Adjusting Mass Balance Errors

[OilBoiler]

Hi everyone,

I'm working on a six sigma project for our cryogenic unit. I'm doing a mass balance around our unit with daily averages of flows and component concentrations. Because I'm doing it with daily averages, obviously I have to leave some room for error, but I have a question regarding adjusting this error in order to determine for sure what is the % error or standard deviation of my balance. I need to calculate the % recoveries of C3+ in our liquid stream, so I'm doing a molecular balance around the unit. I have component analyzers at the inlet and outlet gas streams, but I don't have any component analyzers on my liquid stream so I need to predict somehow what are the compositions of the liquid stream.

Here's my approach: Since I do have the compositions for the gas streams I did noncondensables balance, because they should go in and out and not be absorbed/recovered by any stream. For example the balance on Hydrogen I get:

Hydrogen in (inlet gas): 15000 lb/day
Hydrogen out (outlet gas): 14000 lb/day

Because Hydrogen should take a free ride and not go with the liquid stream, there are 1000 lb/day that I'm missing (or going with the liquid, in theory). The % error for the mass balance here would be 6.7%, because this number should be zero. For heavier components such as propane, I get:

Propane in (inlet gas): 134,000 lb/day
Propane out (outlet gas): 61,000 lb/day
Propane out (liquid): 134,000 - 61,000 lb/day = 73,000 lb/day

I'm assuming in the calculation above, that the mass balance doesn't have errors and that the differential between what comes in and leaves the unit in the gas stream goes to the liquid stream, which is not realistic, because the balance for hydrogen showed a 6.7% error on the same stream. My question is: Do I incorporate the 6.7% error or whatever average error I get on noncondensables to the heavier components? For instance:

Assuming the % error in noncondensables is 7%, do I substract 7% of the total lbs/day of the heavier components to account for the error in the balance?:

134000 lb/day of propane x 7% error = 9380 lb/day
Then, 73,000 - 9380 lb/day = 63,320 lb /day (accounting for the % error)

Hopefully that makes sense and if not, I appreciate your feedback. Thanks!

 

[katmar]

This is a common problem when trying to set up models for Process Integration. The people who sell Process Integration software often include utilities for closing mass balances in the most appropriate way. If you Google "Process Integation" you will find plenty of information.

It's quite a while since I did any of this sort of work and my files are a bit out of date. Some old references that you may find useful are

Joseph Rosenberg et al, Ind. Eng. Chem. Rs. 1987, 26, 555-564

JE Albers, Hydrocarbon Processing, March 1994, 65-66

CM Crowe et al, AIChE Journal, Vol 29, No 6, Nov 1983, 881-888

CM Crowe, AIChE Journal, Vol 32, No 4, Apr 1986, 616-623

CM Crowe, AIChE Journal, Vol 34, No 4, Apr 1988, 641-550

 

[DickRussell]

Tell us about the unit around which you are making a balance. Tell us also what measurements, other than compositions, are being used. At some points you are dealing with flow measurements, and they, too, are sources of error. Hydrogen will be absorbed into condensed liquid, although its volatility relative to C3 is perhaps 200, depending on conditions. In absolute terms, the C3 could absorb enough hydrogen in a single flash stage to warrant considering it in the balance. If the C3 product is from the bottom of a column, then of course the hydrogen would be stripped out to negligible.

There could be enough variability in the operating data over the averaging period that your balance is as good as you will get. If the operation is rock steady, you can use your spreadsheet to look at whether changing a single measurement would bring multiple errors in line fairly well. Sometimes such analyis can point the finger at a flow meter in need of calibration.

 

[OilBoiler]

This is a cryogenic unit - we feed fuel gas (mainly made up of C1, H2, C2, and traces of some heavier components to C4+). We have orifice flowmeters for our inlet and outlet gas streams as well as our liquid stream. We measure mole compositions on inlet and outlet gas streams and only C2 on the liquid stream. The unit is composed of three parts: dehydration, separation, and compression. The water is first removed from the gas so the equipment downstream doesn't freeze up, because of the subzero temperatures. The gas is put through cold temperatures to remove lighter components through a deethanizer. The bottom liquids are C3s and C4s. The deethanizer offgas is made up of H2, N2, C1, C2, C2-, etc., and is compressed to be exported. We also have CO2 in the inlet gas and it has been brought to my attention that some of the CO2 may be absorbed by the glycol during the dehydration process, but my balance is showing that more CO2 is coming out than what's coming in.

