A semi-analytical model for computation of capillary entry pressures and fluid configurations in uniformly-wet pore spaces from 2D rock images

A novel semi-analytical model for computation of capillary entry pressures and associated fluid configurations in arbitrary, potentially non-convex, 2D pore space geometries at uniform wettability is developed. The model computes all possible centre positions of circular arcs, and physically sound criteria are implemented to determine the set of these arcs that correspond to geometrically allowed interfaces. Interfaces and pore boundary segments are connected to form closed boundaries of identified geometrical regions. These regions are classified as either oil regions, located in the wider parts of the pore space, or as water regions located in pore space constrictions. All possible region combinations are identified and evaluated for each radius value in an iterative procedure to determine the favourable entry radius and corresponding configuration based on minimisation of free energy. The model has been validated by comparison with known analytical solutions in idealised pore geometries. In cases where different analytical solutions are geometrically possible, the model generates several oil and water regions, and the valid solution is determined by the region combination that corresponds to the most favourable entry pressure, consistent with the analytical solution. Entry pressure radii and configurations are computed in strongly non-convex pore spaces extracted from an image of Bentheimer sandstone, which demonstrates that the model captures successfully well-known characteristics of capillary behaviour at different wetting conditions. The computations also demonstrate the importance of selecting the fluid configuration of minimum change in free energy. In some cases, a merged region formed by a combination of oil and water regions corresponds to the favourable entry configuration of oil, whereas in other cases, an individual oil region may correspond to the favourable oil entry configuration. It is also demonstrated that oil entry configurations may constitute merged regions for weakly water-wet conditions and individual oil regions for strongly water-wet conditions in the same pore space. The computations show that the ratio of pore area to perimeter multiplied by the cosine of the contact angle under-predicts the entry pressure radii in Bentheimer sandstone pore spaces. An alternative formula is proposed for prediction of entry radii for nonzero contact angles based on the entry radii obtained for zero contact angles.     

Characteristics of petroleum accumulation in syncline of the Songliao basin and discussion on its accumulation mechanism

The relation between oil and water in reservoirs with low and ultra-low permeability is very complicated. Gravitational separation of oil and water is not obvious. Normal reservoirs are located in depression and structural high spot, oil and water transitions are located in their middle. Stagnation is the key fact of oil-forming reservoir in the axis of a syncline based on the research of oil, gas and water migration manner, dynamics and non-Darcy flow in the Songliao basin. In low and ultra-low permeable reservoir, gas and water migrate easily through pore throats because their molecules are generally smaller than the pore throats; but the minimum diameter of oil droplets is larger than pore throats and they must be deformed to go through. Thus, gas and water migrate in advance of oil, and oil droplets remain behind. Pressure differential and the buoyancy force in a syncline reservoir are a main fluid driving force; and capillary force is the main resistance to flow. When the dynamics force is less than resistance, oil is immobile. When the buoyancy force is less than the capillary force, a gravitational separation of oil and water does not occur. The reservoir in the mature source rock of a syncline area with the low and ul- tra-low permeability belongs to an unconventional petroleum reservoir.     

部分饱和孔隙岩石中声波传播数值研究

利用基于Biot理论的孔隙弹性介质的高阶交错网格有限差分算法,模拟了具有随机分布特征的多种流体饱和岩石中声波在中心频率分别为25,50,75,100kHz时的声场特点. 对于一个由两种成分（气和水）饱和的岩石模型, 假设含不同流体的孔隙介质随机分布在不同的宏观区域,该区域尺度远小于计算的声波波长;组成模型的两种随机分布介质具有相同的固体骨架参数、渗透率和孔隙度,但分别被具有不同压缩性、密度和黏滞系数特性的水和气饱和. 计算和统计分析结果表明,在两种孔隙成分随机分布的部分饱和条件下纵波速度比较复杂,除骨架参数外,其变化主要依赖于中心频率、各种孔隙成分饱和度及饱和介质的速度. 比较该随机分布模型、Gassmann理论模型和White的“气包”模型,发现三种模型得到的纵波速度和衰减规律有较好的定性对应关系. 其次,按照这种随机计算模型的处理方法,本文还首次计算了一个三种流体成分充填饱和的例子,即岩石模型中的孔隙被水、油和气部分饱和,计算时保持模型含水饱和度不变而只改变含油和含气饱和度. 在这种计算条件下,纵波速度随中心频率呈增大的趋势但有起伏变化. 声场快照显示了各种转换波在多种孔隙成分充填（两种和三种孔隙成分）岩石中的声场特征,复杂的水-油-气界面的非均匀分布对声场有重要影响,纵波能量主要转换形成了较为复杂的多种慢纵波和横波.     

