Estimation of Dynamic Relative Permeability and Capillary Pressure from Countercurrent Imbibition Experiments

Direct laboratory measurements of in situ water-phase saturation history are used to estimate relative permeability and capillary pressure functions. The magnitude of so-called nonequilibrium effects during spontaneous imbibition is quantified and, if significant, these effects are incorporated within the estimation technique. The primary constraint employed is that curves must increase or decrease monotonically; otherwise, no predetermined functionality is assumed. The technique is demonstrated using water saturation profile histories obtained for diatomite (a low-permeability and high-porosity rock). Results indicate that nonequilibrium effects detected at laboratory scale in low-permeability rocks influence the estimation of unsteady-state relative permeability and capillary pressure.     

Immiscible Displacement in the Interacting Capillary Bundle Model Part II. Applications of Model and Comparison of Interacting and Non-Interacting Capillary Bundle Models

In the first part of this work (Dong et al., Transport Porous Media, 59, 1–18, 2005), an interacting capillary bundle model was developed for analysing immiscible displacement processes in porous media. In this paper, the second part of the work, the model is applied to analyse the fluid dynamics of immiscible displacements. The analysis includes: (1) free spontaneous imbibition, (2) the effects of injection rate and oil–water viscosity ratio on the displacement interface profile, and (3) the effect of oil–water viscosity ratio on the relative permeability curves. Analysis of a non-interacting tube bundle model is also presented for comparison. Because pressure equilibration between the capillaries is stipulated in the interacting capillary model, it is able to reproduce the behaviour of immiscible displacement observed in porous media which cannot be modelled by using non-interacting tube bundle models.     

Three-Phase Capillary Pressure and Relative Permeability Relationships in Mixed-Wet Systems

A simple process-based model of three-phase displacement cycles for both spreading and non-spreading oils in a mixed-wet capillary bundle model is presented. All possible pore filling sequences are determined analytically and it is found that the number of pore occupancies that are permitted on physical grounds is actually quite restricted. For typical non-spreading gas/oil/water systems, only two important cases need to be considered to see all types of allowed qualitative behaviour for non-spreading oils. These two cases correspond to whether water or gas is the intermediate-wetting phase in oil-wet pores as determined by the corresponding contact angles, that is, cos ^o _gw > 0 or cos ^o _gw < 0, respectively. Analysis of the derived pore occupancies leads to the establishment of a number of relationships showing the phase dependencies of three-phase capillary pressures and relative permeabilities in mixed-wet systems. It is shown that different relationships hold in different regions of the ternary diagram and the morphology of these regions is discussed in terms of various rock/fluid properties. Up to three distinct phase-dependency regions may appear for a non-spreading oil and this reduces to two for a spreading oil. In each region, we find that only one phase may be specified as being the intermediate-wetting phase and it is only the relative permeability of this phase and the capillary pressure between the two remaining phases that depend upon more than one saturation. Given the simplicity of the model, a remarkable variety of behaviour is predicted. Moreover, the emergent three-phase saturation-dependency regions developed in this paper should prove useful in: (a) guiding improved empirical approaches of how two-phase data should be combined to obtain the corresponding three-phase capillary pressures and relative permeabilities; and (b) determining particular displacement sequences that require additional investigation using a more complete process-based 3D pore-scale network model.     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.     

高温高压气体在低含水率介质中迁移的数值模拟

针对气液两相非等温渗流模型高度非线性的特点,发展了适宜的数值离散方法。根据相态转换准则和控制方程的性质,采用最低饱和度法简化算法。空间离散方面,使用有限体积法;时间离散方面,设计了一套包含合理求解顺序的Picard迭代法,解决了方程组强耦合的问题。利用上述数值方法对高温高压气体的迁移行为进行数值模拟,证明了气体在低含水率介质和等效孔隙度的干燥介质内的运动基本一致,并分析了空腔内的气液相态转变过程。在此基础上,研究了多孔介质孔隙度和渗透率对气体压强演化和示踪气体迁移的影响。研究表明,孔隙度越小（相同渗透率）、渗透率越高（相同孔隙度）,示踪气体的迁移距离越远,并给出了估算不同孔隙度和渗透率下迁移距离的半经验公式。     

