Percolation Effects of Grain Contacts in Partially Saturated Sandstones: Deviations from Archie’s Law

We study the resistivity index of Fontainebleau and Bentheimer sandstones at ambient conditions down to low water saturations both experimentally and numerically. Numerical simulations are in good agreement with experimental measurements of capillary drainage resistivity index by the porous plate method down to water saturations as low as S _w = 10 %. Fontainebleau sandstone exhibits a percolating network of grain contacts, while the higher porosity Bentheimer sandstone does not. We show that this difference in the topological connection of conductive films at low water saturations is responsible for the non-Archie behaviour of Fontainebleau sandstone. Furthermore, it is necessary to attribute a grain contact conductivity to the grain contacts in Fontainebleau sandstone to reconcile experiment and numerical simulation. Conductive films organised as pendular rings around grain contacts are not able to explain this result.     

土壤水分布的孔隙尺度格子玻尔兹曼模拟研究

土壤水控制着陆地生态系统几乎所有的物理和生物化学过程,准确描述土壤中水的分布与运动状态对人类发展和生态环境保护均有重要意义.土壤水分布不仅与孔隙结构有关,而且受土壤固相表面润湿性的影响.一般对土壤水分布都是从宏观尺度进行描述,但土壤中的物理及生化过程都发生在孔隙中,从孔隙尺度分析土壤水的分布规律,有助于更准确地理解土壤...     

储层含水条件下致密砂岩/页岩无机质纳米孔隙气相渗透率模型

页岩及致密砂岩储层富含纳米级孔隙,且储层条件下页岩孔隙(尤其无机质孔隙)及致密砂岩孔隙普遍含水,因此含水条件下纳米孔隙气体的流动能力的评价对这两类气藏的产能分析及生产预测具有重要意义.本文首先基于纳米孔隙内液态水及汽态水热力学平衡理论,量化了储层孔隙含水饱和度分布特征;进一步在纳米孔隙单相气体传质理论的基础上,考虑了孔隙含水饱和度对气体流动的影响;最终建立了含水饱和度与气相渗透率的关系曲线. 基于本文岩心孔隙分布特征,计算结果表明:储层含水饱和度对气体流动能力的影响不容忽视,在储层含水饱和度20%的情况下,气相流动能力与干燥情况相比将降低约10%;在含水饱和度40% 的情况下,气相流动能力将降低约20%.      

An Analysis of Three-Phase Pore Occupancies and Relative Permeabilities in Porous Media with Variable Wettability

In three-phase flow, the macroscopic constitutive relations of capillary pressure and relative permeability as functions of saturation depend in a complex manner on the underlying pore occupancies. These three-phase pore occupancies depend in turn on the interfacial tensions, the pore sizes and the degree of wettability of the pores, as characterised by the cosines of the oil–water contact angles. In this work, a quasi-probabilistic approach is developed to determine three-phase pore occupancies in media where the degree of wettability varies from pore to pore. Given a set of fluid and rock properties, a simple but novel graphical representation is given of the sizes and oil–water contact angles underlying three-phase occupancies for every allowed combination of capillary pressures. The actual phase occupancies are then computed using the contact angle probability density function. Since a completely accessible porous medium is studied, saturations, capillary pressures, and relative permeabilities are uniquely related to the pore occupancies. In empirical models of three-phase relative permeability it is of central importance whether a phase relative permeability depends only on its own saturation and how this relates to the corresponding two-phase relative permeability (if at all). The new graphical representation of pore sizes and wettabilities clearly distinguishes all three-phase pore occupancies with respect to these saturation-dependencies. Different types of saturation-dependencies may occur, which are shown to appear in ternary saturation diagrams of iso-relative permeability curves as well, thus guiding empirical approaches. However, for many saturation combinations three-phase and two-phase relative permeabilities can not be linked. In view of the latter, the present model has been used to demonstrate an approach for three-phase flow modelling on the basis of the underlying pore-scale processes, in which three-phase relative permeabilities are computed only along the actual flow paths. This process-based approach is used to predict an efficient strategy for oil recovery by simultaneous water-alternating-gas (SWAG) injection.     

