Keywords

1 Introduction

The Studsvik nuclear reactor analysis code, SIMULATE-3, has been extended to transient applications for both engineering analysis and real-time operator training. The physics models used in S3R are much the same as those used for steady-state core design/safety analysis, except that no core design or depletion calculation are done, and some simplifications are introduced to run in real-time under the control of real-time executive.

S3R has become the standard in 3D real-time core models for training simulator. It has been installed in more than 90 sites worldwide. The neutronics model of S3R has been coupled to several real-time thermal hydraulic models, including RELAP5, used in training simulators.

2 Neutronic Model Description

2.1 Features

The neutronics model used in S3R solves the 3-D, two-energy group, neutron diffusion equation with one radial node to represent each fuel assembly. In the axial direction, 24–25 nodes are typically used to represent the active portion of each fuel assembly, and one node is used to represent the upper and lower reflectors.

The S3R core model uses a fourth-order flux expansion to represent the neutron flux distribution within each node (in each of the three directions), and the spatial gradient of the flux can then be taken analytically (a third-order function, rather than the traditional first-order function). This results in a much more accurate representation for the flux than that of simpler methods.

The S3R core model uses explicit nodes (both radially and axially) to model the PWR baffle/reflectors. This permits direct solutions for the fluxes and leakages into the reflectors, without need for introduction of albedos (which are often used in simpler models) to treat the leakage out of the core. The baffle/reflector nodes are treated like any other node in the S3R core model.

2.2 Nuclear Data

Accuracy of the S3R core model depends not only on detailed 3-D neutronic and thermal- hydraulic modeling, but also on accurate representation of feedback parameters. These parameters include:

  • Two-Group Macroscopic Cross Sections

  • Fission Product Yields and Microscopic Cross Sections

  • Assembly Discontinuity Factors (ADFs)

  • Kinetics Data (Betas, Lambdas, Velocities)

  • Spontaneous Fission/Alpha-n Neutron Sources

  • Decay Heat Data (Fission Fractions by Isotope)

  • Pin Power Distributions

  • Detector Data

The functional dependence of the nuclear parameters is expressed as “base cross-section” and several “delta cross-sections” in the form:

$$ \begin{array}{*{20}l} {NP^{S3R} \left( {\rho ,\sqrt {TF} ,N_{xe} ,N_{sm} ,N_{Bo} ,wfct_{2} ,wfct_{3} } \right) = } \hfill \\ { = NP_{Base} (\rho )} \hfill \\ { + \frac{\partial NP}{{\partial \sqrt {TF} }}(\rho ) \cdot \left( {\sqrt {TF} - \sqrt {TF^{REF} } } \right) + } \hfill \\ { + \frac{\partial NP}{{\partial N_{Bo} }}(\rho ) \cdot \left( {N_{Bo} - N_{Bo}^{REF} } \right) + } \hfill \\ { + \frac{\partial NP}{{\partial CR2}}(\rho ) \cdot wfct_{2} + \frac{\partial NP}{{\partial CR3}} \cdot wfct_{3} + } \hfill \\ { + \delta NP(Xe) + NP(Sm)} \hfill \\ \end{array} $$

For a given core life, all the history effects are frozen and only the instantaneous effects are input to S3R. The only instantaneous dependence is due to the moderator density, fuel temperature, control fractions, and boron. By freezing all history dependence, the calculation of the base cross-section is reduced to a set of 1D interpolations in density.

2.3 Decay Heat

Following a fission event in the fuel, about 93% of the heat of fission is immediately released, and the remaining 7% is released slowly over time. Modeling of this decay heat is very important in transients which have large changes in power level (e.g., Reactivity excursions, SCRAMs, and LOCAs). The fission product heat generation in S3R is modeled by using the ASNI/ANS-5.1, 23-group data. The decay heat sources are initialized as part of the steady-state solution in S3R by assuming infinite-time operation at constant power. It can be reset at any time after shutdown (see example in Sect. 5.1).

The predominant isotopes that contribute to decay heat are U-235, U-238, Pu-239, and Pu-241. The split among these isotopes varies from node to node with exposure. Effect of neutron capture in fission products and contributions from heavy elements (U-239 and Np-239) are also included.

2.4 Detectors

For in-core detectors, the detector responses are predicted as the power average from the surrounding nodes. The geometrical weighting factors account for the axial position of the detector. The detector constants are specified individually for each detector string and its surrounding channels and are obtained from the data library. Their radial locations as well as the number of axial strings and axial locations at each radial location are provided in the S3R input file. Flux data at these locations will be accessible from the instructor station and process computer.

