Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Pore-scale simulation of water/oil displacement in a water-wet channel

Water/oil flow characteristics in a water-wet capillary were simulated at the pore scale to increase our understanding on immiscible flow and enhanced oil recovery. Volume of fluid method was used to capture the interface between oil and water and a pore-throat connecting structure was established to investigate the effects of viscosity, interfacial tension (IFT) and capillary number (Ca). The results show that during a water displacement process, an initial continuous oil phase can be snapped off in the water-wet pore due to the capillary effect. By altering the viscosity of the displacing fluid and the IFT between the wetting and non-wetting phases, the snapped-off phenomenon can be eliminated or reduced during the displacement. A stable displacement can be obtained under high Ca number conditions. Different displacement effects can be obtained at the same Ca number due to its significant influence on the flow state, i.e., snapped-off flow, transient flow and stable flow, and ultralow IFT alone would not ensure a very high recovery rate due to the fingering flow occurrence. A flow chart relating flow states and the corresponding oil recovery factor is established.     

A theoretical and experimental investigation of trapping in pore doublets

The mechanism for trapping oil in a pore doublet with a finite source and sink is examined both theoretically and experimentally. The characteristics of the source and sink play a crucial role in determining whether there is a potential for trapping in the wider or narrower branch of the doublet and are explicitly treated for the first time. The analysis includes fluids of unequal viscosity and it is shown that the fluid viscosities should affect trapping only in special circumstances. Trapping of the displaced phase is not a function of scale when the external pressure drop is either zero or much larger than the capillary pressure. However, any attempt to control trapping by an external pressure is constrained by the scale of the pores involved.     

Pore network simulation of fluid imbibition into paper during coating—III: modelling of the two-phase flow

Extensive computer simulations have been carried out to model imbibition of a coating fluid into a paper. The microstructure of the paper's pore space is represented by a network of interconnected channels or pore throats that are formed between the paper's fibers. The geometrical characteristics of the channels, such as their effective radius and length, as well as their connectivity, are selected from the experimental data presented in Part II of this series. The imbibition process that we simulate is the result of forcing the coating fluid into the pore space by applying a time-dependent flow-driven pressure distribution to the external surface of the paper, or is driven only by capillary forces. The dynamic pressure distribution is representative of a high-speed coating process. The simulations indicate that the connectivity of the pore throats, the anisotropic structure of the paper's pore space, and the dynamic pressure distribution all have a strong influence on imbibition of a coating fluid into a paper's pore space and, hence, on the quality of the coating.     

Orifice Flowmeter for Measuring Extensional Rheological Properties

Extensional rheological properties play an important role in processes in which the fluid is subjected to highly decelerated or accelerated flows. This paper describes an orifice flowmeter used to measure extensional properties of rheologically complex fluids at high strain rates. The operating principle of the flowmeter is based on the pressure drop due to the flow through a small size orifice. The flowmeter was first calibrated, by plotting the pressure drop‐flow rate curve of the orifice, in terms of a dimensionless Euler number versus Reynolds number. Newtonian fluids consisting of aqueous solutions of corn syrup were used as calibration fluids. The calibration curve was then used to determine the apparent extensional viscosity of three different paper coating colors. The apparent extensional viscosity is compared to the shear viscosity in terms of the Trouton ratio. The Trouton ratio for one coating color is shown to exceed considerably the theoretical value of 3 expected for Newtonian fluids.     

A stochastic analysis of the flow of two immiscible fluids in porous media: The case when the viscosities of the fluids are equal

A new stochastic theory is developed to explain the flow of two immiscible fluids in porous medium when the viscosity difference between two fluids is zero. In an individual micropore the radius of curvature of the interface separating the fluids is assumed constant and flow is modeled by the random jumping of microscopic interfaces. A one dimensional model composed of an array of parallel capillary tubes of constant radius is analyzed in detail. For the case in which two fluids have equal viscosity an analytical solution is obtained. The fluid displacement process is Fickian and dispersion is described in terms of a diffusion or spreading constant.     