地层模量分解及在流体识别中的应用

储层流体识别是确定油气水分布,合理布设井位,提高钻井成功率的关键之一.本文基于流体饱和孔隙介质岩石物理模型,对地震反演的地层体积模量进行分解,获得孔隙流体体积模量,并依据油、气、水(尤其是气-油、气-水)模量的显著差异进行识别.文中简要分析了Gassmann模型和Kuster-Toksz模型的特征,详细讨论了孔隙形态和饱和度对弹性模量的影响,提出了联合Kuster-Toksz方程和Gassmann方程的体积模量分解方法.该方法通过Kuster-Toksz方程从测井数据中反演地层骨架固体和干骨架的弹性模量,再利用Gassmann方程对地层体积模量进行分解,既考虑了孔隙形态,又充分利用了Gassmann方程的易用性.理论模型结果表明方法是可行的.方法应用于西部地区某气田,流体识别与地层含气性预测结果与钻井基本一致,进一步证实了方法的有效性.     

含不同孔隙流体的砂岩地震波速度随压力变化的实验研究

岩石的地震波性质是区域构造研究和浅部地震勘探应用的基础.延长油田是我国重要的油气生产基地之一,但目前仍缺乏地震波性质方面的基础资料.作者利用Autolab2000多功能岩石物性自动测试设备,在0~180MPa及饱含不同孔隙流体(干燥、饱水及饱油)条件下,研究了三种来自延长油田砂岩岩芯的纵波、横波速度.结果表明:三种砂岩的V_p、V_s1和V_s2均随压力增加(或降低)而基本呈对数曲线增大(或减小);干燥、饱水和饱油三种波速间的关系因砂岩类型不同而不同,这主要取决于岩石的有效弹性模量、孔隙流体性质以及岩石的内部结构等;含同种孔隙流体的不同类型砂岩,其V_p、V_s1和V_s2随压力变化的规律主要受岩石孔隙度和粒度的影响;而含不同孔隙流体的同种砂岩,其V_p、V_s1和V_s2随压力变化的规律则主要受控于岩石的有效弹性模量和流体密度.另外,含水或含油饱和度的变化对V_s1和V_s2基本没有影响.实验结果可以为该地区地震资料的解释及与声波测井之间的对比提供重要的基础数据和参考依据.     

Poisson's ratio at high pore pressure

Laboratory investigations suggest that a precise relationship exists between Poisson's ratio, pore pressure and fluid type. Values of Poisson's ratio for dry samples are significantly smaller than those for fluid-saturated samples. The values are anomalously high for high pore pressure, with the possibility of differentiating between gas-saturated, brine-saturated and oil-saturated porous rocks.
The present study considers two overpressure models, based on oil/gas conversion and disequilibrium compaction, to obtain Poisson's ratio versus differential pressure (confining pressure minus pore pressure). The model results are in good agreement with experiments. Poisson's ratio is approximately constant at high differential pressures and increases (decreases) for saturated (dry) rocks at low differential pressures. Fluid type can be determined at all differential pressures from Poisson's ratio. The analysis is extended to the anisotropic case by computing the three Poisson's ratios of a transversely isotropic rock versus differential pressure. While one of them is practically independent of effective pressure, the others increase with increasing pore pressure. Experiments performed on cores under different pressure conditions, and calibration of the models with these data, provide a tool for inverting pore pressure from seismic data.     

致密油储层核磁共振测井响应机理研究

中国西部某盆地致密油储层孔隙结构差,而核磁共振测井T2谱宽,其复杂的核磁测井响应认识不清,且响应机理也不明确.本文基于致密油储层的特性,通过对三组岩样不同系列的实验测量,包括核磁共振、毛管压力曲线、X衍射矿物分析和润湿性实验,主要研究了碳酸盐岩矿物含量对T2谱的影响和由润湿性引起的T2弛豫机制.根据实验结果分析和讨论,明确了致密油岩石核磁共振响应的影响因素及孔隙流体的弛豫机制.综合分析认为,所述的核磁测井响应特征是由两方面因素综合作用的结果,一是水的T2信号主要取决于表面弛豫,低表面弛豫率的碳酸盐岩矿物导致水的T2信号的长弛豫分量增多;二是由于岩石亲油孔隙表面的存在且其弛豫率低于亲水孔隙表面的弛豫率,使得油的T2信号由表面弛豫和体弛豫贡献.     

Intercomparison of 3D pore-scale flow and solute transport simulation methods

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based on the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.     

