Critical Entry Pressure Research Articles

Coalescence of an Oil Droplet with a Permeating One over a Membrane Surface: Conditions of Permeation, Recoil, and Pinning.

When a droplet lands over a nonwetting surface it forms a convex interface that makes a contact angle larger than 90°. If the droplet lands over a pore opening, an interface is also formed at the pore opening that can prevent the droplet from permeating. The conditions for permeation and pinning are very much related to a threshold critical pressure that above which the droplet will permeate. This property defines a selectivity criterion for microfiltration processes of oily water systems using membrane technology. Such a feature of the membrane gets compromised, however, due to the permeation of droplets that are relatively smaller in size or whose critical entry pressure is smaller than the applied transmembrane pressure (TMP). In this work, we investigate what happens to a droplet when it coalesces with a droplet that undergoes permeation. Two scenarios are considered: namely, (1) a droplet coalesces with a permeating one whose interface inside the pore has not broken through the pore exit and (2) a droplet coalesces with a permeating one whose interface in the pore has broken through. We show that a larger droplet (that will essentially not permeate if pinned over a membrane opening) will now permeate when the pore is filled with oil from a preceding one or recoils when the interface inside the pore of a preceding droplet has not broken through the exit of the pore. This has interesting implications for the rejection capacity of the membrane, which decreases due to the permeation of droplets that would, otherwise, not permeate. A computational fluid dynamic (CFD) study has been conducted to confirm the conclusions obtained from the theoretical study and to reproduce the fates of the combined droplet after coalescence at the surface of the membrane. Furthermore, a simplified formula for estimating the critical entry pressure is developed.

Critical entry pressure of a droplet pinning over multitude of pore openings

Porous membranes filter by the virtue of their pore sizes in relation to the sizes of dispersals. While this is essentially true for solid dispersals, it needs to be reframed when dispersals are droplets. That is, without the existence of other selectivity criterion (other than pore sizes), droplets are prone to permeation, irrespectively. Fortunately, this extra criterion exists via the use of interfacial phenomena. That is, if the materials of the membrane are cast such that they are nonwetting with respect to droplets, interfaces are formed at pore openings that prevent droplets from permeation if the operating pressure is kept smaller than the entry pressure. Therefore, it is important to estimate such critical entry pressure under the different wettability conditions and droplet to pore ratios. Previous works have looked at droplets pining over single pore openings. In this work, the case in which relatively larger size droplets pin over multiple pore openings is investigated theoretically and via the tools of computational fluid dynamics. An exact formula is derived that account for the volumes of that part of the droplet hanging at the pore openings. An approximate formula is also highlighted that ignores this volume and compares very well with the exact formula. This derivation is based on the assumption that the droplets maintain their spherical shape, which is typically the case for smaller size droplets in produced water applications. The study shows that a pining droplet permeates first through the largest size pore until its size matches the critical size associated with the next larger pore opening when it starts to permeate.

On the estimation of the leaked volume of an oil droplet undergoing breakup in crossflow filtration: CFD investigation, scaling, and a macroscopic model

The fate of an oil droplet at the surface of a membrane in crossflow filtration has been identified as either of four destinies; namely, pinning, permeation, rejection or breakup. These fates are determined according to the operating conditions (transmembrane pressure, TMP, and crossflow velocity, CFV) in relation to the critical conditions (critical entry pressure,pcrit, and critical velocity of dislodgment, vcrit). These conditions have enabled the establishment of fate maps for every combination of pore and droplet sizes. Such maps have been the bases for the newly developed multicontinuum modeling approach, which describes the permeation process not only of the continuous phase but also of the inevitably associated dispersed phase. In the multicontinuum approach, both the droplet and pore size distributions are used to establish multitude of continua that interact according to the previously mentioned maps. Therefore, every oil continuum is checked against all membrane continua to determine how the droplets behave. According to this procedure, the permeation flux of the oil as well as the rejection capacity of the membrane can be estimated. At the moment of breakup, the portion of the droplet that has advanced inside the pore depends on the ratios TMP/pcrit andCFV/vcrit. In this work, we investigate this topic thoroughly by conducting computational fluid dynamics (CFD) analysis of various combination of operating and critical conditions. A macroscopic relationship is developed to allow for the estimation of the volume of the droplet inside the pore opening upon breakup under different conditions. This formula allows the accurate estimation of the permeation flux of those oil droplets that have experienced breakup conditions, which allow its use in the context of multicontinuum approach. From this study it is found that the volume of the droplet inside the pore is large the larger the ratio of the transmembrane pressure with respect to the critical entry pressure. It is also found that the larger the feed velocity compared with the critical velocity of dislodgment the smaller the size of that part of the droplet inside the pore. The latter is a manifestation of the increase in hydrodynamic drag as a result of the increased velocity. A scaling analysis has also been conducted to show how the breakup time is correlated with the ratio of the feed stream velocity and the critical velocity of dislodgment.

