Overall balance vs. differential balance

[gfd43tg]

Hello,

when doing mass and/or energy balances, how does one know when one should use a differential balance over a total balance? It would help when knowing how to approach a given problem.

 

[Bystander]

Experience. Do it both ways until you see the differences.

 

[Chestermiller]

I think what Bystander is saying is that, if you have enough information to do the overall balance(s) and don't need to know details within the equipment, then you can use the overall balance. But, if you are missing information to do the overall balance, and the differential balance can provide that information, then you need to do the differential balance.

Chet

 

[Bystander]

Is there a universal set of rules? No. Any rough, general principles that can be commonly applied? "Small differences between large numbers argue for differential methods."
What balances are interesting/useful/relevant for the system being analyzed? Pipeline: mass out/mass in (a tough problem in custody transfer). Gold mining: recovered metal mass/ore mass or tailings mass/ore mass. Coal desulfurization: sulfur mass/coal mass or treated coal mass/untreated coal mass.
The approach to the problem is dictated by the problem statement.

 

[alphy]

I understand the importance of accuracy and precision in any scientific calculation. In the case of mass and energy balances, both total and differential balances serve different purposes and can be used in different scenarios.

A total balance is used to determine the overall mass or energy in a system, taking into account all inputs and outputs. This approach is useful when the system is closed and there are no changes in the system over time. For example, when determining the total mass of a chemical reaction, a total balance would be appropriate.

On the other hand, a differential balance is used to analyze the changes in mass or energy over time, taking into account the rates of input and output. This approach is useful when the system is open and there are changes occurring over time. For example, when studying the flow of a liquid or gas, a differential balance would be more suitable.

In order to determine which approach to use, it is important to understand the specific problem and the nature of the system being studied. If there are no changes occurring over time, a total balance would be appropriate. However, if there are changes occurring, a differential balance would be more accurate.

In summary, both total and differential balances have their own advantages and should be used based on the specific problem and system being studied. It is important to carefully analyze the problem and choose the appropriate approach to ensure accurate results.