CEE 680

 

Fall 2011

Water Chemistry

 

Homework Set #6

 

Problem #1  (2 points)

In Spring when temperatures are on the rise, it is common for conventional activated sludge wastewater treatment plants to start nitrifying.  When this happens, the pH drops due to the following overall stoichiometry:

 

 

Where  represents bacterial cells.

 

What is the rate of nitrification in moles of ammonia per minute, if the pH drops from 7.3 to 6.9 in 4 hours?  (hint: conventional activated sludge systems are intensively aerated or mixed with air)

 

Solution to #1

This is an open system, because the activated sludge is intensively aerated.  In an open system, total carbonate is not conservative, but alkalinity is.

 

Change in alkalinity is determined by the change in the value of (CB-CA) going from the left side of the above equation to the right side.  On the left side (CB-CA) = (22-0) or +22.  On the right side (CB-CA) = (0-21) or -21.  The net change is therefore -43 equivalents of alkalinity formed per "mole" of cells produced.  We can also conclude that there are 22 moles of ammonia oxidized per "mole" of cells produced.  Combining, this gives us, 22 moles of ammonia oxidized per 43 equivalents of alkalinity consumed.

 

We also can calculate the rate of change of alkalinity from the rate of change of pH.  To do this we need to refer to the open system logC vs pH diagram for the carbonates.  Once we know the pH, we can find alkalinity from the following approximation of the ENE: Alk or (CB-CA) = [HCO3-].

 

 

 

If you use 6.3 as the pK1 value you get:

 

The initial conditions:

            pH = 7.3,

            Alk = 1.0x10-4 or 10-4.0 equivalents/L =

 

Final conditions (after 4 hours):

            pH = 6.9

            Alk = 3.98x10-5 or 10-4.4 equivalents/L

The difference in alkalinity is:

            = (10-4.0 - 10-4.4) = 6.05 x 10-5 equivalents/L

 

Therefore the rate of change of alkalinity is

            = (6.05x10-5)/4 hrs  = 1.51 x 10-5 equivalents/L/hr

 

And combining this with the above stoichiometry, we get:

 

nitrification rate

 =  (1.51 x 10-5 equivalents alkalinity consumed/L/hr) x (22 moles of ammonia oxidized per 43 equivalents of alkalinity consumed)

 

= 7.74 x 10-6 moles ammonia oxidized/L/hr

= 1.29 x 10-7 moles ammonia oxidized/L/min

 

 

If you use 6.35 as the pK1 value you get:

 

The initial conditions:

            pH = 7.3,

            Alk = 8.94x10-5 or 10-4.05 equivalents/L =

 

Final conditions (after 4 hours):

            pH = 6.9

            Alk = 3.55x10-5 or 10-4.45 equivalents/L

The difference in alkalinity is:

            = (10-4.05 - 10-4.45)/ = 5.40 x 10-5 equivalents/L

 

Therefore the rate of change of alkalinity is

            = (5.40x10-5)/4 hrs  = 1.35 x 10-5 equivalents/L/hr

 

And combining this with the above stoichiometry, we get:

 

nitrification rate

 =  (1.35 x 10-5 equivalents alkalinity consumed/L/hr) x (22 moles of ammonia oxidized per 43 equivalents of alkalinity consumed)

 

= 6.90 x 10-6 moles ammonia oxidized/L/hr

= 1.15 x 10-7 moles ammonia oxidized/L/min

 

 

 

 

 

Problem #2 (3 points)

You are treating an alkaline groundwater by alum coagulation followed by base addition for corrosion control.  Your target pH for the water in the distribution system is 8.5.  Analysis of the finished water prior to base addition shows a pH of 7.2, and an alkalinity of 250 mg/L as CaCO3.  How much of either one of the following two bases would you have to add (in mg/L) to reach your target pH.

 

a. Caustic Soda  (NaOH)

 

 

b. Soda Ash  (Na2CO3)

 

 

Solution to #2

This is a closed system.  Recall that:

 

We also know that:

Alk = 250 mg/L as CaCO3  =  5x10-3 equivalents/L

 

a. Caustic Soda

Since caustic soda does not contain carbonates, CT is a constant for this case.

@ pH 7.2,

 

Next, it's a simple matter of calculating the change in alkalinity that accompanies the change in pH.

@ pH 8.5,

 

Alk

= (0.97832+2*0.015505)*5.6245x10-3

 

Alk

= 5.67699x10-3  equivalents/L

 

 

delta Alkalinity

 =  5.67699x10-3 equivalents/L  -  5x10-3 equivalents/L

 

 

=  6.77x10-4 equivalents

 

and this change in alkalinity must come from the caustic soda added:

Caustic Soda Dose =  6.77x10-4 equ. * 40g/equ.

Caustic Soda Dose = 27.1 mg/L

 

b. Soda Ash

This problem is similar to part "a", except that CT is augmented by addition of the soda ash.  It can be directly related to the soda ash dose (SAD), knowing that one mole of soda ash contains one mole of carbonate species:

 

CT-final = CT-initial + SAD

 

We can then use this and estimate final Alkalinity (Alkfinal) as a function of SAD using the two different equations for alkalinity, then solve both for SAD.  (N.B. you can also solve this problem by recognizing that addition of soda ash does not change the acidity.  You then use this acidity to solve for final carbonate concentration which then gives you the SAD).

 

First equation

Second Equation

Combine and Solve

Convert to mg/L soda ash

 

Soda Ash Dose

= (6.83x10-4 moles/L)*(106 g/mole)

 

 

= 0.0724 g/L

 

 

= 72 mg/L

 

 

 

Problem #3 (1 point)

Repeat #2, but this time consider that your water treatment system has a large uncovered finished-water reservoir.  Make the extreme-case assumption that the water will reach equilibrium with CO2 in the atmosphere, after base addition, but before entry into the distribution system.

 

Solution to #3

This is an open system problem.  To solve, you can examine the open system diagram and determine the Alkalinity needed to achieve a pH of 8.5.  This is where the an imaginary horizontal (CB-CA) line would intersect the bicarbonate line at pH 8.5.  The alkalinity level needed is about 10-2.8 equivalents/L or about 1.5 meq/L.  Since this is below the 5 meq/L we're starting with, no additional alkalinity is needed.  In fact, 3.5 meq/L of acidity would be needed if it was deemed undesirable for the pH to exceed 8.5.