Prashant K. Bhattacharya

Multi-objective optimization of reverse osmosis desalination units using different adaptations of the non-dominated sorting genetic algorithm (NSGA)

Multi-objective optimization using genetic algorithm (GA) is carried out for the desalination of brackish and sea water using spiral wound or tubular modules. A few sample optimization problems involving two and three objective functions are solved, both for the operation of an existing plant (which is almost trivial), as well as, for the design of new plants (associated with a higher degree of freedom). The possible objective functions are: maximize the permeate throughput, minimize the cost of desalination, and minimize the permeate concentration. The operating pressure difference, ΔP, across the membrane is the only important decision variable for an existing unit. In contrast, for a new plant, ΔP, the active area, A, of the membrane, the membrane to be used (characterized by the permeability coefficients for salt and water), and the type of module to be used (spiral wound/tubular, as characterized by the mass transfer coefficient on the feed-side), are the important decision variables. Sets of non-dominated (equally good) Pareto solutions are obtained for the problems studied. The binary coded elitist non-dominated sorting genetic algorithm (NSGA-II) is used to obtain the solutions. It is observed that for maximum throughput, the permeabilities of both the salt and the water should be the highest for those cases studied where there is a constraint on the permeate concentration. If one of the objective functions is to minimize the permeate concentration, the optimum permeability of salt is shifted towards its lower limit. The membrane area is the most important decision variable in designing a spiral wound module for desalination of brackish water as well as seawater, whereas ΔP is the most important decision variable in designing a tubular module for the desalination of brackish water (where the quality of the permeate is of prime importance). The results obtained using NSGA-II are compared with those from recent, more efficient, algorithms, namely, NSGA-II-JG and NSGA-II-aJG. The last of these techniques appears to converge most rapidly.

Flux and retention analysis during micellar enhanced ultrafiltration for the removal of phenol and aniline

Studies were done for the removal of organic solutes under aqueous medium through micellar enhanced ultrafiltration (MEUF). The organic solutes selected for experiments consisted of an ionic compound (phenol) and a non-ionic compound (aniline); whereas cetyl pyridinium chloride (CPC), a counter-ionic surfactant was used for the formation of micelles under aqueous medium. UF was carried out under both stirred and unstirred conditions using batch cells. The effect of important operating parameters (applied pressure, solutes and surfactant bulk concentrations) on the extent of separation of the organic solutes were observed and studied. Solubilization of these solutes in CPC micelles were also experimentally ascertained. A mathematical model developed in this study was used to describe the separation of organic solutes by MEUF and predict permeate solute concentrations under varying operating conditions. The effect of pressure and feed CPC concentration on the behaviour of permeate flux was explained as a consequence of the formation of concentration polarized layer of CPC, upstream of the membrane surface. The removal of organic solutes (phenol and aniline) were observed to increase with increase in feed CPC concentration; however, upto about 150 mM, beyond which it was more or less constant. Solubilization equilibrium constant of phenol in CPC micelles was estimated to be around four times that of aniline.

Generalized integral and similarity solutions of the concentration profiles for osmotic pressure controlled ultrafiltration

A mathematical model describing the concentration polarization phenomenon during osmotic pressure controlled ultrafiltration is presented. Generalized integral and similarity solutions of the concentration profile in the mass transfer boundary layer are obtained. The parameters governing the shape of the concentration profile vary with time in case of a batch cell and axial distance in a cross flow cell. The model is used to predict the permeate flux and the solute rejection simultaneously during unstirred batch cell and cross flow UF. The results obtained by integral and similarity solutions are compared with the results of detailed numerical solution of the governing equations for both the systems. The predictions of permeate flux from the generalized integral method are also compared with some approximate solutions in order to assess the limitations of the various approximations. UF experiments were performed with Dextran (T-20) in cross flow system and with PEG-6000 and Dextran (T-40 and T-20) in unstirred batch cell. Predictions of the model are in remarkably good agreement with detailed simulation as well as experimental results. Moreover, the integral solution can also account for the variation of diffusivity with solute concentration. Comparisons show that (a) while the generalized integral method is much simpler than the detailed numerical solutions, it is much more general and accurate than other analytical and semi-analytical solutions, and, (b) the proposed solution predicts the osmotic pressure controlled flux decline accurately over a wide range of operating conditions. The expression for gel layer governed UF (constant membrane surface concentration) is found to be an asymptotic case of the present solution.

Modeling of ultrafiltration process for a two-component aqueous solution of low and high (gel-forming) molecular weight solutes

Filtration of sucrose from a mixture of sucrose and poly(vinyl alcohol) (PVA) was studied in a stirred ultrafiltration cell. PVA formed a gel layer and was completely rejected by the membrane. Two membranes of different molecular weight cut-off, namely, 1 K and 10 K were chosen. By the former, sucrose was partially retained and by the latter, it was completely permeable in the absence of PVA. A mathematical model was formulated for simultaneous prediction of permeate flux and observed rejection of sucrose. The characteristics of the gel layer and other relevant parameters of the model were determined by independent sets of experiments. It was observed that the steady-state flux was independent of pressure and equal to the flux of the gel-forming component alone (in the absence of permeating solute). Profiles of permeate flux and observed rejection of sucrose with time agreed well with the experimental observations.

