Concept

Mass balance

Overview

A mass balance is the accounting statement that, at steady state, the mass entering any defined boundary equals the mass leaving it — for the total and for every individual component — because matter is conserved. It is the primary check that a process model’s streams are physically consistent: a flowsheet that does not balance is wrong somewhere, even if every figure on it looks plausible.

Body

The conservation law. For any region enclosed by a boundary,

in = out + accumulation

and at steady state accumulation is zero, so in = out. The statement holds for total mass and, separately, for each component — which is what makes it a real constraint rather than a single equation.

Component balances and the reaction term. A component that is neither made nor destroyed simply satisfies in = out. A component that reacts carries a generation/consumption term:

in + generated = out + consumed

The full balance is the set of these: the total plus one per component, written around each unit operation and around the whole plant. Total mass is always conserved; moles are not (a reaction can change the number of molecules), so a molar balance must carry the stoichiometry while a mass balance need not.

It is a solvable system. Given enough specifications — feed flows and composition, per-pass conversion, separation split fractions — the balance equations can be solved for the unknown stream flows and compositions. At the maturity anchor this is a deterministic set of linear (or mildly nonlinear) equations solved by arithmetic and back-substitution, often shortcut with a tie component — not a flowsheet simulation.

Any boundary, nested consistently. A balance can be drawn around a single operation, a group of them, or the entire plant by choosing the system boundary. The balances must be mutually consistent: the sum of the unit balances equals the plant balance. This nesting is both a modeling tool (solve the easy boundary first) and a check (the parts must reconcile with the whole).

Every balance rides on a basis. A mass balance is meaningless without a declared basis of calculation — per hour, per tonne of product, per 100 mol of feed — applied uniformly. Recycle couples balances into a loop that must be solved together rather than in a single forward sweep.

Limits & typical error

• The total can close while a component fails. Forcing the overall in = out says nothing about whether each species balances; a wrong split of components across outlet streams leaves the total intact while violating a component balance. Only checking each component separately exposes it — the total alone is a weak test.
• Steady state is an assumption, not a fact. Startup, shutdown, batch operation, and slow accumulation (catalyst inventory, fouling, solvent hold-up) all carry a non-zero accumulation term. Applying a steady-state balance to an unsteady situation mis-assigns the accumulated mass to the in or out streams.
• Missing streams break closure or force a fudge. Vents, fugitive losses, purges, drains, and water of reaction are easy to omit; each omission makes the balance fail to close, and the common “fix” — scaling a stream to force closure — buries the error inside a plausible-looking flow rather than finding the missing line.
• Real data never closes exactly. Measured plant flows carry instrument error, so an industrial balance closes only to a tolerance (often a few percent); treating a small residual as a real stream, or forcing it to zero, both misread measurement noise as physics.
• Recycle makes a naïve forward pass diverge. Solving a loop as a single forward calculation ignores that the return stream adds to the fresh feed, understating internal flows — sometimes badly, since loop flow can be several times the fresh feed (see recycle & purge).

See also

• Stream (mass / energy) — the flows a mass balance is written over; the balance is the consistency check on the stream table.
• Basis of calculation — the per-time / per-product, mass / molar convention every balance must declare.
• Tie component — a component conserved through a step, used to solve a balance by arithmetic instead of simultaneous equations.
• Conversion, yield & selectivity — the reaction metrics that set the generation/consumption terms.
• Recycle & purge ratio — the loop that couples balances and must be solved together.
• Energy balance — the same conservation logic applied to energy rather than mass.
• System boundary — the choice of region a balance is drawn around.

Mini-example

A single pass of the ammonia synthesis reactor, on a basis of 100 mol of 3:1 H₂:N₂ feed (75 mol H₂, 25 mol N₂) at ~20% per-pass conversion (the running-example value). Twenty percent of the N₂ reacts — 5 mol N₂ + 15 mol H₂ → 10 mol NH₃ — so the outlet is 20 mol N₂, 60 mol H₂, and 10 mol NH₃: 90 mol out from 100 mol in.

Moles fell, but mass is conserved. Inlet mass = 75 × 2 + 25 × 28 = 850 g; outlet mass = 20 × 28 + 60 × 2 + 10 × 17 = 560 + 120 + 170 = 850 g. The total mass balance closes exactly (850 = 850) even though the mole count dropped from 100 to 90 — the clean illustration that the conserved quantity is mass, not moles, and that a molar balance only closes once the synthesis stoichiometry is carried explicitly.

Separately, to show the edge: if the inert argon entering with the nitrogen is left off the balance, the total still appears to close on the major species while the argon quietly accumulates with no exit — the missing-stream error that a purge and an argon tie component are there to catch.

See also

• Stream (mass / energy)
• Basis of calculation
• Tie component
• Conversion, yield & selectivity
• Recycle & purge ratio
• Energy balance
• System boundary