White Liquor Reactivity Dependence on Effective Alkali and Sulfidity

White liquor reactivity in kraft pulping is fundamentally governed by the simultaneous presence and concentration of hydroxide and hydrosulfide ions, chemically quantified through two interdependent parameters: effective alkali (EA) and sulfidity. Effective alkali, defined as the sum of sodium hydroxide plus one-half of the sodium sulfide, expressed on an Na₂O basis per TAPPI T 625 cm-14, determines the total driving force for delignification and neutralization of wood acids, while sulfidity—the ratio of Na₂S to NaOH+Na₂S, also as Na₂O—modulates the electrophilic cleavage of lignin β-aryl ether linkages and the suppression of alkaline peeling reactions on carbohydrate reducing ends. The interplay between these two parameters sets the kinetic boundary conditions inside any continuous or batch digester, directly influencing production throughput, pulp yield, bleach chemical consumption, and the sodium-sulfur balance of the recovery cycle. In industrial operation, white liquor is prepared from green liquor via causticizing, where the degree of causticizing efficiency and lime quality impart batch-to-batch variance in both EA and sulfidity; these must be compensated at the digester feed through white liquor make-down with purchased caustic or by adjusting the recirculation of oxidized white liquor. In unstabilized kraft mills, EA values for softwood pulping typically range between 16% and 22% on oven-dry wood, while sulfidity fluctuates from 25% to 35%, each percentage-point shift potentially altering the H-factor required to reach a target kappa number by 30–50 H-factor units, translating into measurable changes in digester residence time when operating at full hydraulic load. Reactivity, therefore, is not an intrinsic liquor property but an emergent response function of chemical concentration, temperature, chip geometry, and liquor-wood mass transfer dynamics, all of which must be managed simultaneously to avoid excursions that degrade pulp quality or compromise equipment integrity.

When liquor analysis systems built on automatic potentiometric titration—such as the Metso Liquor Analyzer or BTG Single Point Titrator—report EA with a repeatability of ±0.2% Na₂O, the plant distributed control system (DCS) can cascade the signal to the white liquor charge flow controller, often through a feedforward model that also incorporates chip moisture measured by an online microwave sensor (e.g., Metso Chip Moisture Meter) and the digester extraction liquor residual effective alkali (REA) reading from an inline conductivity-based sensor calibrated to TAPPI T 624 cm-19. The REA setpoint, typically maintained between 6 and 10 g/L as Na₂O for softwood at the extraction screens, functions as a real-time surrogate for the effective alkali that remains after chip neutralization, primary dissolution, and initial delignification. When the extraction REA drops below 5 g/L, the gradient driving hydroxyl ion diffusion into the chip centre collapses, leading to an increased shive count measurable in the digester discharge pulp as a rise in the Pulmac shive content above 0.5% on a 0.15 mm slot screen, per TAPPI T 278 sp-18. Conversely, REA exceeding 12 g/L indicates overcharging, with excess alkali penetrating deep into the fibre wall and accelerating cellulose chain scission via alkaline hydrolysis and secondary peeling processes, manifesting as a drop in intrinsic viscosity determined according to ISO 5351:2010, from a nominal softwood target of 1,100–1,300 dm³/kg to below 900 dm³/kg. This asymmetric sensitivity landscape—a narrow REA operating window—forms the process control nexus where EA and sulfidity dependencies intersect.

Why Does the Distribution of Active Species Across Chip Thickness Govern Reactor Yield?

