Concurrent flow permeation

Figure 1.9 Concurrent flow permeation. (Source Bravo et al. ...

Of further interest and concern is the operation of a membrane cell as a continuum. Such a view may be referred to as differential permeation. The permeate may be withdrawn at points along the membrane, as illustrated in Figure 1.8. Or the cell may be operated in concurrent flow, as shown in Figure 1.9, or countercurrent flow, as shown in Figure 1.10. There is the possibility, even, of producing two permeate products if two different membrane materials are employed separately in the same unit or module. This is indicated in Figure 1.11. 

In all cases, stream L follows the bubble-point equivalent curve, here embodied as the K line, as in differential vaporization." The stream V represents the accumulation of permeate and may include any stream injected as Vj in concurrent flow or V, in countercurrent flow. 

In concurrent flow, V, and its composition yfj- may also be specified. If Vj = 0, its composition may be determined from a bubble-point type calculation on L, that is, the composition of V, is that of the first drop of permeate produced. Simultaneous numerical integrations can, in principle, be carried out to a specified value for any of the variables at point 2. 

Part (or conceivably all, in the limit) of either or both the permeate and reject products may be recycled or refluxed. For instance, in the case of concurrent flow, part of the reject product L, can be recycled to the feed f, where the composition and rate of L, would be affected. In effect the reject is making another pass through the membrane cell. For that matter, part of the permeate product V, can be recycled to constitute V, The beneficial effects are dubious and can be ascertained only by a more complex mode of calculation. For the case of assuming perfect mixing, the benefits are nil, as already discussed in Section 3.5 of Chapter 3. 

It is assumed that no permeate phase is introduced, whereby in concurrent flow Vj = 0 and in countercurrent flow = 0. 

For the first circumstance, where only reject outflow is produced, F = L] = L2 and the degree of separation is obtained by a bubble-point calculation on F = L, that is, this determines the composition of the drop of permeate representing V, (even though V, - 0). The result necessarily is the same as for concurrent flow. The reject and permeate compositions remain constant along the axis of countercurrent flow. 

The analysis of the spiral-wound module was done by Ohya and Taniguchi [257]. No pressure drop on either side of the membrane and the concurrent flow of the feed and permeate were assumed. Furthermore, Ohya and Taniguchi made the following four assumptions ... 

In the last few years, a third type of microfiltration operating system called semi-dead-end filtration has emerged. In these systems, the membrane unit is operated as a dead-end filter until the pressure required to maintain a useful flow across the filter reaches its maximum level. At this point, the filter is operated in cross-flow mode, while concurrently backflushing with air or permeate solution. After a short period of backflushing in cross-flow mode to remove material deposited on the membrane, the system is switched back to dead-end operation. This procedure is particularly applicable in microfiltration units used as final bacterial and virus filters for municipal water treatment plants. The feed water has a very low loading of material to be removed, so in-line operation can be used for a prolonged time before backflushing and cross-flow to remove the deposited solids is needed. 

Of special consideration is the investigation of the cell as a continuum, first with point withdrawal of the permeate, then in both concurrent and countercurrent flow for the permeate and the reject phases. For this treatment, differential permeation is the mode of attack. The differential... 

The permeate so withdrawn may subsequently be accumulated, but this is independent of the permeation process per se. Furthermore, the accumulation may be withdrawn as if concurrent to the flow of the reject phase or as if countercurrent to the reject phase. The total accumulation and its composition are the same in each situation it is after the fact. ... 

For membrane systems in concurrent or countercurrent flow of the reject and permeate, the concept of differential permeation applies. Here we consider the flow of the feed and reject stream as diagrammed in Figure 5.1. The end of the membrane cell where the feed stream is introduced... 

The relationships between composition and flow rates can be set forth, based on the rate equations, for both concurrent and countercurrent flow, and based either on the permeate phase V or the reject phase L. The boundary conditions may make one preferable to the other. 

Following this, more rigorous derivations for differential permeation are pursued. That is, permeation is viewed as a continuum rather than an operation in discrete stages or cells. In the first case to be considered, there is continuous point permeate withdrawal in another case, the more general case of permeate flow is analyzed, both concurrently and coun-tercurrently. 

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