h1. Stacked Filtration Research
h3. Introduction and Objectives
A vertically stacked filtration system meets many of the AguaClara Project constraints. First of all, both normal filtration and backwash operations are gravity driven and requires no electricity. It is an open system. The construction material, PVC pipes, sand, concrete, and rebar are relatively cheap and abundant in Honduras. Most importantly, sand filtration gives us the ability to consistently lower the effluent NTU standard to below 1 NTU.
h3. Theory
The basic premise of the stacked filtration system is that the flow of filtration is equal to the flow of backwash so that we can use normal plant flow to backwash the filter. A conservative estimate of backwash velocity requires that it be 10 times the normal filtration velocity. We achieve this requirement by stacking layers of filtration on top of each other. Each layer, or plane, consists of a set of inlet tubes that introduce water to a layer of 20 cm of sand. The water once filtered is then collected by a set of outlet tubes. Each layer is essentially its own filtration system. When you stack them on top of each other, area for backwash stays the same and you can technically backwash all of them with the same backwash water. Figure 2 Basic Concept of Stacked Filtration Operation and the mathematical derivations demonstrate this relationship.
{latex}${{Q_{Plant} } \over 2} = V_{BW} A_{BW} ${latex}
{latex}${{Q_{Plant} } \over {N_{Filter} }} = V_{Filter} A_{Filter} ${latex}
!Clear Well Basic Concept.png|align=centre,width=600,height=400!\\
Figure 1: Clear Well Basic Concept
\\
\\
h3. Method
1) Review of existing filtration/backwash technology and research
We conducted a literature and online review. We determined the flow rate needed to sufficiently expand and clean the sand filter bed. This will help us determine how high the clear well needs to be above the filter, how large the flow pipes should be, and how much water should be in the clear well.
[Research of Existing Work.|Research of Existing Work]
2) Develop a MATHCAD file that generates backwash and filtration design parameters
We needed this for both an actual AguaClara plant and a bench-scale or pilot plant model of the plant for testing.
[MATHCAD File and description.|MATHCAD File]
3) Experiments of bench-scale model to confirm design success
Bench scale modeling tests the effectiveness of a filtration design by shrinking the design parameters of the system (filter bed depth, filter bed surface area, and etc) to a smaller scale that is easier to test. For example, we would simulated a filter bed of 50 cm of sand with 5 cm of sand with the porosity and specific gravity of the sand being constant. This would also enable us to test the validity of the empirical equations that are behind our design.
Our Mathcad design created two designs; one which was a conservative approach (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.|Fluidiziation Velocity Experiment]\\
h3. Results and Discussion
*MathCad Results: Empirical vs. Simple Hydraulics (Conservative) Approach*
|| || Conservative || Empirical \\ ||
| Filter Square Side \\ | 1.5m | 1.5m \\ |
| Filter Height \\ | 3.95m | 2.56m |
| Clear Well Diameter \\ | 6m | 6m |
| Clear Well Height \\ | 1.37m | 1.23m |
\\ !ClearWellTopView.png|width=600,height=400! !ClearWellSideView.png|width=600,height=400!\\
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) and will not be sustainable economically. The material cost for construction will be too high.
\\
2) The design based on the empirical Weber equation is smaller and less expensive. However, the validity of the empirical equations is not yet certain, in spite of our Fluidization Velocity Experiment. Therefore more testing needs to be done in pilot scale models.
\\
3) If the empirical equations are valid, then we can change parts of the design, by changing the sand parameters. For example, lower the dimensions of the clear well by lowering the backwash velocity by decreasing the d60 and specific weight of the media.
\\ !Orgd60.png|width=600,height=400! !Changed60.png|width=600,height=400!\\
Figure 3: Small Change in D60 can fix the error at 30% Expansion by over 100%
\\
\\
4)An additional advantage to Clear Wells is that the distribution tank does not have to be below the filtration tank, and in fact, it could be the clear well as well.
!ClearWellIsDistrTank.png|align=centre,width=600,height=400!\\
Figure 4: Distribution Tank can be the Clear Well Tank
\\
\\
*Experiment Results*
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 30% expansion (our target expansion), the degree of error was 110%.
