Monte Carlo Code Serpent Research Articles

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

We investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the keff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

Radiological characteristics of spent nuclear fuel from small modular reactors under consideration for deployment in Ukraine

Small modular reactors represent a promising technology for power generation, offering solutions to the energy crisis and mitigating greenhouse gas emissions. As Ukraine considers the deployment of NuScale, UK SMR, and SMR-160, it is crucial to address the safe management of spent nuclear fuel. This study focuses on evaluating the radiological characteristics of spent nuclear fuel from the selected small modular reactors and for comparison, from the VVER-1000 reactor. Using the Monte Carlo code Serpent, depletion calculations were performed for an assembly in an infinite 2-D geometry, and the activity, decay heat, and inhalation toxicity of the spent nuclear fuel were assessed. We determined the main nuclides contributing to the radiological characteristics and quantified the mass content of these nuclides. The total number of spent nuclear fuel assemblies produced during the entire life of each small modular reactor type was estimated. The radiological characteristics assessed for the three small modular reactors do not exceed those observed for VVER-1000 reactors currently operating in Ukraine. So, spent nuclear fuel generated by the selected small modular reactors will introduce no new challenges to Ukraine's radioactive waste management system. The results of this work provide valuable insights for identifying the optimal small modular reactor technologies for Ukraine concerning safe spent nuclear fuel management.

Proof of concept for hyper-fidelity depletion of full-scale pebble bed reactors

Pebble bed reactors, either gas-cooled or fluoride-cooled, are among the most promising advanced reactor concepts with active development worldwide. The relatively small size of the pebbles and the fact that they are continuously recirculated makes the task of simulating fuel burnup particularly challenging. Most solutions proposed thus far suggest dividing the core into spectral zones within which fuel composition is assumed uniform, ignoring differences between the different pebbles in the zone. This work suggests that it is possible with current computing tools and with relatively modest computing resources to perform depletion of pebble bed reactors by depleting each pebble individually. The feasibility of this approach, named hyper-fidelity depletion, is demonstrated using a simplified model that assumes static pebbles in a regular lattice and employing the Monte Carlo code Serpent 2 that provides multiple features suitable for hyper-fidelity depletion, among which the most important is domain decomposition. The obtained results show that the spectral zone methods compared to hyper-fidelity can predict average trends, but are not adequate to determine distribution for quantities of interest such as burnup, fission products, etc.

Alternatives to the burnup strategy and fuel material of the EM2 modular reactor

The Energy Multiplier Module (EM2) is a modular high-temperature helium-cooled fast reactor developed by General Atomics (GA). It contemplates a convert-and-burn core, in which fertile fuel is converted to fissile fuel for on-site burning. These features allow the reactor to achieve a core lifetime of 32 years without refueling with different types of fuel materials, like thorium, natural uranium, depleted uranium (DU), and spent fuel. The objective of this study is to evaluate the neutronic performance of the EM2 reactor under four types of fuel material combinations (Low enriched uranium [LEU]/DU, LEU/Th, U-Pu/DU and U/Th) with two burnup strategies. The first strategy was taken from the GA model (configuration 1) and the second was proposed in this paper (configuration 2). The Serpent Monte Carlo code with ENDF/B-VII cross section library was used to perform the calculations. The following parameters were analyzed for each scenario: the effective neutron multiplication factor (keff), the conversion ratio, reactivity coefficients, and the effective delayed neutron fraction (βeff). The fissile inventory and fission rate contribution of the main isotopes were also discussed. The results obtained show that the scenarios with configuration 2 had a higher peak excess reactivity than those with configuration 1. For the scenarios with DU as a fertile fuel, 238U produced ∼20 % of the fission throughout the fuel cycle. In contrast, in the scenarios with thorium as fertile fuel, the 232Th fission rate was negligible. As for the reactivity coefficients, all scenarios presented negative Doppler coefficient and positive void reactivity; both values increased along burnup. On the other hand, the βeff decreased with burnup on and did not vary significantly between both configurations.

