When permeate passes through membrane, the particles contained originally in the permeate are left on membrane surface. High crossflow velocity (CFV) such as 2-5 m/s is required to control the membrane permeability at a proper level. Since the high CFV causes high pressure drop along the channel, maximum allowable channel length exists, which does not cause excess TMP in the channel entrance. In other words, channel length cannot be extended indefinitely without decreasing CFV.
The limited channel length in turn limits the water recovery (Qperm/Qfeed) from the one pass of the feed water through the tubular membrane channel. For example, only 0.15% of feed water is recovered as permeate while the feed solution proceeds 1 m in a tubular membrane, if flux is 100LMH, CFV is 3 m/s, and tube ID is 2.54 cm. If 5% recovery is desired, channel needs to be extended to 33m assuming flux is uniform along the channel. However, it is unlikely that 3m/s is achievable in 33m channel at the maximum allowed feed pressure of 6 bar.
Apparently the length of the channel is limited by the longitudinal pressure drop (ΔPL) that needs to be overcome by circulation pump. Fig. 1 shows the pressure profile in the tubular membrane system, where major pressure loss occurs in the module entrance and exit and the membrane. In general, pressure drop in pipeline can be readily controlled by using properly sized pipes, smoothly curved U-tubes connectors, etc. But, the pressure losses in the headers of multitube modules and in the tube channels are mostly uncontrollable since these are decided by fluid viscosity, velocity, channel dimensions,etc. In fact, the pressure drop in header is very significant in multitube modules, where liquid streams split and gather while velocity changes abruptly, and this is a major cause of pressure loss in multi-tube modules. In addition, slight pressure drop or increase occurs when fluid changes its velocity in the header according to Bernoulli’s theorem. The longitudinal pressure drop is mostly proportional to the number of membrane modules connected serially in a given condition as shown in Fig. 1.
Fig. 1. Longitudinal pressure profile in tubular membrane system with multi-tube modules in MBR.
Meanwhile, the inlet pressure, Pin, is a sum of the total pressure drop in the channel that consists of multiple modules, , and the outlet pressure, Pout, as shown in equation 1. Due to the low , Qperm/Qfeed CFV is almost constant along the entire channel length, thereby the pressure drop in each module, ΔPL,i , is almost constant regardless of the position of the module in the channel.
Since Pout is kept low such as <50 kPa while ΔPL,i is 50-100kPa/module, the portion of Pout in Pin is diminishing with an increasing number of modules connected. For instance, if ΔPL,i is 80kPa, Pout is 30kPa, and 5 modules are serially connected, then Pin must be 430 kPa. If one more module is added, Pin increases approximately by 19% to 510 kPa while 20% more permeate is obtained. This means that there is little gain in energy efficiency by extending the number of modules connected in series.
Based on the above discussion, following conclusions can be drawn that are not necessarily in line with the popular notion.
- Adding more modules in series hardly helps increase energy efficiency. However, capital costs may be saved somewhat by reducing the pump capacity and the requirement of ancillary equipment, if the additional modules does not cause excessive feed pressure.
- Inlet pressure must increase with more number of tubular modules connected in series, but flux hardly increases as discussed here. This is because filtration occurs in mass transfer controlled region, where incremental pressure does not increase flux, but make cake layer denser.
© Seong Hoon Yoon