\\ !Error.png|align=centre,width=600,height=400!\\
Figure 5: Error Between Calculated and Actual Expansions
\\
\\
\\
h4. 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.
*Wall Friction:*
We can attribute the increase in error as flow rate increased due to the increase in wall friction on the test vial.
Fix: We can minimize the wall and tube friction by increasing the size of our bench scale experiments.
*Sand Properties & Parameters:*
We might have used an incorrect D60 and porosity for the filter bed in our equations. We show on the Fluidization Velocity Experiment page how small changes in these values could easily account for the error.
Fix: For the next experiment those parameters should be tested for the sand or material before conducting experiments.
*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.
Fix: In the future, this hypothesis can be tested using dye. In addition, precautions can be taken, such as two levels could be clamped on the sides of the filter walls to ensure it is level or also use two clamps, rather than one.
*Expansion Headloss:*
The accuracy of our model also required the headloss occurring through the expanded bed to be more or less constant, which we did not have time to test (but is part of Recommended Future Research below).
Fix: Testing it would involve putting a pressure sensor into the system, connected on either end of the filter.
h3. Recommended Future Research
Future Research should be devoted to the following objectives:
* Repeating the Weber Fluidization Velocity experiment with a larger scale bench model to see if error decreases.
* Repeating the Weber Fluidization Velocity experiment with multiple layer filter media.
* Testing the headloss in the system through the expanded bed to ensure it is constant
* Create pilot scale model to determine any remaining error in the design before creating a plant scale{latex}${\rm{V}}_{{\rm{BW }}} = 10{\rm{V}}_{{\rm{Filtration}}} ${latex}
Where
BW=Back Wash
Q=Flow rate of filtration, backwash, or entire plant depending on the subscript.
V=Velocity of either filtration or backwash depending on the subscript.
A=Area of either filtration or backwash depending on the subscript.
N=Number of any system, pipe, and etc which in this case is the number of filtration unit that receives the plant flow rate.
For our design, we chose a conservative available backwash flow rate of only half of the plant flow rate.
We want the backwash flow rate to equal the filtration flow rate. So we arrange the first two equations for the plant flow rate and set them equal to each other.
{latex}$V_{Filter} A_{Filter} N_{Filter} = Q_{Plant} = 2V_{BW} A_{BW} ${latex}
When we substitute the 10 to 1 relationship between backwash and filtration velocity into the above equation, we derive the following relationship with regards to area.
{latex}$V_{Filter} A_{Filter} N_{Filter} = 2{\rm{x10}}V_{Filter} A_{BW} ${latex}
{latex}$A_{Filter} = {{20} \over {N_{Filter} }}V_{Filter} A_{BW} ${latex}
With the velocity of filtration cancelling each other, we learn that in order to use the same flow rate to backwash and filter we need the area of the filtration to be 10x the time area of backwash. Consequently, if we were to have two filters, then we would need 10 filters stacked of each other. If we were to have four filters, like our design, then we would have 5 layers for each filtration system.
During back wash operations, we will first use valves to close off the water leading to the distribution tank. As shown in the bottom diagram, we would only need to close off 3 valves. Then we would introduce back wash water from the sedimentation tank through the inlet tubes. As the first layer expands, we would close off the water to the top layer of influent tubes. Once the 2nd and 3rd layer expands we will close off the 2nd inlet manifold. Now all of the backwash water will be pouring through the bottom inlet manifold. These tubes will be designed to handle that flow and, since they are purposely located at the bottom, they would be able to elevate the entire sand bed.
IV. Assumptions
In order for our design to work, we made the following assumptions. First we assumed that 20 cm of sand will effectively filter 5-10 NTU effluent water from the sedimentation tank to lower than 1 NTU without clogging at a reasonable rate. Second, we assumed that the unfiltered water from the sedimentation tank would be able to backwash the filter so that it can continuously filter water to 1 NTU or lower standard. Third, we assumed that, as long as the distance between the filtration tubes in a layer, is small compared to the layer of sand, the flow of water coming out of the tubes will converge and form a plane of filtration. Consequently, a layer of inlet tubes sandwiched between two layers of sand would effectively have two plane areas of filtration. Please see Figure 3 Plane Area. All of the assumptions will be tested as described in more detail in the Future Challenge section.
