Alumina Caustic Ratio Deviation Control with Digestor Caustic Inventory

In a continuous Bayer digestion circuit processing gibbsitic bauxite at 140–150 °C or boehmitic bauxite at 200–240 °C, the molar Al₂O₃/Na₂O_caustic ratio in pregnant liquor is the state variable that couples bauxite feed rate, spent liquor return, evaporation load, residue washing, and downstream precipitation stability. The digestor caustic inventory is not a simple level measurement or a single concentration reading; operationally it is the product of the live liquor volume contained in the digestion train and the titrated caustic concentration expressed as grams per litre Na₂O, corrected to 20 °C and to the nominal density reference used by the plant laboratory. A plant operating with 2,500 m³ of live digestion liquor at 230 g/L Na₂O_caustic carries an inventory of approximately 575 t Na₂O. An unmeasured spent-liquor flow imbalance of 10 m³/h sustained over 24 h therefore changes inventory by roughly 55 t Na₂O, or 9–10% of the total, before any ratio deviation is detected by delayed laboratory titration. Because the pregnant-liquor molar ratio is calculated from the gravimetric quotient by multiplying the Al₂O₃/Na₂O_caustic mass ratio by 0.608, a change in caustic concentration of 4 g/L from 230 g/L to 226 g/L can be sufficient to shift a steady molar ratio from 0.68 to approximately 0.69 if the alumina concentration is constant. The kinetic significance of that shift is nonlinear in boehmitic circuits, because alumina solubility is strongly temperature-dependent and the precipitation tendency of the high-ratio liquor increases as the liquor is flash-cooled through pressure letdown and clarification.

The control requirement is therefore to maintain caustic inventory stability within a band that is much narrower than the laboratory cycle time, usually ±0.5–1.0% of total inventory. That band must absorb bauxite moisture swings, residue wash-water return, spent-liquor ratio changes, fresh caustic additions, and acid cleaning or water flushing of online analyzers. It is not sufficient to control digestor level alone; level is a volume signal with no information about caustic concentration. Nor is it sufficient to control caustic concentration alone; concentration can remain within specification while total inventory drifts through volume changes, so that a subsequent disturbance in liquor flow produces an amplified ratio excursion. The central control loop must therefore combine a level controller, a caustic flow controller, a bauxite feed controller, and a slow model-based inventory corrector that adjusts the bauxite-to-spent-liquor ratio setpoint using measured pregnant-liquor Al₂O₃/Na₂O_caustic ratio from automatic titrators, density meters, or reconciled laboratory inputs, with a dead time of 20–60 min depending on sample transport and digestion residence time.

Why Does Caustic Inventory Drift Occur Before the Ratio Analyser Registers a Disturbance?

In multi-vessel digestion trains arranged as a series of heated stirred reactors, the hydraulic capacitance creates a first-order lag between a change in spent-liquor flow and the resulting change in pregnant-liquor ratio at the blow-off flash vessel. A typical three-vessel train with a total live volume of 2,500 m³ and a combined liquor advance rate of 800–1,000 m³/h has a mean residence time of 2.5–3.1 h. If a spent-liquor flow change is made at the inlet of the first vessel, the response measured at the blow-off line is delayed by the plug-flow residence time of the first vessel, typically 40–60 min, and is further attenuated by backmixing in the remaining vessels. During that period, the only available evidence of the disturbance is a change in digestor level, a change in liquor density, or a change in steam demand. Caustic inventory therefore acts as an integrating variable: a persistent imbalance of 5 m³/h appears first as a level trend, then as a caustic concentration trend, and only later as a shifted molar ratio. The reverse is also possible. A bauxite feed increase adds reactive alumina and water to the front end, increasing pregnant-liquor alumina concentration and simultaneously lowering caustic concentration by reaction consumption and dilution. The level may rise or fall depending on the water balance, while the caustic inventory may remain temporarily unchanged because volume and concentration move in opposite directions. That masking effect is the principal reason simple level control cannot be used as a surrogate for caustic inventory control in high-temperature boehmitic digestion.