Pore Network Modelling of Electrical Resistivity and Capillary Pressure Characteristics

In order to model petrophysical properties of hydrocarbon reservoir rocks, the underlying physics occurring in realistic rock pore structures must be captured. Experimental evidence showing variations of wetting occurring within a pore, and existence of the so-called 'non-Archie' behaviour, has led to numerical models using pore shapes with crevices (for example, square, elliptic, star-like shapes, etc.). This paper presents theoretical derivations and simulation results of a new pore space network model for the prediction of petrophysical properties of reservoir rocks. The effects of key pore geometrical factors such as pore shape, pore size distribution and pore co-ordination number (pore connectivity) have been incorporated into the theoretical model. In particular, the model is used to investigate the effects of wettability and saturation history on electrical resistivity and capillary pressure characteristics. The petrophysical characteristics were simulated for reservoir rock samples. The use of the more realistic grain boundary pore (GBP) shape allows simulation of the generic behaviour of sandstone rocks, with various wetting scenarios. The predictions are in close agreement with electrical resistivity and capillary pressure characteristics observed in experiments.     

A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase Flow in Porous Media

It is well known that the relationship between capillary pressure and saturation, in two-phase flow problems demonstrates memory effects and, in particular, hysteresis. Explicit representation of full hysteresis with a myriad of scanning curves in models of multiphase flow has been a difficult problem. A second complication relates to the fact that P ^c–S relationships, determined under static conditions, are not necessarily valid in dynamics. There exist P ^c–S relationships which take into account dynamic effects. But the combination of hysteretic and dynamic effects in the capillary relationship has not been considered yet. In this paper, we have developed new models of capillary hysteresis which also include dynamic effects. In doing so, thermodynamic considerations are employed to ensure the admissibility of the new relationships. The simplest model is constructed around main imbibition and drainage curves and assumes that all scanning curves are vertical lines. The dynamic effect is taken into account by introducing a damping coefficient in P ^c–S equation. A second-order model of hysteresis with inclined scanning curves is also developed. The simplest version of proposed models is applied to two-phase incompressible flow and an example problem is solved.     

Discussion of Techien Chen, 1997, ‘An Integral Method to Calculate Water Saturation in a Centrifuge Experiment to Determine Capillary Pressure’

That discussion recognizes that the above paper deals with one of the main problems for reserves and reservoir evaluation, i.e. the determination of capillary pressure curves using the centrifuge technique. However, it is explained that the subject was not properly addressed and that sections of the paper are out of date, confusing or eventually wrong. For a more relevant overview on the subject, it is recommended to refer to the corresponding survey by the Society of Core Analysts.     

冠状毛细血管长度非线性变化及渗透作用下的毛细血管血液流动

建立冠状毛细血管内血流的血液动力学模型,研究毛细血管长度沿轴向的非线性变化及冠状毛细血管与周围组织的渗透和物质交换对血液流动的影响。考虑单根长弹性并具有通透性的冠状毛细血管,毛细血管长度非线性变化,毛细血管内血液为粘性不可压缩牛顿流体,跨壁滤过遵循Starling定律,血浆胶体渗透压和血浆蛋白浓度成线性关系。建立血管半径的无量纲方程,数值求解不同生理参数情况下,左心室壁不同层中毛细血管沿长度平均的无量纲半径和不同层毛细血管的平均流量。结果显示,冠状毛细血管与周围组织的渗透和物质交换及毛细血管长度沿轴向的非线性变化对平均无量纲半径和平均出口流量几乎没有影响;而对弹性模量较小的毛细血管,则对心脏收缩期时的平均进口流量有不同程度的影响。     

