**Lesson 18:**

**Water Chlorination Calculations**

**Objective**

In this lesson we will learn the following:

- Calculate chlorine dose, demand and residual.
- Calculate breakpoint chlorination.
- Calculate dry and solution feed rates for hypochlorite.
- Calculate percent strengths.
- Calculate chemical use.

**Lecture**

**Water Chlorination**

Chlorine deactivates microorganisms through several mechanisms that can destroy most biological contaminants, including:

- damaging the cell wall
- altering the permeability of the cell
- altering the cell protoplasm
- inhibiting enzyme activity so it's unable to use its food to produce energy
- inhibiting cell reproduction

Chlorination can be done at any point and time throughout the water treatment process. There isn't one specific time when chlorine must be added. Each point of chlorine application will subsequently control a different water contaminant concern, thus, offering a complete spectrum of treatment from the time the water enters the facility to when it leaves.

Pre-chlorination is when chlorine is applied to the water almost immediately after it enters the treatment facility. In this step the chlorine is usually added directly to the raw water, or added in the flash mixer. It is added at this stage to eliminate algae and other forms of aquatic life from the water so they won't cause problems later on in the treatment process. Pre-chlorination is found to remove taste and odors as well as oxidize any iron, manganese or hydrogen sulfide that might be present.

Chlorination can also be done directly after sedimentation, but before filtration. This would control the biological growth, remove iron and manganese, remove taste and odors, control algae growth, and remove color from the water. This will not decrease the amount of biological growth in the sedimentation cells.

Chlorination may also be done as the final step in the treatment process, which is when it is usually done in most treatment plants. The main objective of adding chlorine is to disinfect the water and maintain enough chlorine in the treated water as it travels through the distribution system (chlorine residual). At times, distribution systems can be a fair distance from the storage tanks and in dead end sections where water is not used, pathogens may re-grow if a proper chlorine residual isn't maintained in the treated water sent out for consumption. This results in poor water quality as well as slime and biofilm growth in the distribution system that will end up contaminating the clean, treated water being distributed.

Chlorine is available in a number of different forms:

- Pure elemental gaseous chlorine: a greenish-yellow gas with a pungent and irritating odor that is heavier than air, nonflammable, and nonexplosive, which is not toxic or corrosive when released to the atmosphere. Typical dosage is 1 - 16 mg/L.

- Solid calcium hypochlorite (tablets or granules). Typical dosage is 0.5 - 5 mg/L.

- Liquid sodium hypochlorite solution (in various strengths). Typical dosage is 0.2 - 2 mg/L.

The strength of one form of chlorine compared to the others that must be used for a system is dependent upon the amount of water to be treated, configuration of the water system, local availability of the chemicals, and skill of the operator.

**Calculations**

**Chlorine Dose, Demand and Residual**

You will hear these terms often pertaining to chlorination. Let's define them:

**Chlorine Dose**- amount of chlorine added to the system. It can be determined by*adding the desired residual*for the finished water*to the chlorine demand*of the untreated water. Dosage can be either milligrams per liter (mg/L) or pounds per day (lb/day). The most common unit used is mg/L. The dose can be determined by:

Chlorine dose, mg/L = Chlorine demand, mg/L + Chlorine residual, mg/L

**Chlorine Demand**- amount of chlorine used by iron, manganese, turbidity, algae, and microorganisms in the water. Since chlorine doesn't kill the microbes instantly, demand is relative to time.

For instance, the demand 10 minutes after applying chlorine will be less than the demand after 30 minutes. Demand, like dosage, is expressed in mg/L and can be determined by:

Chlorine demand, mg/L = Chlorine dose, mg/L - Chlorine residual, mg/L

**Chlorine Residual**- amount of chlorine (determine by testing) remaining after the demand is satisfied. Residual, like demand, is based on time. The longer the time period after the dosage, the lower the residual will be, untill all of the demand has been satisfied. This measurement is measured in mg/L as well.

The presence of a*free residual*of at least 0.2 to 0.4 ppm usually provides a high degree of assurance that the disinfection of the water is complete.*Combined residual*is the result of combining free chlorine with nitrogen compounds. Combined residuals are also known as*chloramines*.

