88
Chapter 3
Ethanol
A =1.871
Carbon dioxide
h
= 19.89
Oxygen
h
=9.26
Biomass
h
= 3.36
«
Glucose
A = 4.41
When one of the measurements is left out of the analysis, rank(R) = 1, and the test function should
therefore be compared with the X2 distribution with one degree of freedom. It is evident that when the
ethanol measurement is left out, all signs of trouble disappear from the data set. It seems beyond doubt
that there is a systematic error in the ethanol measurement, and we can obtain a nice statistical
confirmation of the somewhat more qualitative argument of Example 3.5, which strongly indicated that
some ethanol was missing from the mass balance. Using equation (3.48) we find good estimates for the
measurement errors
S
=
10-3
'0.506^
0.115
0.811
,0.035,
(9)
These are small, and correction of the measured rates (not including that of ethanol) is therefore not
necessary. Using Eq. (3.37), we calculate the three non-measured rates (including that of ethanol)
M
r- 0.01
2"
<\c
=
qp
=
0.100
j
, 0.076 ,
The calculated volumetric rate of ethanol production is thus 0.100 C-moles of ethanol per liter per hour,
which corresponds to 0.357 C-moles of ethanol per C-mole of glucose. This is identical to the sum of
Yip
and the calculated
Yipl
found in Example 3.5. The method for error diagnosis illustrated here is very
simple and quite powerful. It is, however, advisable not to embark on a mechanical error analysis
without first using the intuitively simple engineering approach of Example 3.5.______________________
PROBLEMS
Problem 3.1. Rate of uptake of gas phase substrates. Experimental errors in determination of rates.
Consider a well stirred laboratory reactor of volume 2 L which is used for continuous cultivation of
S.
cerevisiae.
The reactor is sparged with vgf =1.3 L air m in1
The volume fraction of Oi in vgf is 20.96
%. T = 30° C , and p = 1 atm. Assume, that vg = vgf.
a.
Determine the rate of oxygen transfer q0' when the volume fraction of oxygen in the exhaust gas
is 8.15%.
b.
The oxygen tension in the reactor is measured to 2511 M.
s0*
is 1.20 mM when
\
= 1 atm.
Determine the mass transfer coefficient
kp.