development of on-line reactivity meter for parr

35 Pages·2009·0.98 MB·English

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PINSTECH-112
DEVELOPMENT OF ON-LINE REACTIVITY METER FOR PARR
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SALEEM A. ANSARI
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NUCLEAR ENGINEERING DIVISION
Pakistan Institute of Nuclear Science & Technology
P. O. Nilore, Islamabad
June, 1988
PINSTECH-112
DEVELOPMENT OF ON-LINE REACTIVITY METER FOR PARR
SALEEM A. ANSARI
NUCLEAR ENGINEERING DIVISION
PAKISTAN INSTITUTE OF NUCLEAR SCIENCE k TECHNOLOGY
P.O. N1I.OHE, ISLAMABAD
JUNE, 1988
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Abstract
An on-line digital reactivity meter has teen developed for
PARR for continuous monitoring of system reactivity. The
reactivity meter has a prompt response to any change in system
reactivity and gives the reactivity worth of fuel or sample
loading in the reactor directly in terms of %£>k/k. The reactivity
meter comprises of two main parts. The first part is the hardware
and software for on-line acquisition of standard in-plant neutron
flux signals, while the second part is high level, Fortran-77,
real- time programming for the computation of reactivity by
simultaneous solution of neutron kinetic equations. The plant
computer PDP-1123 Plus is used for this purpose on time sharing
basis with its regular data logging function. This report
describes the reactivity meter results for the determination of
sample worth, control rod calibration and power coefficient of
reactivity. The rod calibration resuLts are compared with those
obtained by positive period method currently employed in the
reactor. Reactivity characteristics of the reactor auto-controller
is also discussed.
CONTENTS
.No. Description Page
INTRODUCTION 2
1 Noise Analysis 2
2 Point Kinetic Method 2
Theoretical Consideration 3
Description of Reactivity-Meter 7
1 Data Acquisition 7
2 Algorithm for Reactivity Calculation 9
Digital Filtering 10
1 Filter Design 11
Results and Discussion 13
i Selection Criteria of the Input Signal 13
2 Effect of Digital Filtering on Input Signals 14
3 Reactivity Determination during approach to Full 15
Power
4 Determination of Reactivity worth of Irradiation 16
Samples
5 Determination of Reactivity Coefficient of PARR 17
6 Control Rod Calibration 18
7 Determination of Reactor Auto-Controller 18
Characteristics
8 Determination of Reactor Transfer Function 19
Introduction
The advantages of using a reactivity meter in a reactor are
manifold. In the start-up and operation of nuclear reactors
continuous reactivity surveillance is necessary to safely and
efficiently reach the operating power level. Critics.1 experiments
on zero power reactors require attaining many states of reactivity
in a short time. At higher power levels careful monitoring of
reactivity is needed to determine tha temperature, poison and
power coefficient of reactivity. Reactivity meter is also very
useful in determining the reactivity worth of new fue^ elements
or the irradiated samples added to the core.
There are two methods for determining reactivity from the output
history of a neutron detection system. One is the more standard
method of solving the point reactor kinetic equation. The other
method is based on the frequency analysis of fluctuations in the
neutron detector signal and determination of the break frequency
of reactor transfer function. A brief description of t! ase methods
is given in ensuing sections.
1.1 Noise Analysis
In critical and sub-critical reactor systems the fluctuations in
neutron density or reactor power arise primarily due to inherent
reactivity fluctuations in the reactor. Neglecting the
uncorrelat.ed part of the detector signal the frequency behavior of
the neutron signal is governed by the relation [1J
n(w) = -r--—r- (1.1)
w* + az
2
>
where n< « ) is the magnitude of neutron density at frequency w,
A is the normalized amplitude and a is a constant given by the
relation
a = -j-- (1.2)
where,
H = delayed neutron fraction
J* = system reactivity
1 = neutron mean life-time
From Eq.(l.l), at the value of frequency w = a, n< w) = n<0)/2.
a is thus the break frequency of the neutron density spectrum.
In the noise method the neutron density fluctuations in time
are transformed into the frequency domain by Fourier transform and
the break frequency, a, of the neutron density spectrum is obtained
exper i men Lai iy. Since delayed neutron fraction, (i, and neutron mean
life-time, 1, are constants for a particular core configuration,
reactivity can be evaluated directly from the break frequency
information (Eq. 1.2).
The noise analysis method for reactivity determination has been
applied successfully at PARR and reported elsewhere 12J. The poor
signal-to-noise ratio of the detector signal fluctuations requires
data averaging for longer periods of time which renders this
method rather difficult for on-line reactivity determination.
1.2 Point Kinetic Method
The inverse kinetic calculation of reactivity provides a fast and
flexible method of monitoring the reactivity of reactor core 13 J.
