Module Flow Patterns

In Example 9.2, perfect mixing was assumed on both sides of the membrane. Three other idealized flow patterns, common to other mass-transfer processes, have been studied countercurrent flow, cocurrent flow, and crossflow. For a given cut, the flow pattern can significantly affect the degree of separation achieved and the membrane area required. For a given membrane module geometry, it is not always obvious which idealized flow pattern to assume. Hollow-fiber modules are the most versatile since they may be designed to approximate any of the three flow patterns mentioned above. 

A material balance for A, combined with equation (9-20) gives 

The definition of the separation factor, equation (9-10), can be used to eliminate y from equation (9-22). After some algebraic manipulation, we have 

Equation (9-23) can be integrated numerically using equation (9-24) to evaluate aAB at each value of x for which the integrand is evaluated. When the upper limit of integration in equation (9-23) is x = xR, L = LR = LF(1 - 0). Then, 

Equation (9-25) establishes the relation between the cut and the concentration of the retentate leaving the module. Furthermore, the relation between the local permeate and retentate concentrations can be easily derived (Seader and Henley, 2006)  

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For a defect-free ideal membrane, the selectivity is independent of thickness, and either permeability ratios or permeance ratios can be used for comparison of selectivi-ties of different materials. Nonideal module flow patterns, defective separating layers, impurities in feeds, and other factors can lower the actual selectivity of a membrane compared to tabulated values based on ideal conditions (Koros and Pinnau, 1994). 

Flow inside the capillary membranes, depicted in the lower half of the plot and indicated by positive velocities, shows a regular pattern. The single capillaries are resolved, and flow inside each capillary possesses almost identical maximum velocities. Flow outside the membranes (upper half, negative velocities) reveals a different pattern. Flere, the different flow characteristics between the SMC and SPAN modules become distinct. Obviously, the capillaries in the SMC module are not packed in a regular manner. Large spaces in between the capillaries cause an irregular flow pattern in the dialysate-side with a maximum velocity of about -15 mm s-1 (Figure 4.6.2(a)), which is comparable to the maximum velocity in... 

A3/X°i, C° = X°3/X°, and 03= X 3/X°3. reverse osmosis system involving longitudinal feed flow pattern in the module (such as in spiral wound or tubular modules), let... 

Figure 19.3. Tubular and plate-and-frame membrane modules for reverse osmosis and ultrafiltration, (a) Construction and flow pattern of a single 1 in. dia tube with membrane coating on the inside in Table 19.4, the Ultracor model has seven tubes in a shell and the Supercor has 19 [Koch Membrane Systems (Abcor)]. (b) Assembly of a plate-and-frame ultrafiltration module (Danish Sugar Co.), (c) Flow in a plate-and-frame ultrafiltration module.

Figure 19.5. The Permasep hollow fiber module for reverse osmosis, (a) Cutaway of a DuPont Permasep hollow fiber membrane module for reverse osmosis a unit 1 ft dia and 7 ft active length contains 15-30 million fibers with a surface area of 50,000-80,000 sqft fibers are 25-250 pm outside dia with wall thickness of 5-50pm (DuPont Co.), (b) The countercurrent flow pattern of a Permasep module.

The effect of concentration polarization on specific membrane processes is discussed in the individual application chapters. However, a brief comparison of the magnitude of concentration polarization is given in Table 4.1 for processes involving liquid feed solutions. The key simplifying assumption is that the boundary layer thickness is 20 p.m for all processes. This boundary layer thickness is typical of values calculated for separation of solutions with spiral-wound modules in reverse osmosis, pervaporation, and ultrafiltration. Tubular, plate-and-ffame, and bore-side feed hollow fiber modules, because of their better flow velocities, generally have lower calculated boundary layer thicknesses. Hollow fiber modules with shell-side feed generally have larger calculated boundary layer thicknesses because of their poor fluid flow patterns. 

Although in general the calculation of 8hm for modulation is difficult, a simplistic understanding can be obtained through consideration of the flow pattern above an oscillating infinite plate [13]. The velocity profile u(y,t) parallel to the wall, at a distance y above the wall, is a lagged, damped simple-harmonic motion ... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

A number of factors can lead to high pressure drop, including membrane scaling, colloidal fouling, and microbial fouling. These three factors all involve deposition of material onto the surface of the membrane as well as onto components of the membrane module, such as the feed channel spacer. This causes a disruption in the flow pattern through the membrane module, which, in turn, leads to frictional pressure losses or an increase in pressure drop. 

