Name:
Student #:
Q1: Q2: Q3: Q4: Total:
CHE222S – Process Modeling and Dynamics
Midterm Test – Solution
February 28, 2023
Closed Book
All work to be marked must appear on front of page. Use back of page for rough
work only.
Do not write more than what is necessary. When asked to provide a justification,
please keep your answers to less than 2 sentences.
1 of 12
, 1. (25 Marks)
Consider the following schematic which describes two surge tanks used to dampen
fluctuations caused by the erratic operations of a large air compressor that feeds into a
furnace.
Compressor Furnace
Here Pd(t) is the discharge pressure of the compressor and Pf is the operating pressure of
the furnace, which you can assume is maintained at a constant value and the surge tanks
are operated isothermally. Here wa, wb, wc are the mass flow rates and you can also
assume that the valve resistances are constant, and the valve flow characteristics are
linear. Therefore, the mass flow rate wa can be calculated by the following equation 𝑤𝑎 =
𝑃 −𝑃
[ 𝑑𝑅 1 ]. Assume that one can write a similar equation for wb and wc.
𝑎
a) Write down the equations relating wb and wc as a function of the pressures P1 , P2 ,
Pf and the resistances Rb and Rc. (4 Marks)
𝑃1 − 𝑃2
𝑤𝑏 = [ ]
𝑅𝑏
𝑃2 − 𝑃𝑓
𝑤𝑐 = [ ]
𝑅𝑐
b) Develop a dynamic model for the pressures in the two surge tanks (Tank 1 and
Tank 2), P1 and P2 respectively. Remember to list the variables and any
assumptions that you make. (10 Marks)
Variables:
m1 – mass of gas in surge tank 1
m2 – mass of gas in surge tank 2
P1 - pressure in surge tank 1
P2 - pressure in surge tank 2
Assumptions:
The gas is ideal, and the temperature and volume remain constant in the surge tanks.
Mass balance:
𝑑𝑚1
= 𝑤𝑎 − 𝑤𝑏
𝑑𝑡
𝑑𝑚2
= 𝑤𝑏 − 𝑤𝑐
𝑑𝑡
2 of 12
Student #:
Q1: Q2: Q3: Q4: Total:
CHE222S – Process Modeling and Dynamics
Midterm Test – Solution
February 28, 2023
Closed Book
All work to be marked must appear on front of page. Use back of page for rough
work only.
Do not write more than what is necessary. When asked to provide a justification,
please keep your answers to less than 2 sentences.
1 of 12
, 1. (25 Marks)
Consider the following schematic which describes two surge tanks used to dampen
fluctuations caused by the erratic operations of a large air compressor that feeds into a
furnace.
Compressor Furnace
Here Pd(t) is the discharge pressure of the compressor and Pf is the operating pressure of
the furnace, which you can assume is maintained at a constant value and the surge tanks
are operated isothermally. Here wa, wb, wc are the mass flow rates and you can also
assume that the valve resistances are constant, and the valve flow characteristics are
linear. Therefore, the mass flow rate wa can be calculated by the following equation 𝑤𝑎 =
𝑃 −𝑃
[ 𝑑𝑅 1 ]. Assume that one can write a similar equation for wb and wc.
𝑎
a) Write down the equations relating wb and wc as a function of the pressures P1 , P2 ,
Pf and the resistances Rb and Rc. (4 Marks)
𝑃1 − 𝑃2
𝑤𝑏 = [ ]
𝑅𝑏
𝑃2 − 𝑃𝑓
𝑤𝑐 = [ ]
𝑅𝑐
b) Develop a dynamic model for the pressures in the two surge tanks (Tank 1 and
Tank 2), P1 and P2 respectively. Remember to list the variables and any
assumptions that you make. (10 Marks)
Variables:
m1 – mass of gas in surge tank 1
m2 – mass of gas in surge tank 2
P1 - pressure in surge tank 1
P2 - pressure in surge tank 2
Assumptions:
The gas is ideal, and the temperature and volume remain constant in the surge tanks.
Mass balance:
𝑑𝑚1
= 𝑤𝑎 − 𝑤𝑏
𝑑𝑡
𝑑𝑚2
= 𝑤𝑏 − 𝑤𝑐
𝑑𝑡
2 of 12
