Simulation, Parameter Estimation and Optimization of an Industrial-Scale Evaporation System - Simulation and Modeling Methodologies, Technologies and Application - page 74

5 x 10 −3

s

4

linear

3

2

1

0

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

τ [bar]

Fig. 4. Deviation between the trajectories of ξ C calculated with the smooth model and the hybrid
model (Eq. 12) as a function of the smoothing parameter

1 x 10 −3

0.5

0

−0.5

−1

2 4 6 8 10 12 14

x 10 −3

τ [bar]

(a) Deviation between the trajectories of T evap .

1 x 10 −3

0.5

0

−0.5

−1

2 4 6 8 10 12 14

x 10 −3

τ [bar]

(b) Deviation between the trajectories of p evap .

Fig. 5. Deviation between the trajectories calculated with the smooth model and the hybrid model
(Eq. 12) as a function of the smoothing parameter

it is positive when p>p c . In Figure 6, the sensitivity is calculated at the rather large
parameter value τ =0 . 01 bar. A smaller τ yields a narrower transition region (not
shown). The effect of the smoothing on the the pressure (dotdashed line) and the tem-
perature (dashed line) can be neglected in accordance with the findings reported above
in Figure 5.
As an illustrative example of parameter estimation we will estimate below the coef-
ficient k of the heat transfer from the heat exchanger to the tank, the valve throughputs