Storage and conveying of solids: belt, screw, pneumatic conveyors

Why it matters

Every solids plant stores raw materials and products in piles, bins and silos and moves them between units by belts, screws, elevators or pipelines. Poor bin design causes arching, rat-holing, flooding and even structural failure; a badly chosen conveyor degrades the product, wears out quickly or wastes power. These are routine design decisions for a process engineer.

Key ideas

Properties of bulk solids. Granular solids differ from liquids in three ways that drive design:

• They can sustain shear stress at rest, so a pile stands at the angle of repose (typically 30–45° for free-flowing solids) instead of levelling out.
• Pressure in a bin does not increase linearly with depth: wall friction carries much of the weight, and pressure tends to a maximum value (Janssen).
• The pressure on the walls is lower than the vertical pressure, by the ratio K' (lateral pressure ratio, typically about 0.35–0.6). Bulk density, particle size, cohesiveness, moisture, abrasiveness and friability all affect choices. The internal friction angle and wall friction angle should be measured (shear cell) or taken from data.

Storage. Coarse, robust solids are stored in outdoor piles. Valuable or fine solids go into bins (short) or silos (tall) with a conical hopper. Two flow patterns occur on discharge:

• Mass flow: all the material moves when any is withdrawn; first-in, first-out; no dead zones; needs steep, smooth hopper walls.
• Funnel (core) flow: only a central channel moves; cheaper, shorter hopper, but stagnant zones, segregation, possible rat-holing and erratic flooding. Cohesive powders may form a stable arch over the outlet; the outlet must be wider than the critical arching dimension, and flow aids (vibrators, air pads) are used. Discharge rate from an orifice is independent of head (unlike a liquid), which makes gravity feeders steady.

Janssen's equation. A force balance on a horizontal slice in a vertical bin, with wall friction coefficient μ' and lateral pressure ratio K', gives the vertical pressure at the base P_B as a function of the solids height Z_T. At large depth P_B approaches r·ρ_B·g/(2μ'K'), so tall silos do not need bottoms designed for the full hydrostatic head — but the walls and the hopper transition must be designed for the high, uneven loads during discharge (from codes of practice).

Conveyors.

• Belt conveyors: an endless belt on idlers, usually troughed. Highest capacity and longest distances (kilometres) at low power per tonne; inclination limited to about 15–20° for most materials; dusty open transfer points unless covered.
• Screw conveyors: a helical flight rotating in a trough or tube. Compact, enclosed, can mix or heat while conveying, and feed at a controlled rate; but power-hungry, short lengths (tens of metres), capacity falls on inclines, and abrasive or friable solids wear the screw or break.
• Bucket elevators: buckets on a chain or belt lift solids vertically, discharging by centrifugal or gravity action at the top.
• Flight, apron and drag-chain conveyors for heavy, hot or abrasive materials.
• Pneumatic conveyors: solids carried by air or gas through a pipe, pushed by pressure or drawn by vacuum. Enclosed, dust-free and flexible in routing; but higher power per tonne and wear at bends. Dilute-phase systems use high gas velocity (above the saltation velocity, roughly 15–30 m/s) with low solids loading, causing attrition; dense-phase systems move solids as slugs or plugs at low velocity, gentler on the product.

Formulas

Janssen: P_B = [r·ρ_B·g / (2·μ'·K')]·[1 − exp(−2·μ'·K'·Z_T / r)] Maximum: P_B,max = r·ρ_B·g / (2·μ'·K') Belt conveyor: ṁ = ρ_B·A·v Screw conveyor: Q = (π/4)·(D² − d²)·S·N·φ, ṁ = ρ_B·Q Lifting power (minimum): P = ṁ·g·H

• P_B: vertical pressure at bin base (Pa); r: bin radius (m); ρ_B: bulk density (kg/m³); μ': wall friction coefficient (−); K': lateral pressure ratio (−); Z_T: solids height (m); ṁ: mass flow (kg/s); A: cross-section of the load on the belt (m²); v: belt speed (m/s); D, d: screw and shaft diameters (m); S: pitch (m); N: speed (rev/s); φ: fraction of trough cross-section filled (typically 0.15–0.45, from the manufacturer's tables); H: lift (m). Friction, idler and drive losses add to the lifting power; use manufacturer or handbook correlations for real drive ratings.

Worked examples

Example 1 (standard): belt conveyor. A troughed belt carries ore (ρ_B = 1600 kg/m³) with a load cross-section of 0.08 m² at 2.5 m/s and lifts it 10 m. Find the capacity and the minimum lifting power.

1. ṁ = ρ_B·A·v = 1600 × 0.08 × 2.5 = 320 kg/s = 1152 t/h.
2. P = ṁ·g·H = 320 × 9.81 × 10 = 31 400 W = 31.4 kW (excluding friction and drive losses).

Example 2 (GATE level): silo base pressure. A cylindrical silo 6 m in diameter holds grain (ρ_B = 800 kg/m³) to a height of 20 m. With μ' = 0.4 and K' = 0.4, find the base pressure and compare with the hydrostatic value.

1. P_B,max = r·ρ_B·g/(2μ'K') = 3 × 800 × 9.81/(2 × 0.4 × 0.4) = 23 544/0.32 = 73 575 Pa.
2. Exponent: 2μ'K'Z_T/r = 2 × 0.16 × 20/3 = 2.133; exp(−2.133) = 0.1184.
3. P_B = 73 575 × (1 − 0.1184) = 64 900 Pa ≈ 64.9 kPa.
4. Hydrostatic estimate ρ_B·g·Z_T = 800 × 9.81 × 20 = 157 kPa, so wall friction carries about 59% of the weight.

Common mistakes

• Calculating bin-bottom pressure as ρ_B·g·h like a liquid; it greatly overestimates base pressure and says nothing about wall loads.
• Writing belt capacity as A·v·ρ and calling the result m³/s. A·v is volumetric (m³/s); multiplying by bulk density gives kg/s.
• Using particle density instead of bulk density in conveyor and bin calculations.
• Using screw conveyors for long distances or highly abrasive solids.
• Assuming pneumatic conveying is gentle; dilute-phase systems cause attrition and wear.

For GATE CH

Expect: Janssen base pressure and its limiting value; belt or screw conveyor capacity; minimum lifting power; conceptual questions on angle of repose, mass versus funnel flow, arching, and choice between belt, screw, bucket and pneumatic conveyors. Practise the Janssen exponent carefully, since the radius (not the diameter) appears.

Quick check

1. Does the base pressure in a tall silo keep increasing linearly with height?
2. What is the volumetric capacity of a belt with load area 0.1 m² moving at 2 m/s?
3. Which flow pattern gives first-in, first-out discharge?
4. Name one disadvantage of dilute-phase pneumatic conveying. Answers: 1. No; it approaches r·ρ_B·g/(2μ'K'). 2. 0.2 m³/s. 3. Mass flow. 4. High power per tonne, or particle attrition and pipe wear.