Energy Balance (chemical engineering)
An energy balance is the application of the first law of thermodynamics to a process system, tracking all energy entering, leaving, generated, and stored within a defined control volume in the forms of enthalpy, heat, work, and kinetic/potential energy. For steady-state, open flow systems (the most common case in chemical plants), the balance relates the enthalpy change of process streams to the net heat added and shaft work. Energy balances are essential for designing heat exchangers, reactors, distillation columns, and assessing process efficiency.
Key Formula
Q - Ws = sum(n_dot_i * H_i)_out - sum(n_dot_j * H_j)_in
LaTeX: Q - W_s = \sum_{out} \dot{n}_i H_i - \sum_{in} \dot{n}_j H_j
| Symbol | Meaning | Unit |
|---|---|---|
| Q | Heat added to the system per unit time | W (J/s) |
| W_s | Shaft work done by the system per unit time | W |
| \dot{n}_i | Molar flow rate of stream i | mol/s |
| H_i | Molar enthalpy of stream i | J/mol |
Worked Example
Problem
A process stream of 2 mol/s of water is heated from 25°C to 100°C at 1 atm. No phase change occurs. The heat capacity of liquid water is C_p = 75.3 J/(mol·K). Calculate the required heat duty Q.
Solution
Step 1: Identify the enthalpy change per mole. ΔH = C_p × ΔT = 75.3 × (100 − 25) = 75.3 × 75 = 5647.5 J/mol Step 2: Apply steady-state energy balance (no shaft work, single stream). Q = ṅ × ΔH = 2 mol/s × 5647.5 J/mol = 11 295 W
Answer
Required heat duty Q = 11 295 W ≈ 11.3 kW
Energy Balance Terms for Common Process Operations
| Operation | Dominant Energy Term | Typical Q Sign | Equipment | Scale |
|---|---|---|---|---|
| Heating | Sensible heat | Positive (+) | Shell-and-tube HX | kW–MW |
| Cooling | Sensible heat | Negative (−) | Condenser, cooler | kW–MW |
| Vaporisation | Latent heat | Positive (+) | Reboiler, evaporator | MW |
| Condensation | Latent heat | Negative (−) | Condenser | MW |
| Exothermic reaction | Enthalpy of rxn | Negative (−) | Cooled reactor | kW–GW |
| Endothermic reaction | Enthalpy of rxn | Positive (+) | Fired heater | MW |
Interactive Tools
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Related Terms
Mass Balance (chemical engineering)
A mass balance (also called a material balance) is the systematic application of the law of conservation of mass to a defined control volume or process unit, accounting for all mass entering, leaving, generated by reaction, and accumulating within the system. It is the foundational tool of chemical process design, enabling engineers to size equipment, determine conversion, specify recycle streams, and detect leaks or unaccounted losses. At steady state with no reaction, the balance simplifies to: mass in = mass out.
Distillation
Distillation is a thermal separation process that exploits differences in the volatility (relative volatility) of mixture components: a liquid feed is partially vaporised, the vapour enriched in the more volatile component rises and is condensed, while the less volatile component concentrates in the liquid bottoms. In a continuous distillation column, repeated vapour-liquid equilibrium stages—either trays or structured packing—progressively sharpen the separation, with the reflux ratio governing the trade-off between product purity and energy consumption. It is the most widely used separation process in the petrochemical, pharmaceutical, and food industries.
Absorption Column
An absorption column (absorber) is a mass-transfer device in which a gas mixture flows upward counter-currently against a descending liquid solvent, causing one or more gaseous components to dissolve into the liquid phase driven by a concentration gradient and governed by vapour-liquid equilibrium. The height of the packed or trayed column is determined by the Number of Transfer Units (NTU) and the Height of a Transfer Unit (HTU), or by the number of theoretical stages. Absorption is widely used to remove acid gases (CO₂, H₂S) from natural gas, SO₂ from flue gas, and ammonia from industrial off-gas streams.
From Greek "energeia" (activity, operation), coined by Thomas Young in 1807, and Latin "bilanx". The first law of thermodynamics was formalised by Rudolf Clausius and William Thomson (Lord Kelvin) in the 1850s; its systematic application to open chemical processes was codified by engineers in the early 20th century.