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Our Mathcad design created two designs; one which was a conservative approach and another (most commonly used), based on the simple hydraulics that the necessary velocity of the backwash is 10 times the velocity of filtration. The second design was based upon empirical equations, called the Weber Equation. The accuracy of the empirical fluidization velocity equations needed to be tested so we developed a bench-scale model of our filtration system and conducted an experiment measuring the expansion of a filter bed as backwash velocity is varied. We then compared the empirically calculated fluidization velocities with the actual fluidization velocities required.
Fluidization Velocity Experiment.
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MathCad Results: Empirical vs. Simple Hydraulics (Conservative) Approach
| Conservative | Empirical |
Filter Square Side(m) | 1.5 | 1.5 |
Filter Height(m) | 3.95 | 2.56 |
Clear Well Diameter(m) | 6 | 6 |
Clear Well Height(m) | 1.37 | 1.23 |
Figure 2: Agalteca Plant with Filter Designed from the Conservative Approach
1) Our design based on simple hydraulics will work. However, it is a very large filter (see exact dimensions in Figure 2, below) and will not be sustainable economically. The material cost for construction will be too high.
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3) If the empirical equations are valid, then we can change parts of the design, by changing the sand parameters. For example, lower BW the dimensions of the clear well by lowering the backwash velocity by lowering decreasing the d60 and specific weight of the media.
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We had mixed results with regards to Weber's equation for filter bed expansion. At low levels of filter bed expansion, the Weber equation accurately predicted the fluidization velocity required to achieve the targeted bed expansion. As the target bed expansion increased, so did the degree of error. At 9% expansion, the degree of error was at 14%. At 38% expansion, the degree of error was at 37%.
Figure 2: Agalteca Plant with Filter Designed from the Conservative Approach (Velocity of Backwash is 10 times the Velocity of Filtration)
Sources of Error
Human error:
Despite our best attempt at being consistent (by measuring and marking heights on the test tube, while also holding a ruler on the test tube wall), there will always be human error in observing the bed expansion visually.
Fix:The next expansion experiment should use a camera so there is record of the heights at each flow rate, and also tape a ruler to the filtration bed wall, rather than holding the ruler or drawing it on.
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