Nonequilibrium thermomechanical modeling of liquid drainage/imbibition in trickle beds

We extend the macroscopic nonequilibrium thermomechanical multiphase flow theory proposed by Hassanizadeh and Gray for porous media to analyze a set of drainage and imbibition experiments in trickle beds. The nonequilibrium model rests on inclusion of mass and momentum conservations for the gas‐liquid interface, nonequilibrium capillary pressure, Helmholtz free energy gradients in the body supply of momentum for fluid bulk phases and gas‐liquid interface, and mass exchange rates between interface and fluid bulks accounting for production and destruction of gas‐liquid interfacial area. To solve the nonequilibrium model, entropy‐consistent constitutive relationships are derived and calibrated using liquid holdup and bed pressure drop measurements in drainage and imbibition. The model captures very well the decay (drainage), and breakthrough (imbibition) curvatures of liquid holdup and pressure drop kinetics, while model closer inspection allows assessing the role of nonequilibrium capillary pressure and of dynamic interfacial mass exchanges for the production/destruction of interfacial area. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3123–3134, 2012     

Toward A Mechanistic Understanding of Re-Infiltration in Naturally Fractured Reservoirs with Surfactant-Aided Gravity Drainage Process

Surfactant-aided gravity drainage is an improved oil recovery technique for water-invaded zone in fractured carbonate reservoirs, which are mostly oil-wet or mixed-wet rocks. The re-infiltration mechanism in water-invaded zone has a considerable effect on oil vertical movement in gravity drainage processes. In this work, a mechanistic understanding of re-infiltration in surfactant-aided gravity drainage, in comparison to oil–water gravity drainage is presented using an experimentally and numerically validated model. A column model is constructed from three matrix blocks. These blocks are separated from each other by horizontal fractures. A storage tank is considered on top of the model to store depleted oil from matrix blocks. The stacked-blocks model for re-infiltration is validated and verified to simulate water and chemical flooding using a mesh independency study and experimental flooding data in a composite core experiment. Using this model, several analyses are performed to investigate effects of rock and fluid properties, rock saturation functions, wettability alteration, surfactant adsorption, and capillary continuity on re-infiltration.     

气液分离强化传热多孔结构毛细上升特征

气液分离强化传热多孔结构,由于气体、液体在多孔壁面有着不同的力学行为,使得气液两相在多孔壁面发生分离,气体不能进入多孔壁面结构,液体则能自由进入,从而形成气体始终沿管壁运动,液体则在管中心流动这一高效传热流态。多孔壁面的毛细力对气液分离有着重要的影响。采用一种新颖的毛细力测试方法--红外热像测试法测试了多孔强化结构的毛细力。研究发现,多孔结构的毛细力与使用的粉末材料形状、颗粒尺寸及填充孔隙率有关。其中对毛细力影响最大的是粉末颗粒形状,颗粒尺寸次之,孔隙率最弱。     

Investigation of the dynamic capillary pressure during displacement process in fractured tight rocks

This work investigates the dynamic capillary pressure during the displacement process in fractured tight rocks, through specially designed experiments on fractured and intact core samples. The dynamic capillarity coefficient of matrix and the multiphase flow behaviors are also obtained. Results have shown that the dynamic capillary pressure of the matrix becomes around 5–20% higher after the fracturing treatment. The lower and less variable values of dynamic capillarity coefficient of matrix illustrate a weakened dynamic effect and a more uniform displacement front. Moreover, time derivative of water saturation is increased significantly with fractures. Finally, oil relative permeability after fracturing is lower than its value of the intact core at high water saturations. A dynamic capillarity coefficient model for matrix, which includes the influence of fractures, is derived and verified with the average R² more than 0.95. This wok helps to understand and predict multiphase flow in fractured tight porous media.     

功能性多孔介质中气泡输运调控的格子Boltzmann分析

为提高毛细蒸发海水淡化技术中的蒸发效率,多孔介质层需要维持一定的毛细压力,同时还要确保气泡能够快速通过。基于此背景,本文建立了多孔介质参数化模型,探究了气泡穿越多孔介质间隙过程的运动特征,研究在保持一定孔隙毛细压力的同时,通过调控孔道尺寸及排布从而使气泡能够更快速地通过多孔介质层。基于格子Boltzmann伪势模型分析了多孔介质孔隙率、壁面润湿特性、孔道排布及气泡水平方向初速度等对气泡形貌、上升速度、与壁面平均接触面积及孔隙毛细力的影响,获得了多孔介质的孔隙率设计范围,骨架润湿特性调控以及孔道排布方式的选择依据。同时还获得了在实际蒸发过程中,可以使气泡存在一定的水平方向初速度,从而能够更快地脱离多孔介质的策略。     

