Effect of water temperature on flux (Temperature correction)

Theory 

Flux is inversely proportional to the viscosity of the permeate passing through the membrane pore, if all other conditions including TMP and filtration resistances stay constant. Since the MBR permeate has little dissolved materials, its viscosity is virtually same as that of clean water.

Based on the relation between flux and viscosity, flux can be corrected against a reference temperature for trending the true membrane flux. Typically flux is corrected against 20 oC using the following equations based on the normalized viscosity.

 

1                   ———— (1)

1                                                                                                        ———— (2)

where
μT     :     Water viscosity at current temperature (cP or 10-3 kg/m/s)
μT0   :     Water viscosity at reference temperature (cP or 10-3 kg/m/s)
J       :      Flux observed  (LMH or gfd)
JT0   :      Flux at reference temperature
T       :      Water temperature (oC)
T0     :       Reference temperature (oC)

Alternative equation is also available (Wilde, 2007)

1                                                                                              ———— (3)

where
J      :      Flux observed  (LMH or gfd)
JT0  :     Flux at reference temperature (LMH or gfd)
T      :      Water temperature (oC)
T0     :       Reference temperature (oC)

Caution

Although above correction method is widely used to trend membrane flux (or permeability), it has a significant limitation especially in MBR. The above equation (Eq.2) counts on permeate viscosity effects in membrane pores, but mixed liquor viscosity, biological activity, oxygen transfer efficiency, and even microbial metabolism can change at different temperatures. For instance, at low temperature, high mixed liquor viscosity hampers turbulence on membrane surface that increases membrane fouling. Due to the increase of fouling resistance (Rc here), flux can decrease more than expected by the water viscosity. Therefore temperature correction is meaningful only in a narrow temperature range around the reference point especially when rheological changes of liquid affects membrane performance.

If the range of water temperatures fluctuates widely, temperature correction becomes increasingly inaccurate. For instance, when temperature decreases from 30oC to 5 oC in a full scale MBR plant, the sustainable average daily flow (ADF) declines by 63% from 2,650m3/d to 984m3/d (GE Water, 2011) while the correction equation predicts only 48% decline.

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Temperature effect on permeability

Fig. 1 shows the long-term fluctuation of TMP, permeability, and water temperature in a drinking water plant. The permeability of membrane is highest in summer and lowest in winter due to the seasonal water viscosity changes.

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Fig. 1. Permeability, trans-membrane pressure and flux of the drinking water treatment line and temperature of the reservoir water (all parameters are not temperature corrected) (Dautzenberg, 2011)

 

© Seong Hoon Yoon