A. The General Balance Equation
Consider a continuous process where methane is a component of both the input and the output streams, and to determine if the unit is working as designed, it is found that the mass flow rates of the methane input and output measured are different (m ̇_in≠m ̇_out).
The following can cause the difference between the measured flow rates:
- The methane is being consumed as a reactant or being generated as a product within the unit.
- The methane is accumulated in the unit, meaning adsorbing on the walls.
- The methane is leaking from the unit.
- The measurements is wrong.
All that can be considered and cause a difference between the output and the input is the generation or consumption in a reaction and the accumulation within the process unit only if the measurements is correct and there are no leaks.
The following is the general way of writing a balance of a conserved quantity – mass of a particular species, total mass, energy and momentum – in a system (a single process unit, a collection of units, or entire process):
input + generation - output - consumption = accumulation
Input: enter system boundaries
Generation: produced within the system
Output: leaves the system boundaries
Consumption: consumed within the system
Accumulation: build-up in the system
The two types of balances, differential and integral balances can be written:
1. Differential balances:
This balance indicates what is happening in a system at an instant time. In this balance equation, each term is a rate and has units of the balanced quantity unit divided by a time unit. A differential balance is usually applied to a continuous process.
2. Integral balances:
This balance shows what happens between two instants of time. In the balance equation, each term is an amount of the balanced quantity and has a corresponding unit. An integral balance is applied to a batch process, with the two instants of time being after the time the input takes place and the time before the product is withdrawn.
It is rather a concern taking into consideration that differential balances applied to continuous steady-state systems and integral balances applied to batch systems, have a huge difference between their initial and final states. The following rules can be used to reduce the material balance equation:
1. Set generation = 0 and consumption = 0, if the balanced quantity is total mass.
Except: nuclear reactions (mass cannot be destroyed or created)
2. Set generation = 0 and consumption = 0, if balanced substance is nonreactive (no reactant or product)
3. Set accumulation = 0, if system is at steady state, regardless what being balanced (nothing can change with time, thus amount of quantity does not change).
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