Filtration of highly compactible filter cake: Variable internal flow rate

Conventional analyses used to interpret filtration data assume a constant internal liquid flow rate (qL) and a negligible solid velocity (the constant‐qL approximation). To interpret such data, the upper bounds of errors to estimate αav and kav were analytically derived by the constant‐qL approximation. The solution of the filtration model that incorporates a nonzero solid velocity was then analytically derived. When filtering a highly compactible filter cake, the cake was first compacted toward the filter medium that forms a skin layer and, in doing so, rapidly reaches the steady‐state distribution predicted by the constant‐qL approximation. Except at the first stage of the filtration, the approach of Tiller et al. (1999) is valid for interpreting filtration data of a highly compactible filter cake. Furthermore, the constant‐qL approximation provides the upper limit of errors in terms of estimating cake characteristics regardless of the solid velocity effect.