Template:Model theory (Text, Hydrocyclone, Roping)

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, $M_{\rm {SU}}$ (m³/h), exceeds a solids capacity limit:

$M_{\rm {SU}}>0.35{D_{\rm {u}}}^{2.35}$

Plitt further proposed a limit to the volume fraction of solids in cyclone underflow, $\Phi _{\rm {L}}$ (% v/v), of:

$\Phi _{\rm {L}}=62.3\left[1-\exp \left(-{\dfrac {d_{\rm {u}}}{60}}\right)\right]$

where $d_{\rm {u}}$ is the mass median particle size of the underflow, computed here as the P₅₀ (μm).

The SPOC criterion indicates roping may occur when:

$C_{\rm {VU}}>56+0.2(C_{\rm {V}}-20)$

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

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

Table 1. Transition from spray to roping discharge (after Gupta and Yan, 2016).

Source	$D_{\rm {u}}/D_{\rm {o}}$	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