Chromium-Coated Zirconium Cladding Neutronics Impact for APR-1400 Reactor Core

The accident-tolerant fuel concept involves replacing the conventional cladding system (zirconium) with a new material or coating that has specific thermomechanical properties. The aim of this study is to evaluate the neutronics performance of a chromium coating concept and design solutions. A Zircaloy–uranium fuel system (Zr–U) is currently used as a standard fuel system in pressurized water reactors around the world. This investigation presents the benefits of utilizing an alternative cladding material such as chromium coating and the effects on the thermal neutron parameters of the way in which the chromium coating is introduced in the reactor fuel. Among these significant benefits is an increase in the reactor fuel’s thermal conductivity, which improves reactor safety. Two types of fuel-cladding systems were investigated: Zircaloy–uranium (Zr–U) and Zircaloy–chromium (Zr–Cr–U) coating fuel systems. Neutronics analysis evaluations were performed for the selected fuel assemblies and a two-dimensional full core based on an APR-1400 reactor design. Neutronics analyses were performed for the application of the new fuel-cladding material systems using the reactor-physics Monte Carlo code Serpent 2.31.

Calculation of the VENUS-3 benchmark experiment by response-matrix and Monte Carlo methods

VTT is currently working on the development of the deterministic computer code REMS for reactor dosimetry calculations. The transport solution in REMS is based on a response-matrix formalism, with multi-group responses pre-computed by Serpent 2. In this sense, the Serpent-REMS sequence embodies a two-step approach. Reaction rates for three threshold nuclear reactions were calculated by REMS and compared against measured values in the context of the VENUS-3 benchmark experiment. For the 383 experimental values available, the average and standard deviation of calculated-to-experimental reaction rate ratios were (1.03 ± 0.11). This work also reports on the ongoing validation of the Monte Carlo code Serpent 2 for reactor dosimetry applications. The VENUS-3 benchmark problem was also calculated with Serpent 2. The average reaction rate ratios and standard deviations were (1.02 ± 0.06). Execution times for REMS are considerably lower than those of Serpent 2. Furthermore, parallel scalablitity tests suggest promising prospects for the solution of multi-step irradiation scenarios with REMS. Future work will focus on means of improving the accuracy of the REMS solution by refining the Serpent 2 models used in response-matrix generation, as well as on uncertainty qualification.

Steady-state analyses of an smDFR with coupled Serpent-OpenFOAM calculation

The small modular dual fluid reactor (smDFR) adopts a mixture of liquid uranium and plutonium chloride as fuel, with lead as a coolant. With its smaller size, lower weight, and inherent safety, the smDFR can be used as a mobile energy supply for vehicles or ships. Analyses of the smDFR are still in the early stage based on a single or separated physical field, which can hardly capture the impact of the flowing fuel on the neutron field. The coupled neutronic-fluid dynamic calculation is needed for reliable multidimensional, multi-field distribution of the steady-state smDFR core property. In this work, the Monte Carlo code Serpent 2 and the CFD code OpenFOAM are coupled via a Python interface, whereby the neutron field information can be exchanged with the fluid field in a region-average manner. The correctness and reliability of the coupled code are verified with two cases in the pressurized water reactor background, and the results show good agreement. The coupled code is applied to the steady-state analyses of an smDFR, a single-channel case, and a 1/6-core case. The results show that the temperature distribution of the fuel and coolant caused a lower drift of the axial power peak compared to the uncoupled cosine shape power distribution. The 1/6-core results show that the peak temperature of the fuel reaches 980 K at the top-center of the reactor core. Moreover, the influence of fuel thermal properties and inlet velocity are studied with rated power. Through the comparison of mapping schemes, the results can identify the dependence of specific parameters and help to reduce mapping errors. This work shows that through a coupled neutronic-CFD code, the multidimensional and multi-physical fields of the smDFR can be better represented, providing important references for the future design and analyses of smDFR systems.