Effect of liquid characteristics on the wetting,capillary migration,and retention properties of fibrous polymer networks

Fluid penetration through porous networks consists of two different phenomena: (1) pore fluid displacement and (2) fluid flow through the pores. The first phenomenon depends on the pore size, the fluid–fluid interfacial tension, and the contact angle. The second phenomenon is pore‐size‐ and viscosity‐dependent. We adapted an experimental methodology often used for measurements of liquid permeability and hydraulic conductivity of soils and applied it to polymeric medical textiles. The methodology made use of a pressure/flow cell in which a sample was mounted. The flow rates were measured during sequences of increasing and decreasing pressures applied to the displacing nonwetting fluid (aqueous solution). The effects of the liquid parameters on penetration were investigated. Surface tension effects were studied with water and two solutions with surface tensions lower than that of pure water; the liquids with lower surface tensions had lower displacement pressures. To study viscosity effects, we used water and two solutions with viscosities higher than that of pure water. Increasing the viscosity not only caused the flow rate to decrease but also caused deformation, that is, enlargement, of the pores. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 282–292, 2005     

Pressure‐driven displacement flows of yield stress fluids: Viscosity ratio effects

We numerically investigate pressure‐driven, density‐unstable displacement flows of two miscible fluids along a near‐horizontal 2D channel. The displacing fluid is a Newtonian fluid, slightly heavier than the displaced yield stress (Bingham) fluid. The imposed displacement flow is laminar. We show that the displacement flow is mainly governed by five dimensionless numbers, and their combinations, including the Reynolds number (Re), the Bingham number (Bn), the densimetric Froude number (Fr), the viscosity ratio (m), and the channel inclination angle (β). In this work, we primarily focus on the viscosity ratio and provide a detailed understanding of the flow behaviours via studying the effects of m on displacement flow patterns, regime classifications based on slump‐type and centre‐type displacement flow regimes, leading and trailing displacement front features, and finally the effects of m at different inclination angles.     

Pore-network analysis of two-phase water transport in gas diffusion layers of polymer electrolyte membrane fuel cells

A pore-network model was developed to study the water transport in hydrophobic gas diffusion layers (GDLs) of polymer electrolyte membrane fuel cells (PEMFCs). The pore structure of GDL materials was modeled as a regular cubic network of pores connected by throats. The governing equations for the two-phase flow in the pore-network were obtained by considering the capillary pressure in the pores, and the entry pressure and viscous pressure drop through the throats. Numerical results showed that the saturation distribution in GDLs maintained a concave shape, indicating the water transport in GDLs was strongly influenced by capillary processes. Parametric studies were also conducted to examine the effects of several geometrical and capillary properties of GDLs on the water transport behavior and the saturation distribution. The proper inlet boundary condition for the liquid water entering GDLs was discussed along with its effects on the saturation distribution.     

多孔介质内两相流体流动的核磁共振成像研究(英文)

Measurement of two phase flow in porous medium for sequestration was carried out using high-resolution magnetic resonance imaging (MRI) technique. The porous medium was a packed bed of glass beads. Spin echo multi sequence was used to measure the distribution of CO2 and water in the porous medium. The intensity images show that the fluid distribution is non-uniform due to its viscosity and pore structure of porous medium. The velocity distribution of fluids is calculated from the saturation of water and porosity of porous medium. The experimental results show that fluid velocities vary with time and position. The capillary dispersion rate donated the effects of capillary, which was largest at water saturations of 0.45. The displacement process is different between in BZ-02 and BZ-2. The final water residual saturation depends on permeability and porosity.     

Visualizing multiphase flow and trapped fluid configurations in a model three‐dimensional porous medium

We report an approach to fully visualize the flow of two immiscible fluids through a model three‐dimensional (3‐D) porous medium at pore‐scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the nonwetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium, forming disconnected oil ganglia. Some of these ganglia remain trapped within the medium. By resolving the full 3‐D structure of the trapped ganglia, we show that the typical ganglion size, as well as the total amount of residual oil, decreases as the capillary number Ca increases; this behavior reflects the competition between the viscous pressure in the wetting fluid and the capillary pressure required to force oil through the pores of the medium. This work thus shows how pore‐scale fluid dynamics influence the trapped fluid configurations in multiphase flow through 3‐D porous media. © 2013 American Institute of Chemical Engineers AIChE J, 59:1022‐1029, 2013     

Capillary Condensation and Surface Flow in Microporous Vycor Glass

Depending on the size of the pores and on the temperature and pressure of the fluid, flow in microporous materials can be through gas diffusion, surface diffusion, and viscous liquid flow driven by capillary forces or by hydraulic pressure. We have studied these flow regimes with toluene in untreated Vycor glass with a pore radius of 31 Å and Vycor glass with a pore radius of 21 Å whose pores were derivatized with C₁₈H₃₈. The observed increase in viscosity with decreasing pore size is ascribed to the attractive interaction of the monolayer adsorbed on the pore walls. The surface diffusion coefficient at 22°C is 5 × 10⁻⁵ cm² s⁻¹ for both the derivatized and underivatized Vycor, with an activation energy of 3 kcal in the temperature range 22–100°C.     