Prediction of Vapor‐Liquid Equilibrium inside Capillary Porous Plates

Capillary distillation is a relatively new separation process which uses capillary porous media for the separation of mixtures. It utilizes the solid‐liquid interfacial forces to alter the vapor‐liquid equilibrium (VLE) of mixtures inside the capillary porous plates. Previous studies have shown that capillary porous plates could significantly alter the VLE of binary mixtures. It was shown that the main factors affecting the alteration of VLE of binary mixtures are the polarization of the liquids and the porous plates as well as the polarization difference between the mixture components. In this study, the VLE data for the mixtures inside capillary porous plates have been predicted using the Wilson model and the theory of Abu Al‐Rub and Datta on VLE inside capillary porous media. The validity of the developed model has been assessed by comparing predicted VLE results of some binary mixtures inside capillary porous plates with experimental VLE data. The comparison showed that the model developed could predict the VLE of the studied systems accurately.     

Fundamental understanding of liquid water effects on the performance of a PEMFC with serpentine-parallel channels

A three-dimensional and unsteady proton exchange membrane fuel cell (PEMFC) model with serpentine-parallel channels has been incorporated to simulate not only the fluid flow, heat transfer, species transport, electrochemical reaction, and current density distribution but also the behaviors of liquid water in the gas-liquid flow of the channels and porous media. Using this general model, the behaviors of liquid water were investigated by performing the motion, deformation, coalescence and detachment of water droplets inside the channels and the penetration of liquid through the porous media at different time instants. The results showed that: tracking the interface of liquid water in a reacting gas-liquid flow in PEMFC can be fulfilled by using volume-of-fluid (VOF) algorithm combined with solving the conservation equations of continuity, momentum, energy, species transport and electrochemistry; the presence of liquid water in the channels has a significant impact on the flow fields, e.g., the gas flow became unevenly distributed due to the blockage of liquid water where the high pressure would be suddenly built up and the reactant gas transport in the channels and porous media would be hindered by liquid water occupation.     

DRYING GRANULAR POROUS MEDIA - THEORY AND EXPERIMENT

From a general theory of drying granular porous media, we have constructed a simplified theory that consists of a set of coupled, volume-averaged transport equations for the temperature and the saturation. The theory incorporates the liquid and vapor phase continuity equations, combines the liquid, solid and vapor phase thermal energy equations into a single temperature equation and makes use of Darcy's law for the liquid phase to account for moisture transport owing to capillary action. By purely qualitative reasoning, one can show that combined heat and mass transfer theories of drying cannot provide a complete theoretical explanation of drying phenomena and a detailed comparison between theory and experiment supports this point of view. Speculation concerning the logical course of subsequent theoretical studies is provided.     

裸眼压裂水平气井产能计算及裸眼段贡献研究

对压裂水平井的大部分传统研究认为,其产能计算问题可转化为一种“基质-裂缝-井筒”的双重介质模型,即认为地层中的流体先全部流入裂缝,再沿裂缝流入井筒。根据文献[9]的研究成果,对于水平段为裸眼的压裂水平井,这一假设并不符合事实。本文以国际上使用较多的Guo＆Evans的裸眼压裂水平井产能模型“’为基础,分析了它的未全部贯穿油藏的压裂水平井拟稳态产能解,并讨论在水平井的总产量当中,水平段和裂缝各自所占的比例。     

Capillary-bridge forces between solid particles: Insights from lattice Boltzmann simulations

Liquid capillary-bridge formation between solid particles has a critical influence on the rheological properties of granular materials and, in particular, on the efficiency of fluidized bed reactors. The available analytical and semi-analytical methods have inherent limitations, and often do not cover important aspects, like the presence of non-axisymmetric bridges. Here, we conduct numerical simulations of the capillary bridge formation between equally and unequally sized solid particles using the lattice Boltzmann method, and provide an assessment of the accuracy of different families of analytical models. We find that some of the models taken into account are shown to perform better than others. However, all of them fail to predict the capillary force for contact angles larger than π/2, where a repulsive capillary force attempts to push the solid particle outward to minimize the surface energy, especially at a small separation distance. We then apply the most suitable model to study the impact of capillary interactions on particle clustering using a coupled lattice Boltzmann and Discrete Element method.     

