Question 1 of 4: Kraft Recovery Cycle — Evaporation, Recovery Boiler, Tall Oil, Digesters & Batch-Digester Mass Balance

Question 1: Kraft Recovery Cycle — Evaporation, Recovery Boiler, Tall Oil, Digesters & Batch-Digester Mass Balance (a)–(e) 10 marks each, (f) 20 marks

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Multiple-effect evaporation of kraft black liquor

Weak black liquor leaves the brown-stock washers at roughly 12–18% dissolved solids (DS) — far too dilute to burn. A multiple-effect evaporator (MEE) train concentrates it to 45–55% DS (the feed to a direct-contact or non-direct-contact recovery boiler) using the vapour boiled off one effect as the heating medium for the next, so only the first effect needs live (prime) steam. Liquor and vapour normally flow counter-currently: the thinnest liquor enters the coolest, lowest-pressure effect (fed by vapour bled from the hotter effects upstream) and is progressively concentrated as it is pumped forward through hotter effects, while the vapour train runs the opposite direction from the hottest (first) effect — heated by live steam — down to the coolest (last) effect, whose vapour is finally condensed in a surface condenser under vacuum. Concentrating the liquor in the LAST (hottest) effects, rather than the first, avoids scaling/boiling-point elevation problems at the point where the liquor is most viscous and most prone to organic fouling.

Steam economy is the ratio of water evaporated to live (prime) steam consumed, $\text{SE}=\dot m_{\text{evap}}/\dot m_{\text{live steam}}$. Each successive effect re-uses the latent heat already paid for once, so steam economy scales roughly with the number of effects: an N-effect train approaches a theoretical steam economy of about N kg evaporated per kg live steam, discounted for boiling-point elevation, flash losses and non-condensables. For a well-designed 6-stage kraft black-liquor evaporator section, a typical achieved steam economy is 4.5–5.5 kg water evaporated per kg of 100 psig live steam (vs. a theoretical ceiling near 6), the shortfall coming mainly from the liquor's boiling-point rise (BPE, which grows with % DS) and from any effects vented rather than cascaded forward.

(b) Kraft recovery boiler — steam generation and chemical recovery

The recovery boiler is simultaneously a power boiler and a chemical reactor. Concentrated (45–80% DS) black liquor is sprayed through liquor guns onto the lower furnace walls, where it forms a char bed on the floor. Combustion is staged: primary air enters low (below/at the char bed) in a reducing, oxygen-starved atmosphere so the inorganic sodium/sulphur species are reduced rather than oxidized to sulphate; secondary and tertiary air, admitted higher up, complete combustion of the organic (mostly lignin-derived) fraction of the liquor solids, releasing the heat that raises high-pressure steam in the boiler's water-wall tubes and superheater — steam typically used to drive a back-pressure/extraction turbine-generator, i.e. the recovery boiler is the mill's principal source of both process steam and electrical power.

Chemically, the furnace's job is to convert the spent (organically-bound and oxidized) sodium and sulphur compounds back into a re-usable, smeltable form. The dominant reduction reaction in the char bed is $$Na_2SO_4 + 2C \rightarrow Na_2S + 2CO_2$$ (sulphate reduced to sulphide by the carbon in the char), while sodium bound in organic salts is oxidized and released as inorganic sodium carbonate. The molten mixture of Na₂CO₃ and Na₂S that collects on the furnace floor (the smelt) is drained continuously through smelt spouts into the smelt dissolving tank, where it is dissolved in weak wash (dilute wash-liquor from the causticizing plant) to form green liquor, which is then causticized (reacted with lime) to regenerate white liquor (NaOH + Na₂S) for the digesters.

(c) Tall Oil

Tall oil (Swedish for "pine oil") is a mixture of fatty acids, resin (rosin) acids and unsaponifiable neutral compounds recovered as a by-product of kraft pulping. During alkaline (kraft) cooking, the extractives naturally present in the wood — principally the fatty- and resin-acid esters in resin canals — are saponified by the free NaOH in the white liquor, forming sodium soaps. These soaps are far less dense than the black liquor and, being surface-active, rise and skim off as a separate layer on top of the liquor in the storage/evaporator feed tanks; this skimmed material is crude tall oil soap. The soap is collected, acidulated (typically with sulphuric acid) to convert the sodium soaps back to the free fatty/resin acids and split the emulsion, yielding crude tall oil (CTO), which is then fractionally vacuum-distilled off-site into fatty-acid, rosin-acid and pitch/head fractions for use in inks, soaps, adhesives, and oleochemicals.

