The mass and energy balance is the first engineering document of a commercial design. It states how much of everything goes in and comes out, and how much heat must be added and removed. Equipment sizes, utility demand and operating cost are all calculated from it.
Post 1 showed why the commercial reactor needs a longer addition time than the lab. Post 2 covered the pilot campaign and its design yield of 87%. This post turns those results into a balance for a plant making 5,000 tonnes of product a year.
Step 1: set the basis
A balance needs a stated basis. For a batch process the natural basis is one batch.
Table 1. Basis for the commercial balance
| Item | Value | Source |
|---|---|---|
| Annual production | 5,000 t/y of product | Business plan |
| Operating time | 8,000 h/y | Design basis |
| Batch cycle time | 8 hours | Charge 1 h, addition 3 h, hold 2 h, transfer 1 h, clean 1 h |
| Batches a year | 1,000 | 8,000 h ÷ 8 h |
| Product per batch | 5,000 kg | 5,000 t ÷ 1,000 batches |
| Yield | 87% | Mean of ten pilot runs |
The three-hour addition comes from Post 1: the 10,000 L reactor needs at least 2.7 hours to remove the heat of reaction. A one-hour addition would have given a six-hour cycle and a smaller reactor, and the jacket could not have kept up.
Step 2: scale the pilot mass balance
The pilot runs used 100 kg batches. Each quantity is scaled by the ratio of product required, 5,000 kg ÷ 50 kg = 100.
Table 2. Mass balance: pilot batch, commercial batch and annual totals
| Stream | Pilot batch | Commercial batch | Annual |
|---|---|---|---|
| Raw material A | 30.0 kg | 3,000 kg | 3,000 t/y |
| Raw material B | 27.5 kg | 2,750 kg | 2,750 t/y |
| Solvent, fresh | 2.5 kg | 250 kg | 250 t/y |
| Solvent, recycled | 40.0 kg | 4,000 kg | 4,000 t/y |
| Total in | 100.0 kg | 10,000 kg | 10,000 t/y |
| Product | 50.0 kg | 5,000 kg | 5,000 t/y |
| Waste: by-products and unreacted material | 7.5 kg | 750 kg | 750 t/y |
| Waste: solvent losses | 2.5 kg | 250 kg | 250 t/y |
| Solvent recovered for recycle | 40.0 kg | 4,000 kg | 4,000 t/y |
| Total out | 100.0 kg | 10,000 kg | 10,000 t/y |
The check on yield: raw materials A and B together are 5,750 kg, and 5,000 kg becomes product. That is 87%, which matches the pilot result. The totals in and out agree, so the balance closes.
Two results stand out. The reactor must hold a 10,000 kg batch, about 10 m³, so the vessel needs roughly 12.5 m³ of total volume at 80% fill. And the plant produces 1,000 t/y of waste, one tonne for every five tonnes of product, which sets the size of the waste handling system and the permit application.
Step 3: add the energy balance
Each heating or cooling step is calculated from the masses in Table 2 and the properties measured in the pilot plant.
Table 3. Energy balance for one batch
| Step | Calculation | Heat | Utility |
|---|---|---|---|
| Heat the batch from 20°C to 60°C | 10,000 kg × 2.0 kJ/kg·K × 40 K | 0.8 GJ | 375 kg of steam |
| Remove the heat of reaction | 10,000 kg × 150 kJ/kg | 1.5 GJ | Cooling water on the jacket |
| Evaporate the solvent for recovery | 4,000 kg × 400 kJ/kg | 1.6 GJ | 750 kg of steam |
| Condense the recovered solvent | Same heat, removed | 1.6 GJ | Cooling water on the condenser |
| Total per batch | 1,125 kg of steam, 3.1 GJ of cooling |
Utilities are sized for the peak, which is higher than the average. The reaction heat of 1.5 GJ leaves over the three-hour addition, an average of 139 kW. The jacket can remove 154 kW, so it has about 10% in hand. That margin is thin, and it is the kind of result a design review should question.
Step 4: read the operating cost from the balance
With prices for each stream, the balance gives the variable cost of production. The prices below are illustrative.
Table 4. Variable cost from the mass and energy balance
| Cost element | Per kg of product | Annual | Share |
|---|---|---|---|
| Raw material A | $1.200 | $6,000,000 | 55.7% |
| Raw material B | $0.825 | $4,125,000 | 38.3% |
| Solvent make-up | $0.060 | $300,000 | 2.8% |
| Waste disposal | $0.060 | $300,000 | 2.8% |
| Steam | $0.009 | $45,007 | 0.4% |
| Total variable cost | $2.154 | $10,770,007 | 100% |
Raw materials cost $10.1M a year. Yield therefore matters more than any utility saving. One more point of yield, from 87% to 88%, would cut raw material use by 1.1% and save about $115,000 a year. Halving the steam bill would save about $22,504.
What the balance hands to the next stage
Table 5. Where each result goes
| Result from the balance | Used for |
|---|---|
| Batch size and cycle time | Reactor volume and the number of reactors |
| Raw material and product quantities | Storage tanks, deliveries and shipping |
| Heat loads and their timing | Jacket area, condenser, boiler and cooling water system |
| Recycle and waste streams | Solvent recovery equipment, waste treatment and permits |
| Consumption per kilogram of product | Operating cost estimate and the business case |
These figures become the design basis and the heat and material balance for front-end engineering. The FEED series picks up from here, starting with the design basis.
To practise balance calculations, try the free Mass, Momentum & Energy Exam.
Takeaway. Scale the pilot balance to the commercial batch, check that it closes, then add the energy balance and prices. In the example, a 87% yield and a three-hour addition lead to a 10 m³ batch, 1,000 t/y of waste and a variable cost of $2.15 per kilogram.
The reaction, the vessels and the costs in this series are an illustrative example. The calculations are screening estimates and do not replace process safety testing or a design by a qualified engineer.
