Limiting operating conditions for continuous thickeners

Parameters encountered in idealized thickeners include underflow concentration (esu), flow rate of solids in the underflow (qs), and the sediment height (L). Commonly used design procedures based upon the Coe and Clevenger (CC) (1916 Trans. Am. Inst. Min. Engrs55, 356–384) method only involve the solids rate qs and esu and do not include L. Although valid for freely settling suspensions, the CC method fails when a compression zone is formed. The permeability, porosity, and unbuoyed sediment weight must then be considered. Equations relating qs and L to esu are developed in this paper on the basis of Darcy's law. For a given underflow concentration, it is shown that there is a minimum required sediment height and a maximum underflow solids rate that cannot be exceeded. At the maximum flow rate, a saddle point is encountered in the relation between the solids concentration (es) and the height (x). Placing des/dx=0 and d2es/dx2=0 yields two simultaneous equations which lead to analytical equations relating qsmax to esu. The resulting equations bear a similarity to the standard CC formulas. Examples are presented for a number of constitutive equations appearing in the literature.