Softwood species yield far more tall oil than hardwoods — typically 20–50 kg CTO per tonne of pulp for resin-rich softwoods such as pine, versus essentially negligible amounts from hardwoods. This is because resin (fatty/resin acid) content is concentrated in the resin canals unique to softwood anatomy; hardwoods have no resin canals and correspondingly very low extractives content, so kraft mills that recover tall oil economically are invariably softwood (and especially pine) kraft mills.

(d) Batch digesters vs. the conventional Kamyr (continuous) digester

Batch digesters cook a discrete, weighed charge of chips and liquor as a single closed vessel taken through fill–heat-up–cook–blow steps, then emptied and refilled. Advantages: simple, robust, individually controllable (any one vessel's schedule can be adjusted or shut down without stopping the others), tolerant of chip-quality variability (uniform liquor-to-wood contact within each charge), and lower capital cost per unit for smaller mills. Disadvantages: cyclic (not steady-state) heat and chemical demand causes surges in the recovery cycle and requires blow-heat-recovery equipment to avoid wasting the flash steam released at each blow; lower digester utilization (time lost to fill/heat/blow); and typically higher steam consumption per tonne of pulp than continuous cooking, because each batch's sensible heat is largely lost at blow unless heat is recovered.

The Kamyr (continuous) digester is a single tall pressure vessel through which chips and liquor move continuously (usually co-current in an impregnation zone, then through cooking and counter-current wash/extraction zones) at steady state. Advantages: smooth, steady steam and chemical demand on the recovery cycle; higher thermal efficiency (heat is recovered internally via counter-current liquor extraction, rather than lost at a blow); higher digester capacity per unit of vessel volume/footprint; more consistent pulp quality once at steady state. Disadvantages: much higher capital cost, more complex instrumentation and control, less tolerant of chip-quality upsets (a disturbance propagates down the whole column), and a full outage is required to correct a serious process upset (no way to isolate a single "batch"). In general, a continuous (Kamyr) digester is more advantageous for a large, steady-throughput kraft line because of its lower specific steam consumption and higher utilization, while batch digesters remain more advantageous for smaller mills or those cooking varied furnishes/grades, where flexibility matters more than marginal steam economy.

(e) Raising a low Kappa number out of a continuous digester

Kappa number tracks residual lignin, so a Kappa reading below target means the pulp has been over-delignified relative to setpoint. The operator has several coupled variables to bring the Kappa number back up (i.e. reduce delignification severity): (i) reduce cooking temperature in the cook zone (delignification rate is strongly Arrhenius-dependent on temperature, so even a small reduction slows lignin removal significantly); (ii) reduce residence time in the cook zone, by increasing chip throughput/production rate or adjusting the liquor circulation rate that sets the cook-zone/extraction-zone boundary; (iii) reduce effective alkali charge (lower liquor-to-wood ratio or lower EA% applied at the impregnation/cook circulation points), since less alkali available means less lignin dissolved for the same time/temperature; and (iv) reduce cooking (H-factor) severity more generally — H-factor combines time and temperature into a single control target, and is the parameter most digester control systems actually manipulate to hold Kappa on target. All of these adjustments are made by trimming the setpoints fed to the digester's liquor heaters/circulation loops and to the extraction-zone level (which sets cook-zone residence time), not by any single "valve."

(f) Batch-digester house mass balance

Given.

Find. (1) white liquor volume, L/batch; (2) black liquor volume, L/batch, and its purpose; (3) brown-stock production rate; (4) recausticizing white-liquor flow (L/min), stoichiometric lime (CaO) demand, and lime mud (CaCO₃) produced.

Approach. Work one digester's charge from wet-chip volume down to O.D. wood mass, apply the EA% and L/W definitions to get white- and black-liquor volumes, then scale to a house-wide rate. Parts (3) and (4) both require converting "per batch" quantities to a rate, which needs a batch (cook) cycle time — not stated in the question. Per the exam's own Note 1 ("if doubt exists…submit a clear statement of any assumptions made"), a typical total batch-digester cycle time (fill–cook–blow) of 4.0 hours is assumed and flagged below; with 6 digesters staggered evenly across that cycle, the house discharges one digester's batch every 4.0/6 h, i.e. 1.5 batches/h. For part (4), the white liquor's NaOH/Na₂S/Na₂CO₃ split is backed out from EA and sulphidity, and the causticizing reaction Na₂CO₃+Ca(OH)₂→2NaOH+CaCO₃ (lime slaked in situ, CaO+H₂O→Ca(OH)₂) fixes the lime and lime-mud stoichiometry.

