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Flow & TMP Modeling – Ultrafiltration (UF) modules

Flow & TMP Modeling – Ultrafiltration (UF) modules

We know more flow enters at the top of the module than at the bottom. But how much more? Can we determine a set of equations to answer this question?

How about the pressure drop, known as TMP (trans-membrane-pressure)? How does the TMP varies along the height of the hollow fiber?

The answer is positive. Yes we can, and have already done so. Please see below and follow the link at the end of this post to find out the answers.

In brief, by using a second order differential equation, we determined the flow distribution and trans-membrane pressure function of (x).

As an example, using the above Q(x) expression, the following graph demonstrates the significant difference between the flow rate entering at the bottom of the module compared to the top of module (i.e. 0.18 usgpm vs. 1.5 usgpm). Approximately 8 times more flow passes into the fiber lumen of a clean ultrafiltration module at the top of the module than at the bottom.

Several factors are at play, most notably the fiber diameter. When the fiber diameter is reduced in half, the TMP increases sharply from 3.28 psi to 13 psi.

The model can help designers and process engineers better understand the inner workings of the ultrafiltration module; ultimately, designing a better module by optimizing the different variables, such as lumen diameter, number of fibers per module, porosity, height, etc.

Read the full paper in pdf format: Mathematical Model of TMP vs Flow Rate, Viscosity

Please drop us a line to receive a follow-up paper on the correlation between the temperature correction factor determined mathematically and actual test results.

Here’s a quick pick.

 

 

Water Technologies Canada Inc.

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