Mass transfer of active cooking chemicals into a wood chip follows Fickian diffusion coupled with simultaneous chemical reaction, and the effective alkali concentration in the free liquor dictates the driving gradient for hydroxide and bisulfide ions. In a hydraulic digester with a liquor-to-wood ratio of 3.5:1 to 4.2:1 (volumetric basis), the free-liquor EA at the digester feed is typically 18–22% on wood, but localized depletion within the chip occurs radially as the alkali neutralizes acetyl groups and reacts with lignin monomeric units. Research on Scandinavian softwood chips of 6–8 mm thickness has demonstrated that when free-liquor EA falls below approximately 14% at 155°C, the hydroxide concentration at the chip centre remains insufficient to maintain the bulk delignification rate, resulting in a kappa number gradient exceeding 15 units between chip surface and centre at the blow line, as measured by selective outer-layer shaving and subsequent kappa titration per ISO 302:2015. This gradient directly translates into screen room rejects and bleaching cost escalation, because the uncooked inner fraction requires more aggressive oxygen or chlorine dioxide stages to reach target brightness, potentially violating ECF bleaching sequences by demanding higher kappa factors that may breach mill-specific AOX discharge permits under EU Directive 2010/75/EU. Sulfidity interacts with this mass transfer regime by accelerating the overall delignification rate, thereby reducing the time during which the EA gradient is a limiting factor: at a constant 18% effective alkali, raising sulfidity from 25% to 32% can shorten the bulk cooking phase by approximately 15–18 minutes at 165°C, enabling more uniform lignin removal before significant alkali exhaustion at the chip centre. In countercurrent cooking zones, the upward liquor flow redistributes EA, but the net effect remains dominated by the initial impregnation conditions, which is why modern two-vessel hydraulic digesters incorporate a dedicated atmospheric pre-steaming stage and a high-compression feeder that expels air and saturates the chip pores, after which the chip column enters the impregnation vessel where white liquor charged at 110–120°C is circulated through central pipe screens and a circulation pump, often a Sulzer AHLSTAR type with a capacity of 2,000–4,000 m³/h per circulation, ensuring that the free-liquor-to-wood ratio at the impregnation zone remains above 3.8:1 to prevent EA starvation. Under these conditions, the Damköhler number for the penetration-reaction system shifts such that reaction becomes limiting over diffusion; any reduction in EA below the neutralization demand of the incoming chips, estimated at 3–4% Na₂O for typical softwood, immediately pushes the system back into mass-transfer control, a regime that mill operators recognize by a sudden increase in digester extraction screen delta-P and a rise in blow-line kappa variability.

In mills running close to recovery boiler limits, the white liquor sulfidity is often the variable forced to shift in response to the sulfur balance in the evaporation and combustion loop. When the lime kiln throughput restricts causticizing capacity, the mill may be forced to accept reduced sulfidity, which directly depresses the hydrosulfide ion concentration and alters the pH-dependent equilibrium H₂S ↔ HS⁻. At 150–170°C, the fraction of sulfide species acting as nucleophile is high, but the pKₐ of H₂S shifts such that at pH values below 11, a measurable fraction can volatilize into the digester non-condensable gas stream. This loss of active sulfur can feed back into sulfidity depression unless compensated by makeup sodium sulfate or elemental sulfur in the black liquor. To quantify the relationship between sulfidity, vapor-phase H₂S, and effective alkali, mill process models often incorporate the Pohjanpalo-Rantala equilibrium set, which has been validated against gas-phase measurements from a gas chromatograph equipped with a flame photometric detector, such as a Siemens ULTRAMAT system. Operating data from a northern European softwood mill with the continuous digester rated at 1,500 ADt/d showed that when sulfidity drifted from 30% to 25% due to causticizer inefficiency, the required H-factor to maintain kappa 30 rose from 800 to 950, and simultaneously the oxygen delignification exit kappa increased by 1.5 units, illustrating how sulfidity variability propagates downstream.

Within the digester circulation loops, temperature-driven reactivity amplification interacts nonlinearly with EA and sulfidity. The bulk delignification phase follows an empirical power-law expression dL/dt = k·[OH⁻]ⁿ·(L – L_∞), where n is typically found to be 1.0–1.2 for softwood, and the rate constant k incorporates temperature via an Arrhenius relationship having an activation energy of 60–65 kJ/mol. The integrated H-factor concept, originally developed by Vroom, multiplies the time-temperature profile into a single number, implicitly assuming that the rate constant is independent of alkali concentration; however, mill-scale correlation data has repeatedly demonstrated that the H-factor required to achieve a target kappa is inversely proportional to the effective alkali charged. Empirical correction factors, sometimes termed the “EA-adjusted H-factor”, have been implemented in advanced process control (APC) schemes from vendors like ABB and Valmet, where the APC algorithm solves for a dynamic setpoint of the cooking circulation heater outlet temperature to maintain a target kappa while compensating for measured white liquor strength. In a hydraulic digester with three concentric cooking screens, the lower cooking zone temperature trim is typically limited to ±3°C to avoid excessive sugar degradation and furfural formation, so the primary manipulated variable for reactivity adjustment remains the white liquor charge to the chip chute—directly modulating the effective alkali entering the system. When the white liquor EA is measured at 100 g/L Na₂O and the charge pumps are actuated by a Coriolis flowmeter (e.g., Endress+Hauser Promass F), dosage increments of 1 L/min can shift the effective alkali by 0.3%, a level of precision necessary when the kappa target is 18 for softwood destined for ECF bleaching, because the mill’s oxygen delignification stage can only accommodate an incoming kappa of 14–16 if caustic charge is not to exceed 2.5% on pulp and the temperature is limited to 105°C due to pump seal ratings.

