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### What Courses related?

### Numerical Solution

Website:http://www.engr.usask.ca/classes/CHE/414/index.html

Text: ChE 414.2 Laboratory Manual

(available online at course website)

Office hours: Thurs & Fri 10:00 a.m. – 11:00 a.m.

Rm: 1C129 Eng. Bld.

- Surge Tank Data Acquisition and Process Dynamics
- Fermentation: Kinetics of Yeast Growth
- Packed Column: Pressure Drop and Flooding
- Filtration
- Centrifugal Pump

Surge Tank:CHE 413, 423

(process dynamics and control);

CHE 210, 320 (fluid mechanics)

Fermentation:CHE 461 (biochemical engineering)

Packed column: CHE 315, 421 (mass transfer)

Filtration:CHE 315, 421 (mass transfer);

CHE 210, 320 (fluid mechanics)

Centrifugal Pump: CHE 210, 320 (fluid mechanics)

- Equipment operation

- Data recording

- Analysis of the data using academic theory

- Technical report writing

in the selected typical Chem. Eng. processes

Marking

- Lab performance: (4X2.5%)
- Lab notebook: 10%
- Technical letters: (2X10%)
- Brief report: 25%
- Formal report: 35%

Overall mark: 100%

No exam

Plagiarism is DEFINITELY NOT acceptable!

- Copy other people’s report
- Citing without referencing the source

Plagiarism results in 0 mark for the report

Be aware of & Followthe new University of Saskatchewan Academic Honesty/Dishonesty definitions, rules and procedures www.usask.ca/honesty.

Due Date and Overdue Penalty

- Due date
- 2 weeks after the experiment date.

10 “free” late hand-in days for the whole course

Indicate on your report when use it.

- Penalty
- 10% of the full marks (100) per week (2%/day) deducted from the late reports
- submissions will NOT be accepted after

Dec. 18th, 2006.

Requirements

- Lab performance
- Write-ups: technical writing
- Fundamentals of each lab

Lab performance

Be prepared for:

- Objectives
- Theory / knowledge
- Design of experiment
- Parameters to be measured
- Apparatuses, procedures and principles
- Find out: what to learn

Initiate the contact for the pre-lab help

with the demonstrators & the lab coordinator

During the experiments:

- Follow the experimental procedures
- Record observations in Lab Notebook
- Test the validity of data and/or results
- Pay attention to SAFETY issues
- personnel
- equipment

Write-ups / Reports

- Technical memo
- Brief report
- Formal report
- Lab notebook: during the experiments

Write-ups / Reports

One student is required to hand in

- 2 technical letters
- 1 brief report
- 1 formal report
- 1 lab notebook

In one group, you may label the 4 labs by A, B, C, and D in your own order.

Each member of the group should keep the same order.

Lab Notebook

No sheets of paper

Permanently bounded & recorded

- Briefly outline the title, apparatus, experimental conditions and procedures before labs

Suggest making table for recording data

- Record clearly all original observations

& simple calculations of data

- MUST be examined, dated and initialed by the TAs before leaving the laboratory

Lab Notebook

Refer to ChE 333 class website for

RULES FOR LABORTORY NOTEBOOKS

Submit the lab notebook

at the end of the term for marking

Technical Memorandum

- Body of text: maximum two pages
- Introduction

- concise introduction of the system used

- a brief statement of the objectives of the experiment

- a general description of the procedure followed

- Results

- discussions and comparison of all required results with values from literature

- equations used

- a brief table of results or major graphs attached to support the conclusions.

- Conclusions and recommendations
- Sign your memo on the last page below the text

From: (your name, group X)

Re: (Lab name)

Date: (of the preparation of the memo)

Your group logo

(optional)

The text of memo is put here below the line.

ChE 414 - TECHNICAL MEMORANDUM GRADE SHEET

Student: ______________________________________

Experiment: ______________________________________

Due Date: ___/___/___ Date Rec’d: ___/___/___ Late Penalty: ___ %

Formal Technical Report

- Title page and Table of Contents
- Abstract
- Table of contents, table of figures, table of tables
- Introduction
- Review of theory or literature
- Experimental Section: apparatus and procedure
- Results and Discussion
- Conclusions
- Recommendations
- Nomenclature
- Reference
- Appendices

Formal Technical Report

Title page

- Course number
- Name (Your name and state the partner’s name)
- Lab title
- Prepared for (instructor’s name)
- Date lab done
- Date report due

Table of contents

Formal Technical Report

Abstract

- State briefly the purpose of the investigation
- Describe briefly how the results are obtained
- Give all required results in a concise and quantitative format if possible.
- Use words, no tables, figures and equations
- Normally no more than 250 words.

