Pin Power Research Articles

Application of the PSI cycle check-up methodology for full-core Monte Carlo simulations verified using pin power estimates and validated for hot zero power conditions

Monte Carlo (MC) based neutron transport codes provide high-fidelity numerical solutions to problems beyond the modelling capabilities of conventional core simulation methods. However, performing core-follow calculations with MC codes remains challenging due to the necessity of incorporating thermal-hydraulic feedback and generating evolved fuel composition for the cycle of interest by taking into account the entire irradiation history of loaded fuel assemblies over previous cycles. Nevertheless, at PSI, the neutronic version of a cycle check-up methodology (CHUP) is under development to address this challenge. This methodology involves extracting operating conditions and nuclide compositions from validated reference deterministic core-follow models (CASMO5/SIMULATE5/SNF), subsequently generating MC neutron transport models for selected operating points. This article presents the verification and validation performed for a hot zero power operating condition of a Swiss pressurised water reactor using the updated CHUP methodology, which automates information extraction from reference core models to minimise human intervention. The MC models were verified by assessing their deviation from criticality, consistently found to be supercritical within the [10,60] pcm range. Additionally, radial relative power distribution verification yield deviations in the [−5,4] % range compared to validated nodal results. Finally, additional validation was performed using start-up measurements from two successive cycles. Eight MC models were found to be subcritical, on average by 51 pcm, with a standard deviation of 25 pcm.

Linear Sources and Anisotropic Scattering in the Random Ray Method

An enhanced implementation of the random ray method (TRRM), a stochastic adaptation of the method of characteristics, is presented. This implementation generalizes from a traditional flat source (FS) approximation to a linear source (LS) approximation, and from the standard isotropic scattering approximation to an anisotropic approximation, up to P3. On the two-dimensional C5G7 benchmark, LS alone enables a 1.4× and 1.7× enhancement in run time for parallel and serial executions, respectively, without compromising accuracy. Further testing on the three-dimensional C5G7 Rodded B benchmark demonstrates that LS enables significant axial coarsening and reduction in ray populations. This results in a 5.3× speedup in run time while still offering comparable accuracy. On the Babcock and Wilcox 1484 Core II benchmark, incorporating anisotropic scattering in TRRM up to P3 with a FS decreased keff errors (~110 pcm) and maximum and average pin power errors. LS with anisotropic scattering (LSPN), showed similarly improved keff errors while benefiting from a coarser mesh. The linear isotropic flat anisotropic (LIFA) method, relative to LSPN, offers further run time and memory savings of 4.1× and 1.6×, respectively, for P3, while maintaining comparable accuracy to anisotropic FS on more refined meshes.

Neutronic and thermal–hydraulic coupling of FCM and helium annular fuel as accident-tolerant fuel

The study aims to explore two types of Accident Tolerant Fuel (ATF) (helium annular fuel and Fully Ceramic Microencapsulated (FCM) fuel), both with Silicon Carbide (SiC) used as clad material and as a matrix material for TRISO (TRi-structural ISOtropic particle fuel) particles in FCM fuel. The safety characteristics (such as maximum fuel temperatures) were evaluated and compared against reference UO2-Zr for a Pressurised Water Reactor (PWR) with neutronic and thermal–hydraulic coupling during normal operation for fresh fuel. The results show that both annular and FCM fuels exhibit reduced maximum temperatures compared to the reference fuel, with a reduction of 479 K (25.3 %) for helium annular fuel and 798 K (42.2 %) in the FCM fuel. The annular fuel improved the burnup by 12.4 MWd/kgU (24.2 %) without the cycle length being affected significantly (−5.6 %). The FCM fuel significantly reduced in the cycle length by 44.1 % while the burnup was more than double the reference providing a 163.5 % increased burnup in comparison to the reference fuel assembly. Assembly pin power peaking factors showed no dramatic deviation from the reference and the axial power distribution of ATFs is more symmetrical than that of the reference fuels. In terms of coupling the pin models converged after eight iterations on average with maximum relative power errors per radial node below 2 %.