Polysulfide cooking processes, in which a fraction of the white liquor sulfide is oxidized to polysulfide sulfur, add a further dimension to the EA–sulfidity reactivity landscape. Polysulfide ions (S_x²⁻) stabilize carbohydrate reducing end groups against peeling, thereby allowing mills to push effective alkali to higher levels 20–24% without the typical viscosity penalty, increasing delignification rate and yield. The polysulfide generation step requires oxidizing a side-stream of white liquor in a catalytic reactor, typically employing activated carbon and air at 70–80°C; the degree of oxidation directly alters the effective alkali appearing as NaOH remaining in the stream. Process control must account for the fact that each mole of Na₂S converted to Na₂S₂ or higher polysulfides consumes no NaOH but changes the sulfidity calculation if the sulfide is no longer available for delignification in its monomeric form. In such a hybrid system, the “apparent sulfidity” measured by the standard titration per TAPPI T 625 overestimates the true active hydrosulfide, requiring offline correction via ion chromatography or UV spectrophotometry using the absorbance ratio at 420 nm and 290 nm. Published data from a mill-scale installation of a Metso polysulfide system integrated into a single-vessel hydraulic digester producing 1,100 ADt/d of softwood linerboard pulp showed that when the polysulfide sulfur dose was maintained at 1.5% on wood, the effective alkali could be raised from 18% to 22% with only a 4% reduction in pulp viscosity and a kappa drop from 85 to 72, simultaneously decreasing the black liquor heat value slightly but improving overall cooking economy. This illustrates how the reaction network linking EA and sulfide species can be exploited industrially, but it also reveals the narrow operational window: exceeding 2.0% polysulfide sulfur led to measurable corrosion rates above 0.1 mm/year in the duplex stainless steel (EN 1.4462) digester circulation piping, as documented in inspection reports following a 36-month campaign.

When Effective Alkali Drops Below the Combined Neutralization Demand of Extractives and Acetyl Groups

Wood chips fed to the digester are chemically heterogeneous: the acetyl content of softwood hemicelluloses alone consumes approximately 1.8–2.7% of the charged effective alkali as Na₂O via deacetylation, while acidic extractives (resin acids, fatty acids) consume an additional 0.5–1.0%, and the initial lignin phenolic units consume 2–3% before the bulk delignification rate constant achieves its maximum value. If the total effective alkali charge falls to 13–14% on wood for a typical softwood like Scots pine, the entire alkali inventory can be consumed by side reactions and surface lignin solubilization, leaving no residual hydroxide to drive the fragmentation of high-molecular-weight lignin in the secondary wall. The resulting pulp will exhibit a kappa number well above 60 and can contain unsoftened chip centres visible as brown specks in the final sheet, directly contributing to dirt count failures under ISO 5350-2:2006. Industrial remediation of such an excursion involves not only increasing the white liquor flow but also adjusting the sulfidity, because the selectivity gain from hydrosulfide ions becomes irrelevant if alkali is absent. A corrective action implemented in a South American eucalyptus mill that experienced a series of low-EA events traced to causticizer performance revealed that raising sulfidity from 22% to 30% while simultaneously increasing EA by 2% restored the blow-line kappa from 22 back to 18 within 45 minutes of dwell time, as verified by a Kajaani kappa analyzer on the blow-line. Nonetheless, this transient compensation cannot be sustained indefinitely because the elevated sulfidity increases the sodium-sulfur balance discrepancy, requiring additional makeup saltcake that may stress the recovery boiler’s capacity to reduce sulfate to sulfide under the char bed—an effect particularly acute in boilers operating near their design limit of 1.5 kg black liquor solids per square metre per hour of hearth loading.

Long-term departures from the optimal EA–sulfidity regime also manifest in the paper machine’s refining energy demand. Pulp produced under conditions of high effective alkali with normal sulfidity exhibits a lower hemicellulose content due to secondary dissolution of glucomannan and xylan, which reduces the fibre’s inherent bonding potential and demands more PFI mill revolutions to reach a target tensile index of 80 Nm/g (ISO 1924-2:2008). Conversely, high sulfidity preserves more hemicellulose and promotes a greater degree of sulphonic acid group formation on lignin during cooking, which softens the fibre wall and facilitates internal fibrillation in disc refiners. A systematic mill study conducted over 18 months on a Valmet single-disc refiner (type RGP 268) processing northern bleached softwood kraft at 42° Schopper-Riegler freeness demonstrated that each 1% increase in sulfidity above 30% reduced the specific refining energy by 8–12 kWh/t at constant gap load, while effective alkali changes within the 17–20% range showed a marginal but not statistically significant correlation. However, this benefit must be weighed against the fact that high-sulfidity pulps are more prone to brightness reversion due to residual chromophoric sulfur-containing structures, a complication that can be partially mitigated by post-oxygen washing with 0.3% H₂O₂ in the wash press, as per a process patent by Eka Chemicals.