Formal Technical Report

Introduction

- Include information on the subject of the investigation and its importance in industry
- Cite the references;
- Describe clearly the objectives of the lab.

Formal Technical Report

Literature review or theory

- Provide sufficient theoretical background

to the particular experiments

- Develop the equations or models to correlate your experimental data.

detailed derivation placed in Appendix

- Describe how to obtain the model parameters and predict the particular system
- Cite the references

Formal Technical Report

Apparatus and Experimental Procedures

- Specify the main apparatuses used

make, model and use

- Describe the procedures

Highlight important experimental conditions

- Give the names of quality of the materials.

Make sure other people can repeat your work and obtain the same results if they follow your description.

Formal Technical Report

Results and Discussions

- Present the significant experiment results

required in the Lab Manual in words and graphs.

- State the data treatment processes and the outcomes.
- Discuss the results of experiments and model simulations or predictions.
- Compare your results with that in literatures if available.
- Logically discuss and lead to conclusions.

Attention

- Consistent format
- The unit for every parameters in the equations has to be conformed.
- Figures or Tables in the body of text
- Titles of figures, axes, and tables
- Briefly state the experimental conditions
- Experimental data: represented by unique symbol for each group of data in figures
- Modeling curves: different lines with legends
- Show model significance when fitting models

error bar: 95% confidence interval

Modeling the effect of IS on Cr uptakes40±1 mg AWUS, 20±0.2 mL solution

Formal Technical Report

Conclusions and Recommendations

- Conclusions should be summarized following the discussions.
- Lists your suggestions on how we can improve the labs.

Formal Technical Report

Nomenclature

- Completely lists the symbols that appear in your report, their definition and unit in a professional and consistent format.

Refer to a published paper.

Formal Technical Report

Reference

- Completely lists every reference cited, mentioned or used in the text of the report in a professional and consistent format.
- Follows either the number order or the alphabetical order.

Formal Technical Report

Reference format examples

In the text:

……Adams concluded that ……1. However, that conclusion may be suspicious because ……2

In the Reference section:

References

1. Adams, A. B. title of publication. ……

2. Cook, H. M., Author #2, ……

Ref: Industrial and Engineering Chemistry Research

or in the text:

It was concluded ( Adams, 2001) that ……. However, that conclusion may be suspicious (Davis and Volesky, 2001) because ……(Niu, et. al., 2005)

References

Adams, A. B. year, title of publication, publisher, page (book)

Davis, T. and B. Volesky, year, title of paper, volume, issue, pages (paper)

Niu, C., M. Huang and M.Volesky, year ….

Ref: Canadian Journal of Chemical Engineering

Formal Technical Report

Appendices

- Raw data (neat with tables)
- Calculated data
- Sample calculation (using a set of data to show the steps of calculations)
- Tables and Figures

Brief Technical Report

- Title page and Table of contents
- Summary

a brief introduction stating the nature and purpose of the investigation

a brief explanation of the procedures and apparatuses a summary of all the required results

- Results and Discussion: include major graphs or tables
- Conclusions
- Recommendations
- Appendices: only raw experimental data and a sample calculation

Absence of abstract, introduction, theory/literature review, materials and methods sections

A good report

- Careful measurements
- Correct calculations
- Understanding and use of the theory or models
- Logical discussions
- Correct conclusions

Organized

Clarity

No grammar & typographical errors

- References

Filtration

A Standard Unit Operation:

physical separation of solid particles from liquid or gas.

a porous medium: fluid to pass through

solid particles to be retained.