Snap‐off of a liquid drop immersed in another liquid flowing through a constricted capillary

Emulsions are encountered at different stages of oil production processes, often impacting many aspects of oilfield operations. Emulsions may form as oil and water come in contact inside the reservoir rock, valves, pumps, and other equipments. Snap‐off is a possible mechanism to explain emulsion formation in two‐phase flow in porous media. Quartz capillary tubes with a constriction (pore neck) served to analyze snap‐off of long (“infinite”) oil droplets as a function of capillary number and oil‐water viscosity ratio. The flow of large oil drops through the constriction and the drop break‐up process were visualized using an optical microscope. Snap‐off occurrence was mapped as a function of flow parameters. High oil viscosity suppresses the breakup process, whereas snap‐up was always observed at low dispersed‐phase viscosity. At moderate viscosity oil/water ratio, snap‐off was observed only at low capillary number. Mechanistic explanations based on competing forces in the liquid phases were proposed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

多孔介质中流动泡沫的压力分布计算

将多孔介质简化为一簇变截面毛细管组成的毛细管束,根据多孔介质的颗粒直径、颗粒排列方式、孔喉尺度比以及束缚水饱和度,计算出变截面毛细管的喉道半径和孔隙半径。在考虑多孔介质喉道和孔隙中单个气泡的受力和变形基础上,利用质量守恒定理和动量守恒定理,推导出单个孔隙单元内液相的压力分布和孔隙单元两端的压力差计算公式,最终得到多孔介质的压力分布以及多孔介质中泡沫当量直径计算方法。利用长U型填砂管对多孔介质中稳定泡沫的流动特性进行了实验研究,并对实验结果和计算结果进行了对比。结果表明:稳定泡沫流动时多孔介质中的压力分布呈线性下降,孔喉结构和泡沫干度是影响泡沫封堵能力的主要因素;泡沫的封堵能力随泡沫干度的增加而先增加后降低,在泡沫干度为85%时达到最强封堵能力。     

Capillary forces between two solid spheres linked by a concave liquid bridge: Regions of existence and forces mapping

This article focuses on the capillary interactions arising when two spherical particles are connected by a concave liquid bridge. This scenario is found in many situations where particles are partially wetted by a liquid, like liquid films stabilized with nanoparticles. We analyze different parameters governing the liquid bridge: interparticle separation, wetting angle and liquid volume. The results are compiled in a liquid volume‐wetting angle diagram in which the regions of existence (stability) or inexistence (instability) of the bridge are outlined and the possible maximum and minimal particle distances for which the liquid bridge may be found. Calculations of the capillary forces discriminate those conditions for which such force is repulsive or attractive. The results are plotted in form of maps that allow an easy understanding of the stability of a liquid bridge and the conditions at which it may be produced for the two particle model. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Displacement of residual nonwetting fluid from porous media

Percolation theory of transport in random composites is used to explain the correlation between the residual saturation of nonwetting phase in porous media after displacement by a wetting phase and the capillary number, this number being a measure of the ratio of Darcy-law viscous force in the wetting liquid to interfacial tension force in curved menisci between the two phases. Statistical concepts of percolation theory give estimates of the length distribution of blobs created when the nonwetting phase loses continuity because of displacement by the wetting phase. These estimates agree with the few experimental data. Simple blob mobilization theory and experiments establish that the capillary number required to mobilize a blob is inversely proportional to its length in the direction of the Darcy-law pressure gradient; this and the predictions of percolation theory account for the observed capillary number correlation.     

Experimental determination of capillary forces by crushing strength measurements

Mechanisms that lead to powder agglomeration are in many cases controlled by capillary forces. Indeed, in the earliest stage of agglomeration, minute amounts of liquid join solid particles by liquid bridges. Spontaneous formation of the bridge at contact points is caused by capillary condensation. Depending on solid/liquid interactions, particularly contact angle and spreading, liquid bridges may attract or repel individual particles. Undesired agglomeration may appear during storage and is called caking. On the other hand, powder agglomeration process is often required, for example, in enlargement of the particle size, i.e. granulation. A simple experimental device, designed from usual caking tests, was developed in order to estimate capillary forces transmitted by attracting liquid bridges joining particles. Crushing strength of wet cylindrical agglomerates was estimated. Influence of the low saturations of the void space (0<S<25%) and the surface tension of a liquid have been investigated. A normalised force which does not depend on the surface tension contribution has been calculated from experimental measurements and compared to Rumpf's model. It is possible to roughly estimate the solid/liquid contact angle by comparison with the model.     