*Example: *

**A water is tested and found to have a chlorine demand of 1.5 mg/L. If the desired chlorine residual is 0.6 mg/L, what is the desired chlorine dose, in mg/L?**

Chlorine dose, mg/L = Chlorine demand, mg/L + Chlorine residual, mg/L

Chlorine dose, mg/L = 1.5 mg/L + 0.6 mg/L

Chlorine dose, mg/L = 2.1 mg/L

*Example:*

**The chlorine dosage for a water is 1.8 mg/L. If the chlorine residual after 30 minutes contact time is found to be 0.4 mg/L, what is the chlorine demand, in mg/L?**

Chlorine demand, mg/L = Chlorine dose, mg/L - Chlorine residual, mg/L

Chlorine demand, mg/L = 1.8 mg/L - 0.4 mg/L

Chlorine demand, mg/L = 1.4 mg/L

*Example:*

**If the chlorine dosage for a water is 1.2 mg/L and the demand is known to be 0.8 mg/L, what is the residual amount in the water?**

For this one, just rearrange the formula to get residual on one side of the equation to solve:

Chlorine demand, mg/L = Chlorine dose, mg/L - Chlorine residual, mg/L

demand + residual = dose

residual = dose - demand

Chlorine residual, mg/L = Chlorine dose, mg/L - Chlorine demand, mg/L

Chlorine residual, mg/L = 1.2 mg/L - 0.8 mg/L

Chlorine residual, mg/L = 0.4 mg/L

Let's watch a video showing how to calculate the chlorine demand.

**Chlorine Dosage Feed Rate**

Now that you know the measurements of chlorine in mg/L, you can convert that dosage to pounds per day (lb/day) (or vice versa) with the following formula:

Chlorine, lb/day = Chlorine, mg/L x Flow, MGD x 8.34 lb/gal

*Example:*

**What should the chlorinator setting be, lb/day, to treat a flow of 1.88 MGD if the chlorine demand is 2.1 mg/L and a chlorine residual of 0.6 mg/L is desired?**

First calculate the chlorine dosage in mg/L:

Chlorine dose, mg/L = Chlorine demand, mg/L + Chlorine residual, mg/L

Chlorine dose, mg/L = 2.1 mg/L + 0.6 mg/L

Chlorine dose, mg/L = 2.7 mg/L

Now calculate the chlorine feed rate in lb/day (at a dose of 2.7 mg/L):

Chlorine, lb/day = Chlorine, mg/L x Flow, MGD x 8.34 lb/gal

Chlorine, lb/day = 2.7 mg/L x 1.88 MGD x 8.34 lb/gal

Chlorine, lb/day = 42.3 lb/day

*Example:*

**A pipeline that is 10 inches in diameter and 1800 ft long is to be treated with a chlorine dose of 5 mg/L. How many pounds of chlorine will this require?**

To use the mg/L to lb/day conversion, the gallon volume of the pipeline must first be determined. Remember to convert 10 inches to feet:

10 in x (1 ft/12 in) = 0.83 ft

Volume, gal = 0.785 x (Diameter)

^{2}x Length, ft x 7.48 gal/ft^{3}Volume, gal = 0.785 x (0.83 ft)

^{2}x 1800 ft x 7.48 gal/ft^{3}Volume, gal = 0.785 x (0.69 ft

^{2}) x 1800 ft x 7.48 gal/ft^{3}Volume, gal = 7,292.8 gal

^{}(which equals 0.0073 MG)

Now we can calculte the pounds of chlorine required using the conversion:

Chlorine, lb/day = Chlorine, mg/L x Flow, MGD x 8.34 lb/gal

Chlorine, lb/day = 5 mg/L x 0.0073 MGD x 8.34 lb/gal

Chlorine, lb/day = 0.30 lb/day

*Example:*

**A chlorinator setting is 42.3 lb/day for a flow of 1.21 MGD. What is the chlorine dosage, in mg/L?**

Let's take a look at the feed rate equation for lb/day and maneuver it to get dosage on one side by itself:

Chlorine, lb/day = Chlorine, mg/L x Flow, MGD x 8.34 lb/gal

To get mg/L on one side alone you will divide both sides by: (Flow, MGD x 8.34 lb/gal). This cancels it out on the right and brings it to the left:

Let's watch a video that shows you how to calclate the chlorinator setting.

