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The purpose of this experiment is to test the validity of the compare the experimental results to the empirical fluidization velocity model equation covered in the literature research section (Walter J. Weber).
Concept of Experiment
In this experiment, a bench-scale granular filter was backwashed. backwashing of a granular filter with a sand test vial as the bench scale model. Our bench scale model consists of a 5 cm deep sand filter with a diameter of 2.5 cm (see Figure 1, (b)). The sand (classified as D60) has a diameter of 0.5mm and porosity of 0.4. The diameter of the flow control orifice is 0.2 cm. Please see figure 1 below. We essentially introduced a backwash flowrate of water of known velocity from the bottom and measured the bed expansion. An attentuator attenuator, or small tank filled with water, was installed between the pump is there was installed and the filter to eliminate the pulsing action of the pump . We measured (see Figure 1, (a)). The bed expansion flow rate as we was increased the flow rate from 20 mL/min to 380 mL/min (Can you describe in units that will scale to full-scale such as average velocity?), which is the maximum flow rate possible with our pump configuration.
Figure 1: Fluidization Velocity Experiment-Single Media Diagram
Results and Discussion
0.4-9 mm/s) (380 mL/min being the max rated flowrate for our bench scale pump configuration). The fluidization velocity is based on the ratio of original filter depth to expanded filter depth, so the velocity doesn't change with a larger depth.
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V = K_e (\overline \varepsilon )^{n_e }
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\overline \varepsilon = 1 - {D \over {D_e }}(1 - \varepsilon )
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Figure 1: (a) Fluidization Velocity Experiment Set-Up (b) 5 cm Filter Bed of Sand in Tube Unexpanded & Expanded
Results and Discussion
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 measured fluidization velocity vs the empirically predicted fluidization velocity as as target bed expansion was increased (see Figure 2)We plotted the actual fluidization velocity vs the calculated fluidization velocity as the target bed expansion is increased. As expected, higher bed expansion required high fluidization velocity. The However, the difference between calculated and actual velocity increased as the velocity flow rate increased. (What do you suppose is the reason for this if you stated that head loss once the bed is fluidized is constant? What sort of relationship is exhibited in Figure 2? Also, please reference all figures before you insert them in your document.) Click here for the Experiment 1 therefore, the experimental and the calculated data had a roughly direct relationship with calculated data having a steeper slope.
Experiment results data.
Figure 2:
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Predicted Fluidization Velocity vs
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Measured Fluidization Velocity
We believe the following to be sources of error.>> Human error: Despite our best attempt at being consistent, there will always be human error in observing the bed expansion visually.
>> there are two main sources for the error (more of which are discussed on the main on the Clear Well Filtration Page).
#1)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. (If this is the case, then why not try to fit the empirical equation to different sand diameters or porosities to see if this corrects for the majority of the error?)
>> 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. (This may be true, but has it been confirmed with a dye study? If this is true what is the next step in keeping the column level?)We tested this in our Mathcad code and found that if we increased the porosity from 0.4 to 0.5, the graph changed to Figure 3, thereby decreasing the error at %30 expansion to only 30% error:
Figure 3: Fluidization Velocity Experiment-porosity change
Then we also found that if we instead increased the d60 from 0.55 to 0.9, the graph changed to Figure 4, thereby decreasing the error at 30% expansion to only 16.7% error:
Figure 4: Fluidization Velocity Experiment-d60 change
This shows that small errors in our d60 or porosity term could easily account for the major errors we have. Therefore, future experiments should carefully measure these properties before conducting experiments.
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.