Modeling of Jigs as Gravity Separation Units

 Discuss the modeling of jigs as gravity separation units. (p. 234–243)

Modeling of Jigs as Gravity Separation Units

Jigs are widely used gravity separation devices that utilize pulsating water to stratify and separate particles based on their size and density. Modeling the performance of jigs involves understanding the processes of particle stratification, movement, and separation. Mathematical models are developed to predict their performance, optimize operating conditions, and improve separation efficiency.

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Principles of Jigging

1. Particle Stratification:

   • During the jigging cycle, particles stratify into layers based on density and size, with denser particles moving to the bottom and lighter particles rising to the top.

2. Hindered Settling:

   • Denser particles settle faster, but their motion is hindered by the surrounding lighter particles, forming a stratified bed.

3. Flowing Film Action:

   • The pulsating water flow creates thin layers where finer and lighter particles are carried upward while coarser and denser particles remain at the bottom.

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Modeling Process for Jigs

1. Partition Function

   • The partition function ($P(d)$) defines the probability of particles of size $d$ reporting to the concentrate (denser fraction).
   • It is represented mathematically as: $$P(d) = \frac{1}{1 + \left( \frac{d}{d_{50}} \right)^n}$$ Where:
     • $d_{50}$: Cut size where 50% of particles report to the concentrate.
     • $n$: Sharpness index indicating the precision of separation.

2. Bed Stratification Modeling

   • The stratification process is modeled based on particle density, size, and jigging parameters (e.g., pulsation frequency and amplitude).
   • Settling velocity equations (e.g., Stokes’ law for fine particles) are used to predict particle movement.

3. Mass Balance Modeling

   • Mass balance equations are applied to the feed, concentrate, and tailings streams to determine material flow rates and size distributions.

4. Kinetic Models

   • Time-dependent models describe how particle stratification evolves over multiple jigging cycles, capturing the dynamic nature of the process.

5. Empirical and Semi-Empirical Models

   • Experimental data are used to develop simplified models that correlate jigging parameters with separation efficiency.

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Mathematical Representation

1. Recovery:

The recovery ($R$) of particles in the concentrate is calculated as:

$$R = \int_0^\infty P(d) \cdot f(d) \, dd$$

Where:

• $P(d)$: Partition function.
• $f(d)$: Feed size distribution.

2. Separation Efficiency:

The efficiency of separation is given by:

$$E = \frac{\text{Mass of correctly separated particles}}{\text{Total mass of particles in feed}}$$

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Key Factors Affecting Jig Performance

1. Feed Characteristics:

   • Particle size distribution and density differences between valuable minerals and gangue.

2. Operating Conditions:

   • Pulsation frequency and amplitude.
   • Water flow rate and bed thickness.

3. Jig Design:

   • Screen aperture, bed height, and type of jig (e.g., diaphragm, piston, air-pulsated).

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Applications of Jig Models

1. Performance Prediction:

   • Models help predict concentrate recovery and grade for different feed and operational conditions.

2. Optimization:

   • Adjusting parameters (e.g., pulsation frequency) to maximize recovery and minimize losses.

3. Simulation:

   • Jig models are integrated into process simulation software (e.g., MODSIM) to simulate overall plant performance.

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Example Calculation

Given Data:

• Feed: 100 tons with 60% heavy minerals (density = 4.5 g/cm³) and 40% gangue (density = 2.6 g/cm³).
• Partition curve parameters:
  • $d_{50} = 2 \, \text{mm}$, $n = 3$.

Steps:

1. Calculate $P(d)$ for different particle sizes using the partition function.
2. Use the feed size distribution to calculate the recovery ($R$) and separation efficiency ($E$).

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Conclusion

Modeling jigs as gravity separation units involves combining partition functions, stratification principles, and mass balance equations to simulate their performance. These models help in predicting recovery, optimizing jigging parameters, and improving the efficiency of separation processes.

Reference: R.P. King, Modeling and Simulation of Mineral Processing Systems, p. 234–243.