The modulated swirl combustor decribed here (2) represents a step in this direction when operated with propane or hquid kerosene. It exhibits a very distinct change in flow pattern and potentially can satisfy pollution legislation over a wide operating range of heat release rates, as required, for example, in an aircraft gas turbine engine combustor. 

For calculation of required membrane permeation area, flow patterns for the various module designs must be considered. The cross-flow, counter-current, cocurrent, or complete mixing flow will result in different degrees of purity for the same stage cut, 9 (= qp/qt). This is illustrated in Figure 4.18 below [104]. 

Membrane processes are used to filter liquids. Instead of conventional filter materials (e.g. filter cloth, filter candles,) microporous membranes are employed with molecular size pores. First the industry had to learn how to manufacture membranes with controlled pore sizes. To optimise the filtration capacities specific filter structures had to be designed in which the liquid followed well defined flow patterns on one side of the membrane. Many different systems were developed for the varied applications, all having their advantages and also disadvantages, i.e. plate modules, tubular modules, spiral wound membranes, etc. Research and development in this field is far from being exhausted. Today membrane systems are available which are sufficiently resistant to chemical, mechanical and thermal stress. They are produced from plastic... 

The interfacial and turbulence closures suggested in the literature also differ considering the anticipated importance of the bubble size distributions. It thus seemed obvious for many researchers that further progress on the flow pattern description was difficult to obtain without a proper description of the interfacial coupling terms, and especially on the contact area or projected area for the drag forces. The bubble column research thus turned towards the development of a dynamic multi-fluid model that is extended with a population balance module for the bubble size distribution. However, the existing models are still restricted in some way or another due to the large cpu demands required by 3D multi-fluid simulations. 

The main contribution from the work of Luo [95, 96] was a closure model for binary breakage of fluid particles in fully developed turbulence flows based on isotropic turbulence - and probability theories. The author(s) also claimed that this model contains no adjustable parameters, a better phrase may be no additional adjustable parameters as both the isotropic turbulence - and the probability theories involved contain adjustable parameters and distribution functions. Hagesaether et al [49, 50, 51, 52] continued the population balance model development of Luo within the framework of an idealized plug flow model, whereas Bertola et al [13] combined the extended population balance module with a 2D algebraic slip mixture model for the flow pattern. Bertola et al [13] studied the effect of the bubble size distribution on the flow fields in bubble columns. An extended k-e model was used describing turbulence of the mixture flow. Two sets of simulations were performed, i.e., both with and without the population balance involved. Four different superficial gas velocities, i.e., 2,4,6 and 8 (cm/s) were used, and the superficial liquid velocity was set to 1 (cm/s) in all the cases. The population balance contained six prescribed bubble classes with diameters set to = 0.0038 (m), d = 0.0048 (m), di = 0.0060 (m), di = 0.0076 (m), di = 0.0095 (m) and di = 0.0120 (m). 

The performance of a membrane separator may be predicted on the basis of permeation fluxes and material balances. The formulation of these relationships for a particular module depends on the flow patterns of the fluid on both sides of the membrane. 

The field of membrane separations is radically different from processes based on vapor-liquid or fluid-solid operations. This separation process is based on differences in mass transfer and permeation rates, rather than phase equilibrium conditions. Nevertheless, membrane separations share the same goal as the more traditional separation processes the separation and purification of products. The principles of multi-component membrane separation are discussed for membrane modules in various flow patterns. Several applications are considered, including purification, dialysis, and reverse osmosis. 

Orientational order plays an important role in solid polymers. It is often induced by industrial processing, for example in fibers and injection- or compression-modulated parts. In polymers with liquid-crystalline properties of the melt or solution, the anisotropies generated by the flow pattern are particularly pronounced. In order to improve the mechanical properties of polymer fibers or films, the degree of orientation is intentionally enhanced by drawing. At the same time, anisotropy of mechanical properties can result in low tolerance to unfavourably directed loads. In many liquid-crystalline polymers, in the mesophase near the transition to the isotropic phase, electric or magnetic fields can induce macroscopic orientational order [1]. Natural polymers such as silk protein fibers, which are biosynthesized and spun under biological condition, also have good mechanical properties because of their ordered structure [2]. 

Therefore, the flow kinematics for this case is described by the time modulations between the flow patterns A and B, and could be described as a function of the Strouhal number. 

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