Ergun particle density

In fluidised and fixed beds, knowledge of particle density is necessary for calculation of the effective void bed volume (Ergun equation Ergun 1952) and specific surface areas of solids by permeametry using the Kozeny-Carman equation (BS 4359 Pt 2 1982 Carman 1937). Kozeny-Carman equation 

The Ergun density may be determined from a well-mixed bed of porous, non-cohesive powder of known weight by fluidisation at a known pressure drop, Ap. After the gas flow has been stopped the height of the settled bed is measured. An Ergun density may then be calculated from the Kozeny-Carman equation. Use of the Kozeny-Carman equation for the determination of the Ergun particle density becomes, however, invalid with coarse powders 

ASTM B331-95 (2002) Standard Test Method for Compressibility of Metal Powders in Uniaxial Compaction 

ASTM E9-89a (2000) Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature 

ASTM D1075-96 (2000) Standard Test Method for Effect of Water on Compressive Strength of Compacted Bituminous Mixtures 

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Fluidisation may also be used to measure aerated bulk densities, but this technique is normally used to determine the Ergun particle density (see Section 1.4.4). 

The particle density is the weight of a unit volume of solid, including the pores and cracks (Mahajan and Walker, 1978). The particle density can be determined by any of three methods (1) mercury displacement (Gan et al., 1972) (2) gas flow (Ergun, 1951) and (3) silanization (Ettinger and Zhupakhina, 1960). 

Porosities of char samples were calculated from the particle density and true density. The particle density was determined by Ergun s gas flow method (3), which we shortened by making measurements with only three rates or flow at each of two bed densities. The estimate of the standard deviation from 21 duplicate determinations was 7%. We determined true density by helium displacement in a Beckman air pycnometer. 

The superficial fluid velocity at which the packed bed becomes a fluidized bed is known as the minimum fluidization velocity, Lfmf- This is also sometimes referred to as the velocity at incipient fluidization (incipient meaning beginning). Umi increases with particle size and particle density and is affected by fluid properties. It is possible to derive an expression for Lfmf by equating the expression for pressure loss in a fluidized bed [Equation (7.2)] with the expression for pressure loss across a packed bed. Thus recalling the Ergun equation [Equation (6.11)] ... 

With catalysts, sintered products and porous materials the Ergun gas flow method can determine a particle density of porous material regardless of particle size and porosity because the external gas flows around the porous particles and does not penetrate the porous interstructure of the particle (see Section 1.4.4). 

Calculate the minimum velocity at which spherical particles of density 1600 kg/m3 and of diameter 1.5 mm will be fluidised by water in a tube of diameter 10 mm on the assumption that the Carman-Kozeny equation is applicable. Discuss the uncertainties in this calculation. Repeat the calculation using the Ergun equation and explain the differences in the results obtained. 

The generalized relation for the pressure drop for flows through a packed bed was formulated by Ergun (1952). The pressure loss was considered to be caused by simultaneous kinetic and viscous energy losses. In Ergun s formulation, four factors contribute to the pressure drop. They are (1) fluid flow rate, (2) properties of the fluid (such as viscosity and density), (3) closeness (such as porosity) and orientation of packing, and (4) size, shape, and surface of the solid particles. 

Two-phase flow through a packed bed, gas-solid flow, for example, requires modification of the Ergun equation. The change includes accounting for mixture density and viscosity. Particle-bed interaction factors must also be considered. ... 

If we cannot use the Ergun equation to scale a packed column unit operation, then we must devise a different method for scaling such a unit operation. Since scaling is based on dimensionless parameters, we should base our new scaling procedure for packed columns on dimensional analysis. We can perform a dimensional analysis of fluid flow through packed columns because the variables of the process are well known and have been studied for many decades [13,14]. The variables are fluid velocity v [LT ], column diameter D [L], characteristic length of the material mass Tchar that is dependent upon the size and shape of the material particles [L], pressure difference per physical height of the material column AP/Z [ML T ], fluid density p [ML ], and fluid viscosity p, [ML T ]. The Dimension Table for these variables is... 

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