**Breakpoint Chlorination**

To produce a free chlorine residual, enough chlorine must be added to the water to produce what is referred to as breakpoint chlorination. This is the point at which near complete oxidation of nitrogen compounds is reached. Any residual beyond breakpoint is mostly free chlorine.

When chlorine is added to natural waters, the chlorine begins combining with and oxidizing the chemicals in the water before it begins disinfecting. Although residual chlorine will be detectable in the water, the chorine will be in the combined form with a weak disinfecting power. As you can see from the graph above, adding more chlorine to the water at this oint actually decreases the chlorine residual as the additional chlorine destroys the combined chlorine compounds. At this stage, water may have a strong swimming pool or medicinal taste and odor. To avoid this, add even more chlorine to produce a free residual chlorine. Free chlorine has the highest disinfecting power. The point at which most of the combined compounds have been destroyed and the free chlorine starts to form is the *breakpoint*. The actual chlorine breakpoint can only be determined by experimentation.

Let's watch a video explaining breakpoint chlorination.

When determining breakpoint chlorination, compare the expected increase in residual with the actual increase in residual. Expected increase in residual is reflected directly by the increase in chlorine dose, lb/day. If the water is being chlorinated beyond the breakpoint, then any increase in chlorine dose will result in a corresponding increase in chlorine residual. Use the mg/L to lb/day equation to determine the expected increase in residual that would result from an increase in the chlorine dose:

Expected Increase in Residual:

Increase in chlorine dose, lb/day = Expected Increase, mg/L x Flow, MGD x 8.34 lb/gal

Actual Increase in Residual:

Actual Increase, mg/L = New Residual, mg/L - Old Residual, mg/L

*Example:*

**A chlorinator setting is increased by 1.8 lb/day. The chlorine residual before the increased dosage was 0.3 mg/L. After the increased chlorine dose, the chlorine residual was 0.5 mg/L. The average flow rate being chlorinated is 1.32 MGD. Is the water being chlorinated beyond the breakpoint?**

First calculate the EXPECTED increase in chlorine residual:

Increase in chlorine dose, lb/day = Expected Increase, mg/L x Flow, MGD x 8.34 lb/gal

1.8 lb/day = Expected Increase, mg/L x 1.32 MGD x 8.34 lb/gal

You need to maneuver the equation so the expected increase will be alone to solve for it. This means you will divide both sides by (1.32 MGD x 8.34 lb/gal), cancelling it out on the right and bringing it to the left:

Now calculate the ACTUAL increase in residual:

Actual Increase, mg/L = New Residual, mg/L - Old Residual, mg/L

Actual Increase, mg/L = 0.5 mg/L - 0.3 mg/L

Actual Increase, mg/L = 0.2 mg/L

The answer is yes, it is being chlorinated past the breakpoint because we needed it to increase 0.16 mg/L to fulfill the chlorine demand, but it actually increased 0.2 mg/L in chlorine residual. This means you have **free** available chlorine residual after breakpoint chlorination.

Total residal is a combination of the combined and free residual.

Example:

*Example:*

**A chlorinator setting is increased by 22 lb/day. The chlorine residual before the increased dosage was 1.3 mg/L. After the increased chlorine dose, the chlorine residual was 2.3 mg/L. The average flow rate being chlorinated is 2.2 MGD. Is the water being chlorinated beyond the breakpoint?**

First calculate the expected increase in chlorine residual:

Increase in chlorine dose, lb/day = Expected Increase, mg/L x Flow, MGD x 8.34 lb/gal

22 lb/day = Expected Increase, mg/L x 2.2 MGD x 8.34 lb/gal

You need to maneuver the equation so the expected increase will be alone to solve for it. This means you will divide both sides by (1.32 MGD x 8.34 lb/gal), cancelling it out on the right and bringing it to the left:

The expected increase is actually the chlorine demand. This tells us we need the total residual to be greater than 1.199 mg/L.