Inventory-based control is further complicated by the fact that caustic is consumed by reactions with reactive silica and by the formation of sodium aluminosilicate sodalite-type desilication products. These reactions do not necessarily change digestor level in the short term; they change the total quantity of free caustic. In a high-silica bauxite campaign, the reactive silica content may rise from 4–6% to 8–10% on a dry ore basis. The increased caustic loss to desilication product can exceed 1–2 g/L Na₂O_caustic per hour in the digestion circuit if lime dosage and temperature are not adjusted. The molar ratio can fall even when all flow loops are steady, because the denominator of the ratio is being depleted by a chemical reaction that has no direct flow measurement. The only robust correction is a caustic inventory reconciliation that includes a stoichiometrically estimated caustic consumption term from reactive silica, lime, and soda loss to residue. Published data for specific vendor configurations in boehmitic circuits with variable bauxite silica is limited, but the structural form of the reconciliation follows the general balance: dI/dt = F_spentC_spent + F_causticC_caustic − F_pregnantC_pregnant − R_silica − L, where I is the caustic inventory in tonnes Na₂O, F terms are volumetric flows, C terms are titrated caustic concentrations, R_silica is the reaction consumption rate, and L is the loss to residue washing and entrainment.

Online analyzer placement largely determines the speed and reliability of ratio deviation detection. In circuits where the primary ratio signal is derived from a side-stream density meter and a single conductivity cell, the signal may be sufficiently fast but insufficiently selective, because carbonate, sulfate, chloride, and organic salts affect conductivity without changing the caustic concentration available for alumina dissolution. Automatic titrators that sample clarified pregnant liquor and perform an acid titration with thermal or conductivity endpoint detection are more selective and can have a cycle time of 10–15 min, but they require diligent flush-back and descaling. The most defensible arrangement is a dual-measurement system in which a density meter with temperature compensation is used as a high-speed inferential signal and an automatic titrator or laboratory result is used to update the density-to-composition correlation every 1–2 h. In a liquor containing 210–240 g/L Na₂O_caustic and 150–190 g/L Al₂O₃, density at 90 °C is usually in the range 1.38–1.48 kg/L, but the exact conversion is specific to organic carbon content, sodium carbonate concentration, and solids carryover. Analytical measurements should follow ASTM E291-18 for caustic soda titration or an equivalent validated method, with uncertainty evaluated according to ISO 5725-2:2019 so that the inventory calculation is not corrupted by an undeclared reproducibility error. The same analyzer verification should be linked to the safety lifecycle under IEC 61511-1:2016 if the ratio measurement participates in a shutdown or interlock decision.

When a Digestor Level Change and a Ratio Deviation Occur Simultaneously, Which Controller Moves First?

In a conventional cascade configuration, the digestor level controller is the faster loop because level responds to volume imbalance within minutes, while the molar ratio responds through a multi-hour residence time and analyzer dead time. If the level controller is permitted to manipulate bauxite feed directly, then a rising level caused by excess spent liquor will reduce bauxite feed, which will lower alumina extraction and delay the caustic consumption response, causing the level to rise further and the ratio to fall later. That interaction is unstable if the ratio controller then tries to restore alumina by increasing bauxite feed again. The preferred hierarchy is to separate the fast volume loop from the slow composition loop. The level controller may manipulate the spent-liquor return flow or a letdown flow to precipitation, while the ratio controller manipulates the bauxite feed-to-spent-liquor ratio setpoint. In plants where the spent-liquor return is fixed by precipitation demand, the level controller may manipulate the wash-water addition to the residue circuit or the fresh caustic trim flow, but not bauxite feed alone.