This method has distinct advantage over the stable period metuod
used for the solution of inhour equation. When one is measuring
reactivities through observation of an asymptotic period, a long
waiting time is needed to attain the dynamic equilibrium of
delayed neutron precursor concentrations so that the inhour
equation can be applied correctly. The point kinetic method
requires the neutron density as an input and reactivity is
calculated by means of simultaneous solution of point kinetic and
precursor density equations. Section 2 describes the mathematical
formulation of reactivity with the help of neutron density
information.
2. Theoretical Considerations
Point reactor kinetic equations give the global dependent behavior
of a reactor as 14,5].
dt IB i = l
rir* * ft *
-rL = r* P<»> " XiC t> (2.2)
i(
dt l
Where,
P( t) = reactor power at time t
J<t) = System Reactivity
Ci(t) = Concentration of the delayed neutron precursors belonging
to group i
\> ,iii = Decay constant and fraction of delayed neutrons
respectively for ith group
1 = Neutron mean lifetime in the reactor
S< t) = External neutron source
£.
The first and second tern.s on the right hand side of Eq. (2.1)
designate the contribution of prompt neutrons and delayed neutrons
from the decay of precursors respectively. Eq- (2.2) represents
the build-up and decay of neutron precursors.
This set of coupled differential equations can be reduced to a
signal integro-differentiai equation for P(t) which, in turn, can
be rearranged as
*«>= *+i -LLt)- P- r*->p<*->du - - iiv (2.3)
a
P< t) dt P( t > 1 & P( t)
where,
n<«) = .$, J1 Xi e-*i»
i = l 0
is the delayed neutron kernel. D(u)du is the probability that a
delayed neutron will be emitted in du about u following a fission
event at u=0. Substituting the value of D(u) in Eq. 2.3 and
rearranging one gets
j> n 1 ^ ll>_ I i« Si(t) (2-4)
(t) = + iXi
P(t)d<t) P(t) 1 = 1
where the terra Si(t) describes the power history, i.e.
r"
Si(t) = P(t-u>e->iu du (2.5)
Putting y = t-u. Si<t> becomes
Si(t) = e-Ait |jp( kiydy + j P( ekiydy J (2.6)
y)e y)
-• 0
thus for small increments in time (At)
5
f
I ti +At
;f Si<ti»At) = e"*i t iSi(ti) + e-Ajti P<y>e*iydy ] (2.7)
ti
if we denote the power integral by Ri , i . e.
ti+at
Ri = P( eAiydy (2.8)
y)
Jtl
we get
Si(tHAt) = e-*i6t(Si(ti) +Rie-J>itlJ (2.9)
if the variation of P( t) is linear with time within a small
interval of time, At, it can be expressed by
P(r, = P«,n ?LLLi*U:?Lli \- , .10)
+ y yi (2
Substituting this value of P( y) in the integral Ri we get the
source term as
it l ,1 1 AtllTl P(tl*At ) - P { t l)
Si (t 14 At) = S i ( t n e - * il - r (l-e-Ai*» )lPti) --•
(
Ai Xi At
A»
Eq. 2.11 gives the source term which is recursive in the sense
that the power in the previous time step is used along with the
current power to calculate the reactivity. This value of Si can be
used for real-time calculation of reactivity with the help of Eq.
(2.4). Denoting present and past values by subscript 1 and G
respectively, we can write
? „ 1 ,Pi-Po . 1 6 „ , „
j = JJ + i (-----) - - I BiXiSn (2.12)
Pi t Pi 1 = 1
and
1 P] -Do P] -Po
Sii = Sioe-*iAt) + -(1-e-AiAt )[ _ _i-Ll) + —--I (2.13)
Po
Ai AiAt X»
The initial value of Si is calculated from the mean power level at
which the reactor is assumed to be critical
<Po>
Sio = --- (2.14)
Ai
Eq. (2.12) is the well known inverse kinetic equation. Following
observations must be made about this equation. First of ail it is
non-dimensional in P( t) . Secondly, P<t) must have a physically
acceptable behavior, i.e. P( t> f 0 for all t.
When the reactor is operating at a steady-state power Po, i.e. the
reactor is critical, one gets from Eq. (2.12)
• Po
that is, the reactor has negative reactivity to compensate the
effect of external neutron source.
3. Description of Reactivity Meter
The reactivity meter designed for PARR reads the neutron density
signal from plant instrumentation in real-time and feeds this
information to the algorithm for the calculation of reactivity.
The functioning of the meter can be described in two parts,
namely, data acquisition and data processing. These two functions
are described in the following sections.
3.1 Data Acquisition
The analog output from the neutron flux monitoring channels in
PARR is in the form of 0...20 mA current signal. This current