Digester control systems increasingly rely on software sensors that predict kappa number using first-principles models tuned with online REA and blow-line kappa measurements. These model-predictive controllers, implemented on platforms such as Honeywell Profit® Controller or ABB’s Expert Optimizer, incorporate a dynamic mass and energy balance of the digester zones, solving for the effective alkali concentration along the vertical profile by integrating the local delignification kinetics. The sulfidity term enters the kinetic submodel as a multiplicative factor (1 + β·S), where S is sulfidity fraction and β is an empirical coefficient typically determined from step-test data in the range 1.5–2.0. Plant trials have shown that when such a controller is commissioned, the standard deviation of blow-line kappa—as measured by a Metso Kappa Q analyzer sampling every 5 minutes—can be reduced from 1.8 to 0.7 kappa units, while the EA consumption per ton of pulp decreases by 2–3% relative to manual operation, largely because the controller avoids overcharging and prevents the REA from drifting above 10 g/L. The sustained economic benefit, equivalent to approximately €250,000 per year for a 1,200 ADt/d mill at 2019 European caustic prices, justifies the integration effort, but the model’s fidelity degrades if the white liquor sulfidity varies by more than ±3% without an online sulfidity measurement being fed forward. Therefore, mills that lack a dedicated sulfide ion selective electrode in the white liquor header are often forced to operate with wider kappa targets, directly sacrificing bleaching chemical efficiency.

Filterability of the brownstock wash liquor and the subsequent black liquor evaporator throughput are indirectly linked to the EA and sulfidity setpoints. When effective alkali is too low and pulping incomplete, the residual lignin in the pulp is more hydrophobic, causing higher viscosity of the black liquor and an increased tendency for soap separation problems in the primary weak black liquor tank. On the other hand, when sulfidity is excessive and the cooking temperature is pushed to 172°C to accelerate delignification, the black liquor soluble lignin may condense into high-molecular-weight complexes that precipitate on the heat-transfer surfaces of the falling-film evaporator, a phenomenon tracked by monitoring the evaporator scale-outlet differential pressure. A northern European mill documented that shifting sulfidity from 29% to 27% while increasing EA by 1% reduced the evaporator cleaning cycle interval from 14 to 21 days, restoring designed evaporation capacity. Standard practice in many mills therefore involves a multivariable strategy: the production engineer sets a sulfidity target range of 28–32% to balance selectivity against sulfur cycle losses, and then trims EA to maintain REA within the desired control band, compensating for variations in chip species mix and moisture content as measured by the chip moisture meter. When chip quality deteriorates, e.g., higher seasonal bark content or oversized chip fraction above 40 mm, the mass transfer resistance rises, and the effective alkali setpoint must be biased upward by 0.5–1.0% to ensure full penetration—a feedforward adjustment executed automatically in modern DCS logic that also references the calculated chip bulk density from the chip silo weigh belt.

Published data for the specific configuration of high-compression feeders and their effect on white liquor reactivity is limited, but operational experience consistently shows that air removal efficacy, directly determined by the compression ratio of the plug screw feeder (PSF), alters the accessible pore volume for liquor impregnation. A PSF with a compression ratio of 2:1 to 3:1, compressing chips to 250–300 kg/m³, expells interstitial and cellular air, resulting in a chip stream that can absorb 4–5 m³ of white liquor per tonne of OD wood in the subsequent impregnation vessel. If EA is not tailored to this liquor volume, the concentration of alkali entering the chip mass may be diluted below the critical micelle concentration of some dissolved wood extractives, potentially retarding surfactant-assisted penetration. In mills that have replaced an older PSF with a newer Andritz type that achieves a compression ratio of 3.5:1, an EA reduction of 0.8% was achievable without loss in kappa uniformity, because the enhanced impregnation allowed a lower concentration gradient to suffice for centre cooking. Such hardware-chemistry interactions underscore the complexity of defining a universal “reactivity” metric for white liquor; the metric is always relative to the mass transfer and equipment configuration in which the liquor operates, and declaring a single optimum EA-sulfidity pair independent of digester design is technically unsound.