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Mass transfer coefficient and retention of PEGs in low pressure cross-flow ultrafiltration through asymmetric membranes

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Mass transfer coefficient and retention of PEGs in low pressure cross-flow ultrafiltration through asymmetric membranes
  journal of MEMBRANE SCIENCE E LS EV I ER Journal of Membrane Science 99 ( 1995 ) 1-20 Mass transfer coefficient and retention of PEGs in low pressure cross-flow ultrafiltration through asymmetric membranes P. Prddanos*, J.I. Arribas, A. Herndndez Dpto. de Ffsica Aplicada If, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain Received 28 May 1994; accepted in revised form 19 August 1994 Abstract The flow and retention of 0.1% w/w aqueous solutions of several polyethylene glycols with molecular weights ranging from 300 to 12000 Daltons are studied when they are tangentially filtered through three commercially available asymmetric membranes, with transmembrane pressure differences up to 650 kPa. The mass transfer coefficients are obtained for low applied pressures below 60 kPa, within the frame of the film layer theory for the concentration polarization phenomena. The resulting variation of Kr~ with the feed recirculation velocity and the molecular weight is analyzed. In the transition between laminar and turbulent regime, the experimental dependencies of Km are compared with those predicted by friction and non-friction models for the Sherwood equations. The mass transfer coefficient is used to compute the true retention standard curves, allowing estimate of the mean pore radii of the membranes. Keywords: Mass transfer; Polyethylene glycols; Ultrafiltration 1. Introduction Ultrafiltration is being used increasingly as a con- centration and separation process in a variety of indus- tries. Ultrafiltration is amenable to both continuous and batch operations and offers several advantages over more traditional separation methods. For example, because there is no heat added, ultrafiltration is suitable for heat labile substances. In addition, the products are not likely to suffer chemical denaturation which can be present with solvent extraction methods. The applica- tions of ultrafiltration are determined mainly by the permeability versus molecular weight characteristics of the membranes to be used. Manufacturers of ultrafilters generally specify a nominal "cut-off" for their products to be used in process design. However, in practice, there is not a sharply defined molecular weight below which all the 0376-7388/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI0376-7388(94)00197-9 solutes pass the membrane while those above it are totally retained. On the contrary, in fact there is a grad- ual shift from free permeability to total retention as molecular weight increases. In practice, the permeation versus molecular weight characteristics depend on the process parameters and device characteristics; i.e. on the specific features of the process and cell where the membrane is going to be used. Polyethylene glycols are usually chosen to charac- terize a membrane-cell ensemble, because they are water soluble and can be readily obtained with narrow molecular weight distributions. In addition their adsorption is very low for almost every polymer sur- face. A tangential flow device has some advantages over the dead end design, mainly due to its capacity to reduce  2 P. Prddanos et al./Journal of Membrane Science 99 (1995) 1-20 IP RP 1111 l , 9, Mc I ......................... ] m v or L NV DR Fig. 1. Experimental device with: Thermostat T, feed reservoir R, pump regulator RP, impulsion pump IP, pressure transducers P~ and P2, membrane cell MC, needle valve NV, flowmeters F, or F2, balance B and differential refractometer DR. the formation of a concentration polarization layer, consequently decreasing the levels of fouling and pore clogging. In this case, the molecular weight cut-off has to be carefully defined and studied in terms of the pres- sure difference allowed to act through the membrane and the velocity of recirculation used in the retentate loop. Three asymmetric membranes (thin film membrane, TFM ®) that are commercially available in spiral wound modules (Desalination Systems Inc., CA, USA) are