Stacked Filtration Research

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.

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 1 Basic Concept of Stacked Filtration Operation and the mathematical derivations demonstrate this relationship.

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.

Unable to render embedded object: File (BasicConcept.png) not found.
Figure 1: Basic Concept of Stacked Filtration Operation

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.

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.

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 Concept. All of the assumptions will be tested as described in more detail in the Future Challenge section.

Unable to render embedded object: File (Clear Well Basic Concept.png) not found.
Figure 2: Plane Area Concept

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.

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.

Unable to render embedded object: File (Clear Well Basic Concept.png) not found.
Figure 3: Vertically Stacked Filtration Design

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 to 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 ratio between the sand layer and the space between the tubes needs to be to allow us to model the layer of tubes as a plane.

Unable to render embedded object: File (Clear Well Basic Concept.png) not found.
Figure 4: Bench Scale Model

Unable to render embedded object: File (BasicConcept.png) not found.Unable to render embedded object: File (BasicConcept.png) not found.