Material Balance Fundamentals
Material balance is the foundation of chemical engineering calculations, based on the law of conservation of mass.
Conservation of Mass
The fundamental principle states that mass can neither be created nor destroyed (excluding nuclear reactions):
Input + Generation = Output + Consumption + Accumulation
For steady-state processes without reaction:
Total Mass In = Total Mass Out
Types of Balances
Overall Material Balance
Accounts for total mass flow across the system boundary:
Σ(min) = Σ(mout)
Component Balance
Tracks individual species through the system:
Σ(min × xi,in) = Σ(mout × xi,out)
Where xi is the mass fraction of component i.
Mass vs Mole Basis
| Basis | When to Use | Conversion |
|---|---|---|
| Mass (kg, lb) | Physical processes, mixing, non-reactive systems | n = m / MW |
| Mole (kmol, mol) | Chemical reactions, gas-phase processes | m = n × MW |
Common Unit Operations
Mixer
Multiple streams combine into one. No reaction occurs.
F1 + F2 = Fout
Splitter
One stream divides into multiple streams with same composition.
Fin = F1 + F2, where xin = x1 = x2
Separator
One stream divides into multiple streams with different compositions.
Fin = F1 + F2, where xin ≠ x1 ≠ x2
Reactor
Chemical reaction occurs. Use extent of reaction (ξ) or conversion (X).
ni,out = ni,in + νi × ξ
Reactive Systems
For systems with chemical reactions, the balance includes generation and consumption terms:
Extent of Reaction (ξ)
For reaction: aA + bB → cC + dD
nA,out = nA,in - a×ξ
nC,out = nC,in + c×ξ
Conversion (X)
X = (nA,in - nA,out) / nA,in
Degrees of Freedom Analysis
Before solving, check if the problem is properly specified:
DOF = Unknowns - Independent Equations
- DOF = 0: Exactly determined, unique solution exists
- DOF > 0: Under-specified, need more information
- DOF < 0: Over-specified, check for inconsistencies
Solving Procedure
- Draw and label the flowsheet
- Choose a basis (e.g., 100 kg/h or 1 kmol)
- Identify all streams and components
- Write overall material balance
- Write component balances
- Perform degrees of freedom analysis
- Solve the system of equations
- Check results (sum of fractions = 1, all values positive)
References
- Felder, R.M. and Rousseau, R.W. (2005). Elementary Principles of Chemical Processes. Wiley.
- Himmelblau, D.M. and Riggs, J.B. (2012). Basic Principles and Calculations in Chemical Engineering. Prentice Hall.
- Perry, R.H. and Green, D.W. (2008). Perry's Chemical Engineers' Handbook. McGraw-Hill.