Tight dual models of pore spaces

The pore throats in a porous medium control permeability, drainage, and straining through their pore scale geometry and through the way they are connected via pore bodies on the macroscale. Likewise, imbibition is controlled through the geometry of the pore bodies (pore scale) and through the way the pore bodies are connected via pore throats on the macroscale. In an effort to account for both scales at the same time we recently introduced an image-based model for pore spaces that consists of two parts related by duality: (1) a decomposition of a polyhedral pore space into polyhedral pore bodies separated by polygonal pore throats and (2) a polygonal pore network that is homotopy equivalent to the pore space. In this paper we stick to the dual concept while amending the definition of the pore throats and, as a consequence, the other elements of the dual model. Formerly, the pore throats consisted of single two-dimensional Delaunay cells, while they now usually consist of more than one two-dimensional Delaunay cell and extend all the way into the narrowing ends of the pore channel cross sections. This is the first reason for naming the amended dual model “tight”. The second reason is that the formation of the pore throats is now guided by an objective function that always attains its global optimum (tight optimization). At the end of the paper we report on simulations of drainage performed on tight dual models derived from simulated sphere packings and 3D gray-level images. The C-code for the generation of the tight dual model and the simulation of drainage is publicly available at https://jshare.johnshopkins.edu/mhilper1/public_html/tdm.html.     

Extended Roof snap-off for a continuous nonwetting fluid and an example case for supercritical CO2

A dominant mechanism for residual trapping of a nonwetting fluid in porous media during imbibition is snap-off or the disconnection of a continuous stream of the nonwetting fluid when it passes through pore constrictions and when a criterion based on capillary pressure imbalance is met. While quasi-static criteria for Roof snap-off have been defined for pores based on the imbalance between capillary pressure across the front/tail meniscus and local capillary pressure at the pore throat, and expressed in terms of pore body to pore throat ratio for simplification, we extended the previous quasi-static snap-off criterion by considering the local capillary pressure imbalance between the pore body and the pore throat for both circular and noncircular pores when the wetting film exists. We then used the criterion to analyze results from computational fluid dynamics (CFD) simulations of multi-phase flow with supercritical CO₂ as the nonwetting fluid and water as the wetting fluid. The extended criterion successfully described most situations we modeled. Furthermore, we compared fluid interface shape for a noncircular 3D pore predicted by the minimum surface energy (MSE) theory against 3D CFD simulations. While the fluid interface shape at the pore throat for 3D simulation was consistent with the shape predicted by MSE theory, the shape could not be successfully predicted by the MSE theory at the upstream and downstream pore body. Moreover, film flow existed for the noncircular pore at the downstream pore body.     

Structure of residual oil as a function of wettability using pore-network modelling

In the water flooding of mixed-wet porous media, oil may drain down to relatively low residual oil saturations (S_or). Various studies have indicated that such low saturations can only be reached when oil layers in pore corners are included in the pore-scale modelling. These processes within a macroscopic porous medium can be modelled at the pore-scale by incorporating the fundamental physics of capillary dominated displacement within idealised pore network models. Recently, the authors have developed thermodynamic criteria for oil layer existence in pores with non-uniform wettability which takes as input geometrically and topologically representative networks, to calculate realistic S_or values for mixed-wet and oil-wet sandstones [16, 21]. This previous work is developed in this paper to include (i) the visualisation of the 3D structure of this residual oil, and (ii) a statistical analysis of this “residual/remaining” oil. Both the visualisation and the statistical analysis are done under a wide range of wettability conditions, which is reported for the first time in this paper.The structure of residual oil for strongly water wet systems is well known (where residual = remaining oil) and our model agrees with this but this structure changes radically for mixed wet systems (where residual ≠ remaining) and this has not yet been visualised experimentally. We find that for more water-wet systems high final residual oil saturations are reached at relatively small amounts of water injected and this oil is present in the pores as bulk oil. On the other hand, for more oil-wet systems we find a slow decrease of the amount of remaining oil with increasing amounts of injected water. During the process, the remaining connectivity of the oil phase is increasingly provided by oil layers only, hence the slow drainage. The final residual oil saturation, only reached in the theoretical limit of an infinite amount of injected water, is almost entirely contained in large number of (relatively low volume) oil layers, which are present in pores of most radius sizes.     