Filter cake

Filter medium

Slurry flow

Filtrate

a filtration plant for Water Treatment System

(http://www.carrolltown.pa.us/CBMA/)

Filter medium

L

Filtrate

Slurry flow

Filtration Theory- The driving force of filtration separation:

the pressure upstream of the filter

Filtration

Objectives:

- Determine the relationship between the upstream filter pressure and the flowrate

- Evaluate the applicability of the selected model

- Determine the model parameters

- Demonstrate the effect of filter aid (perlite) on the filtration of CaCO3 slurry

- Develop skills on design of a filtration process

Theory:The upstream filter pressure P (Pa)(Bennett and Myers, 1982) P=(K1V+K2)Q if the cake is incompressibleFor constant flowrate filtration Q, V=Qt, then P=K1Q2t+K2Q Plot P~t, get K1 and K2where V: the volume of filtrate collected (m3) Q: the flowrate of filtrate (m3/s);t: time(s);K1 and K2 : constants, highly dependent on the characteristics ofcake and filter medium, respectively

- Dependent on the characteristics
- of cake, liquid and filter medium
- Determined by measuring
- the upstream filter pressure P
- as a function of time at specific Q
- Evaluate the resistances of the cake
- and filter medium
- for filter design:
- theoretically predict the required driving force

Fermentation: Kinetics of Yeast Growth

- Involves in Yeast growth on substrate glucose
- Major end products:

Ethanol: beer, wine, fuel

yeast biomass: high poundage product 500million pounds/year

Fermentation: Kinetics of Yeast Growth

Objectives:

- Demonstrate the yeast batch growth curve

- Determine the parameters of Monod equation.

- Calculate the yields of the products

- Design a fermentor for ethanol production

Fermentation theory(J.M. Lee, 1992)

C6H12O6→ 2C2H5OH + 2CO2

- Substrate: glucose
- Microorganism: yeast
- Low oxygen concentration
- theoretical yielded ethanol: 51.1% by weight

Surge Tank Data Acquisition and Process Dynamics

(http://www.ih.navy.mil/cbf/images/SurgeTank)

- Common problem: propagation of disturbances between processes
- Solution : surge tank
- Damp out the changes of the inlet flowrate
- Deliver a steadier outlet flowrate to the downstream process

Surge Tank Data Acquisition and Process Dynamics

Objectives:

- Evaluate the applicability of selected models relating the outlet flowrate versus head

- Derive and test mathematical models for the transient behavior of a liquid surge tank

- Record the data with automatic acquisition system - LabVIEW

Surge Tank

- Data acquisition and control: a computer with LABVIEW Software package

Automation, more precise.

- Collect data: water flow rate and water head in the tank

Familiar with the software

h

qout

qin

Surge Tank

h: the height of the liquid level in the surge tank (head) (ft);

qin: the inlet water flowrate (ft3/s);

qout: the outlet water flowrate (ft3/s)

A: the cross sectional area (ft2).

Surge Tank Theory

Mass balance at transient period:

t: time (s),

where the density of the liquid is constant

Theory cont.

- Flow exit a surge tank through a valve follows:

(D. R. Coughanowr and L. B. Koppel, 1965, p.60)

qout~ h½

e. g. qout= C1h½ (qout is linearly proportional to h½ )

qout= Co+C1h½

or

qout= Co+C1h½ + C2 (h½)2 + C3 (h½)3 +…+ Cn (h½)n

(n> 1, qout is non-linearly proportional to h½ )

- Constant Ci is determined by fitting the above equations, respectively, to the experimental data (qout ~ h1/2) at steady state, where qout= qin. (Microsoft Excel)
- Compare the fitting results of different models

Theory cont.

Substituting the qout in the mass balance equation yields

non-linear differential equation:

- Solutions:
- Analytical:
- closed-form, a general picture of the process behavior
- independently of the particular values of the input variables
- process design and control limited to linear processes
- Numerical:
- dependent on the values of the input variables.

- Linearize the non-linear differential equation by Taylor series expansion of the non linear term around a point

(e.q. steady state) (Stephanopoulos, G., 1985, p.116-121)

- Convert the differential equation to algebraic equation by Laplace transforming

(D. R. Coughanowr and L. B. Koppel, 1965, p.13-41, 67-70)

- Invert the transform to get h as a function of time

(D. R. Coughanowr and L. B. Koppel, 1965, p.13-41)

Use this equation to describe the experimental data at unsteady state

For example, qout = C1h½ ,

Linearize the non-linear differential equation:

(Stephanopoulos, G., 1985, p.116-121)

Analytical SolutionTake the first order of Taylor series expansion of the term qout

around a point (e.q. steady state):

Linear form

Subscript s represents the steady state.

