Pebble Bed Reactor Research Articles

Neutronics Analysis on High-Temperature Gas-Cooled Pebble Bed Reactors by Coupling Monte Carlo Method and Discrete Element Method

The High-Temperature Gas-Cooled Pebble Bed Reactor (HTG-PBR) is notable in the advanced reactor realm for its online refueling capabilities and inherent safety features. However, the multiphysics coupling nature of HTG-PBR, involving neutronic analysis, pebble flow movement, and thermo-fluid dynamics, creates significant challenges for its development, optimization, and safety analysis. This study focuses on the high-fidelity neutronic modelling and analysis of HTG-PBR with an emphasis on achieving an equilibrium state of the reactor for long-term operations. Computational approaches are developed to perform high-fidelity neutronics analysis by coupling the superior modelling capacities of the Monte Carlo Method (MCM) and Discrete Element Method (DEM). The MCM-based code OpenMC and the DEM-based code LIGGGHTS are employed to simulate the neutron transport and pebble movement phenomena in the reactor, respectively. To improve the computational efficiency to expedite the equilibrium core search process, the reactor core is discretized by grouping pebbles in axial and radial directions with the incorporation of the pebble position information from DEM simulations. The OpenMC model is modified to integrate fuel circulation and fresh fuel loading. All of these measures ultimately contribute to a successful generation of an equilibrium core for HTG-PBR. For demonstration, X-energy’s Xe-100 reactor—a 165 MW thermal power HTG-PBR—is used as the model reactor in this study. Starting with a reactor core loaded with all fresh pebbles, the equilibrium core search process indicates the continuous loading of fresh fuel is required to sustain the reactor operation after 1000 days of fuel depletion with depleted fuel circulation. Additionally, the model predicts 213 fresh pebbles are needed to add to the top layer of the reactor to ensure the keff does not reduce below the assumed reactivity limit of 1.01.

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. This paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem. Program summaryProgram title: MOOSE Fluid Properties moduleCPC Library link to program files:https://doi.org/10.17632/cwzhsyp6pd.1Developer's repository link:https://github.com/idaholab/moose/tree/next/modules/fluid_propertiesLicensing provisions: LGPLProgramming language: C++, PythonNature of problem: The simulation of thermal hydraulics of advanced nuclear reactor systems, such as heat pipe micro-reactors or molten-salt cooled pebble bed reactors, requires a wide variety of discretizations of the fluid flow equations, from 1D thermal hydraulics to computational fluid dynamics at various levels of fidelity, with a wide variety of coolants. Applications are developed within the MOOSE C++ framework by Argonne and Idaho National Laboratories to simulate these reactors for research and design purposes. These applications (Sockeye, SAM, others) rely on MOOSE for the computation of fluid properties. The fluid properties module contains properties for most advanced nuclear reactor coolants, including an interface to the Molten Salt Thermodynamics Database (MSTDB) developed by Oak Ridge National Laboratory. Single phase, two phase, and gas mixtures fluid properties are computed by the module.Solution method: The fluid properties module includes numerous numerical methods to support the wide range of applications, notably forward automatic differentiation, conversion methods between pressure and density-driven variable sets, spline-based table lookups which are the current state of the art for the fast computation of fluid properties. The integration with MOOSE facilitates uncertainty quantification with regards to the fluid properties and optimization studies with regards to the fluid composition.

Uncertainty Propagation of Monte Carlo Cross-Section Generation for Graphite-Moderated Pebble Bed Reactors

Monte Carlo codes have become increasingly popular for generating homogenized few-group cross-section data, especially for advanced reactor designs that have complex geometries and nontraditional compositions. However, the stochastic nature of Monte Carlo processes has the potential to introduce additional statistical uncertainties in the overall uncertainty in the prediction of core behavior. The work performed in this research quantified the additional uncertainty introduced by the use of Monte Carlo multigroup cross sections into the analysis of graphite-moderated pebble bed reactors. In this research, the objective was achieved by performing uncertainty quantification for the key output parameters in deterministic steady-state and transient safety calculations. The results show that when the homogenized multigroup cross sections are generated with a sufficient number of neutron histories in the Monte Carlo calculation, the uncertainties in the subsequent deterministic simulations caused by the Monte Carlo cross-section uncertainty are negligible compared to the contributions from the uncertainties of other input parameters.