studied here when used in flat sheets in a tangential flow cell. Our aim is to analyze the influence of the operation parameters on the permeation properties. Our specific goal being to characterize these ultrafiltration asym- metric membranes when used in a low pressure range, with recirculation velocities in the laminar range and in the transition to turbulent regime- assuming laminar conditions for Reynolds numbers less than 1800 and turbulent regime starting at Reynolds numbers greater than 4000. In the low pressure range used we are far below the conditions where the flux should be inde- pendent of the applied pressure, therefore there are no significant flow limits acting through the membrane. Although there is a certain accumulation of solute at the membrane surface, we use low feed concentrations, thus this solute accumulation is not high enough for consideration of gelation or osmotic contributions. For these low concentrations, viscosity and density can be taken as substantially equal to the pure water values. In these working conditions of low pressure, the phe- nomenological correlations, normally used to take into account the dependency of the mass transfer coefficient on the diffusion coefficient and the recirculation veloc-  P. Prrdanos et al. / Journal of Membrane Science 99 (1995) 1-20 3 ................................. 4 f /,,,, //llll/,ll//'II'III IIII IIIIIIIII ,,,\ / 11111111 llllh I/ll]lll]l I I/////////\/\/\k, ,,, \ U UU 4 -5 2 :3 Fig. 2. Membrane holder showing the permeate output 1, the retentate output 2, the feed input 3, the membrane 4 and the retentate separator 5. ities, should be carefully analyzed. In fact, they are customarily tested in experiments near gelation; i.e. for high feed concentrations and/or high applied pres- sures. On the other hand, only a few studies have been done for recirculation velocities in the range of transi- tion to turbulence while much work has been devoted to conditions of fully established turbulence. Here we try to test some of these customary correlations with low feed concentrations, velocities and applied pres- sures. Finally, once the mass transfer coefficient has been evaluated, the true retention coefficient can be esti- mated and the standard retention curves obtained in order to find the real molecular weight cut-off for these three filters. 2. Materials and experimental set up Three asymmetric TFM filters consisting of a poly- sulfone porous support and a skin layer of aromatic polyamides have been used. They are commercialized under the names of G-5, G-20 and G-50 (Desalination Systems Ltd.), with increasing nominal molecular weight cut-offs, namely 2000, 3500 and 15000 Daltons as given by a spiral wound ultrafiltration test at 298 K and a 95% polyethylene glycol rejection with a feed concentration of 0.1% w/w at 800 kPa (according to the manufacturers). These membranes can be used within a pH range of 2-11, they have a high chlorine resistance and can be operated upto temperatures near 320 K. In order to avoid any irreversible change during operation, each membrane sample was pressurized at 650 kPa for 2 h before being used. Aqueous solutions of several polyethylene glycols (PEGs) at 0.10% w/w were used; this relatively small concentration assures minimal solute-solute interac- tion. They were prepared with distilled, degasified and deionized (resistivity higher than 18 M,O.cm) water and nine different PEGs supplied by Fluka AG. with molecular weights, Mw, of 300, 600, 1000, 2000, 3000, 4000, 6000, 10 000, and 12 000 Daltons. The solutions were pumped tangentially over the membrane and recirculated with a range of velocities, v, and transmembrane pressures, Ap, up to 650 kPa. The tangential ultrafiltration device used here has been described elsewhere [ 1 ]. As shown in Fig. 1, the solution is extracted from a thermostated reservoir at 298 K by means of a regulatable gear pump. Two pres- sure transducers are placed before and after the membrane holder in the retentate loop, they have a range of 0-1000 kPa relative to the atmosphere and give a maximum error of _ 0.25% full scale. In order to measure the pressure loss along the hydraulic chan- nel, which is always small and almost linear along the duct, a water differential manometer has been used. On the