Problem 129, 2011 NCEES Practice Exam

[DavidPE]

I don't understand the solution to problem 129 of the 2011 NCEES Practice Exam, and I'm hoping someone can 'splain it to me. The problem:

A 4.0-MGD wastewater treatment plant discharges a secondary-treated effluent into a receiving stream. The wastewater has the following characteristics:

BOD5: 20 mg/L

DO: 2.0 mg/L

Temp: 24C

The receiving stream upstream from the point of wastewater discharge has the following characteristics:

Flow Rate: 18 cfs

BOD5: 4.0 mg/L

DO: 6.0 mg/L

Temp: 27C

Cross-sectional area: 36 sf (uniform)

The reaeration rate is estimated to be 0.4/day (base e at 20C) and the temperature correction coefficient is 1.024. The deoxygenation rate constant is estimated to be 0.23/day (base e at 20C) and the temperature correction coefficient is 1.047. Reaeration and deoxygenation are the only major factors affecting the dissolved oxygen concentration in the stream after mixing with wastewater effluent. Assume the time of travel in the stream to reach the maximum dissolved oxygen deficit is 3 days. The dissoved oxygen deficit (mg/L) at this location downstream from the point of discharge is most nearly:

a) 3.2

b) 5.2

c) 7.2

d) 8.4

According to the solution:

1. Calculate the temperature of the mixed flows. Mass balance. T = 26.2C.

2. Correct the rate constants for temperature. kt = k20 * theta^(T-20). kd = 0.305; kr = 0.46.

3. Calculate the BOD5 of the mixed flow. Mass balance. BOD5 = 8.09 mg/L.

4. Calculate the BODu of the mixed flow. BOD5 = BODu * (1-e^(-k*t)). They say that BODu = 11.76 mg/L.

5. Calculate the dissolved oxygen deficit at 3 days (Dc). Dc = [(kd * BODu)/kr] * e^-(k*t). They say that Dc = 3.12 mg/L.

I am with them on everything except the BODu calculation. When they calculated the BODu, they used the uncorrected kd value of 0.23/day. Why is that? Why not use the corrected kd value of 0.305/day? I understand everything else.

Thanks very much for the help, I really appreciate it.

Dave

 

[envirotex]

My guess would be that the testing standard for BODu specifies a temperature of 20C...

 

[HopefulEnv]

I was thinking that maybe this was just an error on their part - and we were supposed to use the corrected kd value...?

 

[Dleg]

This question has changed since the 2004 edition, but there was a similar problem in that one (problem 134). In that problem, the stream temp. was 20 degC. My notes say "no need to correct for temp., stream is 20 degC", so it would appear that I agree with you guys - the kd value needs to be corrected for the stream temp. Do you still get the correct answer if you do that?

One thing I hate about the exam is how the answer choices are often a little off the value you get. I am guessing they do that to allow for more than one method to be used, but geeze.... for example on this one (2004 edition), I got 6.29, but the answer is 6.2. Why not 6.3?? Uggh!! Same thing with the new problem: apparently NCEES says the answer is 3.12, but the correct choice is 3.2 But... you'd have to be pretty far off that to get the next closest answer.

 

[HopefulEnv]

Using the corrected kd value (.306) I get 2.74. I've looked into this... and it seems if the stream temp is 20... than no need to correct- like the 2004 version.

 

[envirotex]

This question has changed since the 2004 edition, but there was a similar problem in that one (problem 134). In that problem, the stream temp. was 20 degC. My notes say "no need to correct for temp., stream is 20 degC", so it would appear that I agree with you guys - the kd value needs to be corrected for the stream temp. Do you still get the correct answer if you do that?

One thing I hate about the exam is how the answer choices are often a little off the value you get. I am guessing they do that to allow for more than one method to be used, but geeze.... for example on this one (2004 edition), I got 6.29, but the answer is 6.2. Why not 6.3?? Uggh!! Same thing with the new problem: apparently NCEES says the answer is 3.12, but the correct choice is 3.2 But... you'd have to be pretty far off that to get the next closest answer.

The stream value should use the corrected temp... but I'm still ambivalent about BODu. The standard 5210C (basically extended BOD5) says it should be 20C...

Not the best question.

 

[DavidPE]

Hopeful, I don't agree with 2.74 mg/L using the corrected kd value (0.305). I come up with 5.36 mg/L (answer B).

If fact, I get 7.13 mg/L (answer C) using the uncorreced kr (0.40) and 8.54 mg/L (answer D) using the the corrected kr (0.46). So, it seems they have all the options covered! :beat:

Anyway, I am going to stick to using the corrected kd value.

 

[DavidPE]

Hopeful, I don't agree with 2.74 mg/L using the corrected kd value (0.305). I come up with 5.36 mg/L (answer B).

If fact, I get 7.13 mg/L (answer C) using the uncorreced kr (0.40) and 8.54 mg/L (answer D) using the the corrected kr (0.46). So, it seems they have all the options covered! :beat:

Anyway, I am going to stick to using the corrected kd value.

Nevermind that entire post, except the part about sticking to the corrected kd value. The lesson of that post is thank goodness we don't have to take the exam with a 2 year old and a 3 year old on our laps.