Kraft Pulping Rate Control by Effective Alkali Rather Than Total NaOH

In a modern softwood kraft fibre line operating at 2,800 air-dried metric tonnes per day, the circulating white liquor in the pressure vessels is routinely reported as total sodium hydroxide by online titrators, yet the pulping rate within the digester cannot be predicted from that single value unless the sodium sulphide hydrolysis equilibrium, the carbonate dead load, and the sodium sulphate/thiosulphate carryover are separated into their respective alkali fractions. White liquor is a mixed alkaline solution in which all sodium compounds are expressed as sodium oxide equivalents; effective alkali (EA) is defined as NaOH + ½ Na₂S as Na₂O, active alkali (AA) as NaOH + Na₂S as Na₂O, and total titratable alkali (TTA) usually as NaOH + Na₂S + Na₂CO₃ as Na₂O. The hydrolysis reaction Na₂S + H₂O ⇌ NaOH + NaHS releases only one mole of sodium hydroxide per mole of sodium sulphide; therefore one half of the sulphide sodium ion is titrated as hydroxide only after the hydrolysis equilibrium, while the other half remains as hydrosulphide. In an industrial white liquor with 90–110 g/L effective alkali, 25–35% sulphidity, and 80–85% causticizing efficiency, a direct total-alkali titration typically reads 115–140 g/L as Na₂O because of the carbonate fraction. Operating a rate control loop on that higher total value introduces a consistent offset that becomes severe in high-closure mills where dead load carbonates accumulate. Because delignification rate in kraft cooking is dominated by the hydroxide and hydrosulphide concentrations rather than by the total sodium inventory, the effective alkali concentration is the chemically meaningful driving force. At cooking temperatures of 150–170 °C, the bulk delignification reaction exhibits an apparent activation energy of approximately 134 kJ/mol, and the relative reaction-rate parameter in the H-factor formalism is calculated from the Vroom expression k = exp(43.2 − 16113/T), where T is in Kelvin. The integrated H-factor target is then controlled using residual EA as the back-calculated chemical state variable. Blind use of total NaOH, or even total titratable alkali, would produce lower chemical efficiency, higher kappa variation, and greater yield loss across chip furnish changes.

When the digester control system receives a total NaOH signal from a conductivity or automatic titrator, the carbonate fraction biases the apparent chemical charge by 20–30 g/L as Na₂O in a typical high-causticizing mill. That bias is not constant across liquor loops because the carbonate concentration rises with black liquor carryover, lime mud filtration inefficiency, and white liquor oxidation. A control target based on total NaOH therefore asks the digester to perform a chemical task and then compromises the measurement before the task is evaluated. Effective alkali, by contrast, is calculated from the sodium hydroxide concentration plus one-half of the sodium sulphide concentration; it is the amount of strong alkali that can be converted to hydroxide during the cook. This distinction is most visible in the early heating phase, where sodium sulphide hydrolysis is rapid but not instantaneous, and the local hydroxide activity within the chip is the variable that drives both lignin fragmentation and cellulose peeling. The total sodium inventory does not distinguish between hydroxide, carbonate, sulphate, or thiosulphate, and therefore cannot be used to control the rate of a reaction that is first order in hydroxide and partly dependent on hydrosulphide.

Why does effective alkali rather than total NaOH govern delignification rate?

At the fibre wall and middle lamella, the rate of phenolic β-O-4 ether cleavage is a function of hydroxide activity and hydrosulphide activity. Total sodium hydroxide, as measured by direct titration without separating carbonate, does not quantify the hydroxide activity that remains after the carbonate-bicarbonate equilibrium and the sulphide hydrolysis equilibrium are established. In a typical mill white liquor with 25 g/L sodium carbonate as Na₂O, the measured total alkali could satisfy a process setpoint while the effective alkali is below the minimum required for bulk delignification. The bulk delignification phase consumes the largest fraction of effective alkali: roughly 60–70% of the initial charge is consumed between 150 °C and 170 °C, while the initial phase consumes 25–30%, and the residual phase consumes 5–10%. The kinetic response to hydroxide is close to first order in the bulk phase, so a 10% reduction in effective alkali concentration produces an undercook that cannot be fully compensated by extending H-factor without shifting the viscosity-yield balance. A change from 20% to 30% sulphidity at constant effective alkali can increase the bulk delignification rate by approximately 15–20% and can reduce the H-factor requirement by 150–300 units for the same kappa; however, the effective alkali definition does not rise when sulphidity alone rises, because the added sodium sulphide contributes only one-half of its sodium to hydroxide and the other half remains as hydrosulphide. A total NaOH loop cannot distinguish between an increase in sodium hydroxide and an increase in sodium sulphide, even though the selectivity and rate effects are different.

