Lesson 17:
Filtration Calculations
Objective
In this lesson we will learn the following:
Lecture
Water Filtration
In the conventional water treatment process, filtration usually follows coagulation, flocculation and sedimentation.
Water filtration is a physical process of separating suspended and colloidal particles from water by passing the water through a granular material. This process involves straining, settling, and adsorption. As foc passes into the filter, the spaces between the filter grains become clogged, reducing this opening and increasing removal. Some material is removed just because it settles on a media grain. One of the most important processes is adsorption of the floc onto the surface of individual filter grains. In addition to removing silt and sediment, floc, algae, insect larvae, and any other large elements, filtration also contributes to the removal of bacteria and protozoans such as Giardia lamblia and Cryptosporidium.
The surface water treatment rule (SWTR) specifies four filtration technologies, although other alternatives are allowed. These mentioned include slow sand filtration, rapid sand filtration, pressure filtration, diatomaceous earth filtration, and direct filtration. Of these, all but rapid sand filtration is commonly employed in small water systems that use filtration. Each type has advantages and disadvantages. Regardless of the technology used, filtration involves the process of straining (where particles are captured in the small spaces between filter media grains), sedimentation (where the particles land on top of the grains and stay there), and adsorption (where a chemical attraction occurs between the particles and the surface of the media grains). When determining if your plant is filtering properly there are numerous calculations involved. Let's take a look at some of them of the filters used in water treatment:
Calculations
Flow Rate Through a Filter, gpm
The flow rate (gpm) can be calculated by taking the meter flow rate (gpd) and dividing by 1440 min/day:
Example:
The flow rate through a filter is 3.28 MGD. What is this flow rate expressed as gpm?
When you are given a specific filter run time, you can determine the flow rate that occurs during that time period with the following formula:
Example:
During a 90 minute filter run, 1.8 million gallons of water are filtered. What is the average flow rate through the filter, in gpm, during this filter run?
You will need to enter the flow as gallons, not million gallons.
Example:
At an average flow rate of 3250 gpm, how long a filter run, in hours, would be required to produce 650,000 gallons of filtered water?
You will write the equation as usual, filling in the information that you are given:
To get "filter run" on one side by itself so you can solve for it you need to do a little swapping by cross-multiplication. Think of 3250 gpm as a fraction: (3250 gpm / 1). Because it's over "1", it's the same number. After cross-multiplication your formula will look like this:
The question asked for the filter run time to be given in hours, so we must now convert our answer from minutes to hours:
200 min x (1 hr/60 min) = 3.33 hours
Now we are going to really test your previous knowledge, bringing in volume and area determination for filtration rate.
Example:
A filter box is 5 ft by 2 ft (including the sand area). If the influent valve is shut, the water drops 2 inches per minute. What is the rate of filtration, in MGD?
First, you must do some "pre-processing" of the information given. You should do this by performing calculations one step at a time, breaking down the problem into what is given and what is to be found. We know the following:
To determine the volume of water passing through the filter, we will use the following formulas:
First, let's determine the filter box area:
Filter box area = 5 ft x 2 ft = 10 ft2
To determine the volume of water passing through the filter, you need to convert the drop in water (2 inches) into feet. This measurement will then be known as your "height" for the volume formula above:
2 in x (1 ft/12 in) = 0.17 ft
Now you can determine the volume of water passing through the filter box in one minute:
Volume = Area x Height
Volume = 10 ft2 x 0.17 ft
Volume = 1.7 ft3
Since the problem wants to know the amount of water in gallons we need to convert cubic feet to gallons:
1.7 ft3 x (7.48 gal/ft3) = 12.72 gal/min
Since the problem asked for the filtration rate in MGD we need to convert gallons per min (gpm) to million gallons per day (MGD):
(12.72 gal/min) x (1 MG/1,000,000 gal) x (60 min/day) = 0.00076 MGD
Filtration Rate
One measure of filter production is filtration rate, which is generally in the range of 2 to 10 gpm/ft2. The filtration rate is used to determine the gallons per minute of water filtered through each square foot of filter area. Along with filter run time, it provides valuable information for the operation of filters and is determined with the following equation:
Example:
A filter 10 ft by 8 ft receives a flow of 1825 gpm. What is the filtration rate in gpm/ft2?
What does this tell you? You see the filtration rate for the filter is 22.81 gpm/ft2, but the range should be between 2 and 10 gpm/ft2. That means the plant needs another filter to handle the flow rate of 1825 gpm, or build a much bigger one.
Example:
A filter 48 inches long and 28 inches wide treats a flow of 175,000 gpd. What is the filtration rate in gpm/ft2?