When a simultaneous level increase and falling molar ratio are observed, the diagnostic sequence should first verify the caustic inventory by reconciling the level change into a volume change and comparing it with the titrated caustic concentration trend. A level increase of 1.5% in a 2,500 m³ circuit represents 37.5 m³ of additional liquor volume. If the caustic concentration simultaneously fell from 228 g/L to 224 g/L, the inventory change is relatively small because the concentration fall compensates for the volume rise. Under those conditions, the root cause is likely a dilute liquor ingress, such as wash-water return or heat-exchanger condensate inleakage, and the immediate action should be to close the dilution source, not to change bauxite feed. Conversely, if the level rise is accompanied by a stable or rising caustic concentration, the inventory is increasing, and the root cause is likely an excess of strong spent liquor or fresh caustic addition. The corrective action is then to reduce caustic input or increase forward flow, while the ratio controller holds its output. If both level and ratio move in the same direction—level rising and ratio rising—the circuit is receiving bauxite-rich feed or the digestion reaction is accelerating due to a temperature rise, and the control response must involve the digestion temperature cascade and bauxite feed reduction.

The tuning values shown in the table are not universal constants; they are order-of-magnitude guidance for a digestion train with a residence time of 2.5–3.5 h and an analyzer cycle time of 10–15 min. Shorter residence-time circuits processing gibbsitic bauxite at 140–150 °C may require faster integral action, while longer residence-time boehmitic circuits above 220 °C require slower integral action to avoid reset windup during delayed analyzer feedback. The ratio controller must be equipped with an external reset feedback or an anti-windup strategy whenever the online analyzer is out of service for more than 30 min, because the loop will otherwise integrate the error over the entire analyser outage and produce a large upset on restart. The level controller should use a measured volume calibration that accounts for vessel geometry, agitator displacement, internal heating coils, and solids accumulation. Radar level transmitters with dynamic vapor compensation are preferred over differential-pressure cells in digestors with internal scaling, because differential-pressure cells are prone to impulse-line blockage and can report a false level when the lower tap becomes coated with sodalite scale. In a vessel with a diameter of 8–10 m, a radar measurement error of ±5 mm corresponds to a volume error of 0.5–0.8 m³ per vessel, which is negligible for a single vessel but significant when multiplied across six or eight vessels and then combined with a caustic concentration measurement error of ±2 g/L.

The interaction between digestion temperature and the alumina-to-caustic ratio is often more important than the flow ratio itself. In boehmitic digestion, a temperature increase of 5 °C can raise the equilibrium alumina solubility by an amount that shifts the molar ratio by 0.02–0.04 under otherwise constant feed conditions. The steam control loop therefore acts as an implicit ratio manipulator. If the temperature cascade is tuned aggressively, steam pressure fluctuations from the powerhouse appear as ratio noise with a period of 10–30 min. A multi-vessel train with individual steam coils on each vessel may experience uneven temperature distribution because the first vessel operates at a higher driving force for heat transfer and the last vessel approaches equilibrium. The temperature difference between the first and last vessel in a boehmitic train can be 10–20 °C if the vessels are not re-staged, and that gradient is a source of local ratio excursions that are not captured by a single blow-off ratio measurement. Published data for specific vessel cascades with forced-circulation heating is limited, but the general practice is to maintain a descending temperature profile from the first preheating vessel to the final hold vessel, with the final vessel temperature controlled within ±2 °C and the first vessel allowed to float within ±10 °C to absorb steam-side variations.

Reactive Silica, Lime, and Caustic Loss Coupling

Reactive silica entering with bauxite consumes caustic and alumina through the formation of desilication product, which removes both components from the pregnant liquor and changes the molar ratio in a direction that depends on the stoichiometry of the precipitation reaction. In a high-silica bauxite with 8% reactive SiO₂ on a dry ore basis, the caustic consumption can be in the order of 30–60 kg Na₂O per tonne of bauxite, depending on the degree of desilication and the final soda content of the residue. That consumption is not seen as a flow imbalance in the spent-liquor return, but it appears as a continuous negative term in the caustic inventory balance. If the inventory controller does not include an explicit reactive-silica feedforward term, it will compensate only after the ratio has fallen, by adding fresh caustic or reducing bauxite feed. The compensation is therefore reactive rather than proactive, and the resulting inventory correction may overshoot if the silica feed changes again before the response is complete.