Simplified Formula for the Critical Entry Pressure and a Comprehensive Insight into the Critical Velocity of Dislodgment of a Droplet in Crossflow Filtration

Produced water treatment remains a challenging issue for the oil production industry. Finding ways to effectively treat oily water systems without incurring higher operational costs is the struggle and focus of recent research work. The success in establishing a modeling approach to study the filtration of oily water systems is dependent upon our understanding of the fate of oil droplets at the membrane surface. It has been determined that four fates confront oil droplets at the membrane surface, namely, permeation, breakup, pinning, and rejection. Conditions for manifestation of any of these four fates depend on two operating conditions (transmembrane pressure and crossflow velocity) in comparison with two critical conditions (entry pressure and critical velocity of dislodgment). In this work, a new simplified formula for the critical entry pressure is introduced. It compares very well with the formula already existing in the literature. Furthermore, the complete model for the critical velocity of dislodgment in crossflow filtration is presented and highlighted. More investigations on the physical processes that are involved during the pinning of a droplet at a pore opening are presented. In addition, a thorough analysis of the forces that are involved during the permeation of a droplet that could lead to its breakup is presented. It is found that, once the droplet reaches the pore opening, the interfacial tension force and the pressure force continue to increase. Following the critical configuration, these forces continuously decline and the drag force due to the crossflow field, therefore, becomes sufficient to break up the droplet.

Investigation of the onset of dislodgment of a nonpermeating oil droplet at a membrane surface: Standard models and a new force balance model

The need to determine the onset of dislodgment of an oil droplet pinning over a membrane surface is important in order to determine the critical conditions at which oil droplets detach. Although, previous studies considered this case in relation to an oil droplet pinning over a single pore, in reality, relatively larger size droplets pin over multitude of pore openings. In other words, droplets contact the surface over an area large enough to render the torque balance, which was devised previously to determine critical velocity, inaccurate. Another framework based on force balance is developed in this study from which critical velocity for the dislodgment of pinned droplet may be estimated. A friction force is assumed to balance the drag force due to crossflow field. The friction force is proportional to the resultant normal force that applies on pinned droplet. The proportionality factor is a friction coefficient that is determined as the ratio of the drag force due to crossflow and the resultant normal force. In this work, we determine these forces in addition to the crossflow velocity required to dislodge pinned droplet through computational fluid dynamic study (CFD). This analysis may be applicable to systems in which the deformation of the droplet is not large enough. In this case the resultant component of surface forces along the surface may be considered small. In this study a rectangular domain is considered with a 9 × 9 vertical tubes representing a pattern of pore openings. An oil droplet is released closer to the surface, where the permeation flux carries the droplet to reside on the membrane surface. The pressure inside the domain is adjusted such that it is less than the critical entry pressure and therefore, the droplet will not permeate. We seek to determine the velocity at the top surface that is barely enough to dislodge the droplet. This velocity, in addition to permeation flux, is used to determine the different hydrodynamic forces required to determine the friction force. In this study a number of droplets of different diameters are considered, namely 8, 10 and 12 microns. A base scenario is considered to determine the friction factor when no pores exist. A formula is suggested to estimate the friction factor for the more complex multipored system using that obtained when no pores exist. The numerical work is validated against the data exist in literature and excellent qualitative and quantitative match are obtained, which builds confidence in the numerical approach.

Investigation of the critical entry pressure values associated with the permeation of an oil droplet through a cascade of pore throats and pore bodies: A quasistatic analysis

In this work the problem of permeation of an oil droplet through a cascade of pore bodies and pore openings is investigated. When the oil droplet becomes totally within the pore cascade, it is called an oil ganglion. The cascade is considered composed of spherical pore bodies and cylindrical pore throats. The capillary entry pressure in relation to the applied pressure difference determines whether the oil ganglion will move or get trapped. Several cases are considered including the case when the leading part of the oil droplet is inside the cascade and the receding part is at the surface, the case when both the interfaces are within pore throats, the case when the two interfaces are within pore bodies, and the case when one interface is in a pore throat and the other is in the pore body. An algebraic equation has been developed to determine the entry pressure when part of the droplet is still at the surface of the cascade. This formula reduces to that found in literature when the whole droplet pins at the surface. This provides confidence in the developed relationship and the modeling approach. The entry pressure associated with all these cases is determined. Several examples have been considered to show how the critical entry pressure may vary throughout the cascade. It is found that, the influence of the receding part of the droplet at the surface of the membrane is not significant on the entry pressure formula. In other words, one can use the critical pressure formula associated with the leading interface to determine the breakthrough through the different parts of the cascade.

