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.     

On Mathematical Modeling and Simulation of the Pressing Section of a Paper Machine Including Dynamic Capillary Effects: One-Dimensional Model

This study presents the dynamic capillary pressure model (Hassanizadeh and Gray, Adv Water Resour 13:169–186, 1990; Water Resour Res 29:3389–3405, 1993) adapted for the needs of paper manufacturing process simulations. The dynamic capillary pressure–saturation relation is included in a one-dimensional simulation model for the pressing section of a paper machine. The one-dimensional model is derived from a two-dimensional model by averaging with respect to the vertical direction. Then, the model is discretized by the finite volume method and solved by Newton’s method. The numerical experiments are carried out for parameters typical for the paper layer. The dynamic capillary pressure–saturation relation shows significant influence on the distribution of water pressure. The behavior of the solution agrees with laboratory experiments (Beck, Fluid pressure in a press nip: measurements and conclusions, 1983).     

Influence of Viscous Fingering on Dynamic Saturation–Pressure Curves in Porous Media

We report on results from primary drainage experiments on quasi-two-dimensional porous models. The models are transparent, allowing the displacement process and structure to be monitored in space and time during primary drainage experiments carried out at various speeds. By combining detailed information on the displacement structure with global measurements of pressure, saturation and the capillary number Ca, we obtain a scaling relation relating pressure, saturation, system size and capillary number. This scaling relation allows pressure–saturation curves for a wide range of capillary numbers to be collapsed on the same master curve. We also show that in the case of primary drainage, the dynamic effect in the capillary pressure–saturation relationship observed on partially water saturated soil samples might be explained by the combined effect of capillary pressure along the invasion front of the gaseous phase, and pressure changes caused by viscous effects in the wetting fluid phase.     

仿鱼尾推进器在动力航向控制上的应用

传统的螺旋桨推进器工作噪声大,效率低,而仿鱼尾推进器技术有望改进这些不足,从而提出利用仿鱼尾推进动力定位的思想。通过对鱼尾推进模式和动力学的研究,设计出了最佳参数的仿鱼尾推进器。首先根据力的分解和拉格朗日动力学方程,计算出了前向推进力和各关节转矩,为课题研究奠定了力学基础;在动力定位控制研究中,通过惯性测量装置获取运动信息,采用卡尔曼滤波的数据融合算法实现姿态信息的解算,建立x方向上的空间运动模型并使用模糊自适应PID算法和传统PID算法仿真模拟。系统稳定性分析显示,PID控制存在14%的超调,而模糊自适应PID控制算法没有出现超调,两者的稳定时间均在240 s左右。最后由仿真分析验证模糊自适应PID算法更适合动力定位控制。     

A Steady-State Upscaling Approach for Immiscible Two-Phase Flow

The paper presents a model for computing rate-dependent effective capillary pressure and relative permeabilities for two-phase flow, in 2 and 3 space-dimensions. The model is based on solving the equations for immiscible two-phase flow at steady-state, accounting for viscous and capillary forces, at a given external pressure drop. The computational performance of the steady-state model and its accuracy is evaluated through comparison with a commercial simulator ECLIPSE. The properties of the rate-dependent effective relative permeabilities are studied by way of computations using the developed steady-state model. Examples presented show the dependence of the effective relative permeabilities and capillary pressures, which incorporate the effects of fine scale wettability heterogeneity, on the external pressure drop, and thereby on the dimensionless macro-scale capillary number. The effective relative permeabilities converge towards the viscous limit functions as the capillary number tends to infinity. Special cases, when the effective relative permeabilities are rate-invariant, are also studied. The applicability of the steady-state upscaling algorithm in dynamic displacement situations is validated by comparing fine-gridded simulations in heterogeneous reservoirs against their homogenized counterparts. It is concluded that the steady-state upscaling method is able to accurately predict the dynamic behavior of a heterogeneous reservoir, including small scale heterogeneities in both the absolute permeability and the wettability.     

Towards a theory of nonequilibrium multiphase filtration flow

A new theoretical model of joint filtration flow of immiscible incompressible fluids is presented. This model takes into account relaxation processes due to the exchange of the fluids between pores of different sizes, and these relaxation processes are driven by capillary forces. The fluids occupy connected regions in the four-dimensional space formed by three coordinates and the pore length scale. When fluid exchange between pores of given sizes is effected by way of successive flow through pores of all intermediate sizes, the fluid pressure within each region is governed by a hyperbolic equation, the role of time being played by the pore linear scale. Pressure jumps across hypersurfaces separating these regions are equal to corresponding values of capillary pressure. A supplementary condition at any such hypersurface requires the speed of its displacement in the four-dimensional space to coincide with the normal velocity components of both the adjoining fluids. As a result, a new formulation of multiphase filtration flow problems is gained with allowance made for capillary relaxation in the porous space.     