Coarse mesh finite difference acceleration of the random ray method

This paper presents the development and evaluation of the Coarse Mesh Finite Difference (CMFD) acceleration method to The Random Ray Method (TRRM). We demonstrate its effectiveness in accelerating the convergence of the fission sources and reducing the real statistical error in neutron transport calculations. TRRM treats the angular variable of the neutron flux stochastically and performs batch sampling of characteristic rays to transform the Method of Characteristics (MOC) into a stochastic process, that is capable of making significant strides in memory efficiency and computational performance for some problems. Despite its advantages, TRRM exhibits a potential challenge with a large number of inactive cycles and inherent inter-cycle correlation much like the Monte Carlo method. To address this, the CMFD acceleration method is explored and demonstrated to dramatically reduce the number of required inactive cycles and diminish inter-cycle correlation. Results from the numerical analysis of a 2D C5G7 core problem indicate that the application of CMFD leads to enhanced convergence, with the integration of a CMFD acceleration step every cycle offering the most substantial reduction in statistical noise and error. The study reveals that applying CMFD with every cycle effectively resolves the issue of needing inactive cycles and significantly lowers the inter-cycle correlation, thereby providing a more accurate estimation of standard deviation for pin power distributions. We conclude that using CMFD not only minimizes the number of inactive cycles of TRRM – much like normal Monte Carlo transport – but also lowers real statistical error effectively. For a targeted maximum standard deviation of 0.1% in the pin power, the addition of CMFD can decrease the number of necessary active cycles by 41% compared to standard TRRM, as demonstrated by the 2D C5G7 benchmark analysis.

Radial reflector macroscopic cross sections preparation impact on the low neutron leakage core Beavrs

Full core nodal calculations are essential for safe nuclear power plant operation. The accuracy and compliance with the calculation and the experiment are based on the proper macroscopic data preparation model. While fuel assembly data preparation is usually based on the simple infinite lattice model simulation, the reflector data preparation is not standardised and the influence of the reflector macroscopic data on full core simulation is not quantified. The paper evaluates the large core with low neutron leakage behaviour with the different reflector cross section preparation models with respect to criticality and power distribution prediction. However, in opposition to the first insight, the different reflector model cannot increase the compliance with the power prediction near the fuel assembly reflector boundary. However, the usage of a special rehomogenization model can be helpful for pin power reconstruction compliance near the edge of the core.

NRC’s methodology to estimate fuel dispersal during a large break loss of coolant accident

Recent experimental findings indicate that under certain transient conditions, high-burnup fuel operating at sufficiently high power can fragment and escape from burst fuel cladding, as discussed in the Nuclear Regulatory Commission’s Research Information Letter (RIL) 2021–13. The escaped fuel fragments could subsequently be distributed throughout a reactor coolant system (RCS), potentially challenging core coolability during a loss of coolant accident (LOCA). Consequently, the NRC has developed a methodology to estimate the mass of fuel that could be dispersed during a large-break LOCA. The methodology involves several NRC-sponsored computer codes, including SCALE/Polaris for lattice physics, PARCS/PATHS for full-core neutronics, TRACE for core and RCS thermal hydraulics, and FAST for steady-state and transient fuel performance calculations. Output from FAST is combined with the models in RIL 2021–13 to estimate fuel dispersal to the coolant.NRC staff have exercised this methodology using a prospective Westinghouse four loop core design with high burnup and extended enrichment that was obtained from the Department of Energy’s NEAMS program. Results demonstrate that the NRC methodology can be exercised to provide fuel dispersal estimates that can subsequently be used to study the potential consequences of FFRD. However, this exercise has also identified several areas for improvements to both the codes and to the modeling approaches used here, including the pin power reconstruction methods in PARCS, the modeling approach used to connect the Cartesian and cylindrical vessel components in TRACE, transient fission gas release and fuel rod upper plenum models in FAST, and tighter coupling between FAST and TRACE.

Neutron-physical characteristics of UO2 and UN/U3Si2 fuels with Zr, SiC and APMT accident tolerant claddings