other hand, the transmembrane pressure can be taken as the average of the values given by the trans- ducers at the inlet and outlet of the membrane cell. In order to measure the retentate flow, two electro- magnetic fiowmeters are alternatively used, whose ranges are 1 × 10-6-1 × 10 -5 m3/s and 1.67X 10 -5- 1.67X 10 -4 m3/s, both with errors lower than a +0.25% full scale. The velocity and pressure in the retentate loop are independently controlled by means of the pump regulation and a needle valve. The permeate flow is measured by timing and weighting with a high precision balance with errors lower than + 1 x 10 -7 kg. The concentration of the  P. Prddanos et al. / Journal of Membrane Science 99 (1995) 1-20 tq ,,,-4 X .<3 5.8 5.3 4.8 4.3 1 I ~ } [f-] , 1 J I J I l I 0 I 2 3 4 ml ) Fig. 3. The ratio (Jv/Ap ) as a function of velocity for PEG-4000 and G5. The curve drawn here is (Jv/Ap ) = 5.74 × 10- '2l i - exp ( - a to q ] with a, = 3.78 5:0.13 and q = 0.25 + 0.01. permeate is measured using a previously calibrated dif- ferential refractometer thermostated a 298.15 K. It uses, as reference the same high quality water utilized to prepare the filtered solutions. The calibration ranges are from 0.0400% w/w to 1.0000% w/w. In order to deal only with the regions where the refractive index depends linearly on concentration with the highest sen- sibility, the samples were diluted or concentrated as necessary. In this way, the concentrations errors were reduced to _ 0.0001% w/w. The membrane cell is a Minitan-S manifold which is schematically shown in Fig. 2. On the membrane, there are nine ducts of rectangular section 0.40 X 7.0 mm and a length of 55.0 mm. The resulting channel hydraulic diameter is dh=0.76× 10 -3 m, giving an effective membrane area of 3.68 X 10- 3 m 2 and a chan- nel cross section of 2.8 x 10 -6 m 2. 3. Volume flow and permeability First of all the volume flow of permeate, Jv, was measured, as a function of transmembrane pressure, for pure water and the nine PEG solutions used, while the average retentate recirculation velocities were kept constant in the range from 0.020 to 4.62 m/s. In all cases linear dependencies of Jv on pressure were observed for pressures upto 650 kPa. The pure water volume flow is independent of tan- gential velocity, leading to the following hydrody- namic permeabilities, Lo ( 1.421-4- 0.0016) x 10- ~ m/s.Pa for G-5, (4.28+0.02)X 10 -~t m/s.Pa for G-20 and (6.29+0.03) X 10 -'1 m/s.Pa for G-50 -- all errors given here corresponding to a 95% confidence level (t-tested). The permeability (i.e. the ratio of volume flow and transmembrane pressure) can be given in terms of sev-  13.0 P. Prddanos et al. / Journal of Membrane Science 99 (1995) 1-20 I ~ 11.0 9.0 7.0 t~ v [] I 5.0 ~ t ~ 1 ~ I 0 1000 2000 3000 4000 Mw (Dalton) Fig. 4. The ratio (Jv/Ap) as a function of the molecular weight for a velocity v=4.62 m/s and the G-5 membrane. The fitted curve is (Jv/ Ap) =a: +a3 exp[ -a4(Mw-300) ~] with a2= (5.74 0.04) × 10 -tz, a3 = (7.27=1=0.08) × 10 -12, a4 =0.0365:0.007 and r= 0.51 4-0.12. eral resistances in the membrane system [2] according to: Jv 1 Ap ~(em +Rd +Rb) (1) with the molecular weight of the solute. As an example, (Jv/Ap) is shown for G-5 as a function of velocity for PEG-4000 in Fig. 3, and versus the molecular weight for v = 4.62 m/s in Fig. 4. where Rm is the membrane resistance, Rd the deposited solute resistance and Rb the boundary layer resistance. Assuming that the solute resistances can be character- ised by means of "specific resistances", we have Rd = a,~/d(t) and R b = abmb, Md(t) being the mass of deposited solute per unit area of membrane at time t, while Mb is the mass of solute held in the boundary layer per unit area. Given that we deal with stationary situations we have that (Jv/Ap) is a constant for a given solute and a fixed recirculation velocity. In prac- tice, the permeability always increases with velocity for any solute while, for a constant velocity, it decreases 4. Observed retention Concerning the output or permeate concentration, %, it is convenient to give it in terms of the input or feed concentration, Co, through the so called observed or apparent retention coefficient Ro 1 cp (2) Co which, of course is always ~< 1.
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