Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979 547
Turbulence Promotion and Hydrodynamic Optimization in an Ultrafiltration Process Joseph J. S. Shen" and Ronald F. Probstein Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139
An optimization of flow conditions is presented to minimize permeate product cost in ultrafiltration in laminar channel flow. The methodology for the pressuredriven membrane system is based on a hydrodynamic optimization scheme developed by Sonin and Isaacson for electrochemical systems. Experimental data are presented for permeate flux as a function of transmembrane pressure for the ultrafiltration of bovine serum albumin solution in laminar channel flow with and without detached strip-type turbulence promoters. Empirical expressions are established for the limiting permeate fluxes as a function of the flow rate and interpromoter spacing. Applying the economic optimization scheme, the performance characteristics of the convection-promoted systems are assessed. The optimum values for the interpromoter spacing, the permeate flux, and the Reynolds number are also determined.
Introduction Ultrafiltration of macromolecular solutions has of late been investigated in some detail. Most of the works have examined flows of relatively simple geometry. Vilker et al. (1975) studied the unsteady flow in a stagnant cell. Kozinski and Lightfoot (1972) studied the steady flow in a rotating cell and extended their analysis to parallel plate channels. Papenfuss et al. (1978) studied flows over a flat membrane surface. Brown et al. (1971), Shen and Probstein (19771, and Probstein et al. (1978) studied laminar flows in thin channel systems. In practice, the hydrodynamic conditions in ultrafiltration are usually not so simple and well defined. It has long been known that judicious manipulation of the flow conditions can lead to improved performance as measured, for example, by flux enhancement. In such flux augmentation arrangements, where the flow conditions are far more complicated than for the geometries mentioned, it has been necessary to rely on empirical or semiempirical results. One popular method to effect permeate flux increases is through the introduction of turbulence promoters in the flow channel. The mass transfer characteristics, hence the permeate flux, will generally increase due to the presence of turbulence promoters which cause high shear and/or additional localized turbulence in the flow channel. However, as in any augmentation technique, flux enhancement is only achieved at the expense of increased frictional pressure drop. It is important, therefore, to be able to determine the effectiveness of the convection promotion technique in relation to the performance characteristics of the system as a whole. In this paper, we shall first briefly survey the reported flux augmentation studies for ultrafiltration and the related pressure-driven membrane separation process, reverse osmosis. We shall then present a simple and rational scheme to evaluate and optimize the hydrodynamic performance characteristics of a promoted ultrafiltration system. This hydrodynamic optimization technique is based on the optimizing scheme developed by Sonin and Isaacson (1974) in connection with the optimization of the flow design in forced flow electrochemical systems, with special application to the electrodialysis of brackish water. Finally, we shall present experimental results on the ultrafiltration of a macromolecular solution (bovine serum
* Address correspondence to this author a t Abcor, Inc., Wil-
mington, Mass. 01887.
0019-7882/79/1118-0547$01.00/0
albumin, BSA) with a systematic variation in the distribution of detached strip-type turbulence promoters placed in a parallel plate flow channel. The hydrodynamic performance characteristics of the promoters tested are then assessed in light of the optimization scheme. Flux Augmentation Studies Augmentation of permeate flux in ultrafiltration and reverse osmosis systems has not been widely reported, when compared with studies on mass transfer augmentation by chemical or electrochemical techniques. Turbulence promoters that cause physical blockage and/or flow alteration can be classified into two types, according to the position of the promoters inside the channel. One type can move inside the flow channel while the other type is fixed relative to the membrane surface. The scouring action of the free turbulence promoters repeatedly disrupts and promotes mixing of the boundary layer formed at the membrane surface, thereby increasing the permeate flux due to the combined effect of thinning the boundary layer and higher mechanical shear at the wall. However, the long-term detrimental effects of the movement of the beads (free promoters) on the membrane surface must be considered. Studies on this type of turbulence promoter have been reported by Lowe and Durkee (1971) in processing orange juice by ultrafiltration, Lai (1971) in desalination by reverse osmosis, and Van der Waal et al. (1977) in both ultrafiltration and reverse osmosis systems. Fixed or static turbulence promoters of various configurations have received more attention. Thomas and Watson (1968) observed marked increases in the salt rejection characteristics of dynamically formed membranes when a wire spiral separated from the tube surface was introduced into the flow. Thomas