Equilibrium facilitated mass transfer in plate type reactive membrane separation devices

The introduction of mobile carrier species which react reversibly with the solute species in liquid membrane mass transfer separation devices can give enhanced mass transfer rate. For one-dimensional laminar boundary layer flow of a Newtonian fluid past a single-membrane separator with equilibrium facilitated transport inside the membrane, the mass transfer rate in the separator was analyzed numerically. For a Damköhler number equal to infinity, the effect of maximum facilitation factor, dimensionless equilibrium constant, dimensionless velocity and similarity transformation parameter on the performance of separators was investigated. The dependence of the membrane-fluid interfacial concentration and equilibrium facilitation factor on dimensionless velocity and similarity transformation parameter was discussed.     

Mathematical modelling of CO2 facilitated transport through liquid membranes containing amines as carrier

An approximate analytical solution for the facilitated transport of carbon dioxide across a liquid membrane containing aqueous primary and secondary amine solutions has been developed in which the reversible reaction A(CO₂) + 2B(amine) AB(carbamate) + BH(protonated amine) occurs inside the liquid membranes. The current approximate analytical solution predicts the facilitated factor of CO₂ through the membrane and is based on the dimensionless, nonlinear diffusion‐reaction transport problem. The approximate analytical solution predicts the facilitation factors for the range from the moderate reaction rate to the equilibrium chemical reaction regime, allowing unequal diffusivities of complexes and carrier and cases of zero and nonzero permeate side solute concentrations. In the present mathematical model, a constant free carrier concentration is assumed throughout the membrane phase. In comparison with the numerically calculated results, the results obtained were found to be in well agreement.     

LIQUID MEMBRANE TRANSPORT OF CEPHALOSPORIN ANTIBIOTICS: EFFECT OF SOLUTE CHEMICAL NATURE ON CARRIER SPECIFICITY

Cephalosporin antibiotics were transported from a dilute aqueous solution (feed phase) through a bulk liquid membrane containing Aliquat-336 as an anion exchange carrier in n-butyl acetate as the solvent to another aqueous solution (receiving phase) of lower pH. Under appreciable pH gradient of the feed and receiving phases, facilitated uphill transport could be obtained. Under the optimal pH condition, the intial solute flux across the bulk liquid membrane could be correlated well with the hydrophobicity of the solutes. A linear correlation exists between the initial solute flux and hydrophobicity, indicating that the solute of higher hydrophobic nature are transported at a higher rate in the bulk liquid membrane involving the specific carrier. The correlation appears to be derived from a linear dependenc of solute hydrophobicity on equilibrium constant of the reactive extraction system being exploited in the bulk liquid membrane.     

Physicochemical criteria for reverse osmosis separation of monohydric and polyhydric alcohols in aqueous solutions using porous cellulose acetate membranes

Reverse osmosis data using different samples of Loeb-Sourirajan-type porous cellulose acetate membranes and single-solute aqueous solution systems involving 16 monohydric alcohols, 4 phenols, 18 polyhydric alcohols, pyrogallol, ethylene glycol monoethyl ether, 6 aldehydes, and 8 carbohydrates (sugars) have been studied. The solute concentrations used were in the range of 0.0005 to 0.003 g mole/l. (～100 ppm), and operating pressure used was 250 psig in all cases. The results show that correlations of acidity and basicity parameters (obtained from IR spectra) with solute separation data are equivalent, and they have predictive capability. A method is given for estimating Taft numbers (Σσ^*) for monohydric and polyhydric alcohols from available data based on the additive nature of σ^*. Data on solute transport parameters (D_AM/Kδ) for the different solutes were calculated from membrane performance data. For all the alcohols studied, the Σσ^*-versus-log (D_AM/K)δ correlation was found to be a straight line with a slope different for different ranges of Σσ^*, but independent of the porous structure of the membrane. Based on this result, it is shown that the parameters of the Taft equation can serve as a basis for expressing solute transport parameter, and this basis offers a means for predicting membrane performance for all alcohol–water systems from a single set of experimental data for a reference solute system. This prediction technique is illustrated using experimental data for 1,3-butanediol taken as the reference solute. The general applicability of the technique has been tested for predicting the separation of some aldehydes and carbohydrates.     

