memo example resume

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John Contreras Page 1 Nuclear Engineering Texas A&M University Technical Memorandum To: Dr. John Ford From: John Contreras Date: October 1, 2014 Re: NUEN 405 Laboratory 3, Control Rod Calibration Introduction The purpose of this experiment was to learn and understand how control rods are calibrated in a general setting. Before conducting the experiment the reactor operations checklist was completed to ensure safety. Using the Difference Method of calibration the transient and regulating differential and integral rod worth was calculated. For the transient rod the differential was at 100% was 0.5544 ¢/% and the integral worth was 370¢. For the regulating rod the differential and integral rod worth was 0.42582 ¢/% and 74.8¢ respectively. These results were then compared to the ideal plots given in the perturbation theory and analyzed. Procedure To start the calibration for Shim Safety 1 the transient rod was withdrawn to its upper limit (100%) and the regulating rod was withdrawn to its mid-range (50% for this experiment) Shim safety rod 4 (SS4) was then raised to 100% followed by raising SS2 and SS3 while close attention was given to watching the Log Power Channel and the period meter. Upon reaching criticality a 20 second period or longer was maintained. Once the period responded properly to the power increase, the shim safety rods were taken out to establish a period of 10 seconds or more. When the 300W range was reached the linear channel was switched into “MAN” mode (manual mode), and SS2 and SS3 were at equal heights resulting in a constant power level. SS4 was then lowered by 30¢. Only SS1 was raised to reestablish the constant 300W of power. The previous two steps were repeated until SS1 reached 100% and a constant power of 300W was

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Page 1: Memo Example Resume

John Contreras Page 1

Nuclear Engineering

Texas

A&M University

Technical Memorandum

To: Dr. John Ford

From: John Contreras

Date: October 1, 2014

Re: NUEN 405 Laboratory 3, Control Rod Calibration

Introduction

The purpose of this experiment was to learn and understand how control rods are calibrated in a

general setting. Before conducting the experiment the reactor operations checklist was

completed to ensure safety. Using the Difference Method of calibration the transient and

regulating differential and integral rod worth was calculated. For the transient rod the differential

was at 100% was 0.5544 ¢/% and the integral worth was 370¢. For the regulating rod the

differential and integral rod worth was 0.42582 ¢/% and 74.8¢ respectively. These results were

then compared to the ideal plots given in the perturbation theory and analyzed.

Procedure

To start the calibration for Shim Safety 1 the transient rod was withdrawn to its upper limit

(100%) and the regulating rod was withdrawn to its mid-range (50% for this experiment) Shim

safety rod 4 (SS4) was then raised to 100% followed by raising SS2 and SS3 while close attention

was given to watching the Log Power Channel and the period meter. Upon reaching criticality a

20 second period or longer was maintained. Once the period responded properly to the power

increase, the shim safety rods were taken out to establish a period of 10 seconds or more.

When the 300W range was reached the linear channel was switched into “MAN” mode (manual

mode), and SS2 and SS3 were at equal heights resulting in a constant power level. SS4 was then

lowered by 30¢. Only SS1 was raised to reestablish the constant 300W of power. The previous

two steps were repeated until SS1 reached 100% and a constant power of 300W was

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maintained. After calibrating SS1, the regulating rod was calculated using the same procedure as

before. This was done by leaving the regulating rod at 0% instead of SS1.

Theory

Movement of the control rods is responsible for adjusting the neutron flux or power of the reactor. The

rods have the property of reducing or increasing the thermal utilization factor (f) which depends on

whether the controls rods are inserted or taken out of the core[1]. Moving the controls and changing the

reactivity of the core also change the keff value; therefore, the worth of a control rod is directly related to

the effect it has on the reactivity of the reactor and is usually measure in the same units[2]. The effect of

controls on the flux of a reactor can be seen in Figure 1 in the appendix[3]. There are two types of control

rod worth, integral rod worth and differential rod worth. The integral rod worth is the total reactivity

worth of the rod at a certain degree of withdrawal, and is usually at the maximum when the rod is fully

withdrawn as can be seen in Figure 2[3]. The differential rod worth is the reactivity change per unit

movement of a rod and is expressed in units of /inch, ∆k/k per inch, or pcm/inch[2]. The summation of all

the differential rod worth is the integral rod worth at a given withdrawal. The worth of any control rod at

any position in the core can be calculated using the perturbation theory[3].

By using this theory Eq. 1 below shows the rod worth is:

(1)

Where z is measured from the top of the core of the reactor. Eq.1 is called the integral rod worth. If the

derivative of the integral rod worth is taken, as shown in Eq. 2, the differential rod worth curve can be

determined.

(2)

The differential rod worth curve can be estimated by either a sine function or a cosine function as seen in

Figure 3.

To calibrate the rods the period must be determined by fitting the power level curve using the equations

below:

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(3)

(4)

Based on the characteristic s1, the reactivity insertion required to produce the period determined can be

obtained using the in hour Equation (Eq. 5) below:

(5)

Where l is the prompt neutron lifetime, βk is the delayed neutron fraction, and λk is the decay constant.

For the NSC core βeff was used instead of β as shown in Eq. 6 below:

(6)

After obtaining the reactivity, the reactivity can be divided by the distance of the pull to obtain the

differential rod worth. The integral rod worth can then be calculated by integrating the differential rod

worth function as mentioned previously. There are six different types of delayed neutrons precursors and

βeff is the average of them all. Each type of fuel has its own βeff that is determined by the delayed neutron

precursors for that fuel.