Development and assessment of an integrated multigenerational energy system with cobalt-chlorine hydrogen generation cycle

This study aims to develop and assess a new multigeneration system where nuclear heat is utilized as the energy source. The multigeneration system is further designed to generate power, cooling, freshwater and hydrogen. In the present multigeneration system, five main subsystems, including high-temperature gas-cooled pebble bed nuclear reactors, a Rankine cycle, a cobalt-chlorine thermochemical cycle, a multi-effect desalination system and an ammonia-water absorption refrigeration system are integrated for synchronized operation. The analyses of the present system are carried out with the approaches of energy and exergy. This integrated system uses a total of 1000 MW thermal energy that is obtained from four units of high-temperature gas-cooled pebble bed nuclear reactor. Using all the thermal energy that comes from the nuclear reactors, a total of 346.99 MW of electricity, a total of 1.59 MW of cooling, a total of 384.67 kg/s of freshwater, and a total of 0.25 kg/s of hydrogen are produced. The energetic and exergetic performance coefficients of the ammonia-water absorption refrigeration system are 0.74 and 0.83, respectively. While the energy efficiency for the overall system is calculated as 37.83%, the exergy efficiency is found to be higher as 46.32% with the multiple useful outputs which help exergetically improve the overall system.

Identification of TRISO pebbles at arbitrary orientation using pairs of X-ray radiographs

TRISO (tri-structural isotropic) fuel is anticipated to be one of the fuel types for future small modular reactors. A TRISO-fuelled pebble in a pebble bed reactor (PBR) consists of thousands of TRISO fuel particles embedded inside a graphite sphere. The diameter of each of the fuel particles is approximately 1 mm. A PBR can contain hundreds of thousands of pebbles, each with a diameter of approximately 6 cm. Unlike in traditional reactor designs, which have a relatively small number of discrete fuel assemblies, the large number of pebbles inside a PBR makes the tracking of individual fuel pebbles difficult. The distribution of TRISO particles within the pebble provides a unique fingerprint that identifies a pebble and can be used to track it. This fingerprint can be determined using a standard X-ray radiograph or a more time-consuming X-ray computed tomography scan. When an individual radiograph is used, the pebble image is compared to a library of reference images of the pebbles. To obtain a good match, the orientation of the pebble must be close to the orientation used for the reference image. As a pebble exits the reactor in a random orientation, the pebble must be reorientated before its identification can take place. This paper discusses the addition of a reference particle in the non-fuelled region of the pebble, as well as the simultaneous acquisition of pairs of radiographs at 90° with respect to each other, to aid pebble reorientation and the development of an identification framework. The framework follows a hybrid approach in which the pebble is first reorientated using machine learning techniques before being identified using traditional computer vision techniques. Other effects such as the impact of transmutation of the elements inside the fuel and the radioactivity of irradiated pebbles are also discussed.

Heavy metal loading effects on special nuclear material and waste of an uprated Indonesian Reaktor Daya Eksperimental

This technical policy study investigated the effect of heavy metal loading (HML) quantity in the pebble fuel on the special nuclear material (SNM) and waste quantities in an uprated Indonesian pebble bed reactor design, the Reaktor Daya Eksperimental (RDE). A set of Monte Carlo simulations, performed using OpenMC, was deployed to simulate the pebble fuel depletion using an infinite lattice reactor calculation. This study considers HML, fuel residence time, leftover 235U, total Pu, medium- and long-lived wastes, number of depleted pebbles, and volume of waste at different HML values, at attainable discharged fuel burnup, at a target burnup of 80 GWd/MTU and at different reactor powers (10 and 40 MWt). Due to an over-moderation effect, a higher HML quantity shortened the attainable discharged fuel burnup level, which also translated to a lower fuel utilization. An 80% higher HML quantity resulted in about a 25% lower burnup level. Assuming a five-pass refueling scheme, this resulted in approximately three times more leftover 235U, 2.4 times more Pu, 1.4 times more medium-lived waste, and 1.5 times more long-lived waste collections per year. The study showed that a power uprating by a factor of four increased the SNM and waste quantities by four times.

