1. March 8, 2016
Austin Canaday
Dalton Dunlap
Yen Nguyen

2. 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.

3. Rationale
To obtain a better understanding of basic characteristics of
industrial process equipment by independently
comprehending mixing process in continuous stir tank
reactors (CSTR).

4. CSTR Mixing Equations
Ideal Model:
𝜃 𝑡 = 𝜃 𝑜 𝑒
−
𝐹
𝑉 𝑇
∗𝑡
Non-ideal Model:
𝑇𝑎 𝑖+1
= 𝑇𝑎 𝑖
+
Δ𝑡
𝑉𝑎
𝐹 𝑇𝑖𝑛 − 𝑇𝑎 𝑖
+ 𝑓(𝑇𝑑 𝑖
− 𝑇𝑎 𝑖
)

5. Equipment Process Flow Diagram

6. Experimental Equipment
Electrical SwitchboardCSTR Unit

7. Experimental Equipment (continued)
Mixer 1 (M1) Metering Pump 1 (P1) Reactor 1 (R1) Tank 1 (T1)

8. 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

9. ExperimentalTesting 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
8Total ExperimentalTrials

10. 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

11. Expectations
88
90
92
94
96
98
100
102
104
0 10 20 30 40 50 60
Temperature(ᵒF)
Time Counter
Temperature vsTime
Ideal Model
Non-Ideal Model

12. 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 fromTank 1 (TK1)
• k is the heat transfer coefficient

13. Theory: Ideal Model
Ideal Model:
𝜃 𝑡 = 𝜃 𝑜 𝑒
−
𝐹
𝑉 𝑇
∗𝑡
where
• θ (t) is the temperature deviation from the nominal at time t
• θo is the temperature difference between the inlet cold water fromTK1 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

14. Theory: Non-ideal Model
Energy balance in temperature:
Active zone:
𝑉𝑎
𝑑𝑇𝑎
𝑑𝑡
= 𝐹 𝑇𝑖𝑛 − 𝑇𝑎 + 𝑓(𝑇𝑑 − 𝑇𝑎)
Dead zone:
𝑉𝑑
𝑑𝑇𝑑
𝑑𝑡
= 𝑓(𝑇𝑎 − 𝑇𝑑)
Dead Zone
Active Zone
Baffle

15. Theory: Non-ideal Model
Non-ideal Model:
Active zone:
𝑇𝑎 𝑖+1
= 𝑇𝑎 𝑖
+
Δ𝑡
𝑉𝑎
𝐹 𝑇𝑖𝑛 − 𝑇𝑎 𝑖
+ 𝑓(𝑇𝑑 𝑖
− 𝑇𝑎 𝑖
)
Dead zone:
𝑇𝑑 𝑖+1
= 𝑇𝑑 𝑖
+
Δ𝑡
𝑉𝑑
𝑓(𝑇𝑎 𝑖
− 𝑇𝑑 𝑖
)

16. Theory
Ideal Model:
𝜃 𝑡 = 𝜃 𝑜 𝑒
−
𝐹
𝑉 𝑇
∗𝑡
Non-ideal Model:
𝑇𝑎 𝑖+1
= 𝑇𝑎 𝑖
+
Δ𝑡
𝑉𝑎
𝐹 𝑇𝑖𝑛 − 𝑇𝑎 𝑖
+ 𝑓(𝑇𝑑 𝑖
− 𝑇𝑎 𝑖
)

17. Data Processing
MIXER LEVEL 5
Total Volume VT (cm3
)
3350
Pump % 85
Tin (ᵒF) 75.9
Target Temp. To (ᵒF) 103.1
∆t (minutes) 0.1
use
Solver
F (cm3/min) 378.0
f (cm3/min) 0.195
Vd (cm3) 0.010
Va (cm3) = VT - Vd 3350.0

18. Results
88
90
92
94
96
98
100
102
104
0 20 40 60
Temperature(ᵒF)
Time Counter
Temperature vsTime
Experimental data
Non-Ideal
Ideal
*Above Graph Conditions: Mixer 5, 85% Pump,To=103.1ᵒF

19. 86
88
90
92
94
96
98
100
102
104
0 10 20 30 40 50 60
Temperature(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
Temperature(ᵒF)
Mixer 7 ,100% Pump, To=131.4ᵒF
Time CounterTime Counter

20. Uncertainty
𝜀 𝑇,95% = 0.8
𝑑𝑇
𝑑𝑉 𝑇
2
𝜀 𝑉 𝑇
2 +
𝑑𝑇
𝑑𝑡1
2
𝜀𝑡1
2 +
𝑑𝑇
𝑑𝑡2
2
𝜀𝑡2
2 +
𝑑𝑇
𝑑𝑇 𝑖𝑛
2
𝜀 𝑇 𝑖𝑛
2 +
𝑑𝑇
𝑑𝑇𝑜
2
𝜀 𝑇𝑜
2 = 0.793
2 sigma limit = 0.789

21. T-test
𝑡 =
𝑟−0
𝑠/ 𝑁
= 2.89
Two-tailed
95% confidence level
Degree of freedom 60
t critical = 2.00
N = the number of residuals
𝑟 = the average residual
s = standard deviation of the residuals
Terms Critical value

22. R-lag-1Test
-1
0
1
0 10 20 30 40 50 60
Residuals
Time Counter
R-lag 1 Mixer 5, 85% Pump, To=103.1ᵒF

23. Conclusions
• Model fails to passT-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.
𝑇𝑎 𝑖+1
= 𝑇𝑎 𝑖
+
Δ𝑡
𝑉𝑎
𝐹 𝑇𝑖𝑛 − 𝑇𝑎 𝑖
+ 𝑓(𝑇𝑑 𝑖
− 𝑇𝑎 𝑖
)

24. 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.

25. Conduction Between Reactor 1 andWater
• 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.

26. Reactor 1 Ambient Heat Loss
80
90
100
110
120
130
140
0 50 100 150 200 250
Temperature(ºF)
Time (min)
Ambient Heat loss vsTime
127
127.5
128
128.5
129
129.5
130
130.5
131
131.5
132
0 1 2 3 4 5 6
Temperature(ºF)
Time (min)
130F Ambient losses
95
96
97
98
99
100
0 1 2 3 4 5 6
Temperature(ºF)
Time (min)
100 ºF Ambient Heat lossVsTime

27. 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

28. 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.

29. Mixing Dynamics Non-IdealCST
88
90
92
94
96
98
100
102
104
0 20 40 60
Temperature(ᵒF)
Time Counter
Temperature vsTime
Austin Canaday Dalton Dunlap Yen Nguyen