Group A: Thomas Witt, Dominique Taylor, Zachery Kienle[1]

Modeling Non-Ideal CSTR

An engineering analysis bridging the gap between ideal and reality by quantifying non-ideal mixing, dead zones, and bypassing in a Continuous Stirred-Tank Reactor.[1]

Explore Project View Presentation

Introduction & Apparatus

This project explores the physical realities of industrial mixing by developing a Two-Parameter Model to analyze a Continuous Stirred-Tank Reactor (CSTR).[1] By experimenting with variables such as injection height, space time, and impeller speed, we aimed to quantify non-ideal behavior.[1]

Experimental Setup & Controls

  • • Parameters were carefully controlled by computer.[1]
  • • A conductivity probe allowed constant monitoring of the solution.[1]
  • • The CSTR was equipped with two feed inputs, one with adjustable height.[1]
  • • The feed pump drew water from two 8-gallon tanks.[1]
  • • A 20 ml syringe was used to inject the 0.0022183 g/ml NaCl salt solution.[1]
Insert Figure 1: Industrial Glass-lined CSTR Replace with `image_path.jpg`
Insert Figure 3: GIF of Apparatus Setup Showing water tanks, conductivity monitor, syringe, feed pump, and CSTR.

Theory & Governing Equations

Basic engineering and scientific principles include a mass balance on the injected NaCl.[2]

Mathematical Modeling

Mass Balance Equation[1]

In - Out = Accumulation

\[ v_{s}C_{T0}-v_{s}C_{T}=V_{s}\frac{dc_{t}}{dt} \]

Combined Effluent[1]

\[ \frac{C_{T}}{C_{T0}}=1-(1-\beta)e^{-\frac{1-\beta}{\alpha}(\frac{t}{\tau})} \]

Linearization for Visualization[1]

\[ \ln\frac{C_{T0}}{C_{T0}-C_{T}}=\ln\frac{1}{1-\beta}+\left(\frac{1-\beta}{\alpha}\right)\frac{t}{\tau} \]
Insert Figure 2: Model of a CSTR with dead volume and bypass

Two-Parameter Model Parameters[1]

  • • Mixing Flow: \(v_{s}=(1-\beta)v_{0}\)[1]
  • • Bypassing Flow: \(v_{b}=\beta v_{0}\)[1]
  • • Dead Volume: \(V_{d}=(1-\alpha)V\)[1]
  • • Stirred Volume: \(V_{s}=\alpha V\)[1]

Experimental Procedure & Safety

A comprehensive plan including calibration, replicates, and strict safety controls.[2]

Safety Hazards & Controls

Hazards include mechanical, electrical, and spillage risks.[2]

  • Ensure no loose clothing or hair can get caught in the stirrer axel.[2]
  • Wear safety glasses to prevent salt solution from getting into eyes during a spill.[2]
  • If a large spill occurs, immediately turn off the main power.[2]
  • Because it is an NaCl solution, paper towels can be safely used for cleanup.[2]

Methodology Outline

  1. Calibrate the conductivity probe by rinsing in water, drying it, and placing it in calibration solution.[2]
  2. Fill a large beaker with water and place the pump inlet tube inside.[2]
  3. Set the pump to the desired power level and turn it on.[2]
  4. Wait for the CSTR to fill up.[2]
  5. Measure water flow rate by filling a graduated cylinder and timing it.[2]
  6. Fill the syringe with salt solution and push into the upper inlet tube, injecting it into the CSTR.[2]
  7. Measure the change in conductivity over time (every 5 minutes).[2]
  8. At steady state, repeat the steps using different injection heights.[2]

Calibration & Raw Data Processing

To develop the calibration curve, we made 0.25M, 0.5M, 0.75M, and 1M salt solutions to measure conductivity.[2]

Insert Figure 4: Calibration Curve v0 vs Pump Power (%) to calculate salt solution concentration.[1]
Insert Figure 5: Raw Conductivity Results Plots of Conductivity vs Time demonstrating raw data collected.[1]

Jupyter Notebook Preliminary Analysis

R-Squared Value[3] 0.947
Beta (b) Calculation[3] 1 - np.exp(intercept)⁻¹
Alpha (a) Calculation[3] (1-b) / slope / τ
Insert Python Plot: Tracer Concentration vs Time
Insert Python Plot: Cumulative Concentration (Linear Zone Highlighted)

Results: Variable Relationships

Flow rate immensely changes α and β positively, while greater injection depth and impeller speed reduce bypass.[1]

Insert Figure 6: β vs Impeller Power & Flow Rate
Insert Figure 7: α vs Impeller Power & Flow Rate
Insert Figure 8: β vs Injection Depth & Flow Rate
Insert Figure 9: α vs Injection Depth & Flow Rate
Insert Figure 11: β vs Impeller Power & Injection Depth
Insert Figure 12: α vs Impeller Power & Injection Depth

Aspen Plus Extra Credit Modeling

The experiment was modeled to determine how enabled vs. un-enabled reaction kinetics affect residence time, assuming ideal mixing conditions.[1]

Insert Figure 10: Aspen Model Flowsheet Showing CSTR1 (Kinetics On) and CSTR2 (Kinetics Off)
Parameter CSTR 1 (Kinetics On) CSTR 2 (Kinetics Off)
Residence Time 2.05 min 2.01 min
Heat Duty -2.69 KW 0 KW
H2O Flow 5.83285 kmol/hr 5.65985 kmol/hr
NaCl Flow 1.7261e-05 kmol/hr 0.173017 kmol/hr
Na+ & Cl- Flow 0.172999 kmol/hr 0 kmol/hr

Project Presentation

Review the complete slide deck detailing our non-ideal CSTR modeling process, results, and conclusions.

Conclusions & Recommendations

To achieve ideal CSTR parameters, the full volume must be active (α = 1) and nothing should go through bypass (β = 0).[1] We recommend optimizing the flow rate for a more active volume, while optimizing injection height and propeller speed for fine tuning.[1]

References

  1. "Modeling Non-Ideal CSTR", Group A Presentation: Thomas Witt, Dominique Taylor, Zachery Kienle.
  2. "Preliminary Questions", Methodology, Safety Protocols, and Experimental Plan.
  3. "CHEN 3702 EXP 3 Preliminary Analysis", Jupyter Notebook Data and Python Processing.