Engineering & Technology · Process Balances, Flowsheets & Design
Process boundaries, streams, composition and flowsheets
A process diagram shows a mixer, a heater and a separator. The boxes name functions, but they do not yet state how much material moves, what it contains or which conditions apply. A useful flowsheet connects the picture to a consistent stream account.
Use the earlier material, thermodynamics and fluid-engineering chapters for quantities, energy and flow. Ratios, elementary algebra, units and chemical amount are enough for the constructed calculations here.
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Read a flowsheet as a set of connected material streams with explicit boundaries, quantities and composition bases.
A process function is part of a network
Define the system of interest and what crosses its boundary. The boundary can surround one unit, several connected units or the whole process. Streams inside a whole-process boundary are internal transfers; the same streams can be external inputs or outputs for a single unit. State the chosen boundary before writing an account.
A flowsheet records connectivity and relevant process functions. A stream table supplies identifiers, flow basis, composition, temperature, pressure and phase where needed. A simple teaching flowsheet is not a complete equipment, piping or control design. Its arrows should identify direction without implying quantitative widths or physical layout unless that encoding is explicitly provided.
A fraction requires a denominator
Our original steady nonreacting mixer receives 40 kg/h with A mass fraction 0.25 and 60 kg/h with A fraction 0.10. The A rates are 10 and 6 kg/h; total product is 100 kg/h containing 16 kg/h A. Its A mass fraction is 0.16. Adding the inlet fractions would incorrectly ignore the different stream amounts.
A mass fraction divides a component’s mass by total mass; a mole fraction divides its amount in moles by total moles. In a separate conversion using supplied molar masses M_A=20 and M_B=40 kg/kmol, the 16 kg A and 84 kg B correspond to 0.8 and 2.1 kmol. A’s mole fraction is 0.8/2.9≈0.2759, different from its 0.16 mass fraction.
Conditions and time basis matter
A volumetric flow requires a density or state relationship before it can supply a mass flow. Gas volume in particular depends on its reference temperature and pressure. Do not compare a volumetric rate at one stated condition with another rate at a different condition as if equal volumes necessarily represented equal material.
Distinguish a batch amount, an instantaneous rate and an average over an interval. A recorded 100 kg/h does not mean 100 kg is present in the vessel. Mixtures can have phase-specific compositions, and a homogeneous stream assumption must be stated. Keep assumptions and missing stream properties visible so later material and energy accounts refer to the same physical description.
Reconstruct the mixed stream
The total account gives 40+60=100 kg/h. The A account gives 40(0.25)+60(0.10)=16 kg/h. B occupies the remaining 84 kg/h, also checked as 40(0.75)+60(0.90). The component sum agrees with the total. These are original supplied quantities rather than observations from a plant.
Using the separate hypothetical molar masses, total molar amount per 100 kg is 16/20+84/40=2.9 kmol. The mole fractions are 0.2759 for A and 0.7241 for B and sum to 1. The correct conversion preserves the composition basis instead of silently relabelling a mass fraction as a mole fraction.
Try the reasoning
Why do internal streams disappear from a whole-process material balance?
Show the answer and reasoning
Their transfer leaves one included unit and enters another, so it cancels when the accounts are summed.
Why is the product fraction not 0.25+0.10?
Show the answer and reasoning
The component amounts must be added and divided by the combined total; fractions alone lack that weighting.
Does 100 kg/h specify the vessel inventory?
Show the answer and reasoning
No. It is a rate. Inventory is an amount inside the boundary and needs its own information.
What to carry forward
Connect every stream to a boundary, time basis, composition basis and relevant state before treating a diagram as a calculable process.
References
Teaching resources and research supporting this lesson’s explanations and examples.