Prediction of mass-transfer coefficient with suction in the applications of reverse osmosis and ultrafiltration

Sherwood-number relations for prediction of the mass-transfer coefficient for developing concentration boundary-layer have been obtained for laminar flow-regime from first principles. The common flow-modules, namely, rectangular channel, tubular and radial cross-flow are considered. The relationships developed include the effect of suction through the membrane. Relevant relations for estimation of mass-transfer coefficient for cross-flow reverse osmosis and ultrafiltration are formulated. The Sherwood-number relations developed are compared with the standard correlations to quantify the effect of the suction. The proposed Sherwood relations are used in conjunction with the osmotic-pressure model to predict the permeate flux in reverse osmosis and osmotic-pressure governed ultrafiltration.

A unified model for flux prediction during batch cell ultrafiltration

An analysis of the flux decline encountered during ultrafiltration (UF) in a batch cell is presented by including the combined influence of the osmotic pressure and the gel layer. A predictive model for the flux decline in unstirred and stirred batch cell UF processes is developed by unifying the osmotic pressure and gel layer models. UF experiments were performed in a batch cell with polymeric solutes (PEG, dextran and PVA) and a protein (BSA), ranging widely in molecular weights and physico-chemical properties, under various operating conditions (pressure, solution pH, and stirrer speed). The present unified model predictions match closely with the experimental flux behaviour for all cases, while individual osmotic pressure and gel layer models are found to be inadequate.

Phenol solubilization by cetyl pyridinium chloride micelles in micellar enhanced ultrafiltration

Abstract An attempt has been made to analyze the ultrafiltration data of cetyl pyridinium chloride solution. Solubilization of phenol in the micelles and consequent micellar enhanced ultrafiltration is also studied. Experiments were carried out in both stirred and unstirred cells. For a particular experimental conditions, flux was obtained invariant with time for surfactant solution. There was a distribution of organic solute between aqueous and micelle phase. The solute solubilization capacity of the micelles decreased with increase in applied pressure during ultrafiltration. With increase in surfactant concentration the extent of solubilization of organic solute increased but at the same time, the permeate concentration of the surfactant with respect to the concentration in the feed solution also increased, which is not desirable for industrial applications. Therefore, there must exits an optimal surfactant to solute ratio to conduct the most efficient micellar enhanced ultrafiltration.

Prediction of limiting flux in ultrafiltration of kraft black liquor

Abstract Ultrafiltration of black liquor was carried out using an asymmetric membrane in a stirred batch cell, modified to work on a continuous mode. Poly (ethylene glycol)-6000 was used as a standard macromolecule to compare the results. An attempt was made to predict the flux using a generalized formulation which takes into account the unsteady-state behaviour during the initial stages of continuous stirred ultrafiltration. The model combines film theory, gel theory and filtration theory to predict permeate flux as a function of time. The governing partial differential equation, based on the unsteady-state mass balance concept, was solved numerically. The predicted flux values were compared with experimental data and the average deviations were found to be less than 7%.

Ultrafiltration of sugar cane juice for recovery of sugar: analysis of flux and retention

Raw sugar cane juice was pretreated by cold liming. Clarified juice was then subjected to ultrafiltration (UF) in a stirred cell using three different membranes (Spectra Por 10 K (M1) and 20 K (M3); commercial diffused cut-off 15 K (M2) membranes). The filtration studies were carried out with the aim of retaining the solids except the sugar compounds, present in juice as well as maximizing the flux. Permeate flux and retention of sugars as well as total dissolved solids in permeate stream were measured. Performances of these membranes were evaluated in terms of permeate flux and its quality. It was observed that the permeate flux obtained using M1 membrane was higher than M2 and M3 for most of the operating conditions. However, the retention of sugars was minimum for M3 membrane, which is desirable. A modified resistance-in-series model has been used to analyze both short and long term flux decline behavior under various operating conditions.

Flux decline during ultrafiltration of kraft black liquor using different flow modules : a comparative study

Ultrafiltration of black liquor was studied in three different modules, namely, radial cross flow, rectangular cross flow and stirred cell over a wide range of operating conditions. Effects of different cut-off membranes on the permeate flux and observed rejection were also studied in the stirred cell module. Effects of operating conditions, e.g. pressure difference, Reynolds number and feed concentration on the permeate flux and observed rejection were also investigated. Such comparative study may be useful to select a suitable module, membrane and a set of optimum operating conditions to achieve a desired quantity and quality of permeate flux. A comparative analysis of flux decline for different modules is also presented using a simple resistance-in-series model.