Modeling of backpulse filter cleaning: the small particle filter cake fragments

A fine-scale, quasi-static model has been developed to describe the removal of a layer of filter cake from a cylindrical filter by backpulses of compressed gas. The model includes the bonding forces of adhesion between the layer and a substrate, as well as the forces of cohesion between imaginary “gridblocks” within the layer. For stresses greater than a threshold value, some of the layer is removed. The amount of the layer removed and the fragmentation of this part of the layer depends upon the stress, the average adhesive and cohesive forces, and the distribution of these forces about their averages. Increasing the cohesive force does increase the size of the fragments removed, but the percentage of the layer removed in the smallest fragments saturates at around 13%, decreasing no further with increasing cohesive forces. Furthermore, increasing the cohesive forces both reduces the threshold in the cleaning pressure well below the average strength of the adhesive force and sharpens the threshold so that the threshold is much sharper than the distribution of adhesive strengths. Indeed, the threshold becomes step-like when the cohesive forces exceed a value approximately equal to twice the adhesive forces, with no cleaning immediately below the threshold and nearly complete cleaning immediately above. Although the threshold becomes step-like for large enough cohesive forces, the fragment size distribution seems to be a smooth function of the cohesive force. Surprisingly, there is only a weak dependence of the fragment size upon pressure. Further, the fragments themselves are compact with a rough boundary.