Template:Model theory (Text, Hydrocyclone, Roping): Difference between revisions

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Several methods are available to identify the potential for ''roping'' discharge from a hydrocyclone underflow.
Several methods are available to identify the potential for ''roping'' discharge from a hydrocyclone underflow.


'''Plitt''' proposed that roping may occur when when the volumetric feed rate to the cyclone, <math>M_{SU}</math> (m<sup>3</sup>/h), exceeds a solids capacity limit:{{Dubey et al. 2017}}
'''Plitt''' proposed that roping may occur when when the volumetric feed rate to the cyclone, <math>M_{\rm SU}</math> (m<sup>3</sup>/h), exceeds a solids capacity limit:{{Dubey et al. 2017}}


:<math>M_{SU} > 0.35 {D_u}^{2.35}</math>
:<math>M_{\rm SU} > 0.35 {D_{\rm u}}^{2.35}</math>


'''Plitt''' further proposed a limit to the volume fraction of solids in cyclone underflow, <math>\Phi_L</math> (% v/v), of:
'''Plitt''' further proposed a limit to the volume fraction of solids in cyclone underflow, <math>\Phi_{\rm L}</math> (% v/v), of:


:<math>\Phi_L = 62.3 \left [ 1 - \exp \left ( - \dfrac{d_u}{60} \right ) \right ]</math>
:<math>\Phi_{\rm L} = 62.3 \left [ 1 - \exp \left ( - \dfrac{d_{\rm u}}{60} \right ) \right ]</math>


where <math>d_u</math> is the mass median particle size of the underflow, computed here as the ''P<sub>50</sub>'' (μm).
where <math>d_{\rm u}</math> is the mass median particle size of the underflow, computed here as the ''P<sub>50</sub>'' (μm).


The '''SPOC''' criterion indicates roping may occur when:{{Napier-Munn et al. (1996)}}
The '''SPOC''' criterion indicates roping may occur when:{{Napier-Munn et al. (1996)}}


:<math>C_{VU} > 56 + 0.2 (C_V - 20)</math>
:<math>C_{\rm VU} > 56 + 0.2 (C_{\rm V} - 20)</math>


where <math>C_{VU}</math> is the percentage volume fraction of solids in the underflow stream (% v/v). The SPOC criterion is only valid when <math>C_{VU}<35 \text{ }\%\text{ v/v}</math>.
where <math>C_{\rm VU}</math> is the percentage volume fraction of solids in the underflow stream (% v/v). The SPOC criterion is only valid when <math>C_{\rm V}<35 \text{ }\%\text{ v/v}</math>.


Investigations by '''Bustamante''' (1991) and '''Concha''' et al. (1996) led to the limiting values of cyclone geometry in Table 1:{{Gupta and Yan (2016)}}
Investigations by '''Bustamante''' (1991) and '''Concha''' et al. (1996) led to the limiting values of cyclone geometry in Table 1:{{Gupta and Yan (2016)}}


:{| class=wikitable style="width: 24%;"
:{| class=wikitable style="width: 30%;"
|+ Table 1. Transition from spray to roping discharge (after Gupta and Yan, 2016).{{Gupta and Yan (2016)}}
|+ Table 1. Transition from spray to roping discharge (after Gupta and Yan, 2016).{{Gupta and Yan (2016)}}
! Source
! Source
! <math>D_u/D_o</math>
! <math>D_{\rm u}/D_{\rm o}</math>
! Condition
! Condition
|-
|-

Latest revision as of 13:22, 2 March 2023

Several methods are available to identify the potential for roping discharge from a hydrocyclone underflow.

Plitt proposed that roping may occur when when the volumetric feed rate to the cyclone, (m3/h), exceeds a solids capacity limit:[1]

Plitt further proposed a limit to the volume fraction of solids in cyclone underflow, (% v/v), of:

where is the mass median particle size of the underflow, computed here as the P50 (μm).

The SPOC criterion indicates roping may occur when:[2]

where is the percentage volume fraction of solids in the underflow stream (% v/v). The SPOC criterion is only valid when .

Investigations by Bustamante (1991) and Concha et al. (1996) led to the limiting values of cyclone geometry in Table 1:[3]

Table 1. Transition from spray to roping discharge (after Gupta and Yan, 2016).[3]
Source Condition
Bustamante <0.34 Roping discharge
0.34 - 0.5 Roping or spray
>0.5 Spray discharge
Concha et al. <0.45 Roping discharge
0.45 - 0.56 Roping or spray
>0.56 Spray discharge
  1. Dubey, R.K., Singh, G. and Majumder, A.K., 2017. Roping: Is it an optimum dewatering performance condition in a hydrocyclone?. Powder Technology, 321, pp.218-231.
  2. Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.
  3. 3.0 3.1 Gupta, A. and Yan, D.S., 2016. Mineral processing design and operations: an introduction. Elsevier.