Lime addition complicates the silica control because lime may reduce the loss of caustic to the desilication product by forming a calcium-containing phase that alters the phase equilibrium, but lime also adds a calcium input that can increase scaling on heater tubes. Lime dosage is usually controlled by a molar CaO/SiO₂ ratio in the feed, with typical ranges of 0.2–0.6 for high-temperature boehmitic circuits. A change in lime dosage from 0.3 to 0.5 CaO/SiO₂ molar ratio can reduce the caustic loss to residue by several percent, but it can also change the apparent viscosity of the slurry and the heat-transfer coefficient in tube digestors. The caustic inventory controller must therefore interact with the lime feed controller through a coordinated constraint: the lime dosage is adjusted to maintain the residue soda target, while the caustic inventory is adjusted through fresh caustic addition or spent-liquor flow. If the two controllers are not coordinated, a period of high silica feed can cause both high lime addition and high fresh caustic addition, which may improve the ratio temporarily but increase the total soda load and eventually raise the residue soda loss above the target.

On the downstream side, the pregnant-liquor ratio at the blow-off flash vessel is not the same as the ratio at the first clarifier underflow, because further reaction and cooling occur during pressure letdown. The flash train reduces the temperature from digestion conditions to near atmospheric boiling, and the sudden cooling can cause some dissolved alumina to re-precipitate as gibbsite or boehmite scale if the molar ratio is above the stability limit for the new temperature. A circuit digesting boehmitic bauxite at 230 °C and reducing pressure through two or three flash stages to 100–105 °C passes through temperature windows in which the liquor is supersaturated. If the molar ratio at the blow-off line is above 0.72, the risk of scale formation in the flash vessel and transfer piping increases significantly. The caustic inventory control loop must therefore set its ratio target not only for extraction in the digestor but also for stability in the flash and clarification section. The target of 0.65–0.70 molar Al₂O₃/Na₂O_caustic at the blow-off line is a compromise that preserves extraction while avoiding excessive scaling. If the circuit is forced to operate at the upper edge of that band because of bauxite composition, the flash-line heat exchanger may require more frequent descaling and the run length may be limited by the rate of scale accumulation rather than by the digestor itself.

A feed-forward scheme for boehmitic digestion with delayed laboratory ratio verification should use the measured bauxite feed mass, the measured spent-liquor flow, the titrated spent-liquor caustic concentration, and the available bauxite composition model to compute a molar ratio setpoint trajectory that anticipates the effect of reactive silica and available alumina. The strongest element in such a scheme is the bauxite feed conveyor weight signal, which is usually available as a mass flow in tonnes per hour. The weakest element is the bauxite composition, which is often known only from a daily composite sample and therefore lags the actual reactive silica content by several hours. A realistic middle ground is to separate the control calculation into a fast component based on feed mass and spent-liquor flow, and a slow component based on the measured ratio error and the estimated caustic consumption from silica. The fast component can manipulate the spent-liquor flow to maintain a target caustic-to-bauxite ratio, while the slow component adjusts the target caustic inventory itself. That structure reduces the interaction between level control and ratio control because the fast loop handles the primary flow balancing and the slow loop handles the chemical consumption balance.

Equipment behaviour on actual production lines shows that the most common failure mode in digestor caustic inventory control is not a control algorithm deficiency but an inaccurate volume measurement caused by solids accumulation in the bottom of a vessel. In a stirred digestor with a diameter of 10 m and a working volume of 700 m³, a settled solids layer of 0.5 m displaces roughly 39 m³ of liquor volume and can bias the level measurement by an equivalent amount if the level transmitter is calibrated to the original vessel bottom. That bias is not constant because the solids layer may increase during high-silica campaigns and decrease after a shutdown or after a period of high agitation. The result is a caustic inventory estimate that drifts without any change in the actual inventory, leading the controller to add or remove caustic in response to a phantom error. For this reason, inventory-based control requires periodic re-zeroing of the level measurement during isolated vessel drain-down or during a scheduled wash. The re-zeroing cycle should be matched to the solids loading, with more frequent checks when the reactive silica content of the bauxite exceeds 6% or when the residue settlement rate is high.

