Chemical Engineering World

Balances

The General Balance Equation

1. Methane is being consumed as a reactant or generated as a product within the unit
2. Methane is accumulating in the unit, possibly adsorbing on the walls
3. Methane is leaking from the unit
4. The measurements are wrong

If the measurements are correct and there are no leaks, the other possibilities (generation or consumption in a reaction and accumulation within the process unit) are all that can account for a difference between the input and output flow rates.

A balance on a conserved quantity (total mass, mass of a particular species, energy, momentum) in a system (a single process unit, a collection of units, or an entire process) may be written in the following general way :

There are 2 types of balances :

1. Differential balances. A balance that indicates what is happening in a system at an instant in time. Each term of the balance equation is "rate" (rate of input, rate of generation, etc) and has units of the balanced quantity unit divided by a time unit (people/year, gr/s, barrels/day, etc). This is the type of balance usually applied to a "continuous process."
2. Integral balances.  A balance that describe what happens between two instants of time. Each term of the equation is an "amount" of the balanced quantity and has the corresponding unit (people, gr, barrels). This type of balance is usually applied to a "batch process", with the two instants of time being the moment after the input takes place and the moment before the product is withdrawn.

The following rules may be used to simplify the material balance equation :

• If the balanced quantity is total mass, set generation = 0 and consumtion = 0. Except in nuclear reactions, mass can neither be created nor destroyed
• If the balanced substance is a nonreactive species (neither a reactant nor a product), set generation = 0 and consumption = 0
• If a system is at steady state, set accumulation = 0, regardless of what is being balanced. By definiton, in a steady-state  system nothing can change with time, including the amount of the balanced quantity

From : Elementary Principles of Chemical Processes 3rd Edition, Felder & Rousseau