Parametric Estimation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 300

(2) the Eadie e Hofstee plot ( r ~ r / S )

r
S

r ¼ r max K m (7.38)

The regression model is linear: y ¼ r max þ K m x . Here, y ¼ r and x ¼ r / S .And

(3) the Hanes e Woolf plot ( S / r ~ S )

S
r ¼

1
r max

K m
r max

S þ (7.39)

In terms of two new parameters ( a 1 ¼ 1/ r max and a 0 ¼ K m / r max ), the regression model is

linear: y S .

These classic approaches have contributed to the early successes in the “slide rule” age
when computing power is nonexistent. We will examine the validity of such approaches in
the following.

¼ a 0 þ a 1 x . Here, y ¼ S / r and x ¼

7.8.1. Integral Methods
In the integral method approach, Eqn (7.35) is first integrated to obtain an algebraic equa-
tion. In this case, one can assume an order before starting the process. For example, we
assume n ¼ 2, Eqn (7.35) can be integrated to obtain

0
@

1
A ¼ 26
29

C A 0 3
58

C C

ln k f C A 0 t (7.40)

C A 0 55
58

C C

Letting

0 1

C A 0 3
58

C C

@ A

y ¼ ln (7.41)

C A 0 55 C C

58

Equation (7.40) is reduced to

y ¼ 26
29

k f C A 0 t (7.42)

or

(7.43)
By converting the data of C C in Table 7.3 to y using Eqn (7.41) , one can transform the initial
differential model to a linear model using Eqn (7.43) . If this procedure fails, a different n can
be selected to repeat the process.
Table 7.4 shows the transformed data set from Table 7.3 using Eqn (7.41) . With this
approach, the regression becomes very simple and visually favorable. There might be

y ¼ at