Biomedical Engineering Reference
In-Depth Information
sincewehavelearnedthatthereactionratenormally increases with the concentrations of
reactants. Therefore, if there is a region where an increase in the concentration of A can
lead to a decrease in the rate of reaction, MSS is possible. Recall the kinetics we have
learned so far, this type of rate law is possible for at least three cases: 1) surface reaction
with adsorbed A decomposing requiring an additional free active site; 2) enzymatic reac-
tion with substrate inhibition; and 3) cell growth with substrate inhibition. Figs. 16.3
through 16.5 are based on the kinetics given by case 1) and case 2) with no loss of enzyme
from the reactor.
16.1.2. Stability of Steady State
Fig. 16.3 shows that there is at least one intercept between the mass consumption
rate of A and mass supply rate of A, and there could be three intercepts. When more
than one intercepts exist, we call this system MSS system. Although, there are MSS solu-
tions, not all the steady states are stable that could be operated at. Points I, II, and III all
satisfy steady-state conditions: MC A ¼ MS A . The operating characteristics of each point
are different.
1) CSTR operating at I
When the system is experienced with a fluctuation from feed, the CSTR could be upset in
two ways. If the feed fluctuation caused the concentration in the reactor to shift left
(i.e. lower) and then the fluctuation stopped, the mass consumption rate of A is decreased
while the mass supply rate of A is increased: MC A <
MS A . The net effect is an increase in
the availability of A in the reactor and thus the reactor-operating conditions shift gradually
back to point I. If the feed fluctuation caused the concentration in the reactor to shift right (i.e.
higher) and then the fluctuation stopped, the mass consumption rate of A is increased while
the mass supply rate of A is decreased: MC A >
MS A . The net effect is a decrease in the avail-
ability of A in the reactor and thus the reactor-operating conditions shift gradually back to
point I. Therefore, CSTR operated at point I has the ability to dampen the feed fluctuation
caused steady-state shift. This is a stable-steady state.
2) CSTR operating at II
When the system is experienced with a fluctuation from feed, the CSTR could be upset also
in two ways. If the feed fluctuation caused the concentration in the reactor to shift left (i.e.
lower) and then the fluctuation stopped, the mass consumption rate of A is increased while
the mass supply rate of A is increased less: MC A >
MS A . The net effect is a decrease in the
availability of A in the reactor and thus the reactor-operating conditions shift toward lower
C A and away from point II. On the other hand, if the feed fluctuation caused the concentra-
tion in the reactor to shift right (i.e. higher) and then the fluctuation stopped, the mass
consumption rate of A is decreased while the mass supply rate of A is decreased less:
MC A <
MS A . The net effect is an increase in the availability of A in the reactor and thus
the reactor-operating conditions shift toward higher C A which is again as from point II.
Therefore, CSTR operated at point II is not able to sustain any feed fluctuations. In other
words, the CSTR cannot be operated at point II, although MC A ¼ MS A at point II. This is
an unstable steady state.
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