In the case of ex-core detectors, top and bottom detector signals are constructed based on weighted sums of the flux at the core boundary and reflect accurately power imbalances and flux tilts. Detector response is based on flux value at the location of the detectors. A weighting is used to relate the ex-core detector response to the powers of the bundles contributing to it. Changes in the downcomer density cause changes in the attenuation of neutron escaping from the core and reaching the detectors and its effect is accounted for by using an empirical function of downcomer density.

3 Coupling to System Code

This section describes the algorithm and software used to expand thermal-hydraulic data from an RCS model, such as RELAP5, to S3R and collapse nodal powers from S3R to RELAP5-3D. RELAP5-3D is used as an example herein; however, the coupling algorithm may be applied to any system code which can model core channels. The RELAP5-3D model uses a coarser nodalization in the active core regions than S3R and a method for expanding the RELAP5-3D data from this coarse nodalization to the fuel assembly wise data needed for S3R is needed. The axial nodalization may also be different between the models and this is addressed by the algorithm.

For a 3-loop PWR, typically RELAP5 groups the assemblies into 4 active channels (each representing 39¼ assemblies). The channels assignment is illustrated in the figure below. S3R uses 5 radial power zones. The fifth zone receives the average properties from the 4 RELAP5 channels. This is illustrated below.

figure a

In the axial direction, a possible nodalization used in RELAP5 is:

  • 6 hydraulic cells per channel

  • 24 heat structures per channel

S3R uses 24 axial levels per assembly (see illustration below).

A mapping scheme that takes the RELAP5 data and expands it from the RELAP5 geometry to the S3R nodalization and collapses the S3R data for use in RELAP5 has been implemented in S3R.

The algorithm is comprised of three parts. The first part takes the thermal-hydraulic data and expands it to S3R axial nodalization utilizing an axial power weighting scheme in each thermal-hydraulic channel. The second part uses a power-weighting scheme to expand the fuel temperatures in the radial direction using the last time step 3D power distribution. The third part uses a simple enthalpy rise model and last time step 3D power distribution to calculate the nodal moderator densities.

figure b

A few assumptions are made:

  • The number of axial subdivisions in the RELAP5 volumes and/or heat structures for the active fuel shall be such that an integer multiple of S3R axial nodes are bound by a volume or heat structure height.

  • The number of axial subdivisions in the RELAP5 volumes and/or heat structures shall not be greater than the S3R axial nodalization.

  • The number radial flow paths used in the RELAP5 model shall only include full assemblies, assemblies may not be subdivided.

  • Thermal-hydraulic data shall be provided for the lower and upper plenum regions of the RELAP5 model for use in the reflector cross-section calculations.

4 Interfface with Executive

S3R is used as a library used during the generation of the load regardless of the real-time executive used on the simulator. There are basically two interface routines used to transfer data back-and-forth between S3R and the rest of the simulator. An illustration of what is exchanged at each time step is shown here.

figure c

5 Cycle Update and Initial Conditions

The key factor in updating the core data on the training simulator for S3R is that all the information needed for such an update is contained in the SIMULATE nuclear data library and restart files. The transfer of data from core depletion calculations to the simulator is automatic and does not require any intermediate program or additional data manipulation.

To update the core model with data for a new cycle, the following information needs to be supplied by the organization that maintains the CASMO/SIMULATE model:

  1. a)

    Nuclear data library for the new cycle from Studsvik’s CMS system.

  2. b)

    Restart file(s) for the new cycle with enough exposure points to be able to model all core lives of interest (e.g., BOC, MOC, EOC, etc.).

  3. c)

    Input and output files from the S3 core depletion calculations. This is needed to conveniently determine the conditions used at each depletion point and the exposure points saved on the restart file.

  4. d)

    The boron concentration used during the core depletion calculations for the core lives of interest.

  5. e)

    Updated S3R input files (essentially only the ‘RES’ and ‘LIB’ cards) to provide names of the new data files and point to the exposure of interest.

The process of updating ICs with new core data is straightforward and includes the following steps:

  • Acquire the nuclear data files (S3 restart and library files) for the new cycle

  • Edit the S3R input file to point to the new nuclear data files

  • Reset to an existing IC

  • Set the boron concentration

  • Snap to a temporary location

  • Reset to snapped IC to reinitialize (this step accesses the new core data)

  • Run until steady state has been established at the desired power level, while using the fast xenon flag to force xenon to equilibrium.

