PARTICIPATION IN CHEMICAL ENGINEERING LABORATORY

The Chemical Engineering Laboratory course has been set up as an open-ended learning experience rather than the traditional data sheet oriented laboratories you may have had in other courses. You will normally receive assignments in the form of memos, and you are expected to respond with reports as might be written if you were working in industry.

Pre-Lab Preparation

Each laboratory experiment has a well-defined objective. This objective will be represented by a numerical value, or a correlation allowing the calculation of this value, for the unit operation under study. This objective is accomplished through data taking, reduction, and analysis. These tasks may be successfully completed and the objective achieved only when the nature of the desired result is known, before the experiment is undertaken. Otherwise insufficient data may be taken, the results may be incorrectly analyzed, or preposterous results may be reported.

Read your current assignment. Familiarize yourself with the theory relevant to the experiment and the equipment necessary to take the required data. Read the appropriate sections of your textbook and references such as Perry's Handbook. When you are sure you understand the problem, prepare in writing, a Pre-Lab Plan. This exercise is intended to provide the preparation necessary to undertake a successful experimental study.

The written plan should include a sketch of the experimental equipment, showing vessels, interconnecting piping, valves, and relevant instrumentation. Make sure you understand the purpose and safe operation of each of these equipment items before you start the experiment. The correct analysis of data, its accuracy, and correction for nonstandard operating conditions all require a thorough understanding of the instrumentation. The written plan should discuss the independent and dependent variables and how and over what range these independent variables will be measured. The plan should address the experimental procedure and the sequence of operations undertaken during the experiment. The plan should describe how the data would be correlated, based on what models and which literature information. This pre-lab must be completed before coming to lab. Bring the completed plan to the lab and have the instructor approve your work before undertaking any experimental work. Include the exercise as an appendix in your laboratory report.

In the Lab

Attendance:All students are to report to the lab at the start of the period. Attendance in all sessions for the full 2 hours 50 minutes of each period is required, unless you are excused by the instructor. Unauthorized absences for part or all of any laboratory session will result in a reduced course grade. Normally work will be performed in the lab; work in another area requires prior approval by the instructor.

Safety and Housekeeping: Good safety practices must be observed at all times in the laboratory. This practice includes the wearing of proper clothing, footwear, and eye protection. All equipment must be safely operated and all chemicals must be safely handled. Broken or damaged equipment should be reported to the instructor immediately. You are reminded that all equipment is to be cleaned and returned to its proper location after you finish the day's work. A clean laboratory is the responsibility of all group members. Do not leave the lab until it is clean.

Lab Rules:

1. Come to lab dressed properly. Appropriate dress is required for safety reasons. Wear shoes that cover the feet. Long pants are required. No sleeveless shirts or tank tops are permitted. Long sleeve shirts are preferred. Do not wear a hat. Do not wear long flowing clothes (that includes a tie). Long, lose hair must be restrained. Wear safety glasses. When required wear a face shield. When required wear gloves appropriate for the task.

2. At all times good safety practices must be observed in the laboratory. An individual

who violates this rule will not be permitted in the lab.

3. Come prepared and bring your Pre-Lab Plan.

4. Every group must have a lab notebook (with duplicate numbered pages). During each lab make notes of everything you are doing and every measurement you make. Your notebook will be evaluated so make sure it is legible and understandable. Each page of the notebook should be signed by the data taker and witnessed by a group member and the instructor. Original data sheets should appear in the lab report appendix while the carbon copies should be given to the instructor at the end of each data taking session. In your lab notebook:

Write in ink and record all observations directly in the notebook

Do not erase. If necessary line out errors with one line

At the top of each page put the date and the experiment name

When you finish a page, sign and witness your name with date

Never write on a page after you have signed it

Rotate recording among group members

Making the most out of your time in the lab

- Good experimental work demands that data and runs be replicated. Since we cannot duplicate all conditions exactly, we make replicate runs, meaning that the conditions are almost the same but not necessarily identical. Not only should individual data be replicated (for instance a second, third, and fourth measurement of a flow rate) but also the whole run (something from which you can calculate an experimental result) should be replicated.

- When first doing a new experiment, try different things and become familiar with the experiment and the equipment. Then determine the widest possible ranges of the independent variables. In almost all cases you will want to take data over wide ranges of the independent variables. If the independent variables can easily be changed over a wide range, it is often good practice to conduct the first three experimental runs at the lowest, intermediate, and highest levels of the independent variable.

- Summarize and record in your laboratory notebook the information obtained from automatic data collection (by computer, by recorder, or whatever) as soon as possible.

- Get in the habit of working up your data as you go. Sometimes you can plot preliminary data to see trends. Other times you can calculate the experimental values and see if you are in the ballpark.

- In almost all cases you will be able to compare experimental calculations with theoretical and/or correlated values. In presenting your data and comparisons plan to use graphs if at all possible. If you are using tables, aim to make them concise, clear, and informative.

