Environmental Engineering FOURTH EDITION

190 ENVIRONMENTAL ENGINEERING

Q +W+Q V X

Figure 9-18. A biological reactor without microorganism recycle.

completely mixed the influent is dispersed within the tank immediately upon introduc-
tion, so that there are no concentration gradients in the tank and the composition and
water quality of the effluent are exactly those of the tank contents. In such a continuous
reactor there are two retention times: for liquids and for solids. The liquid, or hydraulic,
retention time, usually expressed in minutes, is.

-v

‘=e-

(9.16)

The solids retention time, also known as sludge age, is the average time a solid (micro-
organism) particle stays in the system. Sludge age in wastewater treatment is also the
mean cell residence time 0, and is &fined as

Mass of SS contained by the aeration tank

Mass rate of solids leaving the aeration tank *

0, =

For the system pictured in Fig. 9- 18, the mean cell residence time is

vx

0, = -

ax ’

(9.17)

which in this case is equal to T. The mean cell residence time is usually expressed in

days.

We now assume that, in the system under discussion, there are no organisms in the

influent (X-= 0), and that the reactor has attained a steady state, in which the micro-

organism growth rate is balanced by the rate of microorganism loss in the effluent.

Death of microorganisms is ignored.

A mass balance for the system is

Rateofchange - Rateof - Rateof Netrateofgrowth

in the reactor - inflow outflow + of microorganisms

-V=QXo-QX+

dX

dt

(9.18)