  • Snap IC. Process completed.

Depending on the real-time executive, it may be possible to automatize this process using scripts. An example from one site includes the different parts in which the conditions of the existing ICs are used to generate an IC-specific restart file to be used in updating the ICs with the new cycle core data. This is illustrated below.

figure d

6 Physics Testing

The S3R core model has been validated against CMS results, vendor codes, and plant data when available. As part of the implementation of S3R on a training simulator, standalone physics testing is conducted to compare, in the case of PWRs, power distributions, critical boron concentrations, boron coefficients, temperature coefficients, bank worths, and xenon and samarium worths.

This is done by running S3R (with its own internal TH model) and compare it to the design code (SIMULATE-3 or SIMULATE5). Results from the vendor’s code, typically available in the Nuclear Design Report, are also used to validate the S3R model.

Finally, S3R predictions are validated against plant data, such as data collected during the Low-Power Physics Tests conducted during the plant startup and flux maps when these are generated.

Examples of comparison results are show below for boron letdown, temperature coefficient, and bank worths.

figure e
figure f
figure g

7 Core Monitoring

Many LWRS use a core monitoring system in the plant control room. These core monitor systems combine measured data and physics calculations to provide operations assistance information. For a variety of reasons, these systems are frequently not available in the simulated control room or are available only via a simplified emulation.

Although conceptually simple, there have been obstacles to implementing core monitoring in the simulator control room. Besides cost and hardware, one important issue from a training point of view is accuracy. The simulator core models take the place of measured data in the plant. The core monitoring system takes measured data and performs calculations to predict things that are not measured. If the simulator is generating inaccurate “plant data,” the simulator core monitoring system will generate an inconsistent plant state, and the predicted results will be unusable.

Since S3R is an engineering-grade core model and replicates closely design calculations, it can be used to provide data to a core monitoring system in lieu of the process computer in the plant. This has been demonstrated in several sites which use the simulator version of the Studsvik Core Monitoring product GARDEL. This version, called GARDEL-SIM, runs on its own server (PC, Linux, or Unix) and responds consistently to executive commands such a run, init, freeze, etc. It also responds to numbered Initial Conditions (ICs) or backtracks and gets “plant data” directly from the simulator database.

The data requirement for GARDEL-SIM is the same data required by S3R. No additional data is required.

8 Additional Items

8.1 Decay Heat Reset

S3R includes several fast flags to advance the fission products (Xe and Sm) solution or the decay heat solution faster than real time. One option for decay heat is to be able to reinitialize to a representative decay heat at a given time after shutdown. An example is shown below. This figure shows three curves:

  • The base case in red with the expected decrease of decay heat after shutdown

  • The case with multiple reinitialization in blue with:

    1. (1)

      Reinitialization to 10 days after shutdown

    2. (2)

      Reset to about 52 s after shutdown

    3. (3)

      Reset to about 17 s after shutdown

    4. (4)

      Reinitialization to 1 day after shutdown

  • Verification that time behavior after reset to 52 s after shutdown is preserved (broken green line)

This code feature makes the control of the amount of decay heat after shutdown and its impact on the response of the system very straightforward alleviating any need for guessing or tuning.

figure h

8.2 Xenon Worth

In most cases, the calculation of xenon worth edit is assumed to be proportional to the average xenon concentration. This is a valid assumption in typical LWRs and is one of the methods used in S3R. Not this is only used for providing a xenon.

One case where this assumption shows its limitation is when the core uses mixed UO2 and MOX assemblies. The MOX fuel assemblies have higher initial (equilibrium) Xenon number density due to larger yield and smaller absorption cross section, which dominates the total xenon in the core. On the other hand, the Xenon worth is larger in UO2 fuel (due to softer spectrum) than MOX, and this dominates the core reactivity. Therefore, the time to peak differs between MOX and UO2.

The figure below show change in xenon concentration (red) and the change in xenon worth (blue) following a scram. The largest xenon worth change occurs about one hour later than the peak xenon.

figure i

9 Conclusions

S3R and its connection to the design methods of Studsvik has been demonstrated as the go-to tool for training simulators. Since it can directly take data from the depletion calculations, it makes the cycle update automatic and the process of generating new ICs fast and easy. With S3R, training anywhere in the cycle or performing just-in-time training, is readily available.