- Acquire the habit of clearly identifying your experimental runs. Run 1, then 2, then 3 is appropriate. Or you can use letters; A. B. C. etc. If a run is a failure (this sometimes happens) the next run is still given a new number or letter.

- Most of the reference books listed for the experiments, as well as other reference books, will be available for perusal during the laboratory period.

Collection and Analysis of Experimental Data

The fundamental basis for a good laboratory report is data collection and record keeping. It is not uncommon that a considerable amount of time elapses between the data collection phase of an experiment and the eventual presentation of the results. The data, therefore, must be well defined and recorded accurately in a permanent bound laboratory notebook. An important requirement is that the notebook, “should be so clear and complete that any intelligent person familiar with the field to which it relates but unfamiliar with the specific investigation could, from the notebook alone, write a satisfactory report on the experimental work”[1],[2].

1. Always use your data as you are taking it to make sample calculations of your results, dimensioning all numbers with their correct units. This simple step will insure that all the information is being recorded that will be necessary for you to make subsequent calculations for the report. Graph your results, with units, as the experiment progresses, not after you have taken all the data. Graph your data in the same way you intend to present it in your report, although it is not always necessary to make all unit conversions for an initial plot done in the lab. This plot may then be used to determine if the current experimental conditions are in the desired range, if the equipment is being incorrectly operated or is not functioning properly, or if the degree of experimental scatter is unacceptable. The plot may also be used to determine experimental conditions for subsequent data points. More data should be taken under conditions where the dependent variable changes more rapidly and less where the changes are smaller. The independent variable(s) should be changed sufficiently to make noticeable changes in the dependent variable.

Example:

Figure 1. Pressure drop in a bed of particulate solids.

Data can be collected evenly, however the important point of fluidization should not be lost because the gas flow settings, hence Reynolds number, were not properly chosen.

2. Always indicate units of quantities that are measured.

3. Never record a calculation, dimension or note on a loose sheet of paper.

4. Sketches of experimental apparatus should be part of notebook. All important dimensions should be recorded.

5. Data from recorders should be put into a laboratory notebook. Label the data with a title, data, and description of the data. Prepare your data sheet based on your Pre-Lab plan. In many experiments you will be taking a series of readings. Record more data rather than less and, of course, include units with all numerical values. The original data sheet and any graphs should appear in the appendix of your report, and the data sheet carbon copy should be turned in to the instructor at the end of each data taking session. The complete data notebook should be turned in to the instructor at the end of the course for a grade.

Example:

UNSTEADY STATE HEAT TRANSFER

January 18, 1999

Heating curve for water with aluminum cube

6. Always record the reading that you actual measure.

Example:

Manometer

Record left and right readings, not only the derived quantity P = 11 in.

Each table should be numbered, have a title and show all units.

Example:

Table 1.

PRESSURE DROP IN PACKED COLUMN

Column diameter:2 inches

Packed height:24 inches

Column packing:1/4 inch Raschig ring

Flow Rate ofFlow Rate ofPressure Drop

WaterAirInches of water per

kg/m2.skg/m2.sfoot of packing

00.2020.075

00.2790.157

00.3870.275

00.4360.301

00.5580.403

00.6100.471

0.860.1640.107

0.860.1990.159

0.860.2970.262

0.860.3620.471

0.860.5010.785

0.860.5971.247

All graphs should have a Figure number, have clearly labeled coordinates and all parameters labeled. Label symbols should be used for different parameters.

Example:

Figure 1 Pressure drop in packed column.

Dimensionless numbers should be used if possible. For example: a plot of friction factor versus Reynolds number is better than a plot of P versus velocity.

7. Notebooks become legal evidence in patent cases. Therefore, always date, sign and witness.

Example:

Experiment #1January 18, 1999

Extended Surface Heat Transfer

Signed______10/1/02

______10/1/02

______10/1/02

Witness (instructor)______10/1/02

8. Notebooks should be neat. Write in ink. Do not erase. If necessary line out with one line.

Error Analysis of Experimental Data

An error analysis should always be an integral part of your data analysis. It is important to take sufficient replicate data points, where possible, to enable you to perform a subsequent error analysis of the results. The ultimate objective of this analysis is to minimize this error.

The treatment of experimental data does not end when the desired numerical results have been obtained. An important part of the treatment is the determination of the uncertainty associated with the numerical results[3]. Every measurement of data is subject to error that can not be determined exactly. If the exact error were known it would be equivalent to measuring the quantity without error, since correction can be made for any known error. But it is possible to specify the highest amount by which the quantity might be in error.

Inaccuracies in measurements can occur due to mistakes and errors2. A mistake is the recording of a wrong reading (215 recorded as 251). An error can be consistent or random. A consistent error that usually can be corrected might come from a defect in the measuring device or the improper use of an instrument. For example: the use of a flow meter calibrated for air but used for ammonia or the use of a wrong scale on a wet test meter. Random errors are caused by fluctuations and sensitivity of the instrument or the inconsistent judgment of the experimenter. An example would be a fluctuating manometer.

