Methodology
Solves the declared steady-state water network and constituent balance from entered process splits, removals, additions, and same-process/upstream recycle. Water and constituent closure errors are reported explicitly; flows and masses are not normalized to force closure.
The steady-state water network is written as F = b + A F and solved with deterministic pivoted Gauss-Jordan elimination.
Each process forwards its declared fraction of inlet flow to the next process. At the final process, forward flow is the final product stream.
The remainder is the waste-side flow. The entered recycle fraction applies to this waste split and returns only to the same process or an upstream process.
Constituent mass flow is water flow multiplied by concentration with unit conversion. At each node, removal is applied to inlet constituent mass, then the entered addition is applied, then the outlet constituent mass is split using the water-flow fractions.
Accumulation is assumed to be zero at steady state. Water and constituent closure errors are reported separately. Errors within the documented tolerance are reported as zero; the flows and masses are not normalized to force closure.
Water closure tolerance is max(1e-8 m³/d, external feed × 1e-10); constituent mass tolerance is max(1e-8 kg/d, (external mass + entered additions) × 1e-10).