Mineral Processing & Tailings Dewatering, Coe & Clevenger (1916) Continuous Thickener Area
Coe-Clevenger Continuous Thickener Area & Solids Flux
Calculate Coe-Clevenger Thickener Clarification Area (m²), Required Circular Tank Diameter (m), Clarified Overflow Water Rate (m³/h), and Daily Solids Loading Flux (t/m²·d).
Skip flocculant dosing on clay-rich tailings (settling rate drops from 1.35 to 0.38 m/h) and a 19.4 m Coe-Clevenger thickener slimes its overflow launder unless widened to 36.5 m!
**Harry S. Coe and Galen H. Clevenger (`1916`)** established the foundational steady-state water-upflow mass balance for **Continuous Gravity Slurry Thickeners**: when `W` (`t/h`) of dry ore solids enter at **Liquid-to-Solid Mass Dilution `F`** (`t water / t dry solids`, e.g. `4.20` = `19.2 wt%` solids) and rake underflow pumps out at **Target Underflow Dilution `D`** (`e.g. 0.85` = `54.1 wt%` solids), **Upward Clarified Water Overflow `Q_{ovf} = W * (F - D)`** (`m³/h` for `SG_w = 1.0` t/m³) MUST rise slower than the **Limiting Hindered Zone-Settling Velocity `R`** (`m/h`) across every intermediate dilution layer! Applying Design Scale-Up Safety Factor `SF` (`1.20–1.35` for feedwell turbulence) yields **Required Thickener Area `A = ((F - D) * W * SF) / R`** (`m²`), **Tank Diameter `D_{tank} = sqrt((4 * A) / pi)`** (`m`), and **Solids Flux `G_s = (W * 24) / A`** (`t/(m²·day)`)!
Verify on a Flocculated Copper Concentrator Tailings Thickener—Dry_Solids_Feed `W` = 95.0 t/h (B2), Limiting_Dilution `F` = 4.20 w/w (B3), Underflow_Dilution `D` = 0.85 w/w (B4), Cylinder_Settling_Rate `R` = 1.35 m/h (B5), and Area_Safety_Factor `SF` = 1.25 (B6): Required Clarification Area equals `294.7` m² (E2), Circular Tank Diameter equals **`19.37` m** (E3), Reclaimed Overflow Process Water equals `318.25` m³/h (E4), and Solids Loading Flux equals `7.74` t/(m²·day) (E5)!
| Coe-Clevenger Continuous Thickener KPI (95 t/h Solids, F=4.20, D=0.85, SF=1.25) | Formula | Verified Output |
|---|---|---|
| Coe-Clevenger Area A (m²) | ((Dilution_F - Underflow_D) * Solids_t_hr * SF) / R_m_hr | 294.7 m² (1,046.9 m² un-flocculated!) |
| Required Tank Diameter (m) | SQRT((4 * Area_m2) / PI()) | 19.37 m (36.51 m without PAM polymer!) |
| Clarified Overflow Water (m³/h) | Solids_Feed_t_hr * (Dilution_F - Underflow_D) | 318.25 m³/h recycled plant water |
| Solids Flux Loading (t/m²·d) | (Solids_Feed_t_hr * 24) / Area_m2 | 7.74 t/m²·d (2.18 t/m²·d clay-limited) |
Coe & Clevenger (1916) Limiting Dilution Zone-Settling Area & Flux Formula
Validate `Dry_Solids W > 0` t/h, `Underflow_Dilution D` in `[0.25, 5.0]`, `Feed_Dilution F >= D + 0.2` up to `30`, `Zone_Settling_Rate R` in `[0.05, 35]` m/h, and `Safety_Factor SF` in `[1.0, 2.0]`!
=LET(ws_t, B2, fd_w, B3, ud_w, B4, rz_m, B5, sf_a, B6, ar_m, ((fd_w - ud_w) * ws_t * sf_a) / rz_m, IF(OR(ws_t <= 0, ud_w < 0.25, ud_w > 5, fd_w < ud_w + 0.2, fd_w > 30, rz_m < 0.05, rz_m > 35, sf_a < 1, sf_a > 2), "Invalid Thickener Input", ROUND((ws_t * 24) / ar_m, 2)))Clay-Slime Ore Lens / Polymer Pump Trip (`R = 0.38` m/h) Mud-Line Carryover Check
Hit a smectite clay lens or lose polyacrylamide flocculant feed so settling velocity drops to `B5 = 0.38` m/h: Required Area E2 jumps `3.55x` to **`1,046.9` m²** (`36.51` m diameter in E3, Solids Flux E5 = `2.18` t/m²·d)—meaning an existing `19.4` m tank immediately pushes its mud bed over the peripheral weir!
=IF(ISTEXT(E5), E5, LET(ar_m, ((B3 - B4) * B2 * B6) / B5, ROUND(SQRT((4 * ar_m) / PI()), 2)))Try the example
Use the original values or change them to test your understanding.