Assessment of CFD Predictions Using Experiments from a Heated Gas-Cooled Pebble Bed Facility

This paper presents computational fluid dynamics (CFD) simulations of the coolant gas flow in a pebble bed reactor core to assess the suitability of CFD models to accurately predict the temperature distribution and possible occurrence of local hot spots that may affect pebble integrity. This study assessed CFD predictions against temperature distribution measurements from the SANA test facility at the Research Center Jülich in Germany. A realistic pebble bed structure of randomly packed 1584 pebbles was produced using the discrete element method to model the pebble packing in detail. A total of 96 experimental temperature pebble points were used for the assessments, covering a broad range of heating powers (10 kW ≤ Poperation ≤ 35 kW). A good agreement between the CFD predictions and the SANA measurements was obtained for two coolants, nitrogen and helium, along the height of the pebble bed. It is anticipated that a better understanding of the suitability of the existing CFD models gained through this study will aid in the identification of gaps and areas of improvement for CFD to support the design and safety evaluations for pebble bed small modular reactors.

Capturing the run-in of a pebble-bed reactor by using thermal feedback and high-fidelity neutronics simulations

Modeling the run-in of a pebble-bed reactor (PBR) can be challenging as a result of changes in the power, fuel type, and temperatures that occur throughout the run-in period. Previous work utilized high-fidelity neutronics simulations or lower-fidelity coupled neutronics/thermal-hydraulics models to capture the general characteristics of the run-in process. The present work employs high-fidelity neutronics simulations (using Serpent) coupled with thermal-hydraulics simulations (using Griffin–Pronghorn) to capture the thermal feedback present during the run-in and approach to equilibrium for a PBR. Incorporating thermal feedback enables important distinctions to be made about conditions occurring inside the core,as the power distribution, discharge burnup, and isotopic compositions are all affected by the temperature distribution.

Thermohydraulic Analysis of Coolant Entry Patterns in a High-Temperature Pebble Bed Reactor: Insights and Characterization

Thermohydraulic Analysis of Coolant Entry Patterns in a High-Temperature Pebble Bed Reactor: Insights and Characterization

Rotation-invariant rapid TRISO-fueled pebble identification based on feature matching and point cloud registration

The Pebble-bed reactor (PBR) utilizing TRISO-fueled pebbles is a promising Gen-IV reactor design due to its inherent safety and thermal efficiency. Identification of pebbles exiting the core may provide IAEA with additional information enhancing PBR safeguards help validate software predicting pebble flow behavior and burnup, and optimize fuel usage strategies should granular fuel management be needed. We propose a rapid, accurate pebble identification method applicable to commercial PBRs. Our approach relies on the unique spatial distribution of TRISO particles associated with each pebble, which can be extracted through X-ray CT. We developed an algorithm to identify a single pebble from 100,000 pebbles and achieved 100% identification accuracy in 90,000 trials, with arbitrary rotations and high noise levels. Remarkably, the outermost TRISO particle positions within a 0.6-mm shell suffice for unique identification. With an average identification time of under 50s per pebble, our method is compatible with PBR operational demands.

Prototyping of a Machine Learning–Based Burnup Measurement Capability for Pebble Bed Reactor Fuel

The pebble bed reactor is a unique reactor design due to its capacity for continuous multipass circulation of the fuel elements, without causing interruption to reactor operation, with the assistance of the burnup measurement system. Such a system necessarily requires an accurate knowledge of the burnup of each fuel pebble upon ejection from the core so as to inform the reloading decision and to ensure that no pebble exceeds the regulated discharge burnup limit at any point following reinsertion into the reactor core. In this work, we conceptualize, develop, and demonstrate a machine learning–based fuel burnup prediction framework leveraging advanced modeling and simulation capabilities. At its core, machine learning regression models are learned from simulated data to establish the correlation among the irradiated fuel composition (hence burnup), the gamma leakage spectrum, and the gamma spectroscopy results. Sensitivity analysis is conducted to quantify the impact of unknown design parameters, such as fuel enrichment, and irradiation environment, including power density, temperature, and neighboring materials, on the prediction accuracy of various supervised regression algorithms. The effects of a short cooldown period on machine learning prediction accuracy are also investigated. A test data set is used to validate that the data generation methodology proposed in this work successfully results in a machine learning model capable of interpolating its prediction of burnup onto a much wider range of irradiation conditions than were explicitly represented in the training database. The inclusion of a cooldown period of just 2 h leads to a prediction root-mean-square error of <5 MWd/kgU when the fuel enrichment is known and <9 MWd/kgU otherwise.

