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March 8, 2016
Austin Canaday
Dalton Dunlap
Yen Nguyen
Objective
The objective of our project is to determine a mixing model for the continuous stir tank (Reactor 1). In order to do so, the behavior of the water’s temperature inside R1 is analyzed in two cases which are ideal and non-ideal CST.
Rationale
To obtain a better understanding of basic characteristics of industrial process equipment by independently comprehending mixing process in continuous stir tank reactors (CSTR).
CSTR Mixing Equations
Ideal Model:
𝜃 𝑡 = 𝜃𝑜𝑒−𝐹𝑉𝑇
∗𝑡
Non-ideal Model:
𝑇𝑎𝑖+1 = 𝑇𝑎𝑖 +Δ𝑡
𝑉𝑎𝐹 𝑇𝑖𝑛 − 𝑇𝑎𝑖 + 𝑓(𝑇𝑑𝑖 − 𝑇𝑎𝑖)
Equipment Process Flow Diagram
Experimental Equipment
Electrical Switchboard CSTR Unit
Experimental Equipment (continued)
Mixer 1 (M1) Metering Pump 1 (P1) Reactor 1 (R1) Tank 1 (T1)
EHS & LP
Our project entails minimal environmental and safety risks.
• However, things to be conscious of include:
• Slipping hazards could occur from water leaking out on the floor
• All liquid water must be carefully carried away from electrical equipment to prevent electrical shock
• Potential energy waste by excess usage of the CST without running experiments
Experimental Testing for Ideality/Non-ideality
130ºF100ºF
100% 85%85% 100%
5 5 57 7 75
Reactor 1 Initial Temperatures:
% of Pump 1 Flow Rate:
Mixer 1 Speed: 7
Note: Data was measured every 6 seconds for a total of 6 minutes. (60 data points per trial )Reactor 1 total volume was measured with a graduated cylinder
8 Total Experimental Trials
Ideal and Non-Ideal Factors
Ideal
• No ambient losses
• Perfect Mixing
• Uniform and constant cooling
Non-Ideal
• Ambient Heat Losses
• Non-perfect mixing
• Baffles
• Conduction from water to metal reactor/reactor to water
Expectations
88
90
92
94
96
98
100
102
104
0 10 20 30 40 50 60
Tem
per
atu
re (ᵒ
F)
Time Counter
Temperature vs Time
Ideal Model
Non-Ideal Model
Theory: Ideal Model
Newton’s Law of Cooling:
𝑑𝑇
𝑑𝑡= −𝑘(𝑇 − 𝑇𝑖𝑛)
Where: • t is time
• T is the temperature of the water within Reactor 1 (R1) at time t
• Tin is the temperature of inlet cold water from Tank 1 (TK1)
• k is the heat transfer coefficient
Theory: Ideal Model
Ideal Model:
𝜃 𝑡 = 𝜃𝑜𝑒−𝐹𝑉𝑇
∗𝑡
where• θ (t) is the temperature deviation from the nominal at time t
• θo is the temperature difference between the inlet cold water from TK1 and the initial hot water inside R1.
• F is the volume flow rate of the inlet cold water to R1
• VT is the total volume of water in R1
Theory: Non-ideal Model
Energy balance in temperature:
Active zone:
𝑉𝑎𝑑𝑇𝑎𝑑𝑡
= 𝐹 𝑇𝑖𝑛 − 𝑇𝑎 + 𝑓(𝑇𝑑 − 𝑇𝑎)
Dead zone:
𝑉𝑑𝑑𝑇𝑑𝑑𝑡
= 𝑓(𝑇𝑎 − 𝑇𝑑)
Dead Zone
Active Zone
Baffle
Theory: Non-ideal Model
Non-ideal Model:
Active zone:
𝑇𝑎𝑖+1 = 𝑇𝑎𝑖 +Δ𝑡
𝑉𝑎𝐹 𝑇𝑖𝑛 − 𝑇𝑎𝑖 + 𝑓(𝑇𝑑𝑖 − 𝑇𝑎𝑖)
Dead zone:
𝑇𝑑𝑖+1 = 𝑇𝑑𝑖 +Δ𝑡
𝑉𝑑𝑓(𝑇𝑎𝑖 − 𝑇𝑑𝑖)
Theory
Ideal Model:
𝜃 𝑡 = 𝜃𝑜𝑒−𝐹𝑉𝑇
∗𝑡
Non-ideal Model:
𝑇𝑎𝑖+1 = 𝑇𝑎𝑖 +Δ𝑡
𝑉𝑎𝐹 𝑇𝑖𝑛 − 𝑇𝑎𝑖 + 𝑓(𝑇𝑑𝑖 − 𝑇𝑎𝑖)
Data Processing
MIXER LEVEL 5Total Volume VT (cm3)
3350
Pump % 85Tin (ᵒF) 75.9
Target Temp. To (ᵒF) 103.1∆t (minutes) 0.1
use Solver
F (cm3/min) 378.0f (cm3/min) 0.195
Vd (cm3) 0.010Va (cm3) = VT - Vd 3350.0
Results
