
215Homogeneous Reactors
3.2.4.1 Estimation of Parameter N
Given the E-curve (E(θ) versus θ) obtained from the trace test conducted on a reactor, we
have to make an estimate of the model parameter ‘N’ using the E-curve (Figure 3.58).
First, mean
and variance σ
2
of the RTD are calculated from the given E-curve data
using the following equations by numerical or graphical integration:
θθ
=
∫
()
0
(3.299)
and
σθθθ θ
22
2
∫
Ed()
(3.300)
Substituting Equation 3.298 for E(θ) in Equation 3.300, we will derive a theoretical equa-
tion for σ
2
as explained below:
σθ
θ
θθ
θ
θ
θ
22
1
0
1
=
−
−
−
−
∞
∫
N
N
N
e
d
N
N
()!
θθ)
2
(3.301)
σ
θ
θ
θ
θ
2
0
1
1
=
−