Question 4 of 6: Stock Testing, Pulp Cleaning, Paper Machine Drying & Fourdrinier Wet End — Water/Fibre Balance

Question 4: Stock Testing, Pulp Cleaning, Paper Machine Drying & Fourdrinier Wet End — 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) drains a fixed volume (1 L) of a dilute (≈0.3%) pulp suspension through a standard perforated-plate/orifice apparatus under a fixed hydraulic head, and measures the volume of water (mL) that escapes through a SIDE orifice rather than the main bottom orifice — a fast-draining (coarse/unrefined) stock produces a low back-pressure, small side flow, i.e. a HIGH CSF reading; a slow-draining (highly refined, fibrillated) stock backs up and forces MORE water out the side orifice, i.e. a LOW CSF reading. CSF is therefore an inverse proxy for a stock's resistance to drainage/water release rather than a direct physical measurement of fibre structure. As pulp is refined (mechanically treated to fibrillate and cut fibres, increasing bonding surface area), the fibre mat becomes progressively harder to drain, so Canadian Standard Freeness decreases with increasing refining.

(b) Paper strength tests

Tensile index (TAPPI T494, N·m/g) is measured by pulling a standard strip of paper to failure in a tensile tester and normalizing breaking load by sample width and basis weight; typical well-refined Kraft pulp gives 60–100 N·m/g. Tear index (TAPPI T414, mN·m²/g, Elmendorf tester) measures the force to propagate a pre-cut tear through a stack of sheets, normalized by basis weight; typical Kraft values are 8–15 mN·m²/g. Burst index (TAPPI T403, kPa·m²/g, Mullen tester) measures the hydraulic pressure needed to rupture a clamped sheet, normalized by basis weight; typical Kraft values are 3–6 kPa·m²/g. As refining increases, fibres are fibrillated and cut, increasing inter-fibre bonded area: tensile and burst index both increase with refining (more bonding → stronger sheet in tension/bursting), while tear index typically increases to a maximum and then DECREASES at high refining, because tear resistance depends on individual fibre strength and length as much as bonding, and heavy refining progressively cuts/weakens fibres even as it improves bonding. The PFI Mill is a small, standardized laboratory refiner (TAPPI T248) used to refine a lab-scale pulp sample through a controlled number of revolutions, allowing a mill to generate a freeness/strength "refining curve" (strength vs. CSF or vs. PFI revolutions) for a furnish on a small sample before committing to full-scale refiner settings.

(c) Pulp cleaning systems

Pulp cleaning systems remove dense contraries — sand, grit, dirt specks, shives and other high-density debris — from the stock immediately before the pulp or paper machine, protecting downstream equipment (headbox slice, wire, press felts) from abrasive wear and preventing visible sheet defects. The principle of operation is centrifugal (cyclonic) separation: stock is pumped tangentially into a conical vessel (a "cleaner"), setting up a strong vortex; denser contaminants are thrown to the outer wall and spiral down to a small reject (apex) outlet, while the lighter, cleaner fibre stock reports to the overflow (accept) outlet at the top. A typical system is arranged as a multi-stage cascade — primary, secondary and (often) tertiary banks of cleaners — because each individual cleaner's reject stream still carries some usable fibre; that reject is fed to the next stage, whose OWN accept is recycled back to the previous stage, so that only the final-stage reject (concentrated sand/grit/shives) is actually discarded, minimizing fibre loss.

(d) Paper machine drying & condensate removal

In the dryer section, the wet sheet (leaving the press section at roughly 40–50% solids) is passed in a serpentine path over a long train of internally steam-heated, rotating cast-iron dryer cans (cylinders), held against each can by a dryer fabric; heat conducts through the can wall and evaporates the sheet's remaining water, progressively raising solids to ≥90% by the reel. Each can is supplied with steam at its cylinder interior and continuously accumulates condensate on the inner wall as the steam gives up its latent heat; this condensate must be continuously removed (typically by a siphon pipe reaching to the can's inner surface, connected to a rotary joint and blown out under differential pressure) because condensate that is allowed to pool inside a rotating can unbalances the can and, more importantly, forms an insulating water layer between the steam and the can wall that sharply reduces the heat-transfer coefficient (and hence drying rate) for that can — efficient, continuous condensate removal is therefore essential to maintaining both drying capacity and can balance/vibration control.

(e) Fourdrinier wet end & drainage

Stock leaves the headbox as a thin, high-speed jet onto the forming fabric (wire); drainage proceeds through a sequence of elements of INCREASING intensity as the sheet consolidates and can no longer be drained by gravity alone: first the stationary forming board and rotating table rolls (gravity/hydraulic drainage, while consistency is still low, ≈0.5–1%), then stationary foils (each foil's trailing edge creates a small vacuum pulse as the wire passes over it, giving mild vacuum-assisted drainage as consistency rises), then enclosed vacuum boxes (externally-applied vacuum, needed once the sheet is too consolidated for foils alone), and finally the couch roll (a perforated roll under strong internal vacuum that completes sheet formation, typically to ≈20% consistency, before the sheet is transferred to the press section).

(f) Paper machine water and fibre balance

Given.

Find. A, B, C, D, E, F, G (kg/s).

Approach. Solve the junction (Mixed Stock + C → A) as a simultaneous mass/fibre balance (2 equations, 2 unknowns: A, C). Get B from fibre conservation across the headbox (only A enters the headbox). Get D from a total mass balance across the Fourdrinier. Get E directly from the Press-section total mass balance (this closes exactly against the given numbers, confirming those flows are reliable). Get G from the stated final-production spec (converted through the 90%-AD ADMT convention and the stream's own 94% actual consistency), and F follows from a mass balance on the dryer's stock path (steam is a separate utility stream, not part of the stock mass balance).

1. Junction: Mixed Stock + C → A. Simultaneous mass and fibre balance ($A=291.3+C$; $A(0.0065)=291.3(0.04)+C(0.0001)$): $$C=\frac{291.3(0.04-0.0065)}{0.0065-0.0001}=\boxed{1524.8\ \text{kg/s}}\qquad A=291.3+1524.8=\boxed{1816.1\ \text{kg/s}}$$
2. Headbox: A → B (fibre-conserving). Only A enters the headbox, so its fibre content is conserved into B: $$B=\frac{A(0.0065)}{0.0055}=\frac{1816.1\times0.0065}{0.0055}=\boxed{2146.4\ \text{kg/s}}$$
3. Fourdrinier: B → 67.9 (to Press) + D (excess white water). Total mass balance: $$D=B-67.9=2146.4-67.9=\boxed{2078.5\ \text{kg/s}}$$
4. Press section: 67.9 → E (to Dryer) + 28.9 (press white water). This is a simple, exactly-closing mass balance: $$E=67.9-28.9=\boxed{39.0\ \text{kg/s}}$$
5. G: final production spec. $1000\ \text{ADMT/d}\times0.90=900\ \text{O.D. t/day}$ (90% AD convention); dividing by G's OWN actual 94% AD consistency: $$G=\frac{(900/0.94)\times1000}{86{,}400}=\boxed{11.08\ \text{kg/s}}$$
6. Dryer stock-path balance: E → F (moisture to atmosphere) + G. Steam is a separate heating utility, not part of the stock mass balance: $$F=E-G=39.0-11.08=\boxed{27.92\ \text{kg/s}}$$