Jump to content

User:Dhatfield/Sandbox Two - product formula

From Wikipedia, the free encyclopedia

Two product formula

[edit]

To derive the two-product formula, define mass balances and recovery. 1 F= C+U Feed (tph) = Coarse (tph) + Underflow (tph) 2 Ffi=Cci+Uui Mass balance for each size fraction i. 3 Reci=Cci/Ffi Recovery defined for each size fraction i.

Multiply (1) by ui and subtract from (2): 5 Fui=Cui+Uui 2 Ffi=Cci+Uui 6 Ffi-Fui=Cci-Cui+Uui-Uui

Factor (6): 7 F(fi-ui)=C(ci-ui)

Solve (7) for C/F: 8 C/F=(fi-ui)/(ci-ui)

Substitute (8) into (3): 9 Reci=ci(fi-ui)/fi(ci-ui) Two-product formula

Example equations

[edit]

The derivative term is given by:

where

: Derivative term of output
: Derivative gain, a tuning parameter
: Error
: Time or instantaneous time (the present)

Slurry calculations

[edit]

To determine the percent solids (or solids fraction) of a slurry from the density of the slurry, solids and liquid[1]:

where

is the solids density
is the slurry density
is the liquid density.

Flow from % solids

[edit]
  1. ^ Wills, B.A. and Napier-Munn, T.J, Wills' Mineral Processing Technology: an introduction to the practical aspects of ore treatment and mineral recovery, ISBN 978-0-7506-4450-1, Seventh Edition (2006), Elsevier, Great Britain