A Feed-Forward and Reconciliation Structure That Limits Ratio Deviations During Bauxite Moisture Swings

Bauxite moisture is a common unmeasured disturbance because the bauxite feed conveyor weight signal does not subtract the free moisture content unless an online moisture analyzer is installed. A bauxite with 12% free moisture enters the grinding circuit as a high-viscosity slurry, but the mass flow of dry bauxite is only 88% of the belt weight. If the moisture content changes from 10% to 13% without a corresponding change in belt speed, the dry bauxite delivery falls by approximately 3.3% while the water delivery rises. The digestor level responds to the water increase, but the caustic concentration also falls, and the molar ratio may not move immediately because both alumina and caustic concentrations change. The eventual ratio response depends on the digestion extent, which is slower than the water balance. A control structure that uses only the belt weight and the spent-liquor flow will overestimate the dry bauxite mass and underestimate the water input, causing an apparent level rise with stable throughput. The correction should come from an online moisture measurement at the conveyor or from a mill-motor power signature that changes with slurry viscosity. If neither is available, a filtered level-inventory trend can be used as an inferential signal for a step-change in moisture, but the response is sluggish.

In a plant with an evaporator and liquor purification circuit, the caustic inventory is partly distributed outside the digestion train. The total inventory includes the live volume in spent-liquor storage, the evaporator feed tank, the heat recovery circuits, and the residue-wash liquor tanks. A change in evaporator load changes the concentration of the recycled spent liquor and therefore changes the caustic concentration entering the digestor without changing the total sodium mass. If the evaporator is down for cleaning, the spent liquor becomes more dilute, and the digestor must be compensated by higher spent-liquor flow or direct fresh caustic addition. The controller must be aware of evaporator availability and must define the inventory setpoint in terms of total Na₂O mass, not volume. For a plant with a bauxite feed of 250 t/h dry ore and a spent-liquor flow of 1,000 m³/h, a drop in spent-liquor caustic concentration from 220 g/L to 210 g/L reduces the caustic mass delivered by 10 t/h. That missing caustic is equivalent to 2.5–3.0% of a 575 t inventory per hour, so the need for a coordinated evaporator schedule is not an academic detail; it is an operating constraint that can drive the ratio out of the target band within a single shift.

The ratio deadband and the inventory alarm limits should be derived from a quantitative model of the relevant uncertainty rather than from a fixed rule. If the pregnant-liquor Al₂O₃ and Na₂O_caustic measurements each have a reproducibility of ±2 g/L, the molar ratio uncertainty is not merely the sum of the two errors; it is governed by the propagation of variance. At an Al₂O₃ concentration of 170 g/L and a caustic concentration of 225 g/L, a 1% relative error in each measurement propagates to a molar ratio uncertainty of approximately ±1.4% relative, or about ±0.01 in the molar ratio. The controller deadband should be set wider than that measurement noise limitation, typically ±0.015, to avoid moving the spent-liquor valve on noise. If the plant uses an automatic titrator with a reproducibility of ±0.5% relative, the deadband can be narrowed to ±0.01. However, the analyser itself is subject to sample line lag, flushing cycles, and calibration drift, and those dynamic errors can be larger than the laboratory reproducibility. The industrial solution is not to eliminate the deadband but to add a model-based predictor that takes the digestor level trend, the steam flow, and the bauxite feed mass as high-frequency proxies for the ratio. The predictor is reset by the analyzer measurement when it is available.