Now calculate the actual increase in residual:

Actual Increase, mg/L = New Residual, mg/L - Old Residual, mg/L

Actual Increase, mg/L = 2.3 mg/L - 1.3 mg/L

Actual Increase, mg/L = 1.0 mg/L

The answer is no, the water is NOT being treated past breakpoint. The demand told us we needed 1.199 mg/L before we started accumulating a residual in the water. We only increased 1.0 mg/L, therefore more chlorine needs to be added to the system.

**Calculating Dry Hypochlorite Feed Rate**

The most commonly used dry hypochlorite, calcium hypochlorite, contains about 65 to 70% available chlorine, depending on the brand. Because hypochlorites are not 100% pure chlorine, more pounds per day must be fed into the system to obtain the same amount of chlorine for disinfection. The equation below allows you to determine the pounds per day of hypochlorite required:

*Example:*

**A chlorine dose of 7.3 mg/L is required to disinfect a flow of 1.8 MGD. If the calcium hypochlorite to be used contains 67% available chlorine, how many pounds per day hypochlorite will be required for disinfection?**

*Example:*

**A tank contains 480,000 gallons of water and is to receive a chlorine dose of 1.8 mg/L. How many pounds of calcium hypochlorite (65% available chlorine) will be required?**

*Example:*

**A total of 37 lbs of calcium hypochlorite (66% available chlorine) is used in a day. If the flow rate treated is 2,400,000 gpd, what is the chlorine dosage, in mg/L?**

You'll need to work backwards on this one, plugging in what you are given first:

First multiply both sides by 0.66 to cancel it out on the right, leaving:

24.42 lb/day = (x mg/L)(2.4 MGD)(8.34 lb/gal)

Next, divide both sides by (2.4 MGD x 8.34 lb/gal), which cancels it out on the right, leaving:

x mg/L = 1.22 mg/L

**Calculating Hypochlorite Solution Feed Rate**

Liquid hypochlorite (sodium hypochlorite) is supplied as a clear, greenish-yellow liquid in strengths from 5.25 to 16% available chlorine. Often referred to as "bleach", it is, in fact, used for bleaching. Common household bleach is a solution of sodium hypochlorite containing 5.25% available chlorine. The typical concentration (density) of sodium hypochlorite is 144 mg/mL. When calculating the chemical feed pump settling, in mL/min, use the following formula:

*Example:*

**A hypochlorinator is used to disinfect the water pumped from a well. The solution used is sodium hypochlorite. A chlorine dose of 1.85 mg/L is required for adequate disinfection throughout the system. If the flow being treated is 1.28 MGD, what will the feed pump setting need to be in mL/min?**

Remember, that the typical density of sodium hypochlorite is 144 mg/mL:

Another way to calculate the feed pump setting in mL/min is:

If we use the problem above and add in the information that the sodium hypochlorite has a strength of 5.25%, determine the setting in mL/min:

We need to do some converting first to get it into the proper units that it calls for in the formula:

Flow is given in the problem above in MGD. Convert MGD to m^{3}/day with a few given constants, like 1 m^{3} = 264.2 gal:

We know the density of sodium hypochlorite is 144 mg/mL, but the equation asks for the density in g/cm^{3}, so let's do that conversion:

Now we can plug the values into the formula:

Notice that the feed pump setting is higher when the strength of the hypochlorite is only 5.25%.

**Calculating Percent Strength of Solutions**

If a teaspoon of sugar is dropped into a glass of water it gradually disappears as it dissolves in the water. A microscopic examination of the water would not show the sugar. Only examination at the molecular level, which is not easily done, would show the sugar and water molecules intimately mixed. If we taste the liquid, we would know there was sugar in it by its sweetness. We could recover the sugar by evaporating the water. In a solution, the molecules of the sugar (the **solute**) are homogeneously dispersed among the molecules of the water (the **solvent**). This mixture of sugar and water is homogeneous on a molecular level. Such a homogeneous mixture is called a **solution**. The composition of a solution can vary within certain limits. The main states of concern here are the solid form (calcium hypochlorite) and the liquid form (sodium hypochlorite) of chlorine. We can determine the percent strength of the hypochlorite through one of two formulas:

or

**Hint: *If your measurement is given in kg, but you need it in lbs, the conversion to use is (1 kg/2.20 lb). If your measurement is given in lbs, but you need kg, the conversion to use is (1 lb/0.453 kg). Sometimes everything is given in either pounds or kilograms and no conversion is needed. Either way you are determining the percent strength.

