the handbook of food engineering practice crc press chapter 10 ...

A. Two-step method
The most common method to estimate the Arrhenius' parameters is the classic
succesive two-steps ordinary linear least squares fit. The first step is the regression of the
quality function (Table 1; i.e., A o for zero-order, or ln (A t /A o ) for a first-order reaction) vs.
time, at each temperature, to estimate the rate constant k, and the initial concentration A o .
The estimation of A o avoids bias in the determination, and provides an additional croiterion
of the adequacy of the model to describe the experimental data. A significant descrepancy
between the estimated and experimental Ao suggests that a problem exists. The problem
may be due to an inadequate kinetic model, large experimental error, insufficient number of
data, etc. The second step is regression of ln(k) vs. [1/T - 1/Tref] to obtain the estimated of
k ref and E A /R.
B. Non-linear Least Squares (one step method)
The nonlinear regression performs a single regression an all of the data points
(i= 1, ....,n), to estimate E A /R, k ref and A o , without calculating the rates for each
temperature.
C. Results
The Arrhenius' parameters and the initial concentration derived using the two
regression methods are summarized in Table 8 for nonenzymatic browning (zero-order)
and thiamin (first-order) kinetics.
The results show no substantial differences among the derived values of E A /R
and k ref when Methods 1 and 2 were applied. Nevertheless, the values derived by method 2
are closer to the actual values used for the simulation.
D. Confidence contour
As mentioned before the confidence contour for Ea/R and kref can be derived
using a computer program (Draper and Smith, 1981) which incorporates approximation
for a nonlinear regression of Eq.(27):
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