A research on CO2 removal via hollow fiber membrane contactor: The effect of heat treatment

The aim of this work was to investigate the effects of heat treatment applying hot air at different temperatures and durations on the morphology and the performance of polyetherimide (PEI) hollow fiber membrane contactors for CO2 separation. The membranes were fabricated via a wet spinning into non solvent bath technique. Then, the membranes were heat treated by exposing them at 80,120 and 160°C for all time intervals of 5, 15 and 30min under a hot air atmosphere. To study the influence of the hot air on the membranes structural parameters and the performance of the membranes they were characterized by: gas permeation test, membrane overall porosity measurement, critical entry pressure of water (CEPw) and gas absorption via a membrane contacting process. The experimental results revealed that, the greatest effect on the membranes structure was observed in the shortest time duration and the lowest temperature i.e. 5min and 80°C, which exhibited a pore size of 49 (nm), a maximum effective surface porosity of 26.8 (1/m) and a CEPw of 3.4bar. Also, for all the time periods and the temperatures tested, the density of the fibers reduced and the CEPws along with the overall porosities increased. In conclusion, applying heat treatment technique on PEI hollow fiber membranes is a simple and easy approach to improve the performance of hollow fiber membrane contactors for CO2 removal.

Mechanics and stability of vesicles and droplets in confined spaces.

The permeation and trapping of soft colloidal particles in the confined space of porous media are of critical importance in cell migration studies, design of drug delivery vehicles, and colloid separation devices. Our current understanding of these processes is however limited by the lack of quantitative models that can relate how the elasticity, size, and adhesion properties of the vesicle-pore complex affect colloid transport. We address this shortcoming by introducing a semianalytical model that predicts the equilibrium shapes of a soft vesicle driven by pressure in a narrow pore. Using this approach, the problem is recast in terms of pressure and energy diagrams that characterize the vesicle stability and permeation pressures in different conditions. We particularly show that the critical permeation pressure for a vesicle arises from a compromise between the critical entry pressure and exit pressure, both of which are sensitive to geometrical features, mechanics, and adhesion. We further find that these results can be leveraged to rationally design microfluidic devices and diodes that can help characterize, select, and separate colloids based on physical properties.

Characterization of partial pore wetting in hollow fiber gas absorption membrane contactors: An EDX analysis approach

In this work a novel method to evaluate the partial pore wetting of gas absorption membranes is proposed. The method consists of two approaches, one by energy-dispersive X-ray spectrometry (EDX), and the other by calculating the mass transfer resistances from the gas and liquid phase in the pore, using the parameter obtained by He gas permeation experiments. For this purpose, hollow fibers were spun from polyetherimide (PEI) and polyethersulfone (PES). As well, the lumen of a PEI hollow fiber was coated with silicone rubber. The hollow fibers were then characterized by He gas permeation experiments, critical entry pressure of water (CEPw), contact angle, scanning electron microscopy (SEM) and EDX. The hollow fibers were then subjected to CO2 gas absorption using aqueous NaCl solution as absorbent. After drying the hollow fiber was subjected to the EDX analysis. The cross-sectional profile of Na and Cl content in the hollow fiber revealed that the pores of the PES hollow fibers were partially wetted, particularly at the pore inlet. Calculation of mass transfer resistances, on the other hand, revealed that the resistance came from gas phase in most hollow fibers, except for the PES hollow fiber where the liquid phase contribution was significant. Silicone rubber coating of the PEI hollow fiber increased the surface hydrophobicity and reduced the pore wetting considerably. Thus, it was concluded that the proposed method can be used as a powerful tool to investigate the pore wetting for many membrane contactor applications.