中低孔渗储层岩石弹性参数的流体敏感性研究(英文)

本文从WXS凹陷中低孔渗储层岩石声波实验出发,以岩样的纵横波速度和密度为基础数据,求取出一系列的弹性参数,包括纵横波波速比、纵波波阻抗、横波波阻抗、泊松比、拉梅常数、剪切模量、体积模量、杨氏模量,等等。在前人的孔隙流体识别究基础上,综合相关理论和实验分析,构建了一个新的流体识别因子F。以饱和流体岩石弹性参数及其组合参数的相对变化量Ag/w和Ao/w为定量指标,评价各流体识别因子的流体识别效果,并采用交会图技术进行了验证。新流体敏感因子在传统较难分辨的孔隙流体"水"和"油"的区别上具有良好效果,有利于提高中低孔渗储层流体识别的成功率。     

An approach to combined rock physics and seismic modelling of fluid substitution effects

The aim of seismic reservoir monitoring is to map the spatial and temporal distributions and contact interfaces of various hydrocarbon fluids and water within a reservoir rock. During the production of hydrocarbons, the fluids produced are generally displaced by an injection fluid. We discuss possible seismic effects which may occur when the pore volume contains two or more fluids. In particular, we investigate the effect of immiscible pore fluids, i.e. when the pore fluids occupy different parts of the pore volume. The modelling of seismic velocities is performed using a differential effective‐medium theory in which the various pore fluids are allowed to occupy the pore space in different ways. The P‐wave velocity is seen to depend strongly on the bulk modulus of the pore fluids in the most compliant (low aspect ratio) pores. Various scenarios of the microscopic fluid distribution across a gas–oil contact (GOC) zone have been designed, and the corresponding seismic properties modelled. Such GOC transition zones generally give diffuse reflection regions instead of the typical distinct GOC interface. Hence, such transition zones generally should be modelled by finite‐difference or finite‐element techniques. We have combined rock physics modelling and seismic modelling to simulate the seismic responses of some gas–oil zones, applying various fluid‐distribution models. The seismic responses may vary both in the reflection time, amplitude and phase characteristics. Our results indicate that when performing a reservoir monitoring experiment, erroneous conclusions about a GOC movement may be drawn if the microscopic fluid‐distribution effects are neglected.     

Passing gas through the hydrate stability zone at southern Hydrate Ridge,offshore Oregon

We present an equilibrium model of methane venting through the hydrate stability zone at southern Hydrate Ridge, offshore Oregon. Free gas supplied from below forms hydrate, depletes water, and elevates salinity until pore water is too saline for further hydrate formation. This system self-generates local three-phase equilibrium and allows free gas migration to the seafloor. Log and core data from Ocean Drilling Program (ODP) Site 1249 show that from the seafloor to 50 m below seafloor (mbsf), pore water salinity is elevated to the point where liquid water, hydrate and free gas coexist. The elevated pore water salinity provides a mechanism for vertical migration of free gas through the regional hydrate stability zone (RHSZ). This process may drive gas venting through hydrate stability zones around the world. Significant amount of gaseous methane can bypass the RHSZ by shifting local thermodynamic conditions.     

Micro-scale experimental investigation of the effect of flow rate on trapping in sandstone and carbonate rock samples

We present the results of a pore-scale experimental study of residual trapping in consolidated sandstone and carbonate rock samples under confining stress. We investigate how the changes in wetting phase flow rate impacts pore-scale distribution of fluids during imbibition in natural, water-wet porous media. We systematically study pore-scale trapping of the nonwetting phase as well as size and distribution of its disconnected globules. Seven sets of drainage-imbibition experiments were performed with brine and oil as the wetting and nonwetting phases, respectively. We utilized a two-phase miniature core-flooding apparatus integrated with an X-ray microtomography system to examine pore-scale fluid distributions in small Bentheimer sandstone (D = 4.9 mm and L = 13 mm) and Gambier limestone (D = 4.4 mm and L = 75 mm) core samples. The results show that with increase in capillary number, the residual oil saturation at the end of the imbibition reduces from 0.46 to 0.20 in Bemtheimer sandstone and from 0.46 to 0.28 in Gambier limestone. We use pore-scale displacement mechanisms, in-situ wettability characteristics, and pore size distribution information to explain the observed capillary desaturation trends. The reduction was believed to be caused by alteration of the order in which pore-scale displacements took place during imbibition. Furthermore, increase in capillary number produced significantly different pore-scale fluid distributions during imbibition. We explored the pore fluid occupancies and studied size and distribution of the trapped oil clusters during different imbibition experiments. The results clearly show that as the capillary number increases, imbibition produces smaller trapped oil globules. In other words, the volume of individual trapped oil globules decreased at higher brine flow rates. Finally, we observed that the pore space in the limestone sample was considerably altered through matrix dissolution at extremely high brine flow rates. This increased the sample porosity from 44% to 62% and permeability from 7.3 D to 80 D. Imbibition in the altered pore space produced lower residual oil saturation (from 0.28 to 0.22) and significantly different distribution of trapped oil globules.     

