Sludge Settling Model

In this article, Senior Developer, Dr. Gengsheng Wei, discusses the new Sludge Settling Model, available in the upcoming release of FLOW-3D v12.0.

Settling is the first stage for sewage sludge treatment, followed by digestion and disposal. In FLOW-3D v12.0, a sludge settling model has been developed to simulate sludge settlement in septic tanks, clarifiers and other sewage treatment equipment. The sludge motion is governed by both sewage flow and gravity-driven settling. The transport equation for sludge is

\displaystyle \frac{{\partial c}}{{\partial t}}+\nabla \cdot \left( {C{\mathbf{u}_{{sldg}}}} \right)={{\nabla }^{2}}(DC)

where C denotes sludge concentration that is defined as sludge mass per unit volume of sludge-water mixture; D is the sludge diffusion coefficient; \displaystyle {{\mathbf{u}_{{sldg}}}} is the total sludge velocity and can be written as

\displaystyle {{u}_{{sldg}}}=\mathbf{\overline{u}}+{\mathbf{u}_{{settle}}}

where \displaystyle \mathbf{\overline{u}} is the velocity of sludge-water mixture and \displaystyle {\mathbf{u}_{{settle}}} is the sludge settling velocity that is always in the direction of gravity.

In general, the \displaystyle {\mathbf{u}_{{settle}}} value decreases with increasing C. It drops to zero when C reaches a critical value, Cmax, which is the maximum sludge concentration in settling tanks. In the fully settled regions with C= Cmax, sludge stops settling but its advection with fluid flow continues. Cmax is a user-specified input parameter in the model.

Users can define \displaystyle {{u}_{{settle}}} as a function of C using either tabulated data or the Vesilind equation (1968)1,

{{u}_{{settle}}}={{U}_{0}}{{e}^{{-nC}}}

where {{U}_{0}} is the maximum sludge velocity, and n is Vesilind parameter with the dimension of volume/mass. When C= Cmax, \displaystyle {{u}_{{settle}}} is set to zero by the model.

The animation above is the simulation result of sludge settling in a septic tank. Sewage flows into the tank from the inlet for 8 sec at the sludge concentration of 5 kg/m3.  Cmax is specified as 10 kg/m3 and can be found in the fully settled regions at the bottom of the tank. U0=1.144×10-3 m/s and n=0.4317 m3/kg are used in the simulation. It is seen that the newly added sludge largely stays in the main chamber of the tank, with a small amount of it entering the secondary settlement chamber through the hole on the separation wall. The initially-settled sludge is disturbed by the incoming sludge but then resettles with it in about 5 min.

The new sludge settling model will help wastewater engineers to better analyze flow and settling process of sludge and improve their designs for wastewater treatment equipment.

Reference

1Vesilind P. A., 1968, Design of prototype thickeners from batch settling tests. Water Sewage Works 115(7), 302-307.