Preparation and characterization of PVDF-montmorillonite mixed matrix hollow fiber membrane for gas–liquid contacting process

Porous PVDF-hydrophobic montmorillonite (MMT) mixed matrix membranes (MMMs) were fabricated via wet spinning method and used in membrane gas absorption process. The effects of hydrophobic MMT nano-clay loadings (1, 3 and 5wt% of polymer) on the structure and performance were investigated. The fabricated membranes showed both finger-like and sponge-like structure with an increase in the length of finger-like pores in their cross-section, which resulted in higher permeability and lower mass transfer resistance compared to plain PVDF membrane. Also, significant improvements for surface hydrophobicity, critical entry pressure of water and porosity with the addition of filler were observed. The CO2 absorption test was conducted through the gas–liquid membrane contactor and demonstrated a significant improvement in the CO2 flux with MMT loading and the membrane with 5wt% MMT presented highest performance. For example, at the liquid water velocity of 0.5ms−1, CO2 flux of the MMM with 5wt% MMT of 9.73×10−4molm−2s−1 was approximately 56% higher than the PVDF membrane without nano-filler. In conclusion, MMMs with improved absorption properties can be a promising candidate for CO2 absorption and separation processes through membrane contactors.

Estimation of Local Capillary Trapping Capacity from Geologic Models

Local capillary trapping, which is accumulation of CO2 under local capillary barriers, occurs during buoyancy-driven flow through rocks with fine-scale heterogeneity. However, fine-scale flow simulations that resolve the local heterogeneity and show the local capillary trapping have very large and impractical run times. In this work, we find a fast method to estimate these structures from the geologic model assuming a critical capillary entry pressure for the domain. The algorithm uses the capillary entry pressure field and the critical entry pressure as inputs and finds the potential barriers inside the domain and calculates the holes surrounded by clusters of potential barriers. The holes correspond to local capillary traps and will give us an estimate of the local capillary trapping capacity in the domain. This estimate should be an upper bound, since we cannot judge a priori whether CO2 will find its way into these holes.

Preparation and characterization of poly(vinylidene fluoride) hollow fiber membranes for vacuum membrane distillation

AbstractVarious asymmetric microporous poly(vinylidene fluoride) (PVDF) hollow fiber membranes with different pore sizes and effective porosities were prepared by the phase inversion method using dimethylacetamide (DMAc) as solvent and LiCl and water as additives. The membranes were characterized using scanning electron microscopy (SEM) and field emission scanning electron microscopy (FESEM) for its microstructure and surface pore size. A gas permeation method was also applied for determining and comparing the effective surface porosity and mean pore size of the different membranes. Moreover, the contact angle with water, critical entry pressure (CEP) of water and collapsing pressure of the PVDF hollow fibers were also determined. Five membrane modules were prepared using the spun hollow fibers and applied in removing 1,1,1‐trichloroethane (TCA) from its aqueous solution by vacuum membrane distillation (VMD) process. The effects of dope composition and spinning conditions on hollow fiber morphology and TCA separation by VMD process are examined. Post‐treating of the spun fibers by solvent exchange using ethanol produced membranes exhibiting higher porosity and higher permeability. A highly porous hollow fiber membrane with a smaller mean pore size can achieve both high TCA permeation flux and high separation factor. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007

Membrane–solvent selection for CO2 removal using membrane gas–liquid contactors

Membrane gas–liquid contactors can provide very high interfacial area per unit volume, independent regulation of gas and liquid flows and are insensitive to module orientation, which make them very attractive in comparison with conventional equipments for offshore application. However, the membrane adds an additional resistance in the process of mass transfer. The mass transfer resistance of the membrane is affected by the presence of the liquid inside the membrane pores. This wetting of the membrane is determined by the properties of the membrane and the liquid mutually. Hence, a proper choice of the membrane–solvent combination is a critical and determining step in developing membrane gas absorption processes.Important criteria for the selection of the membrane–solvent combination for membrane gas–liquid contactors, such as the critical entry pressure, contact angle and critical solvent surface tension are evaluated in this paper. These characterizing properties of membranes and solvents are experimentally measured for various membrane and solvent combinations for the case of bulk CO2 removal. For selected combinations the actual gas–liquid mass transfer process for CO2 absorption is explored experimentally in the flat sheet as well as in the hollow fiber membrane configuration. The experimental results were compared to the theoretical calculations to determine possible mass transfer limitations due to wetting effects. The polypropylene membrane in combination with propylene carbonate as an absorption liquid was found to be a suitable combination for bulk CO2 removal using membrane gas–liquid contactors.

Critical entry pressure for liquids in hydrophobic membranes

Porous membranes made from a hydrophobic polymer have a minimum entry pressure for water and for some liquids with a contact angle less than 90°. A model was developed to account for this behavior by treating the membrane as a square array of intersecting cylindrical fibers. Experimental data for air-liquid systems in polytetrafluoroethylene membranes showed good agreement with the model, but some liquid-liquid systems gave anomolously low entry pressures.