H2 production due to zirconium hydration was the primary source of explosion in the Fukushima Daiichi nuclear accident. To improve accident tolerance of the new reactor designs, advanced fuel and cladding materials are being extensively investigated. Neutronic evaluation at both the pin-cell and assembly levels are performed for the conventional UO2 and the candidate UN/U3Si2 fuels with traditional cladding (Zr) as well as the accident tolerant claddings (SiC and advanced powder metallurgic ferritic, APMT). The neutronic performance, plutonium inventory, cycle length, radial and pin power distribution, spectrum distribution, spatial self-shielding analysis, plutonium radial distribution, and reactivity coefficients are evaluated and analyzed. Combination of UN/U3Si2 and APMT produces 68% and 66 % more 239Pu and 135Xe than the UO2 and APMT systems. In overall, the reactivity change versus burnup and other main neutronic parameters of SiC cladding are quite similar to the current Zr cladding. Using SiC resulted in an average increase of 0.85 % in reactivity in comparison to Zr conventional cladding (without any change in the enrichment of the fuel). Compared with the traditionally used UO2 fuel assembly, the UN/U3Si2 fuel assembly exhibit a higher (0.2 % at BOC and 0.4 % at EOC) pin power peak value in an assembly, which should be a concern from safety aspects. The negativity of FTC and MTC for the proposed UN/U3Si2 is higher than that of UO2 fuel. These higher and enhanced FTC and MTC values of UN fuels mean an improved inherent safety feature of UN-like high U density fuels.

Application of artificial neural network for assembly homogenized equivalence parameter generation

The development of a new reactor core and optimizations for fuel assembly (FA) structures necessitates the generation of homogenized equivalence parameters, including macroscopic cross-sections (XS), for numerous FA configurations. A feed-forward convolutional neural network, XSNET, has been created to streamline this process. Currently, XSNET can produce these parameters for fresh and burned UO2 fuel, both with and without Gadolinia (Gd) burnable absorber rods. In this study, we integrated XSNET with our in-house nodal diffusion code, RAST-K, to create a conventional two-step approximation code system. This system was tested on various tasks, including analyzing a 3-dimensional pressurized water reactor employing 16 × 16 FA types with Gd rods. Over 1,000 unique loading patterns were considered for nodal calculation, which involved steady-state depletion calculations and pin power reconstruction. The results obtained using XSNET/RAST-K demonstrated good agreement with the reference STREAM/RAST-K code system.

AP-1000 fuel assembly performance with UO2 and UO2/U3Si2 fuels and silicon carbide cladding from the viewpoint of neutronics

ABSTRACT Accident Tolerate Fuels have been highly researched since the Fukushima disaster. To improve the safety of the AP-1000 fuel assembly, an advanced fuel, UO2/U3Si2, is considered. In addition, the silicon carbide (SiC) cladding that has the capability of reducing oxidation is compared with the baseline Zircaloy for AP-1000 fuel assembly along with the two different fuel cases (UO2 and UO2-U3Si2). The present study focuses on the neutronic performance of the UO2/U3Si2 fuel and thus the main neutronic parameters such as the fuel cycle length, pin power distribution, atom density evolution of main isotopes, and the reactivity feedback coefficients are evaluated. An increase of 6.72% in the criticality period is introduced when 70%UO2-30%U3Si2 fuel with SiC cladding is considered. The pin power peaking factors, fuel temperature coefficients, and moderator temperature coefficients of the proposed fuel result in very few changes. For instance, the maximum pin power distribution difference between 70%UO2-30%U3Si2 and UO2 fuel with SiC cladding is 0.001, which is negligible. Thus, its performance is as good as the traditional UO2 fuel from the neutronic aspects and controlling power distribution.

Multi-objective reinforcement learning-based approach for pressurized water reactor optimization

A novel method, the Pareto Envelope Augmented with Reinforcement Learning (PEARL), has been developed to address the challenges posed by multi-objective problems, particularly in the field of engineering where the evaluation of candidate solutions can be time-consuming. PEARL distinguishes itself from traditional policy-based multi-objective Reinforcement Learning methods by learning a single policy, eliminating the need for multiple neural networks to independently solve simpler sub-problems. Several versions inspired from deep learning and evolutionary techniques have been crafted, catering to both unconstrained and constrained problem domains. Curriculum Learning (CL) is harnessed to effectively manage constraints in these versions. PEARL’s performance is first evaluated on classical multi-objective benchmarks. Additionally, it is tested on two practical PWR core Loading Pattern (LP) optimization problems to showcase its real-world applicability. The first problem involves optimizing the Cycle length (LC) and the rod-integrated peaking factor (FΔh) as the primary objectives, while the second problem incorporates the mean average enrichment as an additional objective. Furthermore, PEARL addresses three types of constraints related to boron concentration (Cb), peak pin burnup (Bumax), and peak pin power (Fq). The results are systematically compared against conventional approaches from stochastic optimization. Notably, PEARL, specifically the PEAL-NdS ( ▪ ) variant, efficiently uncovers a Pareto front without necessitating additional efforts from the algorithm designer, as opposed to a single optimization with scaled objectives. It also outperforms the classical approach across multiple performance metrics, including the Hyper-volume. Future works will encompass a sensitivity analysis of hyper-parameters with statistical analysis to optimize the application of PEARL and extend it to more intricate problems.