Equilibrium core modeling of a pebble bed reactor similar to the Xe-100 with SCALE

As the nuclear industry moves towards licensing and constructing advanced reactors, new attention has been focused on the advanced reactor designs that have past operational experience, such as pebble-bed high-temperature gas-cooled reactors (PB-HTGRs). Pebble-bed reactor designs have many advantages, such as their higher operating temperatures and online refueling capabilities. However, high-fidelity computational modeling of pebble-bed reactor designs, from reactor startup to operation at equilibrium, is more challenging compared to conventionally fueled reactors due to the continuous movement of the fuel pebbles through the reactor during operation. In previous work at Oak Ridge National Laboratory (ORNL), the SCALE Leap-In method for Cores at Equilibrium (SLICE) was developed around tools within the SCALE code system. This iterative method can effectively generate pebble-bed reactor zone-wise fuel inventories at equilibrium core operation within a reasonable computational time. The objective of this work was to further verify the ORNL SLICE method and to investigate the impact of considering temperature profiles during the application of the method. The SLICE method was applied to a modular high-temperature gas-cooled reactor design based upon publicly available design specifications of the Xe-100 pebble-bed reactor. Upon comparing the results from the SLICE method to published literature, the differences in the eigenvalue keffective were on the order of several hundred pcm (percent millirho). To investigate one possible cause of these differences, a study looking at the sensitivity of the full-core equilibrium keffective and discharge nuclide inventory to temperature was performed by developing equilibrium cores of two additional temperature profiles. From this temperature study, differences on the order of hundreds of pcm for the full-core equilibrium keffective, and up to 15% difference for the discharge inventories were found. These results indicated the strong dependence on temperature that needs to be considered for future work in equilibrium modeling of PB-HTGRs.

Investigating geometry adjustments for enhanced performance in a PeLUIt-10 MWt pebble bed HTGR with OTTO refueling scheme

This research investigates the impact of changes in reactor geometry to discover more optimal dimensional options for nuclear power plants with potential applications in remote areas of Indonesia. The reactor used is PeLUIt-10, a pebble bed High-Temperature Gas-cooled Reactor (HTGR) with a 10 MWt capacity and a “once-through-then-out” or OTTO fuel loading scheme. The neutronic and thermal–hydraulic performances of PeLUIt-10 were analyzed with its core size altered, first by modifying its height-to-diameter ratio (H/D ratio) and second by reducing its core volume. These analyses were performed using the Pebble Bed Reactor Neutron Diffusion (PEBBED) Code, a specialized tool to analyze HTGR reactor physics parameters, particularly Pebble Bed Reactors.. Neutronic parameters analyzed include total fuel flow, burnup, power peaking factor, and power density distribution. For thermal-hydraulics and safety, parameters include steady-state and transient fuel temperatures, especially in Depressurized Loss of Forced Cooling (DLOFC) accidents. Results show that the optimal design, maintaining a volume of 5 m3, is a reactor with a height of 159.57 cm and a diameter of 200 cm (H/D ratio of 0.8). The fuel can achieve a maximum burnup of 80.97 MWD/kg-HM at this size. Power density distribution at these dimension is better than another dimensions, with a relatively low power peaking value of 1.4. For safety parameters, the fuel temperature in transient conditions remains below the safety limit. Meanwhile, when the core volume is reduced, the minimum burnup target of 60 MWD/kg-HM at a reactor volume of 4.4 m3 with a diameter of 172 cm and height of 189.2 cm. Thus, for OTTO-cycle PeLUIt-10, altering H/D ratio is more beneficial.