Numerical Calculation of Effective Diffusion in Unsaturated Porous Media by the TRT Lattice Boltzmann Method

Numerical models that solve transport of pollutants at the macroscopic scale in unsaturated porous media need the effective diffusion dependence on saturation as an input. We conducted numerical computations at the pore scale in order to obtain the effective diffusion curve as a function of saturation for an academic sphere packing porous medium and for a real porous medium where pore structure knowledge was obtained through X-ray tomography. The computations were performed using a combination of lattice Boltzmann models based on two relaxation time (TRT) scheme. The first stage of the calculations consisted in recovering the water spatial distribution into the pore structure for several fixed saturations using a phase separation TRT lattice Boltzmann model. Then, we performed diffusion computation of a non-reactive solute in the connected water structure using a diffusion TRT lattice Boltzmann model. Finally, the effective diffusion for each selected saturation value was estimated through inversion of a macroscopic classical analytical solution.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

基于核磁共振孔隙划分的致密油藏自发渗吸原油可动性研究

自发渗吸驱油是致密油藏提高采收率的有效手段,但不同的孔隙划分方法会导致原油可动性精细定量表征存在差异性.基于此,以鄂尔多斯盆地延长组致密油藏为研究对象,开展了四种典型致密岩心的自发渗吸驱油实验,利用基于核磁共振分形理论的流体分布孔隙精细划分方法,区分了致密砂岩岩心孔隙类型,明确了不同类型岩心孔隙结构对原油可动性和自发渗吸驱油速率的控制特征.研究结果表明不同类型岩心自发渗吸模拟油动用程度介于22.07%～33.26%,核磁共振T2谱双峰型岩心自发渗吸模拟油动用程度高于单峰型岩心;不同类型致密砂岩岩心中流体分布孔隙可初步划分出P1和P2两种类型, P1类型孔隙则可进一步划分出P1-1, P1-2和P1-3三种亚类型孔隙;致密砂岩岩心中P1和P2类孔隙中模拟油均有不同程度的动用, P1类孔隙作为致密岩心中主要孔隙,尤其是P1类孔隙中P1-2和P1-3类孔隙的数量决定了自发渗吸模拟油动用程度;P1-1, P1-2和P1-3类孔隙结构差异性对自发渗吸模拟油动用程度起决定性作用,较小尺寸孔径孔隙较大的孔隙结构差异性不仅提升了自发渗吸模拟油动用程度,而且提升了自发渗吸驱油速率;流体可动性指数较高的P...     

A Parametric Model for Predicting Relative Permeability-Saturation-Capillary Pressure Relationships of Oil–Water Systems in Porous Media with Mixed Wettability

A parametric two-phase, oil–water relative permeability/capillary pressure model for petroleum engineering and environmental applications is developed for porous media in which the smaller pores are strongly water-wet and the larger pores tend to be intermediate- or oil-wet. A saturation index, which can vary from 0 to 1, is used to distinguish those pores that are strongly water-wet from those that have intermediate- or oil-wet characteristics. The capillary pressure submodel is capable of describing main-drainage and hysteretic saturation-path saturations for positive and negative oil–water capillary pressures. At high oil–water capillary pressures, an asymptote is approached as the water saturation approaches the residual water saturation. At low oil–water capillary pressures (i.e. negative), another asymptote is approached as the oil saturation approaches the residual oil saturation. Hysteresis in capillary pressure relations, including water entrapment, is modeled. Relative permeabilities are predicted using parameters that describe main-drainage capillary pressure relations and accounting for how water and oil are distributed throughout the pore spaces of a porous medium with mixed wettability. The capillary pressure submodel is tested against published experimental data, and an example of how to use the relative permeability/capillary pressure model for a hypothetical saturation-path scenario involving several imbibition and drainage paths is given. Features of the model are also explained. Results suggest that the proposed model is capable of predicting relative permeability/capillary pressure characteristics of porous media mixed wettability.     

