Spirals and Water-Only Cyclones

 Describe the operation and modeling of spirals and water-only cyclones. (p. 263–266)

Operation and Modeling of Spirals and Water-Only Cyclones

Spirals and water-only cyclones are gravity-based separation devices commonly used in mineral processing. They utilize fluid dynamics and particle density differences to separate valuable minerals from gangue. Below is a description of their operation and modeling.

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1. Spirals

Operation

• Principle:
  Spirals use a combination of gravitational and centrifugal forces to separate particles based on density, size, and shape.
• Design:
  • Consist of helical troughs through which slurry flows downward.
  • Lighter particles stay near the outer edge due to lower inertia, while denser particles migrate toward the inner edge.
• Separation:
  • Separation occurs along the spiral’s length, with heavier particles collected at the bottom of the trough and lighter particles carried by the flow to the outer discharge points.

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Modeling of Spirals

1. Partition Function:

   • The partition function describes the probability ($P(d, \rho)$) of particles of size $d$ and density $\rho$ reporting to the concentrate stream.
   • It depends on particle size, density, flow rate, and spiral design.

2. Flow Dynamics:

   • The slurry flow is modeled using hydrodynamic equations to describe the velocity profiles and shear forces along the spiral trough.

3. Stratification Model:

   • Models consider the particle stratification mechanism, where heavier particles are transported closer to the inner edge and lighter particles to the outer edge.

4. Performance Indicators:

   • Recovery ($R$) and grade ($G$) are calculated based on particle distribution in the concentrate and tailings streams.

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2. Water-Only Cyclones

Operation

• Principle:
  Water-only cyclones use centrifugal force to separate particles based on density differences. Unlike conventional hydrocyclones, no dense medium is used.
• Design:
  • Slurry is introduced tangentially at high velocity into a conical or cylindrical vessel.
  • Denser particles are forced outward and downward to the underflow (sink product).
  • Lighter particles are carried by the fluid to the overflow (float product).

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Modeling of Water-Only Cyclones

1. Partition Curve:

   • The partition curve describes the cut density ($\rho_{50}$) and separation sharpness ($n$).
   • The partition function is expressed as: $$P(\rho) = \frac{1}{1 + \left( \frac{\rho}{\rho_{50}} \right)^n}$$ Where:
     • $\rho_{50}$: Density at which 50% of particles report to the underflow.
     • $n$: Sharpness index.

2. Mass Balance Modeling:

   • Mass flow rates of feed, underflow, and overflow streams are calculated using the partition function and feed characteristics.

3. Centrifugal Force Modeling:

   • The particle separation is modeled by considering the balance between centrifugal force and drag force acting on particles.

4. Stokes’ Law and Newtonian Flow:

   • For fine particles, settling velocity is modeled using Stokes’ Law, while for coarser particles, Newtonian flow dynamics are applied.

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Comparison of Spirals and Water-Only Cyclones

Feature	Spirals	Water-Only Cyclones
Operating Principle	Gravitational and centrifugal forces	Centrifugal force
Medium	Water	Water
Particle Size Range	Effective for fine to medium particles	Effective for fine particles
Applications	Coal, iron ore, chromite	Coal, sand, iron ore

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Applications

1. Spirals:

   • Widely used in the beneficiation of coal, iron ore, chromite, and other heavy minerals.
   • Suitable for separating fine to medium-sized particles.

2. Water-Only Cyclones:

   • Commonly used for coal cleaning and the separation of lighter gangue from valuable minerals.
   • Effective for fine particle processing.

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Advantages

• Spirals:

  • Simple design and operation.
  • Low cost and energy consumption.

• Water-Only Cyclones:

  • High separation efficiency for fine particles.
  • No dense medium required, reducing costs.

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Conclusion

The modeling of spirals and water-only cyclones involves partition functions, hydrodynamic equations, and mass balance models. These devices play a critical role in mineral processing by enabling efficient separation of valuable minerals based on density and size.

Reference: R.P. King, Modeling and Simulation of Mineral Processing Systems, p. 263–266.