Treatment of random errors.

The more measurements we take the more likely the average will be the most probable value. Let consider six measurements for the flow rate of a process stream.

ReadingFlow rate F, cm3/s

1139.1

2142.3

3138.4

4140.6

5139.0

6141.5

The estimate mean for the flow rate F is

= 140.15 where N = 6

If N is very large (N --> ) then the mean for the flow rate will be the true mean average m. The estimate standard deviation is given by

s == 1.5579

Note: The estimate standard deviation can be obtained by the Matlab function std(F) where

F = [139.1 142.3 138.4 140.6 139.0 141.5].

Since is an estimated mean from a finite measurement, how confident are we that this is a true mean? The confidence level, (1 - ) is defined as the probability that the measured mean for a small sample lies between a certain confidence interval. A 95 percent confidence means that  = 0.05. The lower confidence interval is

- c/2

and the upper confidence interval is

+ c/2

where c/2 = and t/2 is given from the Student-t distribution for small, finite sample size (N < 30). Student-t distribution and Student-t statistic were developed by W.S. Gosset in 1908 who used the pen name of “Student”. Table 1 gives values of t/2 for various confidence levels and N-1.

Table 1. Values of t/2

N-1 /2 = .05/2 = .025/2 = .01

16.31412.70631.821

22.9204.3036.965

32.3533.1824.541

42.1322.7763.747

52.0152.5713.365

61.9432.4473.143

71.8942.3652.998

81.8602.3062.896

91.8332.2622.821

101.8122.2282.764

In this example, let  = 0.05 which is the normal practice of giving 95 percent confidence limits for random errors based on small sample. Then

t/2= 2.571 for N -1 = 5 from Table 1.

Therefore the lower confidence interval is

140.15 - (2.571)*(1.5579)/61/2= 138.51

and the upper confidence interval is

140.15 + (2.571)*(1.5579)/61/2 = 141.79

Hence, 138.51 141.79

and, we are 95 percent confident that the true flow rate mean, m, lies between 138.51 cm3/s and 141.79 cm3/s and = 140.15 cm3/s is an estimate of the true mean. It must be emphasized, however, that systematic errors may be much higher than the random errors in unfavorable conditions. Therefore the sources of systematic errors must be identified and eliminated if possible.

Linear Regression and Matrix Algebra

Error is inherent in data. When data exhibits substantial error rigorous techniques must be used to fit the "best" curve to the data. Otherwise prediction of intermediate values, or the derivatives of values, may yield unsatisfactory results.

Visual inspection may be used to fit the "best" line through data points, but this method is very subjective. Some criterion must be devised as a basis for the fit. One criterion would be to derive a curve that minimizes the discrepancy between the data points and the curve. Least-squares regression is one technique for accomplishing this objective.

It is easiest to interpolate between data points, and to develop correlation, when the dependent variable is linearly related to the independent variable. While individual variables may not be linearly related, they may be grouped together or mathematically manipulated, such as having their log or square root taken, to yield a linear relationship. Often theory serves as a guide for such manipulations. Since we are mainly interested in these linear relationships, we will discuss only the technique for linear least-squares regression.

We wish to fit the "best" straight line to the set of paired data points: (x1,Y1), (x2,Y2), …, (xi,Yi). The mathematical expression for the calculated values is:

yi = a1 + a2xi

where yi is the calculated (linear) value approximating the experimental value Yi. The model error, or residual, ei can be represented as

ei = Yia1a2xi

where ei is discrepancy between the measured value Yi and the approximated value yi as predicted by the linear equation and shown in Figure 1.

Figure 1. Relationship between the model equation and the data

We wish to find values for a1 and a2to give the "best" fit for all the data. One strategy would be to select values for a1 and a2 to yield a straight line that minimizes the sum of the errors ei's. Since error is undesirable regardless of sign this criterion is inadequate because negative errors can cancel positive errors. The problem may be fixed if one selects a1 and a2 such that the absolute value of the sum of errors is minimized. However one may show that this criterion does not yield a unique "best" fit. A third criterion for fitting the "best" line is the minimax criterion. With this technique one selects a line that minimizes the maximum distance that an individual data point deviates from the calculated line. Unfortunately this strategy gives an undue influence to an outliner, a single point with a large error.

A strategy that overcomes the shortcomings of these previous approaches is to minimize the sum of the squares of the errors or residuals, between the measured Yi's and the yi's calculated from the linear model. This criterion has a number of advantages. A unique line results for a given data set. This criterion also leads to the to the most likely a1 and a2 from a statistical standpoint.

Regression analysis is used to determine the constants in a relationship between variables. We only consider the simple case where y is a linear function of x. In other words we wish to find an equation y = a1 + a2x to best fit the obtained experimental data xi and Yi. At the values xi, the experimental values Yi are subject to random errors. Let’s define