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 { | :<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>\ | '''Plitt''' further proposed a limit to the volume fraction of solids in cyclone underflow, <math>\Phi_{\rm L}</math> (% v/v), of: | ||
:<math>\ | :<math>\Phi_{\rm L} = 62.3 \left [ 1 - \exp \left ( - \dfrac{d_{\rm u}}{60} \right ) \right ]</math> | ||
where <math> | 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 ( | :<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_{V}<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)}} | ||
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|+ 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> | ! <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:
![{\displaystyle \Phi _{\rm {L}}=62.3\left[1-\exp \left(-{\dfrac {d_{\rm {u}}}{60}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/228b752256c0741664e3d5acae2b9f922ae40052)
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
- ↑ 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.
- ↑ 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.
- ↑ 3.0 3.1 Gupta, A. and Yan, D.S., 2016. Mineral processing design and operations: an introduction. Elsevier.