乳化液膜提取柠檬酸及其溶胀的研究

本文研究了采用Ｗ／Ｏ型乳化液膜提取水溶液中的柠檬酸，同时研究了柠檬酸提取过程中水的传质行为（乳液溶胀）。考察了表面活性剂、载体、反萃剂Ｎａ２ＣＯ３、柠檬酸浓度对柠檬酸传质和乳液溶胀的影响。实验结果表明：萃取率随载体和内相试剂浓度的增加而增加；当载体和初始柠檬酸浓度较高时，乳液更易于溶胀，由此得出了除渗透压造成的乳液溶胀外，溶质与载体形成的络合物也能促成乳液的溶胀。提出了分离浓缩柠檬酸的最佳乳液配方     

稀土浸出过程溶质传递的格子Boltzmann模拟

采用耦合传质的格子Boltzmann方法模拟风化壳淋积型稀土矿中稀土浸出的溶质传递过程,在验证模型有效性的前提下,获得了稀土矿填充孔隙中流体流动的速度分布和伴随流动过程的溶质浓度分布. 通过考察浸取流速对溶质传递过程的影响,得到最佳浸取流速,约为0.25~0.35 mm/s,使溶质传递效率最高. 浸取流速小于0.2 mm/s导致浸取周期过长、浸取剂消耗量大;浸取流速大于0.4 mm/s引起沟流,导致稀土不能有效地浸出. 此外,模拟所得传质舍伍德数Sh随雷诺数Re的变化关系与经验关系式吻合,表明提出的模型可用于预测稀土浸出过程的溶质传递规律.     

High-Pressure Gas Chromatography and Chromatography with Supercritical Fluids. I. The Effect of Pressure on Partition Coefficients in Gas-Liquid Chromatography with Carbon Dioxide as a Carrier Gas

Abstract

Gas-chromatographic experiments with CO₂ as a carrier gas, conducted at temperatures of 30 to 40°C and pressures up to 80 atm, showed a pronounced drop of the partition coefficient with increasing pressure. This effect, which can be interpreted as a raise in solute volatility, is proved to be mainly due to nonideality in the gas phase.

The gain in volatility (by a factor of 10 or more) permits gas-chromatographic separations to be carried out at lower temperatures than usual. As partition coefficients were found to drop very fast near the critical point of the carrier gas, operation at pressures well above this point may open up the possibility of handling compounds too heavy for ordinary gas-chromatographic practice.

Interesting possibilities of class separation can be deduced from the study of the pressure effect in homologous series. Some potential non-analytical applications of high-pressure gas chromatography are discussed.     

Droplet evaporation and solute precipitation during spray pyrolysis

The process of spray pyrolysis was investigated theoretically using a model that describes the evolution of the droplet size, solvent vapor concentration in the carrier gas, and both droplet and gas temperatures along the reactor axis. The model also accounts for solute concentration profiles and solute precipitation in the solution droplets. The model was used to describe the evaporation of sodium chloride aqueous solution droplets in diffusion dryers and hot-wall reactors as a function of reactor residence time, droplet size (a few microns), solution molality (up to 2 M), droplet concentration (10⁶–10⁷ cm⁻³), relative humidity of the carrier gas (0–50%) and reactor wall conditions. Decreasing initial droplet size and solution molality accelerated droplet evaporation and resulted in smaller droplets at the onset of solute nucleation. Decreasing droplet concentration and carrier gas inlet relative humidity as well as increasing wall temperature (up to 350°C) or axial wall temperature gradient (up to 100°C cm⁻¹) increased the droplet evaporation rate, but did not change appreciably the droplet size at the point of precipitation for a given droplet size and solute concentration. Thus, control of droplet size at the onset of solute nucleation by varying process parameters other than the solution concentration and initial droplet size is limited.     

Effects of crystal growth rate and heat and mass transfer on solute distribution

The effects of crystal growth rate and heat and mass transfer on solute distribution during solidification of binary melt have been theoretically investigated on the basis of a new theory of solute distribution proposed by the present authors. The solute distribution factor f at the solid-liquid (SL) interface is in inverse proportion to the one-half power of the dimensionless growth rate U. The growth rate U is in proportion to the second power of the normalized concentration difference between the SL interface and bulk melt. A new transport factor K, which describes heat and mass transfer in melt, gives an important contribution to the crystal growth and the solute distribution at the SL interface. The transport factor is used successfully to control the solidification of melt. The flow structure in melt exerts essential influence on the solid purity.     