Safeguards and Security for High-Burnup TRISO Pebble Bed Spent Fuel and Reactors

Several high-temperature thermal neutron–spectrum pebble bed reactors are being commercialized. China has started up two helium-cooled pebble bed high-temperature reactors. In the United States, the X-Energy helium-cooled and the Kairos Power salt-cooled pebble bed high-temperature reactors will produce spent nuclear fuel (SNF) with burnups exceeding 150 000 MWd per tonne. The reactor fuel in each case consists of small spherical graphite pebbles (4 to 6 cm in diameter) containing thousands of small TRISO (microspheric tri-structural isotropic) fuel particles embedded in the fuel of zone these pebbles. The unique isotopic, chemical, and physical characteristics of this high-burnup SNF create a technical case to eliminate safeguards based on the low risk for use in nuclear weapons, while maintaining safeguards in terms of risk for use in radiological weapons. These safeguards could be reduced to the simple counting and monitoring of pebbles in storage. Alternatively, there is the option to create a special category with reduced requirements for this SNF in storage, transport, and disposal. No safeguards would be required for a repository with only this type of SNF. Reactor safeguards are required for fresh fuel, partly burnt fuel, and to identify unconventional pebbles with depleted uranium or other materials that might be used to create weapons-useable materials.

Flow analysis through a randomly packed pebble-bed geometry using computational fluid dynamics

This study presents a comprehensive analysis of the flow behavior in packed pebble-bed reactors using computational fluid dynamics (CFD) simulations. The pebble-bed geometry corresponds to an experimental facility located at the Texas A&amp;M Thermal-Hydraulics Research Laboratory. The unsteady Reynolds-averaged Navier–Stokes (URANS) k−ω shear stress transport (SST) and the large eddy simulation (LES) approaches were selected to model the turbulence at different Reynolds numbers. The numerical models were first validated by comparing the pressure drop results obtained from the simulations against established correlations, finding the simulation predictions in accurate agreement. Secondly, the velocity first-order statistics from the URANS k−ω SST and LES calculations were also contrasted with the available experimental particle image velocimetry data to validate the numerical models. Results were found in reasonable agreement as the mean absolute error achieved values smaller than 10% of the inlet velocity for most of the analyzed velocity profiles. A comprehensive turbulence characterization was performed, including second-order statistics, Reynolds stress anisotropy, and turbulent kinetic energy production. The proper orthogonal decomposition of the fluctuating velocity was examined in the current flow domain. The turbulence characterization revealed the complex nature of turbulence in packed pebble-bed geometries, which is further complicated by the presence of an enclosing wall. Overall, the findings of this study provide a solid foundation for the development of more accurate CFD-based methodologies for predicting the behavior of flow through packed pebble-bed reactors.

Investigation of convective heat transfer in a cold flow pebble bed nuclear reactor using advanced pebble probe heat transfer sensor

The aim of this study was to investigate the local heat transfer coefficients between the pebbles and the coolant gas in a PBR using an advanced measurement technique that consists of a heated pebble probe, a micro-foil heat flux sensor mounted flush on the surface of the heated pebble probe, and a thermocouple in the center of the bed void in front the sensor. In this work, the local heat transfer coefficients were derived at various axial levels, radial and angular locations and at different superficial inlet gas velocities that cover both transitional and turbulent flow conditions. The local heat transfer coefficients were found to be 22-32%, 34-39%, and 18-20% higher near the wall at superficial inlet gas velocities of 0.3,1.2, and 2m/s, respectively. This is due to higher volumetric flow at the wall where larger void in the pebble bed exists compared to the center region of the bed where the flow of the gas in the packed bed follows the least resistance path. Large deviations were obtained between the experimental overall heat transfer coefficients in the bed and the predictions of seven correlations that were selected from the literature. Furthermore, these correlations cannot predict the local heat transfer coefficients inside the PBR. This necessitates the development of new correlations for the prediction of the local heat transfer coefficients using the data obtained in this work. A pseudo-3D correlation was developed and was found to provide predictions that are in good agreement with the experimental values for the conditions used, with an averaged absolute relative error (AARE) of 3.33% at high Reynolds numbers for our operating and design conditions.