Operational boundaries for the control scheme include a minimum liquor advance rate below which the digestor solids settle and the ratio becomes spatially non-uniform. For a vessel in which the slurry density is 1.40–1.45 kg/L and the particle size distribution has a d₅₀ near 150–250 µm, the minimum superficial velocity to maintain full suspension is typically in the order of 1.5–2.5 m/s in transfer lines and 0.5–1.0 m/s in well-stirred vessels, but the exact value is specific to particle density, solids loading, and vessel geometry. If the liquor advance rate is reduced below this range for more than 1–2 h, settling can occur and the level measurement becomes unreliable, leading to a false caustic inventory high or low. The controller should therefore include a liquor-advance-rate interlock that prevents the spent-liquor valve from closing below a minimum flow even if the level is rising. The minimum flow is often set at 60–70% of the normal liquor advance rate for the given vessel train, with the exact value confirmed by tracer residence-time distribution testing or by physical inspection during a scheduled shutdown.

In caustic systems with high organic carbon loadings, the viscosity and density correlations used for inferential measurements degrade because the organics content changes the liquor density at a constant inorganic composition. A liquor with 20 g/L organic carbon and a density of 1.42 kg/L may have the same density as a liquor with 10 g/L organic carbon and a different caustic concentration if the temperature and alumina concentration differ. An inventory controller that relies on density as a caustic surrogate will therefore drift when the organic carbon content changes after residue washing changes or after an evaporator scale removal. The same limitation applies to conductivity-based analyzers, because sodium carbonate, sodium sulfate, and sodium chloride contribute to conductivity but do not contribute to the effective caustic concentration available for desilication or alumina dissolution. The most robust online measurement is therefore a selective titration, which can be automated with a side-stream filter and a validated acid delivery system. In installations where that is not available, the density signal must be corrected by a laboratory titrated composition at least every 4 h, and the correction must be applied through a bias term that is updated only when the analyzer is in service and the plant is at steady state. Under those conditions, the caustic inventory calculation remains reliable if the volume measurement is trusted and the total inventory is not allowed to deviate by more than ±2% from the target.

The final operational constraint is the interaction between the digestion caustic inventory and the precipitation circuit. A high molar ratio in pregnant liquor above 0.72 may be desirable for digestion extraction, but it produces a precipitation feed that crystallises rapidly and can generate fine gibbsite particles and high organic-polymer dispersant demand. A low ratio below 0.60 slows precipitation and shifts the particle size distribution toward coarser product while reducing yield. The digestion ratio target is therefore not selected in isolation; it is selected by the precipitation product-quality requirement and the seed surface area available in the precipitation circuit. In a typical plant targeting a precipitation ratio drop of 0.10–0.15 and a final molar ratio of 0.55–0.60 in spent liquor, the digestion target must remain within 0.62–0.72 to preserve the precipitation driving force. The caustic inventory controller must therefore communicate with the precipitation liquor advance rate controller, because a change in precipitation seed rate or temperature changes the spent-liquor ratio and therefore the caustic concentration returning to digestion. A particularly severe disturbance occurs when the precipitation circuit is started from a low-activity seed inventory, because the ratio drop is smaller and the spent liquor returns to digestion with a higher alumina-to-caustic ratio than normal. In that case, the digestor inventory control must compensate by reducing fresh caustic addition or increasing bauxite feed even though the digestor itself may appear balanced.

Under these process constraints, the practical configuration that reduces inventory-induced ratio noise in several full-scale circuits comprises a radar level measurement with a measured-volume calibration table, a selective online titrator for caustic concentration, a fast density meter for transient detection, a bauxite belt weight with online moisture correction, and a spent-liquor magnetic flowmeter with a density-compensated mass flow calculation. The level controller is tuned for a slow response to avoid fighting the spent-liquor flow controller, and the ratio controller operates on a calculated inventory signal rather than on an instantaneous concentration signal. Fresh caustic addition is used as a trim manipulated variable with a rate limit of 1–2 t/h Na₂O unless a major inventory deficit is confirmed by reconciled mass balance. The digestion temperature controller is tuned as a ratio-manipulation variable only when the ratio controller is at saturation and the flow-based manipulation cannot provide the required correction. That hierarchy maintains the caustic inventory as the primary buffer, uses the bauxite-to-spent-liquor ratio as the secondary manipulated variable, and reserves temperature for the slow disturbances caused by bauxite mineralogy changes.