Relative Permeability Analysis of Tube Bundle Models

The analytical solution for calculating two-phase immiscible flow through a bundle of parallel capillary tubes of uniform diametral probability distribution is developed and employed to calculate the relative permeabilities of both phases. Also, expressions for calculating two-phase flow through bundles of serial tubes (tubes in which the diameter varies along the direction of flow) are obtained and utilized to study relative permeability characteristics using a lognormal tube diameter distribution. The effect of viscosity ratio on conventional relative permeability was investigated and it was found to have a significant effect for both the parallel and serial tube models. General agreement was observed between trends of relative permeability ratios found in this work and those from experimental results of Singhal et al. (1976) using porous media consisting of mixtures of Teflon powder and glass beads. It was concluded that neglecting the difference between the average pressure of the non-wetting phase and the average pressure of the wetting phase (the macro-scale capillary pressure) – a necessary assumption underlying the popular analysis methods of Johnson et al. (1959) and Jones and Roszelle (1978) – was responsible for the disparity in the relative permeability curves for various viscosity ratios. The methods therefore do not account for non-local viscous effects when applied to tube bundle models. It was contended that average pressure differences between two immiscible phases can arise from either capillary interfaces (micro-scale capillary pressures) or due to disparate pressure gradients that are maintained for a flow of two fluids of viscosity ratio that is different from unity.     

Effects of Organic Base Chemistry on Interfacial Tension,Wettability, and Capillary Pressure in Multiphase Subsurface Waste Systems

The presence of surfactants may have profound effects on the transport of organic contaminants in multiphase systems. It is a common practice, however, to model the subsurface migration of liquids independently of the aqueous phase composition. As such, transport in these systems may not be adequately characterized. This study investigates the impact of pH on interfacial tension, wettability, and the drainage capillary pressure–saturation relationship in air–water–quartz and oxylene–water–quartz systems containing dodecylamine, an organic base. In these systems, three mechanisms, speciation, partitioning, and sorption, are important in determining the interfacial tension and contact angle, and consequently, important in determining the capillary pressure. By adjusting the pH above and below, the pK_a of the base, the relative importance of these mechanisms was altered. Below dodecylamine's pK_a of 10.6, the base was primarily in a cationic form resulting in minimal partitioning into the nonaqueous liquid and greater sorption at the quartz surface. Above the pK_a, the base was primarily in a neutral form which did not sorb to the quartz, and, furthermore, partitioned into the organic liquid phase where its surface activity was minimized. The combination of these processes caused the capillary pressure to change in a manner consistent with porescale theory of capillarity. The utility in this approach lies in the possibility of predicting transport properties in multiphase systems while incorporating the direct effects of solution chemistry.     

Experimental study of two-phase flow in three sandstones. II. Capillary pressure curve measurement and relative permeability pore space capillary models

By means of the porous plate method and mercury porosimetry intrusion tests, capillary pressure curves of three different sandstones were measured. The testing results have been exploited jointly with three relative permeability models of the pore space capillary type (Burdine’s model type), these models are widely used and in rather distinct fields. To do so, capillary pressure has been correlated to saturation degree using six of the most popular relations encountered in the literature. Model predictions were systematically compared to the experimentally measured relative permeabilities presented in the first part of this work. Comparison indicated that the studied models underestimate the water relative permeability and over-estimate that of the non-wetting phase. Moreover, this modeling proves to be unable to locate the significant points that are the limits of fields of saturation where the variation of the relative permeabilities becomes consequent. We also showed that, if pore structure is modeled as a “bundle of capillary tubes”, model predications are independent of the capillary pressure curve measuring method.     

硼化硫代磷酸酯胺盐的极压抗磨性能研究

以硫化物、磷化物、氮化物以及硼化物为原料合成了多功能润滑油添加剂--硼化硫代磷酸酯胺盐,对比考察了所合成的添加剂同几种常见商品添加剂的极压抗磨特性,探讨了在添加剂分子中引入B元素对其热氧化稳定性及腐蚀性能的影响,初步考察了硼化硫代磷酸酯胺盐在无灰液压油和齿轮油中的应用性能.结果表明:引入B元素可以显著改善S-P-N类多功能润滑油添加剂的热氧化稳定性和腐蚀性能;含有S、P、N和B等多种活性元素的合成添加剂在无灰液压油及齿轮油中具有广阔应用前景.     

