Systematic Approach for Design of Slurry Mixing Agitators

         Hi Friends,

In various technical forums, process experts as well as equipment manufacturers have opined that the design of agitators for mixing process slurry handled in Chemical industries is complicated and tricky issue. In this paper, we would like to discuss the subject in very simplified manner with systematic approach starting with brief description of involved terminology, associated design parameters and methodology with sample motor rating calculations for the slurry mixing agitator.

Basic Formula Drive Rating Calculations for Agitator:

Power Required for Agitator Drive Motor = N_p X ρ x N³ x D⁵ watt for 1 Impeller.

Where Np = Power number (Dimensionless number dependent on type of impeller),

ρ = Density of Fluid in kg/m3,

N = Revolution per second and

D = Diameter of Impeller in m.

Indicative Power Numbers for Various Types of Impellers:

S.No.	Type of Agitator Impeller	Power Number (Np)
1.	Four bladed 45 degree Pitch Turbine	2.1
2.	Rushtom Turbine	5.5
3.	Propeller Type Impeller	0.70
4.	Hydro-Foil Type Impeller	0.30 to 0.51

Sample Calculations to Arrive at Drive Motor Rating for Agitator: 

Simplified sample calculations have been presented to arrive at the drive motor rating for the agitator of a Process tank having around 3000 m³ gross capacity with key input figures as well as realistic assumptions-

Fluid height in the tank, H = 16 m and Diameter of tank, D_t = 14 m

Slurry volume in tank   = π *D_t²*H/4 =  π * (14)²*16 /4 = 2463 m³   

Solid consistency in Slurry = 50 % (w/w),   Density of slurry, ρ = 1602 kg/m³,

Viscosity of slurry, μ = 550 cp

Agitator Impeller Diameter, D_i= 33 % of tank diameter = 14 * 33% m = 4.62 m

Tip speed of Impeller = π *D_i *N = 3.1416 * 4.62 *20 = 290 m/minute,      

 Drive motor RPM = 1500 rpm, Gear Box Reduction Ratio = 75

∴ Agitator RPM = Drive Motor RPM/Gear Box Reduction Ratio = 1500/75 = 20 rpm,

Thus revolution per second of impeller, N = 20/60 = 0.333 Revolution per second.

Flow Number N_q   = 0.56 and Power Number,     N_p  = 0.51 (assumed figures for Impeller)

∴ Pumping Capacity  =  N_q * N * D_i³  m³/ second

= 0.56 * 0.333 * (4.62)³ = 18.41 m³/sec.

Area of Tank               = π  * D_t²   = 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  * (D_t²- D_i² ) /4  

Where D_t = Diameter of tank      and        D_i = Diameter of impeller in meters.

= 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 N_p    = 0.51

Shaft Power,      P      = N_p* ρ *(D_i)⁵ * N³ /1000 kW

Where N_p = Power number of impeller (Dimensionless number),

D_i = Diameter of impeller in meters, Shaft RPS,             N = revolutions per second,

∴ Shaft Power, P   = 0.51 * 1602 * (4.402)⁵ * (0.333)³ /1000 kW = 49.86 kW

Taking Gear Box Efficiency   = 80% and Drive Motor Efficiency = 95%,

Design margin           = 1.15

∴ Drive Motor Rating = 1.15 * 49.86/(0.80 * 0.95) =73.95 kW.

Thus the drive motor of about 75 kW shall be adequate for successful operation of agitator of 3000 m³ Process tank containing fluid of considered solid content. 

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. 

Trust, you will like the methodology adopted in this technical paper. We would like to have your comments.

In case, your company needs assistance of our team in resolving any technological, process, engineering or operational problems of your plant; we may be contacted. We are operating out of Gurugram, India. You may like to have a look at our website.

Regards.

Rajendra Kunwar

E.Mail: rajendra@ceti.co.in

Our Website: www.ceti.co.in