Theory of Declining Rate Filtration. I: Continuous Operation

Abstract

A theoretical framework for the study of variations in rate, head loss, and concentration during declining rate filtration (DRF) is developed. A simple model for the variable rate filtration is derived in order to formulate the continuous declining rate response of a sand filter in terms of a first‐order nonlinear ordinary differential equation for the dimensionless filtrate volume. This formulation indicates that there are four dimensionless parameters that determine the behavior of a declining rate filter. The differential equation is solved numerically by the Runge‐Kutta method to obtain a single filter response as a function of time. The importance of various parameters is discussed for the true DRF and influent flow‐splitting arrangements. The theoretical framework developed here permits modeling the behavior of a filter bank in terms of oscillations in head loss, rate, and concentration in the DRF mode, which is presented in a subsequent paper.