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

Numerical simulations for core‐scale capillary pressure (P^c)‐saturation (S) relationships have been conducted for a supercritical carbon dioxide‐water system at temperatures between 35°C and 65°C at a domain pressure of 15 MPa as typically expected during geological sequestration of CO₂. As the P^c‐S relationships depend on both S and time derivative of saturation ( ) yielding what is known as the “dynamic capillary pressure effect” or simply “dynamic effect,” this work specifically attempts to determine the significance of these effects for supercritical carbon dioxide‐water flow in terms of a coefficient, namely dynamic coefficient (τ). The coefficient establishes the speed at which capillary equilibrium for supercritical CO₂ (scCO₂)‐water flow is reached. The simulations in this work involved the solution of the extended version of Darcy's law which represents the momentum balance for individual fluid phases in the system, the continuity equation for fluid mass balance, as well as additional correlations for determining the capillary pressure as a function of saturation, and the physical properties of the fluids as a function of temperature. The simulations were carried out for three‐dimensional cylindrical porous domains measuring 10 cm in diameter and 12 cm in height. τ was determined by measuring the slope of a best‐fit straight line plotted between (1) the differences in dynamic and equilibrium capillary pressures against (2) the time derivative of saturation (dS/dt), both at the same saturation value. The results show rising trends for τ as the saturation values reduce, with noticeable impacts of temperature at 50% saturation of aqueous phase. This means that the time to attain capillary equilibrium for the CO₂‐water system increases as the saturation decreases. From a practical point of view, it implies that the time to reach capillary equilibrium during geological sequestration of CO₂ is an important factor and should be accounted for while simulating the flow processes, for example, to determine the CO₂ storage capacity of a geological aquifer. In this task, one would require both the fundamental understanding of the dynamic capillary pressure effects for scCO₂‐water flow as well as τ values. These issues are addressed in this article. © 2014 American Institute of Chemical Engineers AIChE J 60: 4266–4278, 2014     

Darcy's law–based numerical simulation for modeling 3D liquid absorption into porous wicks

Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single‐phase flow in a porous medium where the Darcy's law is combined with the continuity equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE‐FLOW^© based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two‐dimensional (2D) wicking in the altered cylindrical wicks with two different cross‐sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross‐section cases along with the Washburn equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross‐sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross‐sectional area as well as its location vis‐à‐vis the wick entrance. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A NON-FICKIAN SURFACE EXCESS MODEL FOR CHEMICAL TRANSPORT THROUGH FRACTURED POROUS MEDIA

The transport of a solute through fractured rock domains is of major concern in various disciplines. The transport of chemicals in a porous medium is not a very well understood phenomenon, especially if the meidum is fractured. A study was conducted to invertigate the transport process of three selected chemicals in a fractured porous medium. A series of laboratory flow experiments was conducted in silica sand packs using a single fracture. Forty six runs were conducted to investigate the effects of chemical concentration, flow rate, and fractures in the transport process. A numerical model was developed that employed a one-dimensional transport equation combined with the surface excess concept to describe absorption equilibrium in the solid/liquid interface. Functional forms of the dispersion parameter (λ) and the kinetic desorption constant (k₂) were used to take into account the effect of the fracture on the porous medium. This non-fickian simulation results showed excellent agreement with experimental results. The developed model accommodates various interactions between the solid and the liquid phases. Therefore, it can be used for different chemical and rock types with little modification.     

Detection and analysis of transition from annular to intermittent flow in vertical tubes

In vertical co-current gas-liquid flow, the transition from annular to intermittent flow occurs when gas core becomes interrupted by liquid bridges due to the instability of the interfacial capillary waves. An analytical model is formulated to explain the liquid bridging in terms of the growth of finite amplitude interfacial capillary waves. Experimental results show that the longest wave length, which is associated with the transition, is about eight times the wave length of waves moving with the velocity of the liquid film.     

A method to calculate the multiphase flow properties of heterogeneous porous media by using network simulations

A method is suggested to compute the capillary pressure and relative permeability curves of heterogeneous porous media. The broad pore radius distribution (PRD) and throat radius distribution (TRD) are decomposed into relatively narrow component distribution functions which are used for the computer‐aided construction of pore‐and‐throat networks. The quasi‐static motion of menisci in pores and throats is tracked by accounting for capillary forces. The presence of fractal roughness along pore walls ensures the coexistence of both phases in pores. The calculation of the hydraulic conductance of each phase is based on the concept of constricted unit cell. Simulations in component pore networks constructed from narrow PRD and TRD produce a set of capillary pressure and relative permeability functions, the arithmetic averaging of which yields the corresponding functions for a heterogeneous synthetic pore network. This information is used by a dynamic simulator of drainage in permeability networks to predict experimental results of soil columns. © 2010 American Institute of Chemical Engineers AIChE J, 2011