Application of new axial power distribution synthesis method using in-core detector signal in digital core protection system

ABSTRACT A new method for the generation of axial power distributions using artificial neural network (ANN) technique and real-time measured planar radial peaking factor, Fxy (hereinafter ‘Live Fxy’) method for digital core protection system of pressurized water reactors is presented. ANN with Simulated Annealing (SA) technique to find global optimum solution was used to calculate core average axial power distribution. In Live Fxy method, axial node-wise Fxys were calculated by multiplying pin/box factors to the measured assembly powers inferred from in-core detector signals without calculating detailed 3D power distributions. The hot pin power distribution for DNBR and LPD was then obtained by multiplying the core average axial power distribution and Fxys at axial nodes. The validation of the method was performed for various core conditions (e.g. core power levels, control rod positions, etc.) of Korean OPR1000 power plant. The result showed a decrease in RMS errors by 2.2% ~ 7.0% (3.6% on average), and the minimum thermal margins for DNBR and LPD were increased by 6.4% and 15.6%, respectively. The application of the method would improve the accuracy of axial power distribution and thermal margin, contributing to the operability and safety of digital core protection system.

Evaluation of Improved Contribution Function Method in the Compression of CINDER90 Depletion Library

The improved contribution function (ICF) method based on generalized perturbation theory (GPT) is applied to the compression of CINDER90 depletion library. A series of representative problems for PWR are defined with different fuel materials and operation conditions. According to the characteristics that the reactivity indicator is only meaningful in the neutron radiation calculation while the decay heat indicator is affected by both radiation and decay stage, the ICF method is adopted in the selection of candidate nuclides, then actinides and fission product nuclides of compressed system are obtained. In addition, the absorber nuclides of the compressed system are identified by analyzing the depletion process of the poison with a large absorption cross section separately. Finally, a compressed depletion library consisting of 489 nuclides is generated. The numerical results show that the compressed library maintains high precision in the calculation of k‐inf, nuclide concentration, decay heat power, and pin power. Meanwhile, the use of compressed depletion library leads to a significant reduction of computing resources.

Numerical qualification of the GSP3(0) theory using the analytic function expansion nodal method

The simplified P3 (SP3) method is an important way to implement the pin-by-pin neutron transport calculation of the core. This method has the high accuracy but costs twice the computing time of the diffusion method. Recently, the Generalized SPN (GSPN) theory has been developed, and the ad hoc SPN theory is resolved through rigorous theoretical derivation. GSP3(0) theory is the 3rd order and the 0th layer of GSPN theory. Compared with GSP3(0) theory, the SP3 theory with Marshak boundary condition is regarded as the traditional SP3 theory. The equations of the two theories are the same while the interface and the boundary conditions are different. Based on the GSP3(0) theory and the traditional SP3 theory, transport calculation codes have been developed using the analytical function expansion nodal (AFEN) method. The numerical results show that both of the two SP3 theories are more accurate than the diffusion theory, and the GSP3(0) theory can further improve the accuracy of the pin power calculation compared to the traditional SP3 theory.

Validation of Pronghorn’s subchannel code using EBR-II shutdown heat removal tests: SHRT-17 and SHRT-45R

Pronghorn-Subchannel, referred to as Pronghorn-SC throughout this document, is a subchannel code within the Multiphysics Object-Oriented Simulation Environment (MOOSE) developed at the Idaho National Laboratory (INL). Pronghorn-SC was initially designed to model flows in water-cooled, square-lattice, bare subassemblies. Its capability has been extended to model flows in liquid-metal-cooled, triangular-lattice, wire-wrapped subassemblies. To ensure the accuracy of Pronghorn-SC in predicting the behavior of liquid sodium-cooled reactors, the code was validated by comparing calculations with experimental data, obtained from the experimental breeder reactor (EBR-II), Shutdown Heat Removal Tests (SHRT) 17 and 45R. The steady-state calculation at the beginning of the transients was validated using temperature measurements taken at different axial elevations in the instrumented subassembly XX09. The validation exercise was performed in successive stages. First, a comparison between the measured temperature profiles and standalone Pronghorn-SC simulations using a uniform pin power profile was made. The pin power profile was then refined using a Serpent-2 model of the reactor core. Finally, the radial temperature profile was further corrected considering the inter-assembly heat transfer. A Pronghorn Finite-Volume (FV) thermal hydraulic simulation of XX09 and its six neighboring subassemblies; calculated the heat flux on the inner duct surface of the XX09 subassembly to inform the Pronghorn-SC model. Last, a transient validation calculated the peak temperature evolution during the SHRT tests.

