂性和连通性。与CK处理相比,CT、STS和STSM处理显著增加了0~15 cm土层的各向异性和分形维数,降低了欧拉数(P<0.05);STS和STSM处理显著改善了15~35 cm土层土壤孔隙结构。不同处理间玉米产量表现为STSM>STS>CT>CK。结构方程模型结果显示,0~15 cm土层土壤孔隙结构可以直接影响玉米产量或者通过影响容重和饱和导水率间接影响玉米产量,而15~35 cm土层土壤孔隙结构只能通过影响田间持水量间接影响玉米产量。0~35 cm土层土壤物理性质和孔隙结构能够解释玉米产量的81.9%,15~35 cm土层对玉米产量的贡献大于0~15 cm土层。有机物料深混还田通过改变0~35 cm土层草甸土物理性质和孔隙分布,增加孔隙结构的复杂性和连通性,优化耕层结构,具备提高玉米产量的潜力,其中秸秆和有机物配合施用的效果优于单独秸秆还田。如果草甸土分布区有机肥源充足,建议利用秸秆和有机肥料进行深混还田可建立良好的土壤肥力,可以有效增加玉米产量。

分形界面吸附行为初探

煤层气吸附解吸机理研究是揭示煤层气成藏机理及高效开发煤层气的基础。已有研究表明,煤储层孔隙结构非常复杂且具有分形特征,煤层气在孔-固界面的吸附行为明显受到煤孔隙结构特征的影响。对比分析几种常用气-固界面上的吸附模型,总结这些模型的特点和适用条件,指出当前吸附模型在分形界面吸附行为的描述和应用上均未摆脱吸附选择性的平稳假设,尚未考虑吸附厚度的尺度不变特征。而分形拓扑理论可以有效标定分形对象的尺度不变属性,为分形界面的等效表征提供了理论支撑。因此,结合上述模型对气-固界面吸附行为的描述,借助分形拓扑理论提出煤储层孔-固界面上分形吸附行为的相关假设及其控制机理,构建基于吸附拓扑的单层吸附模型。在此基础上,通过设置不同的吸附拓扑参数组合获取其等温吸附曲线,分析得出,随着吸附压力的升高,吸附覆盖率表现出指数、线性和对数3种不同的增长趋势,而吸附热表现为对数减小趋势。结果显示,不同的吸附拓扑参数组合会得到不同类型的等温吸附曲线,在一定程度上弥补了Langmuir方程只能描述单一类型等温吸附线的不足。为了验证吸附模型的适用性,结合沁水盆地武乡区块富有机质泥页岩的液氮吸附实验数据,对比了实际等温吸附曲线与模拟吸附曲线的差异。结果表明,通过调整各吸附拓扑参数之间的组合关系,可以使等温吸附模拟曲线与实际吸附曲线的趋势始终保持一致。最后,探讨了吸附解吸机理的研究方向,类比电子层提出了吸附层的概念,指出发展分形动力学描述模型是解释煤层气吸附解吸规律的关键。