A proposed refueling scheme for the modular pebble bed reactor

In this paper, a suggested design of the fuel pebble and loading pattern in the MIT Modular Pebble Bed HTGR (MPBR) using thorium (232Th) is presented. Using the MCNP5 code model for the MPBR reactor, different compositions of Thorium Low Enriched Uranium (ThLEU) with different Heavy Metal (HM) loading and 235U enrichment were investigated to achieve the maximum thorium utilization with relatively minimum reactivity insertion in case of water ingress accident. Using pure Low Enriched Uranium (LEU) pebbles and ThLEU pebbles with the same HM loading and 235U enrichment, different pebbles loading patterns were studied. One loading pattern was selected to achieve the criticality with enough excess reactivity compensating for the poisoning effect of xenon build-up at the startup of the reactor operation and the negative effect of fuel and reflector temperature coefficients of reactivity. This loading pattern aims also to reduce the radial power peaking in the core and to minimize the axial Power Peaking Factor (PPF) in the central hot channel, with a minimum number of pure LEU fuel batches. A calculation procedure was developed that combines fuel pebble depletion and full core calculations to investigate the impact of a proposed online refueling scheme for the MPBR reactor and to simulate the multicycle refueling mechanism. Using SERPENT 1.1.7, the nuclide concentrations were calculated as a function of pebble burnup for both LEU and ThLEU pebbles. A multicycle online refueling scheme was proposed and the average number of passes required for LEU and ThLEU pebbles to reach their maximum burnup was estimated.

Experimental measurement of stiffness coefficient of high-temperature graphite pebble fuel elements in helium at high temperatures

Graphite material plays an important role in nuclear reactors especially the high-temperature gas-cooled reactors (HTGRs) by its outstanding comprehensive nuclear properties. The structural integrity of graphite pebble fuel elements is the first barrier to core safety under any circumstances. The correct knowledge of the stiffness coefficient of the graphite pebble fuel element inside the reactor's core is significant to ensure the valid design and inherent safety. In this research, a vertical extrusion device was set up to measure the stiffness coefficient of the graphite pebble fuel element by the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University in China. The stiffness coefficient equations of graphite pebble fuel elements at different temperatures are given (in a helium atmosphere). The result first provides the data on the high-temperature stiffness coefficient of pebbles in helium gas. The result will be helpful for the engineering safety analysis of pebble-bed nuclear reactors.

Experimental investigation of the convective heat transfer coefficients at different angular orientations inside the void in a cold flow pebble bed reactor using a non-invasive heat transfer pebble probe

This study focuses on investigating the effect of the surface location of the pebble inside the bed, by varying the angular orientation of the heat transfer pebble probe and the velocity of the gas on the convective heat transfer coefficients in a cold-flow pebble bed reactor. An advanced non-invasive technique consisting of a cartridge heated copper pebble, a micro-foil sensor and a thermocouple probe was used to obtain accurate measurements of the local heat transfer coefficients from three surface locations inside the void. The effect of the wall on the local convective heat transfer coefficients was highlighted due to the low aspect ratio of the bed (bed diameter to pebble diameter (5cm)) used in this work. The local measurements showed, for the first time ever, that the surface location inside the void substantially impacts the heat transfer coefficients, with higher heat transfer coefficients at the center of the void and bottom of the void. Furthermore, the measured overall heat transfer coefficients showed good agreements with the predictions of the correlations of [52,21] and [14]. A second order polynomial model with an R2=0.9807 and an average absolute relative error (AARE) equal to 9.08%, was developed for the prediction of the local heat transfer coefficient within the design and operation conditions of this work. The accurate local heat transfer data collected in this work is valuable as benchmark data for the validation of computational fluid dynamics (CFD) simulations and heat transfer calculations.

A comparative numerical investigation of the thermal-fluid phenomena between helium and nitrogen cooled pebble bed reactors

The study assesses the thermal-hydraulic performance of a pebble bed type nuclear reactor using nitrogen and helium as coolants. The analysis is done in two separate parts using CFD. First, a segment of the pebbles is modeled and later the whole reactor core. The study assesses the core performance under normal and after reactor shutdown conditions using these two different coolants. The assessment concludes that nitrogen as a coolant candidate for PBR behaves in an acceptable manner in both conditions at a cost of increased pumping power consumption. It is found that under steady state conditions, the heat stored in the pebbles (both for the segment and the whole core) is more in the case of the nitrogen cooled bed compared to the helium cooled bed.