Time basis
Declare whether the calculation represents one batch, one campaign, an annual operating year, a continuous hour, or a dynamic interval. Convert schedules and inventories only after the batch basis closes.
Engineering guide · Mass balance
How to Build a Bioprocess Mass Balance (Step-by-Step Guide)
A useful balance is not one plant-wide total. It is a time-resolved component ledger that states its basis, reactions, accumulation, recycle logic, data quality, and closure tolerance.
Define the calculation basis
Fix the boundary before solving the numbers.
Component basis
Track water, substrates, biomass, product, metabolites, salts, gases, solvents, cleaning agents, and waste species. Use pseudo-components only when their definition and conversion factors are explicit.
System boundary
Mark every feed, product, emission, purge, waste, recycle, inventory, and sampling loss. Utilities belong in the energy and LCA boundary even when they do not enter the product-contact mass balance.
Dynamic component balancedMi/dt = ΣFin,i − ΣFout,i + VΣνi,rrr
For each component i, accumulation equals inlet minus outlet plus net generation or consumption by reaction. Batch additions, harvest, evaporation, gas transfer, bleed, sampling, adsorption, and degradation must appear as explicit terms when material.
Close locally, then globally
Find the residual where it is created.
Unit-operation residual
Calculate inlet, outlet, reaction, and accumulation residuals per component and per equipment item. A plant-wide balance can hide equal and opposite errors across two units.
Recycle convergence
Iterate recycle composition, temperature, and flow until the declared convergence norm is met. Report the initial guess, solver method, iteration count, residual, and any purge used to prevent accumulation.
Acceptance tolerance
Define absolute and relative tolerances before reviewing the result. Numerical closure does not validate kinetics, yields, measurements, or the selected process boundary.
Review gate
Minimum evidence for a decision-useful balance
CheckRequired evidenceFailure signal
BasisBatch size, operating mode, time horizon, units, temperature and pressure basisMixed annual and batch quantities
ComponentsComponent dictionary, molecular or pseudo-component definition, phase and sourceUntracked water, gas or cleaning mass
ReactionsStoichiometry, yield basis, rate law, validity domain and parameter sourceYield entered twice or inconsistent biomass basis
ClosurePer-unit and plant residuals, convergence status and agreed toleranceA rounded dashboard total without residuals
UncertaintyLow, base and high values for material assumptions with sensitivity rankingOne precise value for an unmeasured parameter