The permeability prediction of beds of poly-disperse spheres with applicability to the cake filtration

• Filter cake of poly-disperse particles is formed for different flow conditions.
• Permeability of filter cake is measured experimentally.
• Particle size averages (moments) are calculated from the distribution function.
• Harmonic average of the poly-disperse particle sizes best fits the predictive models.

The interactions between the cake and depth filtration of poly-disperse spherical particles is examined by comparing experimentally measured cake permeability to the permeability predictions of analytical models. In the experiments, the influence of the cake forming history on the cake permeability is investigated, where the parameters as (i) different filtration materials, (ii) test suspension flow rates, and (iii) particle concentrations in the suspension are varied. The permeability models are given as product of preset constant, porosity function and square of characteristic particle size. For the poly-disperse porous media, the characteristic particle size has to account for the distribution of particle sizes which is typically accomplished through the use of various moments of the distribution. Clearly, the size distribution function of particles forming the cake has to be utilized which is obtained after correcting the original distribution function of particles used in the test suspension for the particles which pass through the cake. This implies that the particles have to be counted after the test suspension passes the filtering material. Following this framework, a set of experiments is carried out to determine the permeability of poly-disperse cake. For each experiment, the permeability is also evaluated analytically using four different long-established models in combination with different averages for the particle diameter of the poly-disperse particle sample, trying to identify an averaging rule for which the analytical predictions are most close to the experimental results.

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