First convert the flow from gpd to gpm:
(175,000 gal/day) x (1 day/1440 min) = 121.53 gpm
Determine the area of the filter, converting from inches to feet as you go:
48 in x (1 ft/12 in) = 4 ft
28 in x (1 ft/12 in) = 2.3 ft
Area, ft2 = 4 ft x 2.3 ft
Area, ft2 = 9.2 ft2
Now determine the filtration rate:
Example:
A filter 10 ft long and 5 ft wide produces a total of 2 MG during a 72-hour filter run. What is the average filtration rate for this filter run, in gpm/ft2?
First you need to calculate the gpm flow rate through the filter:
Now calculate the filtration rate of the filter:
Example:
A filter is 45 inches long and 25 inches wide. During a test of flow rate, the influent valve to the filter is closed for 5 minutes. The water level drop during this period is 9 inches. What is the filtration rate for the filter, in gpm/ft2?
Just like before, you must do some "pre-processing" of the information given. You should do this by performing calculations one step at a time, breaking down the problem into what is given and what is to be found. We know the following:
We need to convert the dimensions from inches to feet for calculation:
45 in x (1 ft/12 in) = 3.75 ft
25 in x (1 ft/12 in) = 2.08 ft
To determine the volume of water passing through the filter, we will use the following formulas:
First, let's determine the filter box area:
Filter area = 3.75 ft x 2.08 ft = 7.8 ft2
To determine the volume of water passing through the filter, you need to convert the drop in water (9 inches) into feet. This measurement will then be known as your "height" for the volume formula above:
9 in x (1 ft/12 in) = 0.75 ft
Now you can determine the volume of water passing through the filter box in one minute:
Volume = Area x Height
Volume = 7.8 ft2 x 0.75 ft
Volume = 5.85 ft3
Since the problem wants to know the amount of water in gallons we need to convert cubic feet to gallons:
5.85 ft3 x (7.48 gal/ft3) = 43.76 gal/min
We have the flow in gpm, but we need to determine the flow during the 5 minutes the valve was closed:
(43.76 gal/min) / 5 min = 8.75 gpm
Now determine the filtration rate during this 5 minute time period:
Backwash Rate
In filter backwashing, one of the most important operational parameters to be determined is the amount of water, in gallons, required for each backwash. This amount depends on the design of the filter and the quality of the water being filtered. If the chosen filter requires a backwash flow rate of 10 gpm and the pump only produces 7 gpm, the bed will not clean completely and though it may take a few months to a year, the bed will foul prematurely. Water temperature also plays a role in selecting the right equipment. Colder water will expand the mineral bed more than warmer water at the same flow rate. The actual washing typically lasts 5 to 10 minutes and uses amounts of 1-5% of the flow produced.
Sometimes treatment plants do not have a means of determining backwash rates with a flowmeter. These rates need to have a velocity high enough to separate the media so trapped particles that work their way into the filter can be lifted and removed during a backwash. Typically, the backwash rate should be a minimum of three times its filter rate.
Without a meter attached to a backwash pump, physical measurements need to be taken from time to time to establish the backwash flow rate. The backwash filter rise is when the filter level has been dropped low enough to expose the troughs, and then the pump is engaged and a measurement is taken from the water level over a period of time that can be easily calculated. For best results, take two measurements while the pump is running, and then average the rise rate. This way the actual time needed to charge the backwash line is taken into consideration. To do this, an operator needs to be quick with their measurements while taking precautions not to fall into the filter and using proper personal protective equipment (PPE).
Typical backwash rates range from 10 to 25 gpm/ft2 and is determined with the following formula:
Example:
A filter has the following dimensions:
Assuming a backwash rate of 11 gallons per square foot per minute (gal/ft2/min) is recommended, and an 8 minute backwash is required, calculate the amount of water, in gallons, required for each backwash.
Fist convert the dimensions from inches to feet for calculations:
48 in x (1 ft/12 in) = 4 ft
28 in x (1 ft/12 in) = 2.3 ft
Area of filter = 4 ft x 2.3 ft = 9.2 ft2
Gallons of water used per ft2 of filter = 11 gal/ft2/min x 8 min = 88 gal/ft2
Gallons required for backwash = 88 gal/ft2 x 9.2 ft2 = 9.57 gal
Example:
A filter that is 4 ft by 6 ft has a backwash rate of 550 gpm. What is the backwash rate, in gpm/ft2?
Determine the filter area:
Area, ft2= 4 ft x 6 ft
Area, ft2= 24 ft2
Now calculate the backwash rate:
Example:
A filter that is 10 ft long and 6 ft wide has a backwash flow rate of 985,000 gpd. What is the filter backwash rate, in gpm/ft2?