水胶比对混凝土性能及气孔结构的影响分析

通过试验,对不同水胶比下混凝土28 d龄期的抗压强度、氯离子电通量及微观方面的气孔结构和气孔特征参数进行了对比分析,研究了水胶比对混凝土宏观性能及微观孔结构的影响.结果表明:过量的自由水会在混凝土内部产生毛细孔,增大水胶比相当于变相增多了混凝土内部的孔隙数量,能够显著降低混凝土的抗压强度,但较大的水胶比又能够增强局部的水泥水化反应.对氯离子电通量而言,水胶比越大,毛细孔越多,孔含量越多,相对增大了连通孔隙的数量,氯离子电通量会呈现出增大的现象.随着水胶比的减小,孔径分布也有向小孔径方向发展的趋势.此外,抗压强度与较小孔径的孔含量及孔隙率的关联度计算结果较大,氯离子电通量与气孔间距系数的关联度计算结果较大,这说明小孔含量及孔隙率能够用来表征混凝土的抗压强度,气孔间距系数也能在一定程度上表征混凝土的耐久性.     

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.’     

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.'     

T型微流控芯片中微液滴破裂的数值模拟

利用VOF模型对T型结构微流控芯片中微液滴的三维破裂过程进行了数值模拟,获得了液滴发生破裂和不会破裂两种流型。一定轴向长度的微液滴对应着一个临界毛细数,当主流流体的毛细数大于此临界毛细数时,微液滴发生破裂并分别流向T型结构两侧;否则不会发生破裂,微液滴流向任意一侧。通过多个工况的计算,拟合了临界毛细数与微液滴相对轴向长度的关系,探讨了黏度比对微液滴破裂的影响。发现黏度比越小,微液滴越易发生破裂。     

Debinding behaviors of injection molded ceramic bodies with nano-sized pore channels during extraction using supercritical carbon dioxide and n-heptane solvent

Debinding behaviors related on changes in capillary pore structure during extraction with supercritical carbon dioxide and n-heptane, respectively were investigated for injection molded ceramic bodies consisting of skeleton pores of 68 nm. For the debinding processes, both debinding curves showed a square root of time dependence but significantly deviated in the middle or end period of debinding because of structural changes with pores during extraction. The debinding bodies experienced capillary changes having a debinding front separating the undebinded region with fluid state into the debinding region with pendular state in the wax-based green bodies. The debinding rate of the supercritical fluid extraction was five times higher than that of the solvent extraction because of a higher interdiffusion diffusivity and a formation of relatively large pore channels. An abrupt change of pore structures between debinded and undebinded region in the green bodies caused severe defects during the solvent extraction even at a low rate of debinding at 313.15 K, while the severity of the capillary changes was overcome during the supercritical fluid extraction and the debinded ceramic bodies were free from defects even at a high rate of debinding at 328.15 K. It is attributed to a reduction of the capillary stress developed on debinding front during the supercritical fluid extraction.     

Water and methane in shale rocks: Flow pattern effects on fluid transport and pore structure

Using molecular dynamics simulations, the two‐phase flow of water and methane through slit‐shaped nanopores carved from muscovite is studied. The simulations are designed to investigate the effect of flow patterns on fluids transport and on pore structure. The results indicate that the Darcy's law, which describes a linear relation between flow rate and pressure drop, can be violated when the flow pattern is altered. This can happen when the driving force, that is, the pressure drop, increases above a pore‐size dependent threshold. Because the system considered here contains two phases, when the fluid structure changes, the movement of methane with respect to that of water changes, leading to the violation of the Darcy's law. Our results illustrate the importance of the capillary force, due to the formation of water bridges across the model pores, not only on the fluid flow, but also on the pore structure, in particular its width. When the water bridges are broken, perhaps because of fast fluid flow, the capillary force vanishes leading to significant pore expansion. Because muscovite is a model for illite, a clay often found in shale rocks, these results advance our understanding regarding the mechanism of water and gas transport in tight shale gas formations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2993–2999, 2015     

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     

Dispensing of rheologically complex fluids: The map of misery

Rheological effects may complicate the dispensing of complex fluids, when compared to their Newtonian counterparts. In this work, fluids with tailored rheological properties have been studied using high‐speed video‐microscopy. The level of viscosity, the degree of shear thinning, and the elasticity have been varied independently. At low‐flow rates, droplets are formed that pinch off. The drop volumes, breakup mechanisms, and times have been identified. At higher‐flow rates, a continuous jet is observed, with the transition depending on the rheology of the dispensed fluid. The relevant nondimensional groups are the Ohnesorge, Deborah, and elasto‐capillary number, for when viscosity, inertia, or elastic forces dominate flow. In each of these cases, the transition between dripping and jetting dispensing occurs, controlled by a critical Weber, capillary, and Weissenberg number, respectively. This set of six nondimensional groups can be used to construct an operating space and map out areas of potential problems. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3242–3255, 2012