Theory of declining rate filtration: I. Continuous operation

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 equations 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.