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96
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100
102
104
0 20 40 60
Tem
per
atu
re (ᵒ
F)
Time Counter
Temperature vs Time
Experimental data
Non-Ideal
Ideal
*Above Graph Conditions: Mixer 5, 85% Pump, To=103.1ᵒF
86
88
90
92
94
96
98
100
102
104
0 10 20 30 40 50 60
Tem
pe
ratu
re (ᵒF
)
Mixer 5, 100% Pump, To=101.9ᵒF
Measured Data
Ideal Model
Non-ideal Model
95
100
105
110
115
120
125
130
135
0 10 20 30 40 50 60
Tem
pe
ratu
re (ᵒF
)Mixer 7 ,100% Pump, To=131.4ᵒF
Time CounterTime Counter
Uncertainty
𝜀𝑇,95% = 0.8𝑑𝑇
𝑑𝑉𝑇
2𝜀𝑉𝑇
2 +𝑑𝑇
𝑑𝑡1
2𝜀𝑡1
2 +𝑑𝑇
𝑑𝑡2
2𝜀𝑡2
2 +𝑑𝑇
𝑑𝑇𝑖𝑛
2𝜀𝑇𝑖𝑛
2 +𝑑𝑇
𝑑𝑇𝑜
2𝜀𝑇𝑜
2 = 0.793
2 sigma limit = 0.789
T-test
𝑡 = 𝑟−0
𝑠/ 𝑁= 2.89
Two-tailed95% confidence level Degree of freedom 60t critical = 2.00
N = the number of residuals 𝑟 = the average residual
s = standard deviation of the residuals
Terms Critical value
R-lag-1 Test
-1
0
1
0 10 20 30 40 50 60
Re
sid
ua
ls
Time Counter
R-lag 1 Mixer 5, 85% Pump, To=103.1ᵒF
Conclusions
• Model fails to pass T-test and r-lag-1 tests but illustrates CST temperature behavior
• Flow rate Temperature Drop
• Mixing Speed Temperature Drop
• Due to baffles in all experimental trials, ambiguity exists between Ideal and non-ideal models.
𝑇𝑎𝑖+1 = 𝑇𝑎𝑖 +Δ𝑡
𝑉𝑎𝐹 𝑇𝑖𝑛 − 𝑇𝑎𝑖 + 𝑓(𝑇𝑑𝑖 − 𝑇𝑎𝑖)
Suggestions
Accounting for conduction between the water and Reactor 1 as well as ambient heat
losses could potentially make it acceptable for us not to statistically reject our
model.
Conduction Between Reactor 1 and Water
• Initially hot water in Reactor 1 exchanges heat with Reactor 1.
• As cold water flows in, the water in the reactor becomes colder than R1 walls
• Reactor 1 then conducts heat to the water.
Reactor 1 Ambient Heat Loss
80
90
100
110
120
130
140
0 50 100 150 200 250
Tem
per
atu
re (º
F)
Time (min)
Ambient Heat loss vs Time
127
127.5
128
128.5
129
129.5
130
130.5
131
131.5
132
0 1 2 3 4 5 6
Tem
pe
ratu
re (º
F)
Time (min)
130F Ambient losses
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97
98
99
100
0 1 2 3 4 5 6
Tem
pe
ratu
re (º
F)
Time (min)
100 ºF Ambient Heat loss Vs Time
Effects of Ambient losses
100 ºF Heat Loss 130 ºF Heat Loss
Average experimental losses (ºF): 14.15 ºF 27.75 ºF
Ambient Heat loss (ºF): 0.6 ºF 2.75 ºF
Percent of Ambient Losses: 4.25 % 10 %
Conclusion: Negligible Not Negligible
References
• Murrell, Kaston (2015). Standard Operating Procedure: CST Unit & Batch Reactor Experiments. Oklahoma State University
• Myers, Kevin J., Mark F. Reeder, and Julian B. Fasano. "Optimize Mixing by Using the Proper Baffles." People.clarckson.edu, Feb. 2002. Web. Feb. 2016. <http://people.clarkson.edu/~wwilcox/Design/mixopt.pdf>.
• Rhinehart, R. R. (2016). Sketch CST with Dead Zone. Oklahoma State University.
• Skogestad, Sigurd. Chemical and Energy Process Engineering, 1st order. Boca Raton: CRC Press, Taylor and Francis Group, 2009. pp. 274-280. Print.
Mixing Dynamics Non-Ideal CST
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102
104
0 20 40 60
Tem
per
atu
re (ᵒ
F)
Time Counter
Temperature vs Time
Austin Canaday Dalton Dunlap Yen Nguyen