Two-Phase Pore-Network Modelling: Existence of Oil Layers During Water Invasion

Pore-network modelling is commonly used to predict capillary pressure and relative permeability functions for multi-phase flow simulations. These functions strongly depend on the presence of fluid films and layers in pore corners. Recently, van Dijke and Sorbie (J. Coll. Int. Sci. 293:455–463, 2006) obtained the new thermodynamically derived criterion for oil layers existence in the pore corners with non-uniform wettability caused by ageing. This criterion is consistent with the thermodynamically derived capillary entry pressures for other water invasion displacements and it is more restrictive than the previously used geometrical layer collapse criterion. The thermodynamic criterion has been included in a newly developed two-phase flow pore network model, as well as two versions of the geometrical criterion. The network model takes as input networks extracted from pore space reconstruction methods or CT images. Furthermore, a new n-cornered star shape characterization technique has been implemented, based on shape factor and dimensionless hydraulic radius as input parameters. For two unstructured networks, derived from a Berea sandstone sample, oil residuals have been estimated for different wettability scenarios, by varying the contact angles in oil-filled pores after ageing from weakly to strongly oil-wet. Simulation of primary drainage, ageing and water invasion show that the thermodynamical oil layer existence criterion gives more realistic oil residual saturations compared to the geometrical criteria. Additionally, a sensitivity analysis has been carried out of oil residuals with respect to end-point capillary pressures. For strongly oil-wet cases residuals increase strongly with increasing end-point capillary pressures, contrary to intermediate oil-wet cases.     

A Novel Analysis of the Electrical Transport Mechanisms in Porous Media

Effects of water saturation and wettability on the dielectric constant are investigated experimentally using four-electrode impedance measurements, and theoretically using models that account for the electrical double layer polarization. Complex impedance measurements, performed on Berea sandstone and on Ottawa-sand packs in the frequency range 10Hz to 1MHz, appear to indicate that the dielectric constant varies linearly with water saturations above 50%. The rate of change of dielectric constant with saturation is found to be a function of frequency. As the frequency increases this rate of change decreases. The decrease in the slope of the dielectric constant-water saturation profile with frequency is not intuitively obvious, but has been proven theoretically in this work. The dielectric constant of water-wet samples is found higher than that of the oil-wet samples at all water saturations. The difference is more pronounced at high water saturations near unity. The wettability changes have been simulated using a generalized Maxwell–Wagner model by varying the amount of ionic surface charge of rocks. In general oil-wetting agents react with the formation matrix by connecting their positively charged tails to the negatively charged silica surfaces, lowering the surface charge density. Simulations show that the effect of wettability changes on the dielectric constant is very significant. These conclusions are consistent with the experimental results presented in this study.     

Microscale Visual Study of End Effects at Permeability Discontinuities

The physical effect of multiphase fluid distribution and flow at permeability boundaries has not been fully investigated, particularly at the pore scale (1–100 μm), although such behaviour can significantly affect the overall scaled-up reservoir trapping capacity and production performance. In this article, microscale physical models have been used to qualitatively study the pore scale flow events at permeability boundaries, both high to low and vice versa, to gain a better understanding of the role of these boundaries and water saturation on multiphase displacement behaviour at the pore scale. We have used etched glass models of stripes of large and small (a factor of two) pores with circular matrix. Capillary pressure, which is the controlling parameter is itself dependant on pore size and its spatial distribution, the magnitude of the interfacial tensions and the wettability between the fluids and the solid surface of the models. Sometimes, the only way the non-wetting fluid can penetrate the boundary is through a fortuitous leakage, whereby the presence of an initial saturation reduces the controlling capillary pressure. Examples are demonstrated including mechanisms of end-effects and how capillary boundary resistance (due to capillary forces) can be broken down and fluid movement across the boundary can develop. These micromodel experiments show vividly that connate water can assist in these processes, particularly oil trapping and leakage of water across a permeability boundary.     