The Random Ray Method Versus Multigroup Monte Carlo: The Method of Characteristics in OpenMC and SCONE

The Random Ray Method (TRRM) is a recently developed approach to solving neutral particle transport problems based on the Method of Characteristics. While the method previously has been implemented only in closed-source or limited-functionality codes, this work describes its implementation in two open-source Monte Carlo codes: OpenMC and SCONE. The random ray implementations required small modifications to the existing Multigroup Monte Carlo (MGMC) solvers, offering a rare venue for redundant, fine-grained, “apples-to-apples” speed and accuracy comparisons between transport methods. To this end, TRRM and MGMC solvers are evaluated against each other using each code’s native capabilities on reactor eigenvalue problems with different degrees of energy discretization. On the C5G7 benchmark (featuring only seven energy groups), TRRM achieves a maximum pin power error comparable to or lower than that of MGMC for a given run time. On a problem with 69 energy groups, MGMC is found to scale more efficiently, obtaining a lower pin power error for a given run time. However, the defining difference between the two transport methods is found to be their vastly different uncertainty distributions. Specifically, TRRM is found to maintain similar levels of accuracy and uncertainty throughout the simulation domain whereas MGMC can exhibit orders-of-magnitude greater errors in areas of the problem that feature low neutron flux. For instance, TRRM provided an up to 373 times speed advantage compared with MGMC for computing the flux in low-flux regions in the moderator surrounding the C5G7 core.

An attempt to find the optimal loading pattern of minor actinides in the PWR fuel rods

Three approaches of minor actinide (MA) loading in the fuel rods of a pressurized water reactor were examined. They comprised inserting MAs and fuel mixture in the center of duplex fuel rods, coating of MAs and fuel mixture in the outer layer of fuel rods and lastly, mixing MAs homogeneously with the entire fuel rod elements. AP1000 fuel assembly was chosen as the reference design. Two fuel types namely conventional UO2 and UTh MOX fuel were selected as the base fuel models for the study. Although shorter cycle length than the UO2 fuel design was achieved by the UTh fuel design, UTh fuel exhibited more favorable FTC and yielded a lower plutonium stockpile at the end of the fuel cycle. When MAs were added in the outer layer of fuel rods, it resulted in higher rate of transmutation, however it had an adverse impact on the fuel reactivity, discharge burnup and pin power distribution. On the contrary, when MAs were loaded in the central region, it led to incomplete incineration of MAs. Therefore, based on the satisfactory transmutation rate, MTC, most negative FTC and uniform pin power distribution, the homogenous MA loading strategy can be concluded as the optimal loading pattern for the AP1000 nuclear reactor.

AP-1000 fuel assembly performance with cadmium oxide as a new burnable poison

ABSTRACT One of the main nuclear reactor design problems is finding an efficient method for reactivity control. Boron-free small modular reactors and long-life pressurized water reactors need proper neutron absorbers to suppress large initial reactivity and gentle reactivity variation during reactor operation. In this paper, AP-1000 fuel assembly is used to investigate the effect of using cadmium and enriched Cd113 as burnable poisons. The reactivity behavior of the AP-1000 fuel assembly is of interest. The DRAGON code calculates the neutronic performance of the natural and enriched UO2-CdO. The investigation is performed from the standpoint of initial reactivity, reactivity swing, pin power peaking factor, and cycle length. As a further check, the impact of the CdO on the MTC results is also explored. Moreover, the results are compared with those of gadolinia-bearing rods. Fully enriched cadmium oxide (enriched in Cd113) provides 10.5% more initial reactivity suppression than that of gadolinia fully enriched by Gd157 while reaching almost the same cycle length. Also, using cadmium enriched in Cd113 leads to reducing parasitic absorption. The reactivity swing of the case fully enrichment of Cd113 is 21% lower than the case with natural cadmium rods. It is also found that the residual binding of the CdO with 100%Cd113 enrichment and Gd2O3 with 100%Gd157 enrichment are 0.002928 and minus 0.0026 respectively. Moreover, it is seen that, the normalized pin power for 2 w/o concentration of CdO fully enriched Cd113 has been increased by 3.3% relative to the case with Nat. Cd.