IV. Methods
Our design process consisted of 3 major steps. First we designed the individual filter bed itself based on the relationship equations mentioned in the theory section. Second, we sized the pipe in our system so that the head loss experienced by the pipes is never greater than 10% of the head loss experienced by the sand. If the head loss in the sand is not greater than the head loss in the pipes, there will be preferential flow and not all of the pipes in the manifold will have equal flow. Third step was to design the minimum distance between the entrance pipes from the sedimentation tank to the height of the gutter to ensure proper back wash.
!Clear Well Basic Concept.png|align=centre,width=600,height=400!\\
Figure 1: Clear Well Basic Concept
\\
\\
h3. Results and Discussion
Our complete filtration system for Agalteca consists of a four rapid sand filtration system. Please see the below diagram. When arranged side by side with concrete wall with a thickness of 20 cm, the total width will be 2.897m and the total height will be 1.652m. Each filtration unit will be 1.652m in height and the sand portion will be square with a side of 0.474m. Each filter will have 5 layers with each layer, consisting of a set of inlet pipes, 20 cm sand layer, and a set of outlet pipes. Each layer will hold 18 layers except for the bottom inlet layer which will hold only six because they are bigger tubes. As pipe sizing go, all of the inlet and outlet tubes are 0.5 inch while the bottom is 1.5 inch in diameter. All of the manifold that connects to these filtration tubes except for the bottom one will be 3 inch in diameter while the bottom manifold and the rest of the pipe system of the filtration system will consist of 6 inch PVC pipes. All pipes and tubes used are schedule 40. This filter is designed for sands with typical characteristics of D60 of 0.55mm, porosity of 0.4, and specific gravity of 2.65. It will filter at rate of 1.4 mm/s and backwash at 14 mm/s with the expected 30% bed expansion. The filtration system should be located so that there is at least 2.5 m distance from the entrance pipe from the sedimentation tank to the gutter and the effluent pipe of the filtration unit should be slightly higher than the sand bed.
Our design should work as long as the following assumptions hold. First, we need to effectively backwash the sand filter with unfiltered water from the sedimentation tank so that it can continue to filter water to 1 NTU or lower. If there is decreasing filtration efficiency, as evident by high effluent NTU, then this design cannot work. Also we need to know whether or not 20 cm of sand is enough to lower the effluent NTU to 1 or lower. Also we need to find the clogging time of 20 cm of sand. If the 20 cm of sand clogs too frequently then that would be a weakness of this design. Lastly we are depending on the layer of inlet tubes to function as a plane of filtration instead of tubes of filtration if the distance between them is significantly smaller than the distance to the outlet tubes. Modeling the layer of tubes as a single layer that has a top and bottom plane area of filtration has enabled us to greatly reduce the size of our system.
VI. Future Challenge
The future challenge for the Filtration Team is to test the validity of our three assumptions mentioned above. We need to test the efficiency of 20 cm of sand with regards to clogging time and filtration efficiency. Our modeling of the area of filtration as a plane instead of a row of tubes needs to be tested as well. Finally, we need to find out the implications of back washing the sand filter with water that is normally used as an influent. Does the filtration efficiency eventually decrease over time?
Our immediate goal would be design and build a bench scale model of our filtration unit as shown below. Instead of a square unit, we will use a 6 inch diameter test tube. We are currently working on the actual specifications of this model but everything would essentially be scaled down except the 20cm layer of sand. Once this prototype is built, we can push water 5-10 NTU water through and check to see if the effluent NTU is lower than 1. We can also measure the clogging time during this experiment and model the effectiveness of filtration versus time. Using this model, we can also simulate backwash with 5-10 NTU water and then rerun the first experiment to see how backwashing with the unfiltered water effect the filtration efficiency as backwash cycles are repeated. Finally, we can also vary the number of inlet and outlet tubes per plane to see if our modeling of the layer of tubes as planes of filtration is accurate. We can slowly decrease the space between the tubes to see what the necessary |
