Question 3 of 4: Stock Preparation & Paper Machine Wet End — Freeness, Strength Testing, Cleaning, Drying & Fourdrinier Water/Fibre Balance

Question 3: Stock Preparation & Paper Machine Wet End — Freeness, Strength Testing, Cleaning, Drying & Fourdrinier Water/Fibre 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) Canadian Standard Freeness (CSF)

The CSF test (TAPPI T227) measures how readily water drains from a dilute pulp suspension — a practical proxy for the fibres' state of hydration/fibrillation (development) and hence for how the stock will drain on the paper machine wire. A fixed volume (1.0 L) of a standardized (0.3% consistency) pulp suspension is drained through a perforated screen plate in a Canadian Standard Freeness tester; water passing through the screen splits between a direct bottom orifice and a side orifice, and the volume of water that overflows through the side orifice (in mL) is read directly as the CSF value. A freely-draining, coarse, unrefined pulp gives a HIGH CSF (fast drainage, e.g. 700+ mL); as pulp is refined the fibres fibrillate, develop surface fines, and swell (increased water-holding capacity), which progressively slows drainage — CSF decreases as refining proceeds and is used on the mill floor as the primary, fast, on-line proxy for degree of refining/pulp development.

(b) Paper strength testing & refining response

Tensile index (TAPPI T494, N·m/g = breaking tensile strength normalized by basis weight) measures the sheet's in-plane strength, governed largely by inter-fibre bonding; typical unrefined kraft values are roughly 40–60 N·m/g, rising to 80–110+ N·m/g with refining. Tear index (TAPPI T414, mN·m²/g, from Elmendorf tear) measures resistance to crack propagation, governed by individual fibre strength and length; unrefined kraft is typically 10–15 mN·m²/g and, distinctively, tear index initially RISES with light refining (better stress transfer between fibres) then FALLS with heavy refining as fibres are cut/shortened. Burst index (TAPPI T403, kPa·m²/g, from a Mullen burst tester) measures resistance to a multi-directional bursting force and, like tensile, is bonding-dominated; typical unrefined kraft is roughly 2–4 kPa·m²/g, rising with refining to 5–8+ kPa·m²/g. In short: refining monotonically improves tensile and burst (more bonding) at the cost of sheet bulk/porosity and, past an optimum, at the cost of tear (fibre shortening). A PFI mill is a small standardized laboratory refiner (a bar-and-groove rotor against a smooth housing, a fixed number of controlled revolutions at controlled clearance/force) used to refine a lab pulp sample to a series of controlled refining levels so that these strength/freeness properties can be measured and plotted vs. refining energy (a "beating curve"), letting a mill or pulp supplier characterize a pulp's refining response without needing a full-scale mill refiner trial.

(c) Pulp cleaning systems

Centrifugal (hydrocyclone) pulp cleaners remove dense/heavy contaminants (sand, dirt, scale, shives, tramp metal) and low-density contaminants (bark, plastic film) that would otherwise show up as dirt specks or cause web breaks/wire wear on the paper machine, protecting both sheet quality and machine-clothing life. The operating principle is centrifugal separation: stock is fed tangentially into a conical cleaner body, the resulting vortex flings denser-than-fibre particles outward and downward to a small reject (apex) outlet, while the lighter, cleaner fibre stock reports to the overflow (accepts) at the top. A single stage cannot recover all of the good fibre carried out with the rejects, so a full system is staged in cascade — primary cleaners feed their rejects to secondary cleaners, whose rejects feed tertiary cleaners, with each stage's ACCEPTS recycled back to the FEED of the preceding stage — so that essentially all usable fibre is eventually recovered to the primary accepts (to the paper machine) while only a small, concentrated final reject stream is discarded.

(d) Paper machine dryer section

After the press section (typically 40–45% consistency), the remaining water is removed by evaporation, not mechanical pressing: the sheet travels in a serpentine path around a long train of large, steam-heated rotating cast-iron cylinders ("dryer cans"), held in contact with each can's hot surface by a dryer fabric. Steam condensing inside each can (at successively lower pressure/temperature moving down the dryer train, matching the falling drying load as the sheet dries) supplies the latent heat that evaporates water from the sheet surface into the surrounding hood air, which is continuously exhausted (carrying the evaporated moisture away) and made up with fresh, often pre-heated, air.

