Normalized pressure drop

Pressure drop through the RO system can also be used as an indicator of when it is time to clean membranes. Pressure drop is a direct measure of the pressure loss due to friction caused by scale or foulants on the membrane or the feed spacer. 

The energy lost from pressurized feed water is absorbed by the membrane module materials, which can cause the materials to shift within the module when the degree of fouling or scaling is severe. This can lead to telescoping of the membrane leaves, resulting in 

Intel Module 1 Module 2 Module 3 Module 4 Module S Module E B Water Pressure O Axial Load 

Inlet Module 1 Module Z Module 3 Module 4 Module 5 Module 6 Recommended Load O Maximum Load 

As a result, pressure drop should also be considered in making the determination when to clean the membranes to avoid physical damage to the modules. Membranes should be cleaned when the pressure drop increases by 10% to 15% from initial operating conditions. 

Inlet Module 1 Module 2 Module 3 B Water Pressure 

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Normalized pressure drop and NPF should be monitored simultaneously, and the membrane cleaned when the first of these measures reaches the 10% change in performance as compared to initial operating performance. 

Figure 1. Normalized pressure drop factor variation with Remfor a single fluid flow in a porous medium.

Multidimensional Effects. In the previous section, we studied the wall effect on the shear factor. To give a full account of the wall effects, we now look at the no-slip flow effect posed by the containing wall (multidimensional effect) on the total pressure drop. For simplicity, let us rewrite the normalized pressure drop factor, fv, based on the permeability of the medium rather than the particle diameter,... 

Figure 12 shows the multidimensional effect on the normalized pressure drop factor from both the exact solution, equation 121, and its approximation, equation 123. It can be observed that equation 123 gives a fairly good approximation to the exact solution. The multidimensional effect is significant when the normalized bed radius is small, say, F1/2D/2 < 100. When the normalized bed radius is large, Crrul - 1. 

Figures 14 and 15 show the normalized pressure drop factor for a densely packed bed of monosized spherical particles. For Rem < 7,fv is fairly independent of Rern, and at high Rem values, it increases fairly linearly with Rem. The data points are the experimental results taken from Fand et al. (110), where the bed diameter is D = 86.6 mm and the particle diameter is ds = 3.072 mm. One can observe that the 2-dimen-sional model of Liu et al. (32), referred to as equation 107, agrees with the experimental data fairly well in the whole range of the modified Reynolds number. From Figure 14, one observes a smooth transition from the Darcy s flow to Forchheirner flow regime. The one-dimensional model of Liu et al. (32) (i.e., equation 106) showed only slightly smaller fv value. Hence, the no-slip effect or two-dimensional effect for this bed is small. As shown in Figures 14 and 15, the Ergun equation consistently underpredicts the pressure drop. The deviation becomes larger when flow rate is increased.

Figures 21 and 22 show the normalized pressured drop estimated by equation 128 for a packed D = 5.588 mm, ds = 3.040 mm, and e = 0.5916. The experimental data are taken from Fand and Thinakaran (92). We can observe that the approximate solution, equation 128, predicts fairly well the experimental results and is very good in representing the exact numerical solution of the governing equations. For clarity, Figure 21 is an expanded region for the small Rem values. Even with this scale, we observe that the approximate solution is very close to the exact numerical solution.

It was found that equation 128 is a good prediction for the normalized pressure drop factor when used for data in Figures 14-22. The use... 

Figure 22. Normalized pressure drop factor variation with Re m for a packed bed of monosized spherical particles at high flow rate. The symbols represent the experimental data taken from reference 92.

The usage of the flow equations can be summarized as follows. For the case of a one-dimensional single fluid flow, either equation 106 or 108 can be used to predict the normalized pressure drop factor in a porous medium. The determined normalized pressure drop factor is related to the pressure drop by equation 11. For the simple case of packed spherical beads, ds and e are known a priori. The Reynolds number is evaluated using equation 93. For random packs of nonspherical particles, the particle s sphericity needs to be known. Equation 73 can be used to estimate ds. For the case of consolidated porous medium, one can estimate ds from the knowledge of the intrinsic permeability using equation 14. 

Viscosity curve is shifted. There are a number of items that can cause the viscosity curve to shift up or down. Cheek to see that the proper calibration values have been entered for the pressure/force transducer. Check the die to ensure that it is not partially bloeked, eausing greater than normal pressure drops. Lastly, eheek for a shift in either the barrel or die temperature. Burned-out heater bands or maladjusted temperature eontrollers will eause large shifts in experimental results. 

As mentioned in Section 10.5.1, the easiest way to implement flooding diagnosis is to monitor pressure drop. Before beginning the diagnosis, the normal pressure drop curve should be tested for comparison this test will be the baseline for the diagnosis. If the pressure drop is seriously larger than normal, flooding is supposed to have occurred. 

The normal pressure drop across the control valve should be sufficient for the pump to operate (see Fig. 38.3) on the flat part of the pump s performance curve. These curves are published in reference manuals by the pump vendors. The flat portion of the curve in Fig. 38.3 has been labeled "good."... 

Th design pressure drop across the condensei(s) and associated piping should be set at S to 7 pst. When the system is clean, the normal pressure drop will be on the... 

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