Volume Conservation of the Intermediate Phase in Three-Phase Pore-Network Models

Quasi-static rule-based network models used to calculate capillary dominated multi-phase transport properties in porous media employ equilibrium fluid saturation distributions which assume that pores are fully filled with a single bulk fluid with other fluids present only as wetting and/or spreading films. We show that for drainage dominated three-phase displacements in which a non-wetting fluid (gas) displaces a trapped intermediate fluid (residual oil) in the presence of a mobile wetting fluid (water) this assumption distorts the dynamics of three-phase displacements and results in significant volume errors for the intermediate fluid and erroneous calculations of intermediate fluid residual saturations, relative permeabilities and recoveries. The volume errors are associated with the double drainage mechanism which is responsible for the mobilization of waterflood residual oil. A simple modification of the double drainage mechanism is proposed which allows the presence of a relatively small number of partially filled pores and removes the oil volume errors.     

Poromechanics of freezing materials

When subjected to a uniform cooling below the freezing point a water-infiltrated porous material undergoes a cryo-deformation resulting from various combined actions: (i) the difference of density between the liquid water and the ice crystal, which results in the initial build-up of an in-pore pressure at the onset of crystallization; (ii) the interfacial effects arising between the different constituents, which eventually govern the crystallization process in connection with the pore access radius distribution; (iii) the drainage of the liquid water expelled from the freezing sites towards the air voids; (iv) the cryo-suction process, which drives liquid water towards the already frozen pores as the temperature further decreases; (v) the thermomechanical coupling between the solid matrix, the liquid water and the ice crystal. We work out a comprehensive theory able to encompass this whole set of actions. A macroscopic approach first provides the constitutive equations of freezing poroelastic materials, including the interfacial energy effects. This approach reveals the existence of a thermodynamic state function—namely the liquid saturation degree as a function of the temperature only. The macroscopic ice-dependent poroelastic properties are then upscaled from the knowledge of the elastic properties of the solid matrix, of the pore access radius distribution, and of the capillary curve. The theory is finally illustrated by analysing quantitatively the effects of the cooling rate and of the pore radius distribution upon the cryo-deformation of water-infiltrated porous materials. The theory succeeds in accounting for the experimentally observed shrinkage of embedded air voids, while predicting the partial melting of the ice already formed when the cooling suddenly stops.     

厚壁胞体多孔结构接触强度研究

选用H59黄铜为材料,制备了含圆形单孔、双孔、三孔以及四孔的圆柱体试样,采用型号为YE-600的液压式压力试验机对试样进行压缩试验,探讨了布孔方式对厚壁胞体多孔结构接触强度的影响;并用有限元法探讨了多孔结构的破坏机理.结果表明:双孔材料水平布孔方式优于垂直布孔方式;三孔材料斜正三角形布孔方式优于正三角形布孔方式;四孔材料正方形布孔方式优于菱形布孔方式;微孔分布半径的增大和微孔个数的增加均有助于提高厚壁胞体多孔结构的接触强度;裂纹萌生于微孔边缘且离初始接触点最近的地方,它由最大拉伸主应力引起并沿着微孔拉应力集中区进行扩展.     

Numerical Simulation of Diagenetic Alteration and Its Effect on Residual Gas in Tight Gas Sandstones

In this study, we numerically cemented a segmented X-ray microtomography image of a sandstone to understand changes to pore space connectivity, capillary control on gas, and water distributions, and ultimately production behavior in tight gas sandstone reservoirs. Level set method-based progressive quasi-static algorithm (a state-of-the-art direct simulation of capillarity-dominated fluid displacement) was used to find the gas/water configurations during drainage and imbibition cycles. Further, we account for gas?Cwater interfacial tension changes using 1D burial history model based on available geologic data. We have found the displacement simulation method robust, and that diagenetic changes impart a significantly larger effect on gas trapping compared with interfacial tension changes.     

Radon Emanation in Partially Saturated Porous Media

Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.     

