CHEM-E7130 Process modeling Exam 22.10.2020
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5 p max in each question
1. Your task is to model mass transfer from dissolving solid particles into liquid in a stirred tank operated batch-wise. You can assume that heat transfer is very efficient, so that the vessel remains at a constant temperature (heating fluid temperature). Which balances and which constitutive equations you would need at minimum? What kind of model results in (mathematically)? Explain how you would 1) verify and 2) validate your model performance. Maximum answer length is half page (with text editor).
2. Consider the following second order differential equation:
0 dt Bx
A dx dt
x d
2
2 + + =
where A and B are constants. Write it as a system of first order differential equations
( )
=[ ] ( )
dt d
(where ( ) and [ ] are a vector and a matrix that you need to solve) by making a substitution
dt
y
=dx
. How can you evaluate stability of the original system from the matrix [ ]?3. Find out if there is something wrong in the following equations and if needed correct them based on dimensional and physical arguments. Symbols and their dimensions for these equations are given below. Explain shortly in words what the equation describes.
a)
1 E
0exp k L
V
− = − a
b)
n
n 1 n
c
c c dc t
+ = +
dt
∆Symbols
a specific surface area (m2/ m3)
c concentration (mol/m3)
D diffusion coefficient (m2/s)
E efficiency ()
J diffusion flux (mol/m2s)
k mass transfer coefficient (m/s)
L characteristic length (m)
N mass transfer flux (mol/m2s)
r reaction rate (mol/m3s)
T temperature (K)
t time (s)
v velocity (m/s)
V volume (m3)
x space coordinate (m)
y mole fraction ()
ρ density (kg/m3)
λ thermal conductivity (W/mK)
µ dynamic viscosity (Pas = kg/ms)
