Pulp, Paper & Packaging Process Engineering, Fourdrinier Wet-End & Dryer Section Balance
Paper Machine Wet-End Dewatering & Steam Drying Formula
Calculate Bone-Dry Fiber Throughput (t/h), Headbox Slurry Flow (t/h), Dryer-Section Water Evaporation Rate (t/h), and Steam Boiler Demand (t/h) across Press-Felt Solids.
Why losing 6% press-section solids from 44% down to 38% hikes paper-machine dryer-section steam consumption by 30%!
On a high-speed **Fourdrinier or Yankee Paper Machine**, `99.35%` water Headbox Stock (`Consistency C_{hb} = 0.65%` bone-dry fiber) jets onto the forming wire (`~20%` solids at couch roll), squeezes mechanically through shoe presses (`Press Exit Solids S_p = 44%`), and evaporates the remaining bound moisture over steam-heated cast-iron dryer cans to **Pope-Reel Finished Solids `S_r = 94%`** (`6%` equilibrium moisture) at **Reel Production Rate `P_{reel}`** (`t/h` as-rolled)! Because thermal evaporation costs `~10x` more energy per tonne of water than mechanical shoe-pressing, **Dryer Water Evaporation `W_{evap} = P_{reel} * ((S_r / S_p) - 1)`** (`t/h`) is non-linearly sensitive to `S_p`: each `1%` drop in press-exit dryness adds `~4%–5%` to **Dryer Live-Steam Demand `M_{steam} = W_{evap} * R_{steam}`** (`t/h`, where `R_{steam} = 1.30–1.55` t steam / t water evaporated)!
Start on a `28.0` t/h Linerboard Machine—Reel_Paper_Production `P_{reel}` = 28.0 t/h (B2), Reel_Dry_Solids `S_r` = 94.0% (B3), Shoe-Press_Exit_Solids `S_p` = 44.0% (B4), Headbox_Consistency `C_{hb}` = 0.65% (B5), and Specific_Steam_Ratio `R_{steam}` = 1.38 t/t (B6). An independent trap is computing evaporation as `28 * (0.94 - 0.44) = 14.0` t/h (wrong—at `44%` solids, the wet sheet entering the dryers actually weighs `28 * (94 / 44) = 59.82` t/h, NOT `28` t/h!). Ask the in-app assistant for a fiber-conservation mass-balance hint: Bone-Dry Fiber equals `26.32` t/h (E2), Headbox Slurry Feed equals `4,049.2` t/h (E3), True Dryer Water Evaporation equals `31.82` t/h (E4), and Live Steam Demand equals `43.91` t/h (E5)!
| TAPPI Paper Machine Mass-Balance KPI (28 t/h Reel @ 94% Solids, C_hb=0.65%) | Formula | Verified Output |
|---|---|---|
| Bone-Dry Fiber Rate (t/h) | Reel_Prod_t_h * (Reel_Solids_Pct / 100) | 26.32 t/h |
| Headbox Slurry Flow (t/h) | Bone_Dry_Fiber_t_h / (Headbox_Consist_Pct / 100) | 4,049.2 t/h (~99.35% whitewater!) |
| Dryer Water Evaporation (t/h) | Reel_Prod_t_h * ((Reel_Solids_Pct / Press_Pct) - 1) | 31.82 t/h (41.26 t/h @ blinded 38% felt!) |
| Dryer Section Steam (t/h) | Water_Evap_t_h * Steam_To_Evap_Ratio | 43.91 t/h (+29.7% -> 56.94 t/h @ 38%!) |
TAPPI TIP 0404-47 Wet-to-Dry Solids Conservation & Dryer Evaporation Formula
Validate `Reel_Production P_{reel} > 0.5` t/h, `Headbox_Consistency C_{hb}` in `[0.1%, 4.0%]`, `Press_Solids S_p` in `[20%, 60%]`, `Reel_Solids S_r` in `(S_p, 99%]`, and `Steam_Ratio R_{steam}` in `[1.0, 2.5]` t/t!
=LET(pr_t, B2, sr_p, B3, sp_p, B4, ch_p, B5, rs_t, B6, we_t, pr_t * ((sr_p / sp_p) - 1), IF(OR(pr_t <= 0.5, ch_p < 0.1, ch_p > 4, sp_p < 20, sp_p > 60, sr_p <= sp_p, sr_p > 99, rs_t < 1, rs_t > 2.5), "Invalid Paper Machine Input", ROUND(we_t * rs_t, 2)))Blinded Press Felt Drop from 44% to 38% Solids Steam Penalty Check (Set B4 = 38%)
Let pitch/fines blind the 3rd-press felt so Press Exit Solids drops from `44%` to `B4 = 38%`: Dryer Water Evaporation E4 surges from `31.82` to `41.26` t/h and Boiler Steam Demand E5 jumps **`+29.7%`** (`43.91 -> 56.94` t/h)—often forcing machine speed back when dryer cans hit steam-header pressure limits!
=IF(ISTEXT(E5), E5, ROUND(B2 * ((B3 / B4) - 1), 2))Try the example
Use the original values or change them to test your understanding.