memo example resume
TRANSCRIPT
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To start the calibration for Shim Safety 1 the transient rod was withdrawn to its upper limit
(100%) and the regulating rod was withdrawn to its mid-range (50% for this experiment) Shim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
John Contreras Page 2
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:
John Contreras Page 3
(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
John Contreras Page 4
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.
John Contreras Page 5
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.
John Contreras Page 6
Figure 1. Shows the effect of the control rod height on the flux.
Figure 2. Shows the transient rod integral rod worth.
John Contreras Page 7
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
John Contreras Page 8
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 ¢
John Contreras Page 9
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 ¢/%
John Contreras Page 10
Figure 7. Displays individual integral rod worth for the regulating rod in ¢
John Contreras Page 11
Figure 8. Reactor Operations Facility Worksheet
John Contreras Page11
Figure 9. Reactor Operations Genie calculations
John Contreras Page 12