1. Charge mass per digester. Wet-chip volume charged $=0.80\times175=140\ \text{m}^3$, so $$m_{wet}=140\times285=39{,}900\ \text{kg wet wood/batch}\qquad m_{OD}=39{,}900\times(1-0.45)=\boxed{21{,}945\ \text{kg O.D. wood/batch}}$$
2. (1) White liquor volume. EA required $=0.150\times21{,}945=3291.8\ \text{kg EA}$; at 93 g EA/L: $$V_{WL}=\frac{3291.8\times1000}{93}=\boxed{35{,}395\ \text{L/batch}}\ (35.4\ \text{m}^3/\text{batch})$$
3. (2) Black liquor volume. Total liquor required at L/W=4.1 L per kg O.D. wood: $$V_{total}=4.1\times21{,}945=89{,}975\ \text{L/batch}$$ By the standard kraft convention (Smook Ch. 5) the "liquor" in the L/W ratio is ALL the free liquid in the digester — white liquor, black liquor AND the water carried in with the chips. The chips bring $39{,}900\times0.45=17{,}955$ kg $\approx17{,}955$ L of water, so $$V_{BL}=V_{total}-V_{WL}-V_{chip\ water}=89{,}975-35{,}395-17{,}955=\boxed{36{,}624\ \text{L/batch}}\ (36.6\ \text{m}^3/\text{batch})$$ (The white-liquor density of 1.09 g/mL is not needed: EA is quoted per litre and the L/W ratio is on a volume basis.) The recycled black liquor is added to raise the liquor-to-wood ratio to the level needed for adequate chip saturation, uniform liquor circulation and heat transfer through the charge — not to add cooking chemical — while simultaneously returning residual NaOH/Na₂S left in that black liquor to the cook (chemical economy) instead of drawing an equivalent extra volume of fresh white liquor.
4. (3) Brown-stock production rate. Pulp per batch per digester $=0.54\times21{,}945=11{,}850\ \text{kg O.D. pulp}$. With the assumed 4.0 h cycle, the house (6 digesters, staggered) discharges $6/4.0=1.5$ batches/h: $$\dot m_{pulp}=11{,}850\times1.5=17{,}776\ \text{kg/h}=\boxed{426.6\ \text{O.D. tonnes/day}}\ (\approx474\ \text{ADMT/day at 90\% AD})$$
5. (4a) Recausticizing white-liquor flow. $$\dot V_{WL}=35{,}395\ \text{L/batch}\times1.5\ \text{batch/h}\div60=\boxed{884.9\ \text{L/min}}$$
6. (4b) White-liquor NaOH/Na₂S/Na₂CO₃ split. With EA=NaOH+0.5Na₂S (as Na₂O) and sulphidity S=Na₂S/(NaOH+Na₂S): $$\text{Na}_2S=\frac{S}{1-S}\,\text{NaOH}=0.3889\,\text{NaOH}\ \Rightarrow\ \text{NaOH}=\frac{93}{1+0.5(0.3889)}=\boxed{77.86\ \text{g/L (as Na}_2\text{O)}}\qquad \text{Na}_2S=30.28\ \text{g/L}$$ Causticizing efficiency CE=NaOH/(NaOH+Na₂CO₃) gives the residual (uncausticized) carbonate that rides through to the digesters as dead load: $$\text{Na}_2CO_3=\text{NaOH}\left(\frac{1}{CE}-1\right)=77.86(1/0.82-1)=17.09\ \text{g/L (as Na}_2\text{O)}$$
7. (4c) Lime and lime-mud stoichiometry. The slaked-lime causticizing reaction is $\text{Na}_2\text{CO}_3+\text{Ca(OH)}_2\rightarrow2\text{NaOH}+\text{CaCO}_3$ (1:1:1 molar), with lime itself slaked in situ, $\text{CaO}+\text{H}_2\text{O}\rightarrow\text{Ca(OH)}_2$. The lime consumed is set by the carbonate that IS causticized, i.e. by the NaOH formed (the 17.09 g/L left over never meets lime). With Na₂O = 2(23.0)+16.0 = 62.0, CaO = 56.1 and CaCO₃ = 100.1 g/mol from the given atomic masses: $$n_{Na_2CO_3,\ causticized}=\frac{77.86}{62.0}=1.2558\ \text{mol/L WL}$$ $$\text{CaO required}=1.2558\times56.1=70.45\ \text{g/L WL}\qquad \text{CaCO}_3\text{ (lime mud)}=1.2558\times100.1=125.7\ \text{g/L WL}$$ Scaling by the white-liquor flow (884.9 L/min): $$\dot m_{CaO}=70.45\times884.9/1000=\boxed{62.34\ \text{kg/min}}\ (89.8\ \text{t/day})\qquad \dot m_{CaCO_3}=125.7\times884.9/1000=\boxed{111.2\ \text{kg/min}}\ (160.2\ \text{t/day, to the lime kiln})$$ The 92% reduction efficiency does not enter the lime balance: it fixes how much sulphur leaves the furnace as Na₂SO₄ dead load rather than Na₂S, not how much carbonate is causticized.