Fine mesh pin-by-pin analysis of IPWR equilibrium core

Detailed fine mesh reactor physics simulations are warranted for reactor cores in order to estimate the important safety parameters such as detailed pin power distribution in the core and local pin peaking factors. A pin-by-pin reactor analysis code HEXPIN has been developed to perform 3D reactor core analysis with a pincell size mesh. HEXPIN uses the conventional two step calculation methodology for performing reactor calculations. India is developing a 2700 MWth/900 MWe Indian Pressurized Water Reactor (IPWR) for developing indigenous capability for commercial light water technology. It uses enriched uranium oxide fuel. The batch refueling scheme is adopted for fuel cycle management. A fine mesh pin-by-pin analysis of equilibrium core of IPWR has been performed using HEXPIN code system. The pin homogenised parametric cross section library, required for HEXPIN calculation, has been generated using lattice burn up code EXCEL. The equilibrium core calculation has been performed by a set of repeated calculations till a converged core configuration is achieved. The present paper gives the methodology and brief results of the analysis.

Reactivity control optimization of boron-free small modular pressurized water reactor with helical-cruciform metallic fuel

Small modular pressurized water reactors have the advantages of small size, modularity, inherent and passive safety, and flexible power generation for a wider range of users and applications. Helical-cruciform metallic fuel has the potential to be applied to small modular pressurized water reactors capable of its axial self-spacing plane, high power density, increasing heat transfer area, and extending the cycle length. A novel boron-free small modular pressurized water reactor NETH-HCF175M design using helical-cruciform metallic fuel is proposed in this paper. The reactivity of the core is completely controlled by burnable absorbers and control rods. Two different geometric structures of separate pins and integral pins are researched. Results indicate that Gd2O3 is a suitable neutron absorbing candidate, while Er shows the best reactivity control effect in the integral pin structure. The separate pin structure with Gd2O3 is selected as the burnable absorber design and the core depletion result shows that the core can achieve a cycle length of about 1360 effective full power days. Control rods are divided into 60 compensating rods and 60 shutdown rods for excess reactivity controlling and shutting the core. The genetic algorithm is applied to the optimization work of layout and concentration design for burnable absorbers and layout of compensating rods. Based on the optimized burnable absorbers and compensating rod designs, excess reactivity can be controlled and the core can achieve criticality at beginning of cycle. The core can be transitioned from hot full power to cold zero power with shutdown rods at BOC, which obtains a shutdown margin more than 3000 pcm. Finally, the physical characteristics of core are analyzed, including depletion simulation, pin power distribution, and reactivity equilibrium. This paper provides an overview and information practical for the reactivity control design of novel SMPWR with high-enrichment and geometric complex helical-cruciform metallic fuel.

CANDU6 single channel CCP analysis on pressure tube deformation effects with multi-physics coupled calculation

Though pressure tube deformation rigorously and simultaneously affects channel coolability and neutronics behavior, the two effects have never been coupled with each other. In this study, the CUPID code is coupled with the SHAFE code to obtain the Critical Channel Power (CCP) of a designated channel which has high nominal power, a high void fraction, a high flow rate, and high pressure deformation. Even though appendage modeling is not included in this study, adequate cell-wise uniform artificial form loss was sought through iteration and imposed to conserve the header to header pressure drop by considering the inlet & outlet feeder and end fitting pressure drop. Nested loops are included in CCP calculation logic; they are the channel power loop, pin power distribution update loop and flow rate optimization loop from outer loop to inner loop, in sequence. Both CUPID and SHAFE are based on the Fortran computer language; the CUPID code is converted to the Dynamic Link Library (DLL) and the SHAFE code can load the CUPID library whenever it is required. Finally, we found that a CCP decrement for a channel with large pressure tube deformation is not that much, even for a complex deformation case. In addition, the sagging effect for a CCP decrement is significantly different from the expectation before an analysis is completed.