Design Calculations for Slurry Agitators in Alumina Refinery

Design Calculations for Slurry Agitators in Alumina Refinery Rajendra Kunwar, India

Today I am presenting the gist of my technical paper on "Motor rating calculations for slurry mixing agitators in Alumina refinery" which has been published recently in aluminium issue of the magazine "Minerals & Metals Review" (page 30 and 31 in MMR, August 2011 issue). In various technical forums, process experts as well as equipment manufacturers have opined that the design of agitators for mixing bauxite, residue and hydrate in Alumina refinery is complicated and tricky issue. In this paper, we will discuss the subject with brief description of involved terminology, associated design parameters and methodology with sample motor rating calculations for the slurry mixing agitator of a Pre-desilication tank of Alumina refinery. Method to arrive at motor rating: Impeller power for slurry mixing agitator is calculated using following mathematical relations Impeller Power, P = Np * ρ *N3 * Di5/(16*104) h.p. Where Di = Diameter of impeller in meters, N = Revolution per minute for impeller, Np = Power number for impeller and ρ = Specific gravity of slurry. Sample calculations: Simplified calculations to arrive at the motor rating for the agitator of Pre-desilication tank of around 3000 m3 gross capacity with realistic assumptions have been presented belowFluid Height in Tank , H = 16 m Diameter of tank, Dt = 14 m Slurry volume in tank = π *Dt2*H/4 = π * (14)2*16 /4 = 2463 m3 Solid consistency in Slurry = 50 % (w/w), Specific gravity of slurry, ρ = 1.602, Viscosity of slurry, μ = 550 cp Agitator Impeller Diameter, Di= 33 % of tank diameter = 14 * 33% m = 4.62 m Tip speed of Impeller = 290 m/minute,

Drive motor RPM = 1500 rpm. Gear Box Reduction Ratio = 75 ∴ Agitator RPM, N = Drive Motor RPM/Gear Box Reduction Ratio = 1500/75 = 20 rpm Flow Number: Nq = 0.56 And Power Number,

Np = 0.51 (assumed figures)

∴ Pumping Capacity = Nq * N * Di3 m3/minute = = 0.56 * 20 * (4.62) 3 = 1104.44 m 3/min. = 18.41 m 3/sec. Area of Tank = π * Dt2 = π *(14)2 / 4 = 153.94 m2 Bulk fluid Velocity

= pumping capacity/area of tank

= 1104.44 / 153.94= 7.18 m/min.= 23.55 ft./min. Degree of Agitation = bulk fluid velocity / 6 (For 6 ft/min., degree of agitation =1 and Degree of agitation varies from 0 to 10) = 23.55 / 6 = 3.93 ~ 4 Annular Area = π * (Dt2- Di2 ) /4 Where Dt = Diameter of tank Di = Diameter of impeller in meters. Annular Area = 3.14 * (142 – (4.622) / 4 = 137.18 m2 Rising velocity of particles = pumping capacity / annular area = 1104.44 / 137.18 = 8.051 m/min. = 0.1342 m/sec. Tank Turnover rate = Pumping capacity / tank capacity = 1104.44 / 2463 = 0.45 times / min. Power Number Np

= 0.51

Shaft Power,

P

= Np* ρ *(Di)5 * N3 /(16 *104)

Where Np = Impeller power no., Di = Diameter of impeller in meters, Shaft RPM, N = revolutions per minute ∴ Shaft Power, P = 0.51 * 1.602 * (4.402)5 * 203 / (16 *104) = 85.98 h.p. Taking Gear Box Efficiency = 80% and Drive Motor Efficiency = 95%, Design margin

= 1.15

∴ Drive Motor Rating = 1.15 * 85.98/(0.80 * 0.95) =130 h.p. = 97.0 kW. Thus the drive motor of about 100 kW shall be adequate for successful operation of agitator of 3000 m3 Pre-desilication tank in Alumina refinery. Conclusions The developed methodology clearly reveals that motor rating calculations for any slurry mixing agitator can be carried out easily by simply replacing the associated input process conditions, operating parameters, dimensions of tanks / vessel and appropriate power number for impeller in above simplified derivation.