The application of dimensional and statistical analysis to fluidization studies

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Polytechnic Institute


The use of fluidized solids techniques has been very prominent in recent years, especially in the petroleum industry with the increasing use of fluidized systems the need for the study of the relationships existing between the variables of such systems became more important. The application of the principles of dimensional and statistical analysis to such studies have proved very effective.

The purpose of this investigation was to correlate the pressure drop across a fluidized bed of Ottawa sand with the variables of bed height, bed diameter, and particle size by dimensional and statistical means.

In the investigation, the effects of bed height, particle size, and vessel diameter on the pressure drop through the fluidized system were studied. Copper fluidization columns were used having internal diameters of 2 and 4 inches. Standard testing grade of Ottawa sand were employed as the solid. The sand ranges studied were 20 to 30-, 30 to 50-, and 50 to 70-mesh (Tyler standard) with an absolute density of 166.6 pounds per cubic foot. Several bed heights of 1/2-, 1-, 1-1/2-, 1-, 1-1/2-, 3-, and 3-1/2-feet were used in the investigation with the static pressure drop determined at the critical mass velocity at each bed height. Air, varying in temperature from 68 to 76 degrees Fahrenheit and having a maximum humidity of 0.006 pound of water vapor per pound of dry air, was employed as the fluidizing medium.

By means of dimensional and statistical analysis, an empirical equation was developed and the exponents relating pressure drop to the other properties of fluidized systems were evaluated. The equation applies only to velocities of the fluid at the critical mass velocity and is as follows:

Y = 3.173 - 0.186X₁ + 0.039X₂ + 1.017X₃ - 0.297X₄ + 0.151X₅


Y = log Δp/ρfDt dimensionless

X1 = log Uf/ √(gDt) , dimensionless

X2 = log Dp/Dt, dimensionless

X3 = log L/Dt, dimensionless

X4 = log ∈, dimensionless

X5 = log μff√gDt3/2, dimensionless

The pressure drop over the fluidized system was determined to be dependent primarily on the bed height of sand employed. The application of the principles of multiple regression showed that all the dimensionless groups correlated with pressure drop were significant. The pressure drop was shown to decrease as particle diameter decreased, increase as the tube diameter decreased, and increase as the bed height increased.