Results and Analyses

Using Eq. 4 and Eq. 6 the differential rod worth for the transient rod was calculated. When the

rod was 100% withdrawn the differential rod worth was 0.554455446 ¢/% and the integral rod

worth was 370¢. The results for the rod at different points of withdrawal are located in Table 1.

By plotting the calculations for both types of worth Figure 4 and Figure 5 were obtained. When

compared to the ideal curve for the differential worth from the perturbation theory the plot

obtained in Figure 4 does not fit with the ideal curve in Figure 3. Figure 4 is shifted to the left of

the ideal having a ¢/% peak at a lower withdrawal percentage. This deviation from the ideal could

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be due to not having as many points taken, or possibly to taking away too much worth in each

step. The integral plot in Figure 5 however compares favorably to the ideal in Figure 2. Although

the differential rod worth was off, the shape of the curve was still a cosine function so when the

integral was taken to determine integral rod worth the plot of the results came out ideal. Eq. 4

and Eq.6 were again used to determine the differential rod worth for the regulating rod. As seen

in table 2 when the rod was 100% withdrawn the differential rod worth was 0.425824176 ¢/%

and the integral rod worth was 74.8¢. Figure 6 and Figure 7 show the differential and integral rod

worth plots for the regulating rod. Due to taking very few withdrawal points the plot in Figure 6

is very rigid and does not depict a curve very well. The plot does however peak close to the

midpoint, 44% withdrawn, just like the ideal curve peaks when the rod is at 50% withdrawal.

Figure 7 is also rigid due to lack of points but still maintains the same shape as the ideal. Large

jumps in worth were taken in calibrating the regulating rod causing the results to be skewed.

There were various sources of error for the experiment. Once possible source of error is the fact

that he reactor had to be brought up to critical, a steady state in power. If the experiment went

too quickly in between pulls of the control rod, a supercritical state could be misinterpreted as a

steady state. This would skew the results, as the calculations of the next position did not start

when the reactor was at equilibrium. Another source of error could emerge from misreading the

linear power level gauge. The experiment was meant to start and end each pull at the same place,

but often there would be a variation between the previous pull.

The advantage of the Positive Period Method is that it is very accurate. It is very good at obtaining

accurate and precise data for each trial. This makes calibration more consistent, allowing for a

better reference for the next calibration. This is counter-intuitive to the characteristics of the

Negative Rod Drop calibration method.[4] The negative drop method differs from the Positive

Period Method because of its speed, it is very quick to run several calibrations with this method.

Hinders with the Rod Drop method is that it has a relatively high error probability. It is of value

when a time constraint deems other methods impractical. To use the

Rod Drop method, an inaccuracy of about 30%must be accepted.[4] It may be useful to use both in

conjunction with each other, but the control rod method is much more accurate, allowing the

experiment to yield beneficial data.

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References

1. "Control Rods." Education and Training :Nuclear Safety and Security. IAEA, n.d. Web. 1 Oct. 2014.

2. "Figure 10 Differential Control Rod Worth." Figure 10 Differential Control Rod Worth. N.p., n.d. Web. 01 Oct. 2014.

3. W.D. REECE, NUEN 405 Class Notes, Nuclear Engineering Department, Texas A&M University (Fall 2013).

4. Buoni, Frederick B. EXPERIENCE WITH THE USE OF THE ROD-DROP METHOD OF ROD CALIBRATION AT THE ORR AND LlTR. N.p.: Oak Ridge Ntnl. Laboratory, 1963. Print.

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Figure 1. Shows the effect of the control rod height on the flux.

Figure 2. Shows the transient rod integral rod worth.

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Figure 3. Shows the transient rod differential rod worth

Table 1

Differential and integral rod worth for the transient rod is show in the table. These results were

obtained by using Eq.4 and Eq.6.

Transient Rod

%Withdrawn Reactivity (¢) Differential (¢/%) Integral (¢)

0 0 0 0

9.8 30 3.06122449 30

15.7 29.3 4.966101695 59.3

20.7 29.6 5.92 88.9

25.4 30.5 6.489361702 119.4

29.8 29.4 6.681818182 148.8

33.9 27.3 6.658536585 176.1

38.7 32.7 6.8125 208.8

43.5 32.1 6.6875 240.9

48.7 27.7 5.326923077 268.6

56.7 31.8 3.975 300.4

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63.5 26.4 3.882352941 326.8

79.8 32 1.963190184 358.8

100 11.2 0.554455446 370

Figure 4. The plot of the transient rod differential rod worth in ¢/%

Figure 5. Shows the plot of the integral rod worth of the transient rod in ¢

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Table 2

Differential and integral rod worth for the regulating rod is show in the table. These results were

obtained by using Eq.4 and Eq.6.

Regulating Rod

%Withdrawn Reactivity (¢) Differential (¢/%) Integral (¢)

0 0 0 0

27.5 18.5 0.672727273 18.5

44 20.5 1.242424242 39

63.6 20.3 1.035714286 59.3

100 15.5 0.425824176 74.8

Figure 6. Displays the differential rod worth for the regulating rod in ¢/%

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Figure 7. Displays individual integral rod worth for the regulating rod in ¢

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Figure 8. Reactor Operations Facility Worksheet

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Figure 9. Reactor Operations Genie calculations

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