Substitute the first order Taylor series expansion of qout in the differential equation,

Convert the differential equation to algebraic equation by Laplace transforming

(D. R. Coughanowr and L. B. Koppel, 1965, p.13-41, 67-70)

is Laplace transform of derivation variable h-hs

is Laplace transform of derivation variable qin-qin,s

s represents the Laplace function.

When the inlet flowrate is increased or decreased around certain steady state:

t<0

t≥0

Take the transform of Qin

t<0

t≥0

t<0

=

t≥0

Invert the transform,

(D. R. Coughanowr and L. B. Koppel, 1965, p.13-41)

t ≥ 0

Where qout= Co+C1h½ + C2 (h½)2 + C3 (h½)3 +…+ Cn (h½)n

n = 1, …n

Eularian theory: (Rice, RG, 1995)

Compare the analytical model solution with the numerical solution.

Use two equations of qout ~h1/2 at n=1 & n>1 for all cases in this lab.

L in

G in

L out

Packed ColumnGas-liquid counter-current flow in packed column:

- Liquid: downwards flow
- Gas: upwards flow
- Flooding conditions

Design Criteria

- pressure drop: caused by the resistance of packing to fluid flow.
- The flood velocity: an important parameter for gas-liquid packed column design

Packed Column: Pressure Drop and Flooding

Objectives:

- Determine the relationship of pressure drop and the flowrate in a packed column

- Evaluate the applicability of Ergun equation for a single gas flow system

- To determine the pressure drop

and flooding condition in a gas-liquid system

Pressure drop for a single flow through packed bed-Ergun equation

(Treybal, R.E., 1980, P.200.)

Packed Column Theory

Flooding conditions

for a gas-liquid flow through packed bed

(B. Miline, 1994)

Y: a function of gas flowrate

a, b, e: constants for a specific system.

Symbol definition! Units!

Packed Column

- Models are empirical equations.
- Different models fit differential systems.
- Evaluate the applicability of the selected model for the experiment system

Centrifugal Pump

- The most common type of fluid mover in the chemical industry
- To convert energy of a prime mover (an electric motor or turbine) first into velocity or kinetic energy and then into pressure energy of a fluid that is being pumped.

http://www.pumpworld.com/centrif1.htm

Centrifugal Pump

- To determine the characteristics of a centrifugal pump including total head, brake horse power, efficiency and net positive suction power (NPSH) versus flowrate.

- To determine the size of a geometrically similar pump needed to pump against a total head of 100 feet of water at peak efficiency

C.O. Bennett & J.E. Myers, "Momentum, Heat, and Mass Transfer", 3rd Edition, McGraw-Hill, 1982.

D.R. Coughanowr & L.B. Koppel, "Process Systems Analysis and Control", McGraw-Hill, 1965.

G. Stephanopoulos, “Chemical Process Control – Introduction to Theory Practice”, Prentice Hall, 1984.

J.M. Lee, "Biochemical Engineering", Prentice Hall, 1992, pp 100-152.

R.E. Treybal, "Mass-Transfer Operations", McGraw-Hill, 1980.

R.S. Blicq. "Technically-Write!", Prentice Hall, 2nd Edition, 1981.

R.G. Rice, “Applied Mathematics and modeling for chemical engineers”, John Wiley and Sons, Inc. 1995, pp231.

- James R. Welty, Charles E. Wicks, Robert E. Wilson, and Gregory Rorrer, Fundamentals of Momentum, Heat and Mass Transfer. 4th Edition, John Wiley and Sons, Inc. 2001
- Jaime Benitez, Principles and Modern Applications of Mass Transfer Operations. John Wiley and Sons, Inc. 2002
- Donald R. Coughanowr, Process Systems Analysis and Control. McGraw-Hill, Inc. 1991
- Hans, F. Ebel, Claus Bliefert, and William E. Russey, The Art of Scientific Writing. 2nd Edition,John Wiley and Sons, Inc. 2004
- Christie J. Geankoplis, Transport Processes and Separation Process Principles. 4th Edition, Prentise-Hall, Inc. 2003
- Milne, W.E., Numerical Solution of Differential Equations, Wiley, NY, 1953.
- Quinney, D., Introduction to the numerical solution of differential equations, research Studies Press, NY, 1987.

Have your own references to make your report strong!

Important dates

- 19 Sep: Last day to change first term registration.
- 9 Oct: Thanksgiving (University Closed),
- 4 Dec: Last day of classes.
- 18 Dec: Last day to hand in laboratory reports and laboratory notebooks for marking

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