Theoretical Mechanism and Application of Sphere–Cylinder Model in NMR for Oil–Water Porous Media

NMR is a unique logging tool that measures porosity, permeability, fluid components and wettability. It also shows different responses from rocks due to different pore-sizes in reservoirs; this gives opportunities to carry out a further study for pore structures and pore sharps in complicated reservoirs. The theoretical mechanism in NMR used for pore structure study currently is based on the Brownstein and Tarr theory (Phys Rev 19:2446–2453, 1979), but it shows that the pore structures are not sensitive to the connectivity of pores. In order to overcome this, we are proposing a theoretical approach called the Sphere–Cylinder Model to conduct NMR relaxation theories. In addition, a procedure for different pores has been discussed for porous media that is saturated by an oil–water phase. Consequently, considerations for the NMR relaxations for the water and oil phase have been taken into account in our model. The Sphere–Cylinder model has been used based on an NMR log in one of the gas fields in southwest China and shows satisfactory results.     

Effects of wettability and pore-level displacement on hydrocarbon trapping

We use a three-dimensional mixed-wet random network model representing Berea sandstone to extend our previous work on relative permeability hysteresis during water-alternating-gas (WAG) injection cycles [Suicmez, VS, Piri, M, Blunt, MJ, 2007, Pore-scale simulation of water alternate gas injection, Transport Porous Med 66(3), 259–86]. We compute the trapped hydrocarbon saturation for tertiary water-flooding, which is water injection into different initial gas saturations, S_gi, established by secondary gas injection after primary drainage. Tertiary water-flooding is continued until all the gas and oil is trapped. We study four different wettability conditions: water-wet, weakly water-wet, weakly oil-wet and oil-wet. We demonstrate that the amounts of oil and gas that are trapped show surprising trends with wettability that cannot be captured using previously developed empirical trapping models. We show that the amount of oil that is trapped by water in the presence of gas increases as the medium becomes more oil-wet, which is opposite from that seen for two-phase flow. It is only through a careful analysis of displacement statistics and fluid configurations that these results can be explained. This illustrates the need to have detailed models of the displacement processes that represent the three-phase displacement physics as carefully as possible. Further work is needed to explore the full range of behavior as a function of wettability and displacement path.     

Determination of the elastic wave velocities in porous rocks with the change of overburden pressure and its universal significance

Typical rock samples with different lithologic characteristics were collected from exploring wells drilled in sandstone-conglomerate sedimental reservoirs with positive rhythm. In different pore fluid states (fully saturated with gas, water and oil), the velocities of compressional and shear waves (Vp, Vs) were measured under different overburden pressure in laboratory. The effects of pore fluid and different fluid types on the velocities were analyzed. The velocities (Vp, Vs) of the samples fully saturated with water were calculated by use of Gassmann's formula that is suitable for low frequency. The calculated values were compared with the experimental values obtained at high frequency. The result shows that Gassmann's theory can be used to calculate elastic wave velocities in porous rocks saturated with fluid. By this result, the change of elastic velocities with the change of fluid can be predicted. The error is allowable in petroleum engineering. This conclusion is useful for sonic logging interpretation and seismic datum processing.     

A THEORETICAL TREATMENT OF THE EFFECT OF MICROSCOPIC FLUID DISTRIBUTION ON THE DIELECTRIC PROPERTIES OF PARTIALLY SATURATED ROCKS1

Microscopic fluid distribution can have a significant effect on the dielectric properties of partially saturated rocks. Evidence of this effect is found in the laboratory data presented by Knight and Nur in which different methods for controlling saturation produced very different results for the dependence of the dielectric response on water saturation. In this study, previously derived models for the dielectric response of a heterogeneous medium are generalized and the case of a pore space occupied by multiple pore fluids is considered. By using various geometrical distributions of water and gas, it is observed that both the pore geometry in which saturation conditions are changing and the gas–water geometry within a given pore space are critical factors in determining the effective dielectric response of a partially saturated rock. As an example, data for a tight gas sandstone undergoing a cycle of imbibition and drying are analysed. Previous research has demonstrated that significantly different microscopic fluid distributions result from the application of these two techniques to control the level of water saturation. By approximating these microscopic fluid distributions using simple geometrical models, good agreement is found between experimental data and calculated dielectric properties.