Basic Kraft Digester Organic Mass Balance Equations and Chemical Consumption Fundamentals

Chip

Wood furnish enters the digester as a heterogeneous matrix of cellulose, hemicelluloses, lignin, and extractives alongside variable moisture. Incoming kiln-dried or green softwood species such as Pinus sylvestris or Pinus radiata exhibit moisture contents swinging from thirty-five to fifty-five percent of total green weight. Accurately determining the oven-dry mass forms the bedrock of every chemical charging strategy.

Chip dry mass governs the target liquor volume, alkali-to-wood ratio, and ultimate brownstock yield. Running a digester on wet volumetric estimates without automated radiometric or near-infrared moisture tracking introduces immediate drift in chemical charges. The dry mass equation establishes baseline incoming solids:

M_dry = M_wet (1 – MC_wb)

In this equation, M_wet represents total incoming moist chip mass, and MC_wb defines the wet-basis moisture content determined through oven drying at 105 degrees Celsius under ISO 638-1. Chemical processing splits this dry matrix into soluble and insoluble fractions. Softwood chips typically contain forty to forty-five percent cellulose, twenty-five to twenty-nine percent hemicelluloses, twenty-six to thirty-one percent lignin, and three to five percent extractives and inorganics.

Hardwoods such as Eucalyptus globulus shift this balance toward lower lignin contents, typically twenty to twenty-four percent, and higher xylan fractions.

Cold chips absorb liquor unevenly when steam preheating fails.

Chip geometry directly controls the transport kinetics of sodium hydroxide and sodium hydrosulfide into the chip core. Industrial chip screening protocols according to SCAN-CM 40:01 classify fractions into overthick chips exceeding eight millimeters, accept chips between two and eight millimeters, pin chips, and fines below two millimeters. Oversized and overthick fractions induce mass transfer limitations where cooking chemicals fail to penetrate the chip center prior to reaching bulk delignification temperatures.

Incomplete chemical penetration results in uncooked cores, elevating knotter reject levels and shive counts in the unbleached stock.

1. Oversized chips generate high screen rejects exceeding two percent of total pulp yield.
2. Pin chips increase liquor flow resistance and create localized liquor channeling inside continuous digester columns.
3. Fines blind liquor extraction screens, accelerating digester liquor pump cavitation and pressure drops.
4. Accept chips provide uniform diffusion paths, minimizing alkali concentration gradients between liquor and fiber centers.

Overthick chip fractions cause under-sulfidized interior zones. Alkaline hydrolysis proceeds without sufficient hydrosulfide concentration. Carbohydrate peeling accelerates, while lignin condensation produces dark, unbleachable rejects that demand harsh downstream bleaching sequences.

Liquor

White liquor provides the active chemical drive for delignification. The liquor contains sodium hydroxide and sodium hydrosulfide as primary delignification reagents, alongside sodium carbonate, sodium sulfate, sodium thiosulfate, and sodium sulfite as non-reactive or inactive compounds. Industry definitions standardize liquor concentrations expressed on an equivalent sodium oxide basis according to TAPPI T 624 cm-11 or SCAN-N 30:85.

Total titratable alkali includes sodium hydroxide, sodium hydrosulfide, and sodium carbonate. Active alkali encompasses sodium hydroxide and sodium hydrosulfide. Effective alkali calculates total hydroxyl ion concentration assuming complete hydrolysis of sodium hydrosulfide into sodium hydroxide and hydrosulfide anions:

EA = NaOH + 0.5 Na2S (expressed as g/L Na2O)

AA = NaOH + Na2S (expressed as g/L Na2O)

Sulfidity represents the active sulfide proportion:

S = (Na2S / AA) 100

Target sulfidity ranges between twenty-five and thirty-five percent for modern kraft pulping operations. High sulfidity protects carbohydrate chains by accelerating lignin fragmentation through benzyl mercaptide intermediates, which retards alkaline cleavage of glycosidic bonds. When white liquor sulfidity drops below twenty-five percent, pulping selectivity collapses, necessitating higher effective alkali charges to reach a target kappa number.

