What is a heat and material balance? A practical guide
The heat and material balance is the table of numbers behind every process flow diagram. Here is what it contains, how it is built, and how to check it before anyone sizes equipment from it.
A heat and material balance, often shortened to H&MB or HMB, is the set of numbers that describes every stream in a process: how much flows, what it is made of, and at what temperature and pressure. If the process flow diagram is the picture of a plant, the heat and material balance is its data. Pumps, exchangers, vessels and lines are all sized from it, so an error here travels into every later document.
The two principles behind it
Material balance. For each unit and for the plant as a whole, what goes in must come out, plus anything that accumulates. At steady state there is no accumulation, so for total mass:
mass in = mass out
For individual components the same holds, except that chemical reactions create some species and consume others. Component balances therefore include a generation or consumption term set by the reaction stoichiometry and conversion. Total mass, and each element, is still conserved.
Energy balance. At steady state, and neglecting kinetic and potential energy, the enthalpy leaving a unit equals the enthalpy entering it plus the heat added, minus the shaft work done by the unit:
Σ Hout = Σ Hin + Q − W
This is how exchanger duties, reboiler and condenser loads, and outlet temperatures are found.
What the table contains
A heat and material balance is usually a table with one column per numbered stream on the process flow diagram. Typical rows are:
- Phase or vapour fraction
- Temperature and pressure
- Total mass flow and molar flow
- Component flows or composition
- Properties needed downstream: density, viscosity, molecular weight, enthalpy
Equipment duties, such as exchanger heat loads and pump power, are listed alongside or on the diagram itself.
A small worked example
Two streams are mixed: 100 kg/h of water (stream 1) and 50 kg/h of ethanol (stream 2). The mixed stream 3 must carry 150 kg/h, and its ethanol content is 50 / 150 = 33.3 % by mass. Written as a balance table:
| Property | Stream 1 | Stream 2 | Stream 3 |
|---|---|---|---|
| Phase | Liquid | Liquid | Liquid |
| Temperature, °C | 25 | 25 | about 25* |
| Pressure, bar(g) | 3.0 | 3.0 | 2.8 |
| Water, kg/h | 100 | 0 | 100 |
| Ethanol, kg/h | 0 | 50 | 50 |
| Total, kg/h | 100 | 50 | 150 |
*Mixing ethanol and water releases a little heat, so a real balance would show a small temperature rise; it is neglected here to keep the example simple. The outlet pressure allows for a small loss through the mixer.
How a balance is built
- Start from the design basis. Capacity, product specification, feed composition and operating hours fix the overall numbers.
- Close the overall balance on the block flow diagram. Get feeds, products and by-products consistent before adding equipment detail.
- Work unit by unit. Apply component balances, reaction conversions and separation splits to each block, then to the equipment on the process flow diagram.
- Converge the recycles. Recycle loops are solved by assuming a “tear” stream, calculating round the loop and iterating until the assumed and calculated values agree. Inerts that enter with a recycle need a purge, or they accumulate.
- Add the energy balance. With flows fixed, calculate temperatures, duties and phase changes, normally with a property package suited to the system.
Checks before anyone sizes from it
- Overall mass in equals mass out, within a small rounding tolerance.
- Every component closes, allowing for reactions; elements close even where species do not.
- Stream numbers and conditions match the process flow diagram exactly.
- Exchanger temperatures make physical sense: no temperature crosses, sensible approach temperatures.
- Phases are consistent with the temperatures and pressures shown.
- All required cases are covered, such as normal, design and minimum turndown.
Keeping the balance and the diagrams together
A heat and material balance is only useful while it matches the diagrams and the design basis it came from. In Black Owl, the material balance runs from the block flow diagram in the same project, mass flows appear on every stream, and a status shows whether the results are current after something changes. Request early access to see it on your own process, or read BFD vs PFD vs P&ID for how the diagrams fit together.