Environmental Engineering FOURTH EDITION

192 ENVIRONMENTALENGINEERING

and since X =- 0

(9.22b)

Note that in this case 0, # t.
Substrate removal can be considered in terms of a substrate removal velocio q:

= (Microorganism mass under aeration)(hydraulic residence time)

Substrate mass removed

q=- so - s

xf.

(9.23)

The substrate removal velocity is a rational measure of the substrate removal activity,
or the mass of BOD removed in a given time per mass of microorganisms doing the
work, and is sometimes called the process loading factol: It is a useful operational and
design tool.
Substrate removal velocity may also be derived from a mass balance of the system
shown in Fig. 9-19:

Net rate of Rate of Rate of Rate of

changeof = substrate - substrate - substrate

substrate inflow outtlow utilization

dS

-v = QSo - QS - qxv.

dt (9.24)

The rate of substrate utilization is

(Substrate mass removed)(Microorganism mass)(reactor volume)

(Microorganism mass)(time)(reactor volume)

qxv =

Substrate mass removed

Time

qxv =

Solving for q gives

so - s

q=-

Xt.

The Monod rate is defined in Eq. (9.13) as

dX 1 Microorganism mass produced

dt X (Time)(Microorganismmass) *

pL=--=

The yield Y was previously defined as

(9.25)

dX Microorganism mass produced

dS Substrate mass removed '

y=-=