Presenting Test Data Using Normalized Flux Rate
For a side-by-side test comparison between a Coiled Membrane Filter (CMF) and a Straight Membrane Filter (SMF), it seems to make sense to present the test data in terms of flux rate as a function of the accumulated time. After all, the flux rate represents the output of a filter and it provides a direct way for performance comparison. However, presenting the data with a flux rate normalized against the driving pressure may be more accurate in conveying the performance improvement during a comparison test.
The normalized flux rate against the driving pressure is defined as a permeability coefficient and can be found in classical filtration related references. The paragraph below is cited from “Handbook of Filter Media” by Purchas, D. B., Sutherland, K. (Elsevier Advanced Technology P. 27, 2nd Ed, 2002).
"The permeability of a filter medium, a vital measure of the medium’s capability for filtration, is determined experimentally, generally by observing the rate of flow of a fluid under a defined pressure differential. A more fundamental expression is the permeability coefficient of the medium, Kp, which is defined by the Darcy equation describing flow through a porous layer:
P/L = Qµ/AKp or Kp = QµL/AP
A = area; Q = rate of flow; P = differential pressure; L = thickness of the medium; µ = kinematic viscosity"
In the CMF versus SMF side-by-side comparison test, the kinematic viscosity is not playing a role since they “see” the same water at the same time. Also, since both CMF and SMF use the same fibers, the thickness of the medium is not playing a role either. In such a case, Kp can be simplified to Kp = (Q/A)/P for comparison purposes. Where Q/A is the flux (shown as gfd, i.e., gal/ft/day) and P is the feed pressure.
The advantages of presenting data with normalized flux rate instead of flux rate in the CMF versus SMF side-by-side comparison test are:
1. It cleverly ties in energy (which is related to the pressure) to its presentation. This alternative measure further highlights the CMF advantage since it has less pressure resistance compared to the SMF due to the thinner boundary layer controlled by the Dean Flow.
2. The normalized flux provides a good indication regarding the status of membrane fouling. Because a change in pressure resistance is related to the degree of membrane fouling.
3. Examine the data this way eliminates the concern that the test was biased toward the CMF. This concern arose because the distilled feed water was used to begin the test (boundary layer is not playing a role). The data points collected during this test period show the CMF having a slightly higher flux (output) compared to the SMF. This is because the CMF has a higher feed pressure (the intrinsic characteristic of a coiled path) compared to the SMF. However, when the flux is normalized against the feed pressure (permeability coefficient), the normalized flux of the SMF is actually 7-10% higher compared to that of the CMF during the initial test period. This is because the SMF has a more favorable feed pressure distribution compared to the CMF when there is no boundary layer present yet and is discussed in the previous blog "Coiled Membrane Filter (CMF) and a Straight Membrane Filter (SMF)"