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

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104

0 10 20 30 40 50 60

Tem

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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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Time Counter

Temperature vs Time

Experimental data

Non-Ideal

Ideal

*Above Graph Conditions: Mixer 5, 85% Pump, To=103.1ᵒF

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0 10 20 30 40 50 60

Tem

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Mixer 5, 100% Pump, To=101.9ᵒF

Measured Data

Ideal Model

Non-ideal Model

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130

135

0 10 20 30 40 50 60

Tem

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)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

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0 50 100 150 200 250

Tem

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Time (min)

Ambient Heat loss vs Time

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131

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0 1 2 3 4 5 6

Tem

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F)

Time (min)

130F Ambient losses

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100

0 1 2 3 4 5 6

Tem

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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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Temperature vs Time

Austin Canaday Dalton Dunlap Yen Nguyen