Connectivity of Pore Space as a Control on Two-Phase Flow Properties of Tight-Gas Sandstones

We predict capillary-pressure (drainage) curves in tight-gas sandstones which have little matrix or microporosity using a quantitative grain-scale model. The model accounts for the geometric results of some depositional and diagenetic processes important for porosity and permeability reduction in tight-gas sandstones, such as deformation of ductile grains during burial and quartz cementation. The model represents the original sediment as a dense, disordered packing of spheres. We simulated the evolution of this model sediment into a low-porosity sandstone by applying different amounts of ductile grains and quartz precipitation. A substantial fraction of original pore throats in the sediment is closed by the simulated diagenetic alteration. Because the percolation threshold corresponds to closure of half of the pore throats, the pore space in this type of tight-gas sandstone is poorly connected and is often close to being completely disconnected. The drainage curve for different model rocks was computed using invasion percolation in a network taken directly from the grain-scale geometry and topology of the model. Some general trends follow classical expectations and were confirmed by experimental measurements: increasing the amount of cement shifts the drainage curve to larger pressures. This is related to reduction of the connectivity of pore space resulting from closure of throats. Existence of ductile grains in the ductile grain model also reduces the connectivity of pore space but it treats the throats distribution differently causing the drainage curves to be shifted to larger irreducible water saturation when cement is added to the model. The range of porosities in which these connectivity effects are important corresponds to the range of porosities common for tight gas sandstones. Consequently these rocks can exhibit small effective permeability to gas even at large gas saturations. This problem occurs at larger porosities in rocks with significant content of ductile grains because ductile deformation blocks a significant fraction of pore throats even before cementation begins. Predicted drainage curves agree with measurements on two samples with little microporosity, one dominated by rigid grains, the other containing a significant fraction of ductile grains. We conclude that connectivity of the matrix pore space is an important factor for an understanding of flow properties of tight-gas sandstones.     

In-Situ Capillary Trapping of CO<Subscript>2</Subscript> by Co-Injection

Co-injection of water with CO₂ is an effective scheme to control initial gas saturation in porous media. A fractional flow rate of water of approximately 5–10% is sufficient to reduce initial gas saturations. After water injection following the co-injection, most of the gas injected in the porous media is trapped by capillarity with a low fractional volume of migrating gas. In this study, we first derive an analytical model to predict the gas saturation levels for co-injection with water. The initial gas saturation is controlled by the fractional flow ratio in the co-injection process. Next, we experimentally investigate the effect of initial gas saturation on residual gas saturation at capillary trapping by co-injecting gas and water followed by pure water injection, using a water and nitrogen system at room temperature. Depending on relative permeability, initial gas saturation is reduced by co-injection of water. If the initial saturation in the Berea sandstone core is controlled at 20–40%, most of the gas is trapped by capillarity, and less than 20% of the gas with respect to the injected gas volume is migrated by water injection. In the packed bed of Toyoura standard sand, the initial gas saturation is approximately 20% for a wide range of gas with a fractional flow rate from 0.50 to 0.95. The residual gas saturation for these conditions is approximately 15%. Less than approximately 25% of the gas migrates by water injection. The amount of water required for co-injection systems is estimated on the basis of the analytical model and experimental results.     

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.     

Effects of Precursor Wetting Films in Immiscible Displacement Through Porous Media

A computer-aided simulator of immiscible displacement in strongly water-wet consolidated porous media that takes into account the effects of the wetting films is developed. The porous medium is modeled as a three-dimensional network of randomly sized unit cells of the constricted-tube type. Precursor wetting films are assumed to advance through the microroughness of the pore walls. Two types of pore wall microroughness are considered. In the first type of microroughness, the film advances quickly, driven by capillary pressure. In the second type, the meniscus moves relatively slowly, driven by local bulk pressure differences. In the latter case, the wetting film often forms a collar that squeezes the thread of oil causing oil disconnection. Each pore is assumed to have either one of the aforementioned microroughness types, or both. The type of microroughness in each pore is assigned randomly. The simulator is used to predict the residual oil saturation as a function of the pertinent parameters (capillary number, viscosity ratio, fraction of pores with each type of wall microroughness). These results are compared with those obtained in the absence of wetting films. It is found that wetting films cause substantial increase of the residual oil saturation. Furthermore, the action of the wetting films causes an increase of the mean volume of the residual oil ganglia.