Analytical approximate solution of competitive facilitated transport of acid gases through liquid membranes

An analytical approximate solution for the competitive facilitation factor of components A and E across a liquid membrane is developed in the case of instantaneous reactions inside the liquid membranes. This analytical solution solves the dimensionless, nonlinear diffusion-reaction transport problem governing the competitive facilitated transport of two gaseous components through liquid membranes. Prediction of the facilitation factors has been obtained for the equilibrium chemical reaction regime, considering the unequal complexes diffusivities and cases of zero and nonzero permeate side solute concentrations. This mathematical solution leads to analytical expressions for the concentration profiles of the species across the liquid membrane. In comparison with the present numerical solution and also numerical calculations and experimental data from the open literature, the difference between the analytical predictions and those obtained from the numerical solution were found to be in well agreement.     

Analysis of facilitated transport membrane with modified boundary conditions

The performance of the steady state carrier-mediated transport has been investigated. A modified boundary condition is proposed according to the fact that a flowing sweep gas in the receiving phase of the membrane sweeps the permeant molecules, thus the concentration of permeant in the interface of membrane-receiving phases is a function of mass transfer coefficient in the receiving phase. Based on the method of orthogonal collocation, the system of coupled integro-differential boundary value equations is solved. It is confirmed that the facilitation factors calculated by the present approach are much closer to the experimental data. A superior efficiency has also been shown with respect to the previous results of simple Dirichlet type boundary conditions. The proposed method well predicts the system over the entire range of operating conditions, from the physical diffusion to the chemical equilibrium region as well as equal/unequal carrier and complex diffusivities. More studies reveal that increasing Sherwood number and thus reducing the receiving phase resistance would cause an increase in the mass transfer coefficient as well as trans-membrane flux. Also, a decrease in concentration of permeant in the receiving phase, “C_M,b”, shows the same results as increasing Sherwood number.     

Separation and enrichment of carbon dioxide by capillary membrane module with permeation of carrier solution

A novel facilitated transport membrane for gas separation using a capillary membrane module is proposed in which a carrier solution is forced to permeate the membrane. Both a feed gas and a carrier solution are supplied to the lumen side (high pressure side, feed side) of the capillary ultrafiltration membrane and flow upward. Most of the carrier solution which contains dissolved solute gas, CO₂ in the present case, permeates the membrane to the permeate side (low pressure side, shell side), where the solution liberates dissolved gas to form a lean solution. The lean solution is circulated to the lumen side. This type of capillary membrane module was applied to the separation of CO₂ from model flue gases consisting of CO₂ and N₂. Monoethanolamine (MEA), diethanolamine (DEA) and 2-amino-2-methyl-1-propanol (AMP) were used as carriers or absorbents of CO₂. The feed side pressure was atmospheric and the permeate side was evacuated at about 10 kPa. CO₂ in the feed gas was successfully concentrated from 5–15% to more than 98%. The CO₂ permeance was as high as 2.7×10⁻⁴ mol m⁻² s⁻¹ kPa⁻¹ (8.0×10⁻⁴ cm³ cm⁻² s⁻¹ cmHg⁻¹) when the CO₂ mole fraction in the feed was 0.1 and temperature was 333 K. The selectivity of CO₂ over N₂ was in the range from 430 to 1790. The membrane was very stable over a discontinuous one-month testing period.     

Heat Transfer Effects in Facilitated Transport Liquid Membranes

Abstract

Various mathematical models have been developed to describe facilitated transport. There are two limiting regimes where steady-state analytical solutions are available; diffusion-limited (reaction equilibrium) and reaction-limited (frozen condition). For intermediate cases, numerical solutions are available. All of these models are valid for isothermal conditions. It is possible in practice that the system may not be isothermal. The gas streams on each side of the membrane may be at different temperatures and/or there can be heat of reaction effects. These effects can cause the total facilitated flux to deviate from the isothermal case.

The results of including temperature effects are incorporated in a dimensionless factor θ. θ is the facilitation factor for the non-isothermal case divided by the facilitation factor for the isothermal case. Results show that the imposition of a temperature gradient can cause a significant increase or decrease in the facilitated flux. In extreme cases, there can even be a reversal in the direction of the facilitated flux. The heat of reaction had no noticeable effect for the conditions studied.     

Hollow fiber reverse osmosis: experiments and analysis of radial flow systems

The performance of a hollow fiber reverse osmosis system was determined experimentally by measuring the fraction of feed recovered as product, φ, and the concentration reduction ratio, θ_p. A predictive model for these two quantities was developed which yields results that agree with the experimental data very well for applied pressures of 300–450 psig., feed rates from 75 to 525 cc/sec and feed concentrations up to 15000 ppm of sodium chloride.The concept of distributed sinks in a continuum is used for the shell side, and a diffusion model is used to describe solute transport across the fiber wall. The principal assumptions made are negligible concentration polarization, small radial pressure drop in the shell and small solute transport, compared with solvent transport, through the fiber. Simple closed form expressions for φ and θ_p, given by eqns (43a) and (51), were obtained which are accurate over the range of experimental conditions employed.     