*Example:*

**If a total of 86 ounces of calcium hypochlorite (65% available chlorine) is added to 35 gallons of water, what is the percent chlorine strength, by weight, of the solution:**

To use the first equation you will need to convert ounces to pounds of calcium hypochlorite:

86 oz x (1 lb/16 oz) = 5.4 lb

Since the hypochlorite only has 65% available chlorine you would need to multiply the amount (lb) by the strength, in decimal:

5.4 lb x 0.65 = 3.51 lb

For the **solution** (solute + solvent) needed, you will have to remember to add the calcium hypochlorite (3.51 lb) to the amount of water (35 gal). To do this you must convert pounds of hypochlorite to gallons:

3.51 lb x (1 gal/8.34 lb) = 0.42 gal

Solution = 35 gal + 0.42 gal = 35.42 gal

Now plug in the values:

**Chemical Use**

In a typial plant operation, the chemical use (given in lb/day or gpd) is recorded daily. Such data provides a record of daily use from which the average daily use of the chemical or solution can be calculated. To calculate the average use of a chemical use one of the following formulas:

or

To calculate the days' supply you have left in inventory, use one of the following equations:

or

*Example:*

**The amounts of calcium hypochlorite used each day for a week are given below. Based on the given data, what was the average use, in lb/day, of hypochlorite used during the week?**

Monday: 42 lb/day

Tuesday: 40 lb/day

Wednesday: 41 lb/day

Thursday: 40 lb/day

Friday: 45 lb/day

Saturday: 48 lb/day

Sunday: 46 lb/day

**If you know you have 3500 lbs of calcium hypochlorite in storage, how many days' supply do you have?**

**Summary**

Chlorination can be done at any point and time throughout the water treatment process. There isn't one specific time when chlorine must be added. Each point of chlorine application will subsequently control a different water contaminant concern, thus, offering a complete spectrum of treatment from the time the water enters the facility to when it leaves. Chlorine is available in a number of different forms:

- Pure elemental gaseous chlorine: a greenish-yellow gas with a pungent and irritating odor that is heavier than air, nonflammable, and nonexplosive, which is not toxic or corrosive when released to the atmosphere. Typical dosage is 1 - 16 mg/L.

- Solid calcium hypochlorite (tablets or granules). Typical dosage is 0.5 - 5 mg/L.

- Liquid sodium hypochlorite solution (in various strengths). Typical dosage is 0.2 - 2 mg/L.

Chlorine Dose - amount of chlorine added to the system. It can be determined by *adding the desired residual* for the finished water *to the chlorine demand* of the untreated water. Chlorine Demand - amount of chlorine used by iron, manganese, turbidity, algae, and microorganisms in the water. Since chlorine doesn't kill the microbes instantly, demand is relative to time. Chlorine Residual - amount of chlorine (determine by testing) remaining after the demand is satisfied. Residual, like demand, is based on time. The longer the time period after the dosage, the lower the residual will be, untill all of the demand has been satisfied. To produce a free chlorine residual, enough chlorine must be added to the water to produce what is referred to as breakpoint chlorination. This is the point at which near complete oxidation of nitrogen compounds is reached. Any residual beyond breakpoint is mostly free chlorine. The most commonly used dry hypochlorite, calcium hypochlorite, contains about 65 to 70% available chlorine, depending on the brand. Because hypochlorites are not 100% pure chlorine, more pounds per day must be fed into the system to obtain the same amount of chlorine for disinfection. Liquid hypochlorite (sodium hypochlorite) is supplied as a clear, greenish-yellow liquid in strengths from 5.25 to 16% available chlorine. Often referred to as "bleach", it is, in fact, used for bleaching. Common household bleach is a solution of sodium hypochlorite containing 5.25% available chlorine. The typical concentration (density) of sodium hypochlorite is 144 mg/mL.

**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.