Nonisothermal multiphase flow of brine and gas through saline media

We propose a general formulation for nonisothermal multiphase flow of brine and gas through saline media. The balance equations include mass balance (three species), equilibrium of stresses and energy balance (total internal energy). Salt, water and air mass balance equations are established. The balance of salt allows the establishment of the equation for porosity evolution due to solid skeleton deformation, dissolution/precipitation of salt and migration of brine inclusions. Water and air mass balance equations are also obtained. Two equations are required for water: total water in the medium and water present in solid phase brine inclusions. The mechanical problem is formulated through the equation of stress equilibrium. Finally, the balance of internal energy is established assuming thermal equilibrium between phases. Some general aspects of the constitutive theory are also presented.     

The Total Compressibility Condition and Resolution of Local Nonlinearities in an Implicit Black-Oil Model with Capillary Effects

An implicit black-oil model with capillary effects is studied. Various primary unknowns which include one of the phase pressures are considered, and qualitative and quantitative consequences of a choice are discussed. In particular, a total compressibility condition is defined and a local nonlinear problem is studied. A numerical method to solve the local problem is discussed. Dedicated to the memory of John J. Wheeler     

The effect of pore-structure on hysteresis in relative permeability and capillary pressure: Pore-level modeling

The effect of pore-structure upon two-phase relative permeability and capillary pressure of strongly-wetting systems at low capillary number is simulated. A pore-level model consisting of a network of pore-bodies interconnected by pore-throats is used to calculate scanning loops of hysteresis between primary drainage, imbibition and secondary drainage. The pore-body to pore-throat aspect ratio strongly influences the pattern of hysteresis. Changes in the patterns of hysteresis often attributed to consolidation can be understood in terms of changes in aspect ratio. Correlation between the sizes of neighboring pore-throats affects the shape of the relative permeability curves, while the width and shape of the pore-size distribution have only a minor influence.     

高压气瓶工艺残余应力测试和分析

用X射线及磁记忆两种方法对压缩天然气的高压气瓶应力状态进行了系统分析,对一个气瓶整体制造工艺中的残余应力变化用X射线法进行了跟踪检测。考察了气瓶锻造后、淬火后及回火后外表面的残余应力状况,对相同测点进行了三次应力测试。为准确找到测点位置并寻求两种方法之间关系,在每次应力测试之前,均用金属磁记忆方法进行了先期检测。结果表明:锻造后应力水平不高,但磁记忆曲线有小幅波动,显示应力不均匀;淬火后表面具有较大压应力,最大达到0.86σS,且磁场亦有较大变化,个别点有明显应力集中;回火处理有效地消除了淬火残余应力,最大值小于0.17σS,应力均匀化,磁记忆曲线几乎无波动,效果良好。而从定量角度,残余应力和磁记忆两者之间没有明确的对应关系。对于磁记忆所显示的磁场强度变化处,用X射线法进行残余应力测试,结果并没有显示出较高的应力水平。说明两种方法不可互相替代,但以其各自的特点和优势可做互相补充。     

基于连续模型和离散模型的微尺度三维凸台轴承的气体润滑分析

为了考察应用图案化盘片实现超高密度磁存储时磁头/磁盘界面气体润滑设计理论的有效性,本文设计了1种三维凸台轴承构型,分别使用直接模拟蒙特卡罗方法（DSMC）和气体分子薄膜润滑理论（MGL）方法进行了模拟计算,考察了相对滑动速度、轴承最小间隙、凸台高度和入射速度方向对气体轴承压力分布的影响.结果表明：对于三维凸台微尺度气体轴承,MGL方法的计算结果依然与DSMC方法的结果相差不大.存在凸台接触,轴承间隙为零的情况下,气体轴承仍然具有一定的承载能力,且压力分布形状随凸台高度的变化表现出与常规非接触式气体轴承不同的规律.