et al. (1970,1971) found that the use of turbulence promoters markedly affects optimum reverse osmosis plant geometry as a consequence of higher fluxes. Pitera and Middleman (1973) used a Kenics static mixer to study convection promotion in a tubular reverse osmosis module with laminar flow. They observed significantly reduced polarization, leading to improvement in permeate quality and an increase in permeate flux. In applications of turbulence promoters to ultrafiltration, Peri and Dunkley (1971) qualitatively discussed their experimental results of whey protein ultrafiltration in a tubular module fitted with an inserted rod cemented with intermittently-spaced rings. Dejmek et al. (1974) also qualitatively discussed their augmented flux data of whey 0 1979 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 3, 1979
protein ultrafiltration obtained with twisted tape inserts and volume displacement rods. They noted that twisted tape turbulence promoters were superior to the volume displacement rod design. Copas and Middleman (1974) reported experiments on ultrafiltration of a latex suspension in a tube with a Kenics static mixer under turbulent flow conditions. Significant improvement in permeate flux was observed and attributed to reduction of the gel layer resistance at the membrane surface. Based on the published literature, it is obvious that studies of turbulence promoters in ultrafiltration in a systematic and quantitative manner are lacking. No data correlations useful for process design purposes were presented in the ultrafiltration papers surveyed, nor were the performance of the turbulence promoter designs systematically varied and studied. Hydrodynamic Optimization Criteria In what follows is presented a simple and rational method for pressure-driven membrane separation systems adapted from the methodology of Sonin and Isaacson (1974) for electrochemical flow systems. The method determines the extent to which hydrodynamic factors influence product cost and provides a basis to compare various alternative hydrodynamic designs. The approach is based on scaling laws for mass transport and frictional characteristics. Stork and Coeuret (1978) have applied Sonin and Isaacson’s method to electrolysis. Let us consider a typical recirculating system. The working fluid is first pressurized to the operating system pressure by a pump and then circulates through the membrane module. The effluent from the module is a t a lower pressure than the exit pressure of the system pump due to frictional losses incurred in forcing the permeate through the membrane and in pumping the fluid past the membrane. The effluent is recirculated through a booster pump which delivers power to compensate for the frictional losses. In our analysis, we shall for simplicity consider a parallel plate flow channel of membrane area A on both surfaces and a channel height d. The permeate flux through the membrane is taken to be u, for an applied system pressure APa. A working fluid is passed through the channel with superficial velocity U and is assumed to incur a pressure drop AP,over the length of the membrane system L. The interior geometry of the flow channel may be altered to enhance the mass transport characteristics. In operating this system three cost factors must be considered: (1) the cost of mechanical energy to the system pump to pressurize the solution in order to force permeate through the membrane; (2) the cost of mechanical energy required to pump the working fluid past the membrane area; and (3) a “capital” or “ownership” cost, which is assumed to be, a t least to a first approximation, proportional to the membrane area and independent of the two energy costs. The cost of the working fluid itself and the disposal cost of the concentrated effluent are not included in this analysis. Combining the three contributions, the cost of operating the process per unit time can then be expressed as
vw,,m
Applied
(Governed by Flow V e l o c i t y and h l e r n o l Chonnel Design)
Pressure
Figure 1. Schematic of an ultrafiltration flux-pressure excursion curve.
of state-of-the-art ultrafiltration systems. Writing eq 1 to obtain an expression for the cost k , per unit volume of product permeate, we have
k V = -2uwA -K - k p U a + &( uW 1 +
”y)
We note that eq 1 and 2 are of exactly the same form as eq 1 and 2 in Sonin and Isaacson (1974). Therefore, we can easily adopt their methodology with only minor changes. It is clear that the flow conditions in the system influence the product cost through APf and U in the frictional pressure drop term, and also through u, if concentration polarization occurs in the channel. Concentration polarization manifests itself in a departure from linearity of the flux-pressure curve, eventually leading to a flattening-out of this curve as shown schematically in Figure 1. Concentration polarization is a flow dependent phenomenon. Sonin and Isaacson introduced the notion of a hydrodynamically ideal performance by which they meant that the system can be operated with negligible concentration polarization with a flow speed low enough such that the frictional pumping costs contribute negligibly to the total cost. Their two criteria to characterize a hydrodynamically ideal performance when expressed for ultrafiltration membrane processes can be written as L’Wopt,ideal 5 Q U W l i m (3) and
k ,APfUd
kJ
