Permeation simulation

Permeation process of small molecules across lipid membranes studied by molecular dynamics simulations. J. Phys. Chem. 100 (1996) 16729-16738. 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

A = 4.05 X lO " cm/(s-kPa)(4.1 X 10 cm/(s-atm)) and = 1.3 x 10 cm/s (4)//= 1 mPa-s(=cP), NaCl diffusivity in water = 1.6 x 10 cm /s, and solution density = 1 g/cm . Figure 4 shows typical results of this type of simulation of salt water permeation through an RO membrane. Increasing the Reynolds number in Figure 4a decreases the effect of concentration polarization. The effect of feed flow rate on NaCl rejection is shown in Figure 4b. Because the intrinsic rejection, R = 1 — Cp / defined in terms of the wall concentration, theoretically R should be independent of the Reynolds... 

In general, the rate of permeation of the permeating species is difficult to calculate. It is a complex matter which intimately involves a knowledge of the structure and dynamics of the membrane and the structure and dynamics of the complex fluid mixture in contact with it on one side and the solvent on the other side. Realistic membranes with realistic fluids are beyond the possibihties of theoretical treatment at this time. The only way of dealing with anything at all reahstic is by computer simulation. Even then one is restricted to rather simplified models for the membrane. 

The arrows indicate a semi-permeable membrane and the species allowed to permeate is shown within the arrows. The parentheses show a GEMC phase (or region) and the species it contains. The first and the last region are also connected to each other. Using such a scheme, Bryk et al. showed that osmotic Monte Carlo can be successfully used to study the association of two different molecular species when an associating intermolecular potential is included in the simulation. The results agreed well with the more traditional grand-canonical Monte Carlo methods. 

One of the most remarkable results from the molecular simulation studies of aqueous electrolyte solutions was that no additional molecular forces needed to be introduced to prevent the much smaller ions (Na has a molecular diameter of less than 0.2 nm) from permeating the membrane, while permitting the larger water molecules (about 0.3 nm in diameter) to permeate the membrane. This appeared to be due to the large ionic clusters formed. The ions were surrounded by water molecules, thus increasing their effective size quite considerably to almost 1 nm. A typical cluster formed due to the interaction between the ions and a polar solvent is shown in Fig. 7. These clusters were found to be quite stable, with a fairly high energy of desolvation. The inability of the ions to permeate the membrane is also shown... 

MERL s interest in employing these tests has included (1) the quantifying of D to enable certain predictions to be made (see Section 23.4.6), (2) testing at high temperature and pressures to simulate service realism (see Section 23.5.1.3), and (3) to provide data for use in estimating permeation rates while not needing to conduct actual permeation tests (see Section 23.4.4.3). 

Li, K., Acharya, R. and Hughes, R. (1991) Simulation of Gas Separation in an Internally Staged Permeator, Trans IChemE, 69, Part A, 35-42. 

Pal T, Griffin GD, Miller GH, et al. 1993. Permeation measurements of chemical agent simulants through protective clothing materials. Journal of Hazardous Materials 33(1) 123-141. 

Vo-Dinh T, Pal, T. 1992. Development of a fluorescence quenching technique to detect permeation of chemical agent simulants through protective clothing materials. Appl Spectrosc 46(4) 677-681. 

A continuous cross-flow filtration process has been utilized to investigate the effectiveness in the separation of nano sized (3-5 nm) iron-based catalyst particles from simulated Fischer-Tropsch (FT) catalyst/wax slurry in a pilot-scale slurry bubble column reactor (SBCR). A prototype stainless steel cross-flow filtration module (nominal pore opening of 0.1 pm) was used. A series of cross-flow filtration experiments were initiated to study the effect of mono-olefins and aliphatic alcohol on the filtration flux and membrane performance. 1-hexadecene and 1-dodecanol were doped into activated iron catalyst slurry (with Polywax 500 and 655 as simulated FT wax) to evaluate the effect of their presence on filtration performance. The 1-hexadecene concentrations were varied from 5 to 25 wt% and 1-dodecanol concentrations were varied from 6 to 17 wt% to simulate a range of FT reactor slurries reported in literature. The addition of 1-dodecanol was found to decrease the permeation rate, while the addition of 1-hexadecene was found to have an insignificant or no effect on the permeation rate. 

The objective of the present study is to develop a cross-flow filtration module operated under low transmembrane pressure drop that can result in high permeate flux, and also to demonstrate the efficient use of such a module to continuously separate wax from ultrafine iron catalyst particles from simulated FTS catalyst/ wax slurry products from an SBCR pilot plant unit. An important goal of this research was to monitor and record cross-flow flux measurements over a longterm time-on-stream (TOS) period (500+ h). Two types (active and passive) of permeate flux maintenance procedures were developed and tested during this study. Depending on the efficiency of different flux maintenance or filter media cleaning procedures employed over the long-term test to stabilize the flux over time, the most efficient procedure can be selected for further development and cost optimization. The effect of mono-olefins and aliphatic alcohols on permeate flux and on the efficiency of the filter membrane for catalyst/wax separation was also studied. 

In order to develop a continuous flux maintenance procedure, the present study examined the transmembrane flux values from the cross-flow filtration module with a filtration media area of 0.0198 m2 (0.213 ft2), a slurry density of approximately 0.69 g/cm3 at 200°C, 17 kg of simulated FT wax with a catalyst loading of 0.26 wt%, and a TMP between 0.68 and 1.72 bar (10-25 psig). The filtration process was run in a recycle mode, whereas clean permeate was added back to the slurry mixture, thus allowing the catalyst concentration to remain approximately constant over the course of the run (given minor adjustments for about 5 ml permeate and slurry samples collected throughout the test). 

Application of cross-flow filtration for the removal of FT wax products can be a useful technique to maintain a constant catalyst loading in an FTS reactor in continuous operation. Addition of 1-dodecanol (at a concentration of 6 wt%) was found to decrease the permeation rate of the cross-flow filter used for the separation of simulated FT wax and activated iron catalyst slurry. However, additional... 

Of course there are many phenomena that equilibrate on the nanosecond timescale. However, the majority of relevant events take much more time. For example, the ns timescale is much too short to allow for the self-assembly of a set of lipids from a homogeneously distributed state to a lamellar topology. This is the reason why it is necessary to start a simulation as close as possible to the expected equilibrated state. Of course, this is a tricky practice and should be considered as one of the inherent problems of MD. Only recently, this issue was addressed by Marrink [56]. Here the homogeneous state of the lipids was used as the start configuration, and at the end of the simulation an intact bilayer was found. Permeation, transport across a bilayer, and partitioning of molecules from the water to the membrane phase typically take also more time than can be dealt with by MD. We will return to this point below. 

With the Monte Carlo technique, a very large number of membrane problems have been worked on. We have insufficient space to review all the data available. However, the formation of pores is of relevance for permeation. The formation of perforations in a polymeric bilayer has been studied by Muller by using Monte Carlo simulation [67] within the bond fluctuation model. In this particular MC technique, realistic moves are incorporated, such that the number of MC steps can be linked to a simulated time. 

Meanwhile, computational methods have reached a level of sophistication that makes them an important complement to experimental work. These methods take into account the inhomogeneities of the bilayer, and present molecular details contrary to the continuum models like the classical solubility-diffusion model. The first solutes for which permeation through (polymeric) membranes was described using MD simulations were small molecules like methane and helium [128]. Soon after this, the passage of biologically more interesting molecules like water and protons [129,130] and sodium and chloride ions [131] over lipid membranes was considered. We will come back to this later in this section. 

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