An analysis of the falling film gas-liquid reactor

A mathematical model of the falling film reactor is developed to predict the conversion and temperature distribution in the reactor as a function of the gas and liquid flow rates, physical properties, the feed composition of the reactive gas and carrier gas and other parameters of the system. Transverse and axial temperature profiles are calculated for the laminar flow of the liquid phase with concurrent flow of a turbulent gas to establish the peak temperatures in the reactor as a function of the numerous parameters of the system. The reaction rate in the liquid film is considered to be controlled by the rate of transport of reactive gas from the turbulent gas mixture to the gas-liquid interface. The governing equations are solved by reformulating the problem in integral equation form employing Green's functions. The predicted reactor characteristics are shown to agree with large-scale reactor performance, and the effects of the most sensitive parameters are elucidated to provide a basis for reactor optimization. Numerical results are presented for realistic sulfonation reactor conditions.     

Computational scheme for the step growth polymerization of multifunctional monomers in presence of intramolecular reactions

The transport of gaseous ethylene oxide (EtO) in several polymer films is studied using the carrier gas method of measurement. Permeability, solubility, and diffusion coefficients describing ethylene oxide (EtO) transport in polypropylene, polyvinylchloride, Teflon-FEP copolymer, and polyethylene films have been obtained over a 30 Celsius degree range at a low concentration of EtO using the carrier gas method of measurement. The results indicate that the diffusion of EtO in polyethylene is independent of penetrant concentration over the range of concentrations used. However, concentration-independent diffusion could not be verified directly for the other films studied. Two different techniques of determining diffusion coefficients were used, and within the precision of the data both yield the same result. An excess enthalpy of solution for the solubility of EtO in Teflon-FEP copolymer was calculated, an observation that suggests that dual-mode sorption may be taking place.     

Optimal design of combined cycle power plants with fixed-bed chemical-looping combustion reactors

Process intensification options are explored for near-carbon-neutral, natural-gas-fueled combined cycle (CC) power plants, wherein the conventional combustor is replaced by a series of chemical-looping combustion (CLC) reactors. Dynamic modeling and optimization are deployed to design CLC-CC power plants with optimal configuration and performance. The overall plant efficiency is improved by optimizing the CLC reactor design and operation, and modifying the CC plant configuration and design. The optimal CLC-CC power plant has a time-averaged efficiency of 52.52% and CO₂ capture efficiency of 96%. The main factor that limits CLC-CC power plant efficiency is the reactor temperature, which is constrained by the oxygen carrier material. CLC exhaust gas temperature during heat removal and gas compressor to gas turbine pressure ratio are the most important operating variables and if properly tuned, CLC-CC power plants can reach high thermodynamic efficiencies. © 2018 American Institute of Chemical Engineers AIChE J, 65: e16516 2019     

GAS ABSORPTION INTO A LIQUID FLOWING OVER A SPHERE WITH A SECOND-ORDER IRREVERSIBLE CHEMICAL REACTION

The objective of the work presented here is to theoretically investigate the absorption of a gas into a liquid flowing in laminar flow over a sphere with a second-order irreversible chemical reaction occurring between the absorbed gas and a nonvolatile solute present in the liquid. Commonly used simplifications in the diffusion-reaction equations and for the liquid velocity profile and the liquid film thickness on the sphere are investigated, and it is found that, under the experimental conditions usually encountered, these simplifications are justified. Numerical results for the absorption rate are presented graphically in two figures which may be used to estimate the second-order kinetic rate coefficient for the reaction between the absorbed gas and the nonvolatile liquid-phase solute. A criteria is developed for the conditions under which a second-order reaction may be considered to be pseudo-first-order,     

Study of dynamic effects by convective velocity in the membrane process: Operator theoretic approach

This paper studies the dynamic mass transfer effects of solute through fluid-solid interactions in a heterogeneous system. It is found that the convective velocity in internal pores of the membrane can be used to accelerate the speed of the solute by convective velocity at the fluid phase. The theoretical model for the membrane transport is studied in this paper by using the operator theoretic method. A typical example of this dynamic interaction problem is applied in a multi-layered composite membrane. Danckwerts Boundary conditions are analyzed in the inner and outer regions of membrane process. A spectral evaluation of the transport operator is performed by the operator properties in the system. The findings of this paper are useful in guiding the design of membrane separation devices as well as in proving useful to the synthetic performance of composite membrane.