Condensate removal from each rotating dryer can is essential and non-trivial: condensate collects as a rotating pool/rimming layer inside the can and must be continuously syphoned out (traditionally by a stationary syphon pipe reaching to the can's inner wall, or on modern high-speed machines by rotary/turbulence bars that promote condensate pickup) so it can be returned to the boiler house as hot feedwater. If condensate is allowed to accumulate, it reduces the effective steam-side heat-transfer area (the can partly fills with a static or "cascading" water layer that insulates the steel from the steam), cuts drying capacity, and can cause the can to run out of round/vibrate; efficient condensate removal is therefore critical both for maintaining drying rate (production speed) and for capturing that hot condensate's energy value rather than losing it as flash steam or blowdown.

(e) Fourdrinier wet end

The dilute stock jet exits the headbox onto the moving fourdrinier wire at roughly 0.5–1.0% (jet-to-wire matched to wire speed), immediately beginning to drain by gravity over open deckle/forming boards, then over a series of table rolls or hydrofoils, whose rotating/wedge action pulls a small vacuum behind each element to accelerate drainage while the sheet is still very wet and fragile (a sheet is normally formed — fibre network established — within the first metre or two of the wire). Further along, as the sheet has enough integrity to withstand more aggressive dewatering, flat boxes and vacuum boxes apply increasing levels of applied (pump-generated) vacuum from beneath the wire. Finally the sheet, now self-supporting at roughly 18–22% consistency, is lifted off the wire at the suction couch roll (a perforated roll under high vacuum) and transferred to the press section.

(f) Paper machine water and fibre balance

Given.

Find. A, B, C, D, E, F, G.

Approach. Work the balance block by block, from mixed stock through to the layboy: fibre is conserved in every block (white-water fibre at 0.01% is tracked but tiny). In the printed diagram the recycle C joins the mixed-stock line ABOVE the "A" label, so A is the diluted headbox feed and the headbox passes it straight through: A = 1807 kg/s, and C is the dilution water the white-water loop must supply. D then closes the wire-pit split, E the press section, G follows from fibre conservation through the dryer (the dryer removes only water), F closes the dryer mass balance, and B comes from a dryer energy balance (sensible heat to 100°C plus latent heat of evaporation for F, supplied by steam at 175°C).

1. A — headbox mass balance. The headbox neither adds nor removes water, so its feed equals its discharge: $$A=\boxed{1807\ \text{kg/s}}$$
2. C — mass balance at the recycle junction. Mixed stock plus recycle make A: $$C=A-291.3=1807-291.3=\boxed{1515.7\ \text{kg/s}}$$ Fibre check at the junction: $291.3(0.040)+1515.7(0.0001)=11.652+0.152=11.80$ kg/s, and $11.80/1807=0.653\%$, which matches the printed 0.65%.
3. D — Fourdrinier/white-water split. White water drained at the wire $=1807-57.9=1749.1\ \text{kg/s}$, of which C is recycled: $$D=1749.1-1515.7=\boxed{233.4\ \text{kg/s}}$$ Fibre check across the wire: in $1807(0.0065)=11.75$ kg/s; out $57.9(0.200)+1749.1(0.0001)=11.58+0.17=11.75$ kg/s ✓
4. E — press section mass balance. The 57.9 kg/s web loses 28.9 kg/s of fibre-free press water: $$E=57.9-28.9=29.00\ \text{kg/s}=\boxed{1740\ \text{kg/min}}$$ Fibre check: $29.00(0.40)=11.60$ kg/s vs. 11.58 kg/s in the web ✓
5. G — fibre conservation through the dryer. $$G=\frac{11.60}{0.94}=\boxed{12.34\ \text{kg/s}}\ (1066\ \text{t/day at 94\% AD}=1002\ \text{O.D. t/day})$$
6. F — dryer mass balance. $$F=E-G=29.00-12.34=16.66\ \text{kg/s}=\boxed{999.6\ \text{kg/min}}\ (\approx1000\ \text{kg/min})$$
7. B — dryer energy balance (steam flow). Heat is needed to raise F's water from 55°C to 100°C, then evaporate it, supplied by 175°C steam condensing at h_fg,175°C≈2032 kJ/kg: $$Q=F\times[Cp(100-55)+h_{fg,100^{\circ}C}]=16.66\times[4.18(45)+2257]=40{,}735\ \text{kJ/s}$$ $$B=\frac{40{,}735\times60}{2032}=\boxed{1203\ \text{kg/min}}$$ (Sensible heating of the sheet itself and hood losses are neglected, so this is a minimum steam demand.)