The liquor-to-wood ratio sets the liquid phase volume relative to oven-dry chip mass. Continuous digesters run liquor-to-wood ratios from 3.2:1 to 3.8:1, whereas batch systems operate from 3.8:1 to 4.5:1. This volumetric inventory sums four distinct water inputs: chip internal moisture, white liquor volume, black liquor dilution filtrate, and direct steam condensate.

Accurate volumetric tracking prevents liquor dilution, which diminishes hydroxyl ion driving forces.

A mill batch sheet showed forty grams per liter effective alkali despite certified delivery dockets asserting forty-eight.

Alkali charge calculations dictate chemical delivery onto wood dry matter:

EA_charge = (V_WL C_EA) / M_wood_dry 100

Here, EA_charge is effective alkali percentage on dry wood, V_WL is white liquor volume in cubic meters, C_EA is effective alkali concentration in kilograms per cubic meter, and M_wood_dry is oven-dry chip mass in kilograms. Typical bleached softwood kraft grades use fifteen to nineteen percent effective alkali as Na2O. Heavy packaging linerboard grades target eleven to fourteen percent effective alkali to preserve yield.

Suppliers frequently maintain that fluctuating chip moisture accounts for unexpected drops in residual alkali rather than variations in liquor causticity.

Dissolution

Organic dissolution during kraft pulping follows three sequential phases: initial, bulk, and residual delignification. Initial delignification occurs below one hundred thirty degrees Celsius, removing roughly fifteen to twenty percent of total wood lignin alongside substantial extractives and readily accessible hemicelluloses. Diffusion dominates this early step.

Minimal active sulfur consumption takes place.

Bulk delignification initiates as temperatures surpass one hundred forty degrees Celsius. Hydroxyl and hydrosulfide ions cleave alpha- and beta-aryl ether bonds across the phenylpropane network. This phase removes sixty to seventy percent of incoming lignin.

Bulk phase kinetics approximate pseudo-first-order behavior governed by the Arrhenius relationship:

d /dt = -k ^a ^b

Kinetic control over this phase relies on the Vroom H-factor, combining relative reaction rates with cooking time into a single operating variable:

H = Integral from 0 to t of exp(43.2 – 16113 / T) dt

Temperature T is measured in Kelvin. Softwood cooks reaching kappa thirty typically accumulate an H-factor between one thousand two hundred and one thousand eight hundred hours, dependent on target residual alkali and cooking temperature.

Simultaneously, carbohydrate dissolution consumes the vast majority of active alkali. Primary peeling strips reducing end groups from polysaccharide chains molecule by molecule at alkaline pH, creating acidic degradation fragments. An average of fifty to sixty-five sugar monomer units peel away before a stopping reaction, predominantly alkali-promoted beta-elimination forming metasaccharinic acid end groups, stabilizes the chain.

Hydroxyl ions neutralize these acidic dissolution products immediately. Acetic, formic, lactic, and glycolic acids form rapidly. Alkali consumption divides across distinct mechanisms:

• Carbohydrate acid neutralization consumes sixty to seventy percent of the total charged effective alkali.
• Lignin phenolic dissolution consumes twenty to twenty-five percent of charged effective alkali to maintain solubility.
• Extractives saponification consumes two to four percent of effective alkali through fatty acid neutralization.
• Residual alkali retention accounts for ten to fifteen percent of incoming alkali to avoid lignin precipitation.

Residual effective alkali in spent black liquor must stay above five to eight grams per liter as Na2O. Lower residual alkali values trigger lignin condensation and redeposition onto pulp fibers, damaging brightness and elevating bleaching chemical costs.

TAPPI T 236 om-13 kappa testing on unbleached pulp establishes residual lignin content by potassium permanganate oxidation.

High temperatures cause random chain scission via alkaline hydrolysis. Cellulose degree of polymerization drops noticeably. Viscosity loss reflects fiber strength degradation.

Hot white liquor preserves long fibers when alkali concentration remains steady throughout the cook.

Yield

Overall pulp yield represents the dry output mass divided by oven-dry wood input. Yield values determine both wood furnish sourcing costs and black liquor solid loadings directed to the recovery boiler. The mass balance splits the dry wood input into unbleached fiber pulp, dissolved organic solids, dissolved inorganic chemicals, and gaseous byproducts.