First, convert the flow rate from gpd to gpm:
(985,000 gal/day) x (1 day/1440 min) = 684.03 gpm
Determine the area of the filter:
Area, ft2= 10 ft x 6 ft
Area, ft2= 60 ft2
Now determine the backwash rate for the filter:
Backwash Rise Rate
Backwash rate is occasionally measured as the upward velocity of the water during backwashing, expressed as inches/minute rise. To convert from a gpm/ft2 backwash rate to an in/min rise rate use the following equation:
Example:
A filter has a backwash rate of 22 gpm/ft2. What is this backwash rate expressed as an in/min rise rate?
Sometimes the backwash rate needs to be determined in cm/min. In this case, remember that 1 inch = 2.54 cm. To convert the rise rate in the example above to cm/min:
(35.29 in/min) x (2.54 cm/1 in) = 89.63 cm/min
Example:
A filter that is 40 inches long and 30 inches wide has a backwash rate of 99 gpm. What is this backwash rate expressed as an in/min rise rate?
Determine the area of the filter:
40 in x (1 ft/12 in) = 3.3 ft
30 in x (1 ft/12 in) = 2.5 ft
Area, ft2= 3.3 ft x 2.5 ft
Area, ft2= 8.25 ft2
First calculate the backwash rate as gpm/ft2:
Now convert the gpm/ft2 rate to an in/min rise rate:
If you need the rise rate in cm/min, convert the measurement by:
(19.25 in/min) x (2.54 cm/1 in) = 48.9 cm/min
Volume of Backwash Water Required, gal
To determine the volume of water required for backwashing, we must know both the desired backwash flow rate (gpm) and the duration of backwash (min) and use the following equation:
Backwash water volume, gal = Backwash, gpm x Backwash Duration, min
Example:
For a backwash flow rate of 550 gpm and a total backwash time of 7 minutes, how many gallons of water will be required for backwashing?
Backwash water volume, gal = Backwash, gpm x Backwash Duration, min
Backwash water volume, gal = 550 gpm x 7 min
Backwash water volume, gal = 3850 gal
Example:
How many gallons of water would be required to provide a backwash flow rate of 850 gpm for a total of 8 minutes?
Backwash water volume, gal = Backwash, gpm x Backwash Duration, min
Backwash water volume, gal = 850 gpm x 8 min
Backwash water volume, gal = 6800 gal
Backwash Pumping Rate, gpm
The desired backwash pumping rate (gpm) for a filter depends on the desired backwash rate (gpm/ft2) and area of the filter (ft2). The backwash pumping rate can be determined by:
Backwash pumping rate, gpm = Desired backwash rate, gpm/ft2 x Filter area, ft2
Example:
A filter is 6 ft long and 4 ft wide. If the desired backwash rate is 25 gpm/ft2, what backwash pumping rate will be required, in gpm?
Backwash pumping rate, gpm = Desired backwash rate, gpm/ft2 x Filter area, ft2
Backwash pumping rate, gpm = 25 gpm/ft2 x (6 ft x 4 ft)
Backwash pumping rate, gpm = 25 gpm/ft2 x (24 ft2)
Backwash pumping rate, gpm = 600 gpm
Percent Product Water Used for Backwashing
Along with measuring filtration rate and filter run time, another aspect of filter operation that is monitored for filter performance is the percent of product water used for backwashing. This measurement can be determined by:
Example:
During a filter run, 19.2 MG water were filtered. If 75,000 gallons of this produce water were used for backwashing, what percent of the product water was used for backwashing?
Summary
One of the most important processes in a water treatment plant is filtration. Filters trap or remove particles from the water further reducing the cloudiness or turbidity. The surface water treatment rule (SWTR) specifies four filtration technologies, although other alternatives are allowed. These mentioned include slow sand filtration, rapid sand filtration, pressure filtration, diatomaceous earth filtration, and direct filtration. Of these, all but rapid sand filtration is commonly employed in small water systems that use filtration. One measure of filter production is filtration rate, which is generally in the range of 2 to 10 gpm/ft2. The filtration rate is used to determine the gallons per minute of water filtered through each square foot of filter area. In filter backwashing, one of the most important operational parameters to be determined is the amount of water, in gallons, required for each backwash. This amount depends on the design of the filter and the quality of the water being filtered. The actual washing typically lasts 5 to 10 minutes and uses amounts of 1-5% of the flow produced. Backwash rate is occasionally measured as the upward velocity of the water during backwashing, expressed as inches/minute rise. To determine the volume of water required for backwashing, we must know both the desired backwash flow rate (gpm) and the duration of backwash (min). The desired backwash pumping rate (gpm) for a filter depends on the desired backwash rate (gpm/ft2) and area of the filter (ft2).
Assignment
Complete the math worksheet for this lesson. You must be logged into Canvas to submit this assignment. Make sure you choose the appropriate semester.
