Hydrotreating hydrogen recycle and purge balance

RefineryHydrotreatingHydrogenRecycleBalance composes a qualified RefineryHydrotreatingHydrogenSupplyBalance with explicit recovery and purge assumptions. It reports steady-state fresh makeup, reactor-outlet gas, recycle gas, and exported gas for hydrogen, hydrogen sulfide, and the non-hydrogen makeup fraction.

This is component bookkeeping. It is not a separator, phase-equilibrium, solubility, compressor, reactor, or catalyst model. Recovery fractions must come from an independent engineering basis.

Basis and equations

The upstream receipt supplies reactor-inlet hydrogen, consumed hydrogen, once-through unreacted hydrogen, generated hydrogen sulfide, makeup-hydrogen purity, and the average non-hydrogen molar mass. The caller additionally supplies component recovery fractions r_i and one common recovered gas purge fraction p.

The effective recycle fraction for component i is:

k_i = r_i * (1 - p)

Hydrogen recycle and fresh hydrogen are calculated directly from the fixed reactor-inlet target:

nH2,recycle = k_H2 * nH2,out
nH2,fresh = nH2,in - nH2,recycle
nmakeup,fresh = nH2,fresh / yH2

For non-hydrogen makeup and hydrogen sulfide, the steady-state outlet inventory is the fresh or generated source divided by the net rejection fraction:

n_i,out = n_i,source / (1 - k_i)
n_i,recycle = k_i * n_i,out
n_i,export = n_i,out - n_i,recycle

A positive source with k_i = 1 has no purge or rejection path and therefore fails closed. Total mass closes fresh liquid feed plus fresh makeup gas against liquid product plus exported gas; internal recycle cancels from the overall balance.

Java example

The example reuses the public DOE/OEDI Big Hill sulfur case. The 90% H2 recovery, 10% H2S recovery, 50% non-H2 recovery, and 5% purge are illustrative assumptions rather than measured plant or separator performance.

RefineryHydrotreatingSulfurBalance sulfur =
    RefineryHydrotreatingSulfurBalance.calculate(
        1000.0, 0.0040867518, 15.0e-6, 2.0);

RefineryHydrotreatingHydrogenSupplyBalance supply =
    RefineryHydrotreatingHydrogenSupplyBalance.calculate(
        sulfur, 1.5, 0.90, 0.0280134);

RefineryHydrotreatingHydrogenRecycleBalance recycle =
    RefineryHydrotreatingHydrogenRecycleBalance.calculate(
        supply, 0.90, 0.10, 0.50, 0.05);

double freshMakeupKg = recycle.getFreshMakeupGasMassKg();
double recycleGasKg = recycle.getRecycleGasMassKg();
double exportGasKg = recycle.getExportGasMassKg();
double massResidualKg = recycle.getOverallMassBalanceResidualKg();

On this 1000 kg basis, the effective H2 recycle fraction is 0.855. The receipt recycles 108.572702267 mol H2, requires 302.649053102 mol and 1.396916654 kg fresh makeup gas, recycles 149.285217505 mol total gas, and exports 175.663436416 mol and 5.212737927 kg gas. Recycle replaces 28.5% of the once-through hydrogen supply. H2, H2S, non-H2, and overall mass residuals are numerical zero.

A purge fraction of one reproduces the once-through fresh-makeup and outlet-gas receipt exactly. Zero sulfur removal produces a zero-gas receipt.

Provenance and engineering boundary

• The public DOE/OEDI Big Hill crude-oil assay supplies the qualified sulfur basis inherited from the upstream receipts.
• The US Energy Information Administration defines catalytic hydrotreating as contacting petroleum fractions with hydrogen in the presence of a catalyst.
• The AIChE public hydrotreating overview describes excess hydrogen and sulfur conversion to hydrogen sulfide.
• The NIST Chemistry WebBook hydrogen-sulfide entry supplies the H2S molecular weight inherited from the sulfur receipt.
• The NIST Chemistry WebBook nitrogen entry supplies the illustrative non-H2 molar mass used in this public case.

The conservation equations do not estimate recovery. A design claim requires a validated gas-liquid equilibrium and separator model, reactor pressure and temperature, hydrogen solubility, compressor and recycle-loop pressure drops, catalyst and reaction models, contaminant behavior, purge routing, control philosophy, and plant hydrogen-system constraints.