M_wood = M_screened_pulp + M_rejects + M_dissolved_organics + M_volatiles

Kappa number provides an indirect measurement of residual lignin in the pulp matrix. One kappa unit corresponds approximately to 0.147 to 0.150 percent Klason lignin in softwood pulp. A cook terminated at kappa thirty carries roughly 4.5 percent residual lignin on dry fiber weight.

Predicting screened pulp yield from kappa number operates through established empirical linear relationships specific to mill furnish:

Yield_total = Y_0 + b Kappa

For Nordic softwood pulping, constant Y_0 averages forty to forty-one percent, while slope factor b registers between 0.14 and 0.16. Sack paper pulped to kappa forty achieves approximately 47.0 percent total yield. Driving the cook down to kappa twenty-five drops yield to 44.5 percent, sending an extra twenty-five kilograms of dissolved wood organics per oven-dry ton of wood into the recovery cycle.

Carbohydrate yield loss accelerates below kappa twenty-eight. Glucomannan chains undergo rapid dissolution. Pulp tensile and tear strength diverge significantly.

A certified food contact board lot requires extraction values below fifteen milligrams per square decimeter under EN 645 testing.

Chemical consumption balance balances charged mass against consumed active components:

Consumption_EA = (EA_charge / 100) M_wood_dry – (REA V_BL_total)

REA defines residual effective alkali in black liquor, and V_BL_total is total black liquor volume. When process upsets drive residual alkali below target thresholds, fiber rejects multiply, unbleached kappa variance widens across the lot, and downstream converting operations encounter severe fiber stiffness instability that triggers commercial rejection at receiving docks.

Recovery

Dissolved organics combine with spent inorganics to form weak black liquor. Weak black liquor exits the brownstock washing plant at thirteen to eighteen percent dry solids content. The organic fraction comprises degradation products from lignin, hemicellulose, and cellulose, together with aliphatic acids and sulfur compounds including dimethyl sulfide and methyl mercaptan.

Inorganics comprise spent sodium salts: sodium carbonate, sodium sulfate, sodium thiosulfate, sodium sulfide, and bound sodium organic complexes.

Dry solids mass balances trace the inorganic-to-organic ratio, typically thirty-five to forty percent inorganic salts against sixty to sixty-five percent dissolved wood organics. Calculating total black liquor dry solids generated per air-dry ton of pulp follows the organic dissolution equation:

BLS = (M_wood_dry (1 – Yield_fraction) + Chemical_input_inorganics) / ADt_pulp

Bleachable softwood grades yield roughly 1650 to 1750 kilograms of dry black liquor solids per air-dry ton of pulp. This organic mass represents high-energy fuel for the chemical recovery boiler. Gross calorific value ranges from 13.0 to 15.0 megajoules per kilogram of dry black liquor solids, governed directly by the lignin-to-carbohydrate degradation ratio.

Packaging safety standards, including BfR Recommendation XXXVI and Regulation EC 1935/2004, strictly regulate residual chemical carryover from pulping liquor into final packaging substrates. Anthraquinone (AQ), often added at charges of 0.05 to 0.10 percent on wood to accelerate delignification and preserve carbohydrate yield, faces intense regulatory scrutiny. German BfR limits prohibit anthraquinone in food contact papers where migration thresholds exceed analytical limits.

Sourcing officers must verify whether a virgin kraft board supplier employs anthraquinone catalysts to prop up pulp yield, as unlisted AQ charges invalidate food packaging compliance dossiers across European retail supply chains.

Chain-of-custody audits under FSC-STD-40-004 and PEFC ST 2002 require mass balance reconciliation across the fiber supply. When mills declare fiber yields of fifty-two percent on bleachable kraft grades where digester mass balances reflect forty-four percent, chain-of-custody percentage calculations become materially distorted. Inflated yield calculations allow uncertified fiber to enter certified credit accounts undetected.

The operational balance leaves mills balancing the cost of wood chips against the capital throughput ceiling of recovery boilers, asking how far digester alkali charges can drop before unbleached shive content destroys converting efficiency.