The H-factor calculation is only a relative rate integrator. It assumes a constant delignification activation energy, but its use with a setpoint based solely on total alkali propagates errors because the temperature ramp through the hydrolysis zone changes the fraction of sodium sulphide converted to sodium hydroxide. At 170 °C, the autoclave equilibrium of the sulphide hydrolysis reaction is shifted such that the hydroxide concentration corresponding to one-half of the sulphide is available for delignification; the effective alkali definition approximates that equilibrium. In contrast, total NaOH methods may include sodium from sulphide and carbonate but may not include the sulphate and thiosulphate dead load. The rate-control variable should therefore be the effective alkali concentration after the liquor has reached cooking temperature, expressed as g/L Na₂O, and not the initial total sodium hydroxide titre. Furthermore, effective alkali concentration inside the chip is influenced by chip thickness and diffusion. For softwood chips with a thickness of 6–8 mm, the time for hydroxide to reach the chip centre at 150 °C is on the order of 20–30 min, but for overthick chips above 10–12 mm the time can exceed 60 min. In that diffusion-limited case, residual EA in the free liquor may appear adequate while the chip centre remains undercooked. The control system therefore needs an effective alkali setpoint on oven-dry wood, adjusted upward by 0.5–1.0 percentage-point when the overthick fraction exceeds 10% of the furnish.

Operators on a 2,500 air-dried metric tonne per day single-vessel hydraulic digester frequently observe that the total NaOH signal remains stable while the kappa number begins to drift upward during periods of high black liquor carryover. The cause is the additional carbonate entering with the wash liquor: total NaOH remains within range because the titration counts carbonate as hydroxide, while the effective alkali falls. A liquor-to-wood ratio of 3.6 L/kg and an effective alkali charge of 17% on oven-dry softwood produce an initial cooking EA concentration of approximately 47 g/L before heating; after chip moisture and dilution by condensate, the equilibrium cooking-phase EA is typically 14–18 g/L. The digester control loop should therefore calculate EA from the white liquor flow, white liquor EA titre, chip moisture, and carbonate dead load, then trim the white liquor flow to hold the EA concentration rather than holding a total NaOH concentration. Field data from the same digester type show that a 3 percentage-point change in chip moisture changes the effective alkali charge on oven-dry wood by 0.6–0.8 percentage-points, which is enough to shift kappa by 2–4 units if uncorrected. A residual EA titration at 8–12 g/L Na₂O for bleachable softwood, with kappa determined on a blow-line sample every 20 min by a single-point online analyser correlated to ISO 302:2004, provides the feedback needed to adjust the H-factor target by 50–100 units per 1 g/L deviation in residual EA.

When total NaOH masks dead load in high-closure kraft recovery cycles

In a mill operating at a high degree of white liquor oxidation or with high black liquor carryover, thiosulphate and sulphate can reach 15–25 g/L as Na₂O in the white liquor. These species contribute to total sodium but not to effective alkali; they also increase the boiling-point rise and viscosity of the liquor. A control loop based on total NaOH interprets the thiosulphate as available alkali and underfeeds the actual causticising plant. The result is a progressive loss of effective alkali at constant total NaOH, with the sulphidity simultaneously declining because sulphide is oxidised to thiosulphate. Since effective alkali counts only one-half of the sulphide, the loss of sulphide further reduces EA by 0.5 kg Na₂O per kilogram of sulphide sulphur oxidised. The correct analytical basis is the EA titration in TAPPI T 624 cm-15, in which carbonate is excluded and the sulphide contribution is halved. A mill producing 1,800 air-dried metric tonnes per day of bleached softwood pulp with a white liquor TTA of 125 g/L Na₂O but an EA of only 88 g/L Na₂O has a carbonate dead load of 37 g/L Na₂O; if the control target is set at 120 g/L TTA, the digester is chemically starved by 12–15 g/L effective alkali and cannot reach the target kappa without a compensating H-factor increase of 300–500 units. Under these conditions, the normal residual EA control limit of 8 g/L Na₂O is breached, and the dissolved lignin fraction re-adsorbs onto the fibre surfaces, producing a kappa increase of 2–3 units in the final bleached pulp and higher bleach chemical demand. The operational boundary is therefore not total sodium balance but the ratio of effective alkali to total titratable alkali; when that ratio falls below 0.70, the recovery causticising area must be checked for lime quality, carbonate carryover, or excessive white liquor oxidation.

