Material and Energy Balances
Scope
Material balances around a control volume, coupled with the energy balance. Expect flowsheets with recycle, purge, and bypass, multiple units, and reacting systems where extent of reaction or a key component is the right basis.
Concepts to own
- Degrees of freedom = unknowns minus independent equations. Zero means solve; negative means redundant or inconsistent data.
- Recycle loops are solved by combining an overall balance (which ignores recycle) with a balance around the mixing point or the reactor.
- Purge controls inert accumulation. At steady state, inert leaving in the purge equals inert entering in the fresh feed.
- Reactive energy balance: Q − W = Σ(nh)out − Σ(nh)in, with enthalpy from heat capacity, heat of formation, or heat of combustion. Pick one reference state and stay in it.
- Adiabatic: set Q = 0; the temperature rise is heat of reaction divided by sensible heat capacity.
Traps
- Mixing mass and mole fractions in the same balance.
- Forgetting that an element balance (total carbon, total hydrogen) is independent of reaction extent.
- Sign conventions in the open-system energy balance.
- Combining a heat of reaction with formation enthalpies evaluated at different reference temperatures.
Worked example
A fresh feed of 100 mol/h containing 2 mol% inert enters a loop with recycle, and the reactor inlet must stay below 10% inert. Inert out equals inert in, so purge flow = 2/0.10 = 20 mol/h, and recycle = 20 − 2 = 18 mol/h.
Rule of thumb: draw the envelope first, then choose the overall or the local balance by counting unknowns, not by habit.