GPS-X Technical Reference

4 Appendix A – Prefermenter Petersen Matrix
dC L
dt
r
Hence, to obtain the respiration rate only the differential term has to be determined.
This can be done by measuring the decrease in DO due to respiration as a function
of time, which is equivalent to approximating the differential term with a finite
difference term. The consequence of this approach is that the DO becomes
exhausted so that for each new measurement of r a reaeration of the sludge is needed
to bring the DO concentration to a higher level. DO and substrate are limiting when
their concentrations become too low, causing a non-linear DO decrease. The
procedure for the determination of respiration rate according to "Standard Methods"
(APHA, 1989) is based on this principle. The principle can be used for manually
measuring respiration rate or it may be implemented in an automatic respirometer,
which samples activated sludge from an aeration basin and does one or more
measurements of the DO decrease.
The disadvantage of the need for reaeration can be eliminated when the sludge is
continuously aerated. The oxygen mass transfer then has to be included into the
mass balance:
dC
dt
L
K
L
a
x
C
L C
r
L
To obtain respiration rate both the differential term and the mass transfer term have
to be determined. To calculate the latter, the mass transfer coefficient (KLa) and the
DO saturation concentration (CL x ) must be known. These coefficients have to be
determined regularly because they depend on environmental conditions such as
temperature, barometric pressure and properties of the liquid. The simplest approach
is to determine them by using separate reaeration tests and look-up tables. Another
approach is to estimate the coefficients from the dynamics of the DO concentration
whether or not in combination with a close loop adaptive control of the dissolved
oxygen concentration. The advantage of the dynamic method is that the values of the
aeration coefficients can be updated relatively easily. This respirometric principle
allows the measurement of r at a constant DO concentration, thereby eliminating the
dependency of r on the DO concentration. This principle can be implemented in a
separate respirometer or directly in the aeration tank.
Repetitive aeration or estimation of oxygen transfer coefficients, as with the above
principles, can be avoided when activated sludge with a high enough DO
concentration is pumped continuously through a closed completely mixed or plug
flow cell without gas phase. The mass balance becomes:
dC
dt
L
Q
V
in
L
C
C
r
Lin
Lout
Both DO concentrations CLin and CLout can be measured continuously to allow the
calculation of r. In a respirometer Q and VL are instrument constants. This principle
is in fact the continuous counterpart of the first one and it is as such also sensitive to
GPS-X Technical Reference