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Our target expansion was 30% expansion, and we found to achieve this, the flow rate had to be 340 ml/min, or 8 mm/s. However, at this flow rate, the error between calculated and experimental was 110%.
We plotted the experimentally found fluidization velocity vs the calculated fluidization velocity as as target bed expansion was increased (see Figure 2). As expected, higher bed expansion required high fluidization velocity. However, the difference between calculated and actual velocity increased as the flow rate increased. therefore, the experimental and the calculated data had a roughly direct relationship with calculated data having a steeper slope.
Experiment results data.
Figure 2: Calculated Fluidization Velocity vs Actual Fluidization Velocity
We believe the following to be sources of error, which we discuss more in depth there are two main sources for the error (more of which are discussed on the main on the Clear Well Filtration Page.).
#1)>> Human error: Despite our best attempt at being consistent, there will always be human error in observing the bed expansion visually.
>> Wall Friction: We can attribute the increase in error as flow rate increased due to the increase in wall friction on the test vial. We can minimize this by increasing the size of our bench scale experiments.
>> #2) Sand Properties Parameters: We might have used an incorrect D60 and porosity for the filter bed in our equations.
>> Preferential flow: Despite our best attempt to keep the test tube as level as possible, we might have introduced preferential flow in our experiment causing an unbalanced backwash flow.We tested this in our Mathcad code and found that if we increased the porosity from 0.4 to 0.5, the graph looked changed to Figure 3:
The above sources of error will be very difficult to control for the actual filtration design. Consequently, we surmise that we need to apply a safety factor of around 10-30% when applying the empirical fluidization velocity equation. The follow up experiments for multi-media experimentation with larger bench scale model will further specify the safety factor required and we expect the larger scale model to reduce the overall error.