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!

 

[UmeshMathur]

Mass balance reconciliation around a series of interconnected process units is a non-trivial problem and much work has been reported in publications in this area. What is required is a global reconciliation capability that simultaneously adjusts all measurements while enforcing the laws of chemical engineering. There also needs to be a procedure for gross error detection.

The problems with following a manual hit-or-miss procedure are:
(a) Very hard to do for a large problem (global reconciliation is impossible to do by hand)
(b) Error prone (it is easy to misdiagnose the cause of an error)
(c) The whole procedure becomes subjective
(d) New data sets require a replication of the entire effort


Such software is available (unfortunately not in the public domain) that formulates the overall problem as an optimization. As this is a very large problem, I would be happy to discuss it further with you separately at chemgrs@yahoo.com.

Thanks.