Split-alkali profiling in modified continuous cooking provides a direct industrial demonstration of why effective alkali concentration, not total NaOH charge, controls the rate and selectivity. In a single-vessel digester with countercurrent wash, the initial EA in the impregnation zone is held at 5–8 g/L Na₂O to permit liquor penetration without rapid carbohydrate degradation; the cooking-phase EA is raised to 14–18 g/L Na₂O; and the residual-phase EA is held at 10–14 g/L Na₂O. The conventional batch profile, by contrast, produces a peak EA of 22–28 g/L Na₂O early in the heating phase and a residual EA below 6 g/L Na₂O at blow. The modified profile reduces the peak hydroxide activity during the phase where cellulose is most vulnerable to alkaline hydrolysis, while maintaining sufficient EA in the residual phase to keep the fragmented lignin dissolved. Published mill comparisons of batch and modified continuous cooking at the same target kappa show yield gains of 1–2 percentage-points and viscosity improvements of 50–100 mL/g measured according to ISO 5351:2010. These differences are not produced by changing the total NaOH charge; they are produced by redistributing the same effective alkali over the cooking time. A control system that maintained total NaOH would not detect the peak suppression or the residual-phase starvation, because both conditions can exist at the same total sodium inventory.

Residual effective alkali as a rate-dependent kappa control variable

Residual effective alkali at the digester blow is the strongest single liquor-side predictor of kappa stability because it integrates the cumulative hydroxide consumption of the entire cook. For bleachable softwood kappa targets of 25–32 measured by ISO 302:2004, the residual EA should be maintained between 8 g/L and 12 g/L Na₂O; for hardwood kappa targets of 14–18, the residual EA should be 10–14 g/L Na₂O. Below these ranges, the dissolved lignin concentration exceeds the solubility limit for the liquor pH, and precipitation onto the fibre surfaces is kinetically favoured. Above 18 g/L Na₂O, the residual hydroxide activity continues to attack cellulose, especially in the presence of high sodium ion concentration, and the viscosity falls below the 1,200–1,400 mL/g typical of bleachable softwood. The control loop should therefore use a cascaded architecture: the kappa model adjusts the H-factor target, while the residual EA controller adjusts the white liquor charge and the digester washing dilution. A deviation of 1 g/L residual EA at constant H-factor corresponds to roughly 2–3 kappa units in softwood, so the residual EA setpoint must be kept within ±0.5 g/L for a kappa standard deviation below 1.0 unit. Online analysers based on automated titration and conductivity are normally calibrated against TAPPI T 624 cm-15 every 8 h; drift between calibration cycles must not exceed 2% of the measured EA or the cascaded loop will amplify the dead load error.

The use of residual EA rather than total NaOH also changes the interpretation of viscosity loss during a kraft cook. A low total NaOH residual may be due entirely to carbonate accumulation and would not indicate cellulose degradation, whereas a low effective alkali residual with high total sodium indicates that the hydroxide has been consumed by neutralisation of wood acids and carbohydrate degradation products. In that situation, the pulp viscosity measured by ISO 5351:2010 may be below target even though the total NaOH value appears adequate. Process troubleshooting should therefore compare the ratio of residual effective alkali to total titratable alkali against the causticising efficiency; a ratio below 0.60 at blow indicates either excessive carbonate carryover or sulphide oxidation, while a ratio above 0.75 with low residual EA indicates that the wood acid load is higher than the alkali charge can buffer. The control of rate by effective alkali thus extends beyond the digester into the recovery cycle, because the dead load that obscures total NaOH is generated in the lime kiln, the recausticising plant, and the black liquor oxidation system.

In batch digesters with peak EA concentrations exceeding 25 g/L Na₂O, the initial hydrolysis of sodium sulphide is rapid, but the ratio of hydroxide to hydrosulphide inside the chip remains limited by diffusion. At high peak EA, the outer fibre wall delignifies more quickly than the middle lamella, creating a radial kappa gradient that is measured as a kappa bimodality in the blow pulp. The operational boundary for softwood batch cooking is therefore a peak EA of 20–23 g/L Na₂O and a residual EA of 8–12 g/L Na₂O. Hardwood vessels with shorter liquor penetration paths can operate at 16–20 g/L Na₂O cooking-phase EA. When a mill switches from sourwood to oak or from pine to spruce, the acetyl and uronic acid loads differ by 0.3–0.6 mol/kg dry wood, and the EA demand changes by 1–2 percentage-points on oven-dry wood. The compensation must be applied to the effective alkali setpoint, not to the total NaOH setpoint, because the latter includes non-reactive sodium species that do not neutralise wood acids. Failure to apply the compensation produces either an undercook with high rejects and high kappa, or an overcharge with yield loss and reduced viscosity. The practical control boundary in a modern fibre line is therefore a function of residual EA, measured every 2–4 h with a titrator conforming to TAPPI T 624 cm-15, and the corresponding kappa signal from an online analyser calibrated to ISO 302:2004.