*4.5. Optimum Design*

The optimum design of various feed flow rate designs was done in order to illustrate the method. The lower bound for the membrane width is 0.1 m and the lower bound for the module height is 0.5 mm. The results of the design are shown in Table 3.


**Table 3.** Optimum design of the membrane module.

From Table 3, it can be obtained that the operating pressure of the optimum design plant is at a high value when the feed flow rate is not so low. When operating at high pressure, the permeate flux increases, resulting a reduction in the membrane area. However, if the operating pressure is too high, it will a ffect the mechanical stability of the system in addition to the pump cost expression. Therefore, the plant should operate at the maximum allowance of pressure.

Figure 6 shows the total cost per unit flow rate design. The cost per unit flow rate design decreases when the plant size becomes larger. It reflects the economics of scale.

**Figure 6.** The behavior of cost per unit flow rate design in optimum condition with plant capacity.

From the results, it can be shown that the membrane plant should be designed as long in channel length but short in channel width to achieve a high cross-flow velocity. The recirculation flow rate is also operated at a moderate value to maintain relatively high cross-flow velocity, but to not consume too much energy for the pump. The channel height should be configured at several millimeters.

From the results it can also be obtained that at di fferent requirements of the process, such as the desired feed flow rate, the membrane plant configuration and operation condition will significantly change. The tendency is di fficult to predict. Therefore, the design requirement and permeate flux expression strongly a ffect the design, selection, and operation strategy in membrane separation processes. There is no general rule, and for a particular system, the permeate flux and the correlation with operating conditions and membrane geometry should be investigated. The design and operating strategy strongly depend on this correlation.