Falling film flow along steep two-dimensional topography: The effect of inertia

Steady film flow along a vertical wall with isolated step changes is studied numerically for Reynolds numbers Re ∼ O(10⁻³–10²) and capillary numbers Ca ∼ O(10⁻²–10¹). The lengthscale of free surface capillary features upstream of a step-in or step-out decreases uniformly with Re and switches from a −1/3 to a −1/2 power-law dependence on Ca. The height of the capillary features first grows with Re, but eventually diminishes when inertia forces overpower capillary forces. Simultaneously, the key dynamics move from upstream to downstream of the step, and switch from capillary arrest to inertial re-directioning of the falling liquid. The latter mechanism involves a low-pressure region originating from the edge of the step. At a step-out, a new free surface feature appears with increasing Re, which is caused by liquid overshoot in the horizontal direction and is restrained initially by capillary and subsequently by inertial forces. Simple scaling arguments are shown to predict many of the above characteristics.     

Modeling of blood microcirculation processes with allowance for pulse pressure oscillations

Processes of unsteady transcapillary exchange in hemodynamics with allowance for plasma motion in the interstitial space are studied by methods of physical and mathematical modeling. The presence of pulse oscillations of pressure in the network of capillaries is responsible for separation of filtration and re-absorption through capillary walls in space and time. General and specific properties of functioning of the arteriole, intermediate, and venule segments of the capillary network in exchange properties are demonstrated. Pressure oscillations are found to enhance transcapillary exchange.     

An experimental study of planar entry flow of rubber compound

An automated rheometer based on an injection molding machine is developed for the evaluation of entry flow problems. Several entry flow geometries having different contraction and expansion angles and different channel lengths are tested. Two pressure transducers are flushmounted along the die length and a displacement transducer is installed to measure the screw motion. Signals generated by the pressure transducers and displacement transducer are supplied to an A/D converter and an IBM PC/AT computer. The pressure losses for a rubber compound are measured between two cross-sections along the flow direction. The time evolution of pressure with overshoot during flow before and after the entry region is observed. At low flow rates the pressure drops of the expansion flow are larger than those of the contraction flow. At high flow rates the pressure drops of the contraction flow become higher than those of the expansion flow. A ratio of the pressure drop to absolute pressure before the entry is found to be almost independent of flow rate.     

Drop oscillations under simple shear in a highly viscoelastic matrix

Recent two-dimensional numerical simulations and experiments have shown that, when a drop undergoes shear in a viscoelastic matrix liquid, the deformation can undergo an overshoot. I implement a volume-of-fluid algorithm with a paraboloid reconstruction of the interface for the calculation of the surface tension force for three-dimensional direct numerical simulations for a Newtonian drop in an Oldroyd-B liquid near criticalities. Weissenberg numbers up to 1 at viscosity ratio 1 and retardation parameter 0.5 are examined. Critical capillary numbers rise with the Weissenberg number. Just below criticality, drop deformation begins to undergo an overshoot when the Weissenberg number is sufficiently high. The overshoot becomes more pronounced, and at higher matrix Weissenberg numbers, such as 0.8, drop deformation undergoes novel oscillations before settling to a stationary shape. Breakup simulations are also described.     

振动挤出过程中毛细管内聚合物熔体的剪切速率分析

借助自行研制的恒速型毛细管动态流变实验研究装置,对平行叠加振动条件下聚合物熔体经毛细管的挤出过程进行了分析;不依赖现有的任何本构关系,在考虑惯性项影响的前提下,建立了振动力场下毛细管壁处聚合物熔体剪切速率的计算公式;实验测量一定振动频率和振幅下毛细管瞬时入口压力、瞬时体积流量以及体积流量与入口压力波形的相位差,通过上述公式即可求得聚合物熔体在毛细管壁处的剪切速率。     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes

The wicking height of a heated, evaporating meniscus formed by surface-wetting liquid in a vertical capillary tube with dynamic flow has been investigated. Previous experimental results and analytical models for measuring/predicting wicking heights in capillaries are also reviewed. An analytical model is presented that accounts for both major and minor vapor pressure losses along the vertical capillary tube. It is shown that during thermo-mechanical instability, vapor/meniscus interaction can become more prevalent due to increased vapor generation/pressure near the meniscus free surface. A relatively simple procedure for estimating onset of meniscus instability is presented and, when used with the vapor Reynolds number, can estimate whether vapor pressure loss is significant. By comparing the current model with the available experimental data, it is shown that the wicking height of an unstable, evaporating meniscus of n-pentane in a vertical, glass capillary tube is better estimated by considering vapor flow pressure losses – providing a 40% improvement over previous models that neglect vapor flow. In addition to vapor flow pressure loss, the dynamic contact angle and thin film profile must also be calculated to ensure accurate prediction of wicking height. Although the proposed model shows improvement, it is prone to under-predicting the actual meniscus wicking height for stable, evaporating menisci at lower relative heat loads. The proposed model can be used for predicting wicking behavior of heated, vertically-aligned liquid columns in capillary structures – which is relevant to the design of miniature heat transfer equipment/media such as wicked heat pipes, micro-channels and sintered/porous surfaces.     

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.     

Mass transfer enhancement by capillary waves at a liquid–vapour interface

We present experimental results showing that large amplitude capillary waves at a liquid–vapour interface substantially enhance the interfacial heat and mass transfer. The experiments have been conducted in a circular cylinder that is partially filled with a wetting liquid of low boiling point temperature and pressurized by its vapour. The interfacial capillary waves are sub-harmonically excited by oscillating the circular cylinder at 50 Hz with forcing amplitude A in the direction normal to the liquid surface. The upper part of the test cell containing the vapour is heated to a temperature slightly below the boiling point temperature at the operating pressure. When the interface is at rest, the pressure decrease due to condensation is small. However, in the presence of interfacial capillary waves the rate of pressure decrease is substantial. The results show that the vapour condensation rate with respect to the diffusive vapour flux at an undisturbed interface, which is a Nusselt number, increases with the square of the wave amplitude that is proportional to the forcing amplitude. A model is developed that expresses the pressure variation in terms of Jacob number, the temperature gradient in the liquid at the interface and the capillary wave motion. This model allows extrapolation of the results to other fluids and configurations.     

Development of oil inclusions under the action of chemical reagents on the reservoir

Various conditions of formation of motionless closed hydrocarbon inclusions are considered: viscous instability of fluid displacement and inhomogeneous rock structure. Conditions of dynamic equilibrium of the inclusion in a water flow are given for one-dimensional and two-dimensional motion. Distributions of the oil content in inclusions of different shapes are numerically calculated. It is found that the amount of unrecovered oil depends on the ratio of the pressure gradients in the filtration flow of water pumped into the reservoir and the characteristic capillary pressure on the boundary of immiscible phases. It is demonstrated that the use of chemical reagents can substantially reduce the effect of capillary forces and promotes oil entrainment by the overall flow.     

液腔体中气体射流冲击压力的实验测量

对充液腔体中气体射流的冲击效应进行了实验研究. 测量结果表明了冲击压力的瞬态最 大值、稳态平均值和脉动值随喷管进口压比的增加而增加，冲击区是主要的噪声源和动态压 力承载部位. 通过充气与充水两种状态的对比实验，还揭示了腔体充水时气体射流冲击压力 出现一个上冲阶段，其瞬态最大值比充气值有显著的增加.     

电磁场?渗流场耦合作用下离子液体多孔介质流动模型

离子液体是一类可调控、多功能的绿色环保材料, 具有良好的电磁场响应, 有望应用于调控水驱油路径. 在分析离子液体在毛细管中电磁场响应机理的基础上, 建立了电磁场?渗流场耦合作用下离子液体多孔介质流动模型. 通过理论推导与数值分析发现: 电磁场?渗流场耦合作用下毛细管流量大小主要由离子液体电导率与黏度的比值(内因)、电磁场强度与压力梯度(外因)两方面决定; 电磁场产生的洛伦兹力对离子液体施加一个电磁驱动压强, 形成一个类似压力梯度的电磁驱动等效压力梯度, 从而改变离子液体的流量, 当电磁场强度为2.0 × 104 V/m·T时, 电磁场在电导率为0.5 S/m的离子液体上可形成10 kPa/m电磁驱动等效压力梯度. 通过调整电磁场方向即可控制离子液体在多孔介质中的流动方向, 解决常规注水利用压力差难以控制流动路径的难题, 为离子液体智能驱油提供理论依据, 且电磁场产生的热效应会影响离子液体的流动能力及潜在驱油效率.