Hopefully that helps.

 

[DickRussell]

Ok, if the C3+ stream is the bottoms of a deethanizer, then it should be relatively free of hydrogen. 134,000 lb/day of C3+ is "traces"? Well, ok, that could indeed be a couple % of an FCC offgas stream, if that is what you have for "fuel." The 45% propane recovery seems poor if LPG recovery is the point of processing the gas.

It still would be nice to see the actual feed and gas compositions, plus whatever bottoms analysis you have and the flows measured. Are the flows corrected to conditions? Have you done balances for other components? If, say, the ethane, ethylene, or propylene balance is out the same way, and changing one of the measured flows makes everything fall into place, that could be the problem. If propylene is off by a similar amount but in direction opposite to the propane error, then you might suspect analysis error.

You can use reconciliation to get a "best fit" to averaged data, or you can use it to locate suspect sources of measurement error. Variability in process conditions may mean you can't get a really great fit of averaged data.

 

[sshep]

alas, our university educations seem to have barely touched one what to do when we had more data than is needed, and which is not consistent. Experience leads me to believe there are basically two approaches:

1) Pick what you believe to be the most accurate square set of measurements and put all faith in those. This is a very useful approach. Economical effort can thereafter be put into making those measurements as good as possible- for example temp, pressure, and composition correcting your hydrogen stream measurements which are especially susceptible to density errors.

2) Using extra measurements and minimizing the error. This can sometimes be done using only the solver addin in excel. I provide an example below for a case similar to yours where composition and flow is given for the inlet and vapor, but only the bottoms flow is known. For the measured data column the bottoms flow does not match the inlet minus vapor, but in the reconciled column a formula is written to enforce the balance.

example raw data (klb/hr).
Meas CF Recon (M-R)^2
H2 in 15 1 15.0 0.0
CH4 in 20 1 20.0 0.0
C2 in 50 1 50.0 0.0
C3 in 115 1 115.0 0.0
H2 Vap 14 1 14.0 0.0
CH4 Vap 20 1 20.0 0.0
C2 Vap 40 1 40.0 0.0
C3 Vap 40 1 40.0 0.0
Btms 100 86.0 196.0
sum= 196.0

after using solver to adjust correction factors (CF; where R=M*CF) with goal of minimizing the sum of the squared errors:

Meas CF Recon (M-R)^2
H2 in 15 1.10 16.6 2.4
CH4 in 20 1.08 21.6 2.4
C2 in 50 1.03 51.6 2.4
C3 in 115 1.01 116.6 2.4
H2 Vap 14 0.89 12.4 2.4
CH4 Vap 20 0.92 18.4 2.4
C2 Vap 40 0.96 38.4 2.4
C3 Vap 40 0.96 38.4 2.4
Btms 100 98.4 2.4
sum= 21.8

care should be taken to evaluate the results and insert some reason. In this reconcilliation case you see alot of H2 in the bottom, but excel is a math servant not a chemical engineer. If we believe all the H2 goes out as vapor we can add that equation and remove one reconcilliation variable:

Meas CF Recon (M-R)^2
H2 in 15 1.10 16.6 2.4
CH4 in 20 1.08 21.6 2.4
C2 in 50 1.03 51.6 2.4
C3 in 115 1.01 116.6 2.4
H2 Vap 14 16.6 6.5
CH4 Vap 20 0.92 17.4 6.7
C2 Vap 40 0.96 37.4 6.7
C3 Vap 40 0.96 37.4 6.7
Btms 100 97.4 6.7
sum= 42.9

Generally I like to pick a square set of measurements per method #1 because no calculations are needed to "interprete" future data, but sometimes a error minimization approach is useful. You can be as sophisticated as you believe you need to be- if the measurements are believed to have different standard % errors (orifice plates vs mass flow meters, etc), this can be incorporated. For fitting equation parameters to data, using the solver in this manner is great. Anyway you get my drift.

sorry about the length. best wishes as always, sshep