CORE BURN-UP ANALYSIS OF THE RSG-GAS RESEARCH REACTOR USING DETERMINISTIC AND STOCHASTIC METHODSS

Due to several characteristics, such as geometry, compact core, high coolant flow, and high neutron flux, the burn-up study of the RSG-GAS multi-purpose reactor provides challenges when employing a neutronic calculation. For the burn-up analysis, two calculating methodologies are used in the RSG-GAS: deterministic and probabilistic methods. The deterministic codes such as WIMSD-5B and Batan-FUEL are utilized, whereas the continuous-energy Monte Carlo code Serpent 2 is used for the stochastic method. WIMSD-5B is being used to produce a four-group cross-section that is needed by Batan-FUEL to do full core diffusion calculations. Burn-up calculations were performed at the whole fuel assemblies inside the core to see if the deterministic code, WIMSD-5B/Batan-FUEL, could accurately replicate the burn-up behavior of the RSG-GAS research reactor. The Serpent 2 calculation was also done with the exact models to provide a comparison. The results show that both Serpent 2 and WIMSD-5B/Batan-FUEL can perform the RSG-GAS burn-up analysis if appropriate treatments are made to the deterministic codes at both the assembly and core levels. There is a 5% difference in calculated fuel burn-up between deterministic and stochastic approaches.

Possible Implementation of Ex-Core Measurement in TEPLATOR Graphite Reflector

Abstract An ex-core neutron flux measurement is a crucial system for all common power reactors. It is necessary to monitor the neutron flux and control the chain reaction, therefore, the ex-core neutron flux measurement is one of the main safety and control systems. The main advantage of this arrangement of detectors is a fast response to neutron flux change, which determines the reactor power change. Regarding to the new reactor concepts, it is important to deal with improved detection systems suitable for these reactors. Many of the modern reactor concepts are based on a graphite moderator or reflector, which is also the case of the TEPLATOR. The TEPLATOR is a solution of a district heating system based on heavy water as a moderator and graphite as a reflector. The TEPLATOR is designed to use irradiated fuel from the commercial pressurized water reactor or boiling water reactor, which has low to intermediate burnup. This work is focused on the verification of the possible use of the special neutron measuring system placed in the graphite reflector. The Monte Carlo code serpent was used for the calculations performed in this work.

SERPENT CODE POINT KINETIC PARAMETERS ANALYSIS: A NEXUS FOR NIGERIA RESEARCH REACTOR – 1 CORE CONVERSION USING ENRICHED URANIUM DIOXIDE FUEL

The International Atomic Energy Agency (IAEA) requires that all test and research reactors operating on Higher Enriched Uranium (HEU) should be converted to Low Enriched Uranium (LEU) for safety and security purposes. Nigeria having a Miniature Neutron Source Reactor (MNSR) has been long interested in fuel technological research not just to develop the area but also to meet with resolution on the nuclear treaty set out by the global nuclear regulatory body. In this study, reactor kinetic parameters such as effective delayed neutron fractions, prompt neutron lifetime as well as mean neutron generation time were analysed for Nigerian Research Reactor-1 (NIRR-1). Serpent Monte Carlo code 1.17 is used in the analysis. For delayed neutron parameters determination, we used fission probability iteration under one averaged generation time and neutron population rate.The calculated values for delayed neutron were recorded as analogue prompt and implicit prompt neutron lifetime, reproduction time and emission time are in the order of 3×10-7 (s), in agreement with the calculated data from the nuclear data libraries and some literature.The result for delay neutron fraction and other time-based parameters support the fuel core conversion for NIRR-1.The computational and pictorial results obtained from Serpent code simulation described well the transient behavior of the delayed neutron in this reactor.The analytical results also spelled out the relevance and compatibility of low enriched uranium dioxide fuel over higher enriched type.The result of this study conforms with other results obtained from similar reactors but with different Monte Carlo codes and with higher enriched uranium

Code-to-code SIMMER/FRENETIC comparison for the neutronic simulation of lead-cooled fast reactors

This paper presents a neutronic benchmark between the FRENETIC and the SIMMER codes, performed considering the core of the ALFRED lead-cooled fast reactor. FRENETIC includes a nodal diffusion module developed for fast full-core analyses of safety-relevant transients in liquid-metal fast reactors, while SIMMER is a reference tool for qualifying such kind of systems in accidental conditions. In order to highlight the influence of the different numerical methods available in the two codes on the output responses, macroscopic parameters like the effective multiplication factor and the linear power are compared in an increasingly detailed simulation framework. The 3D full-core FRENETIC results are compared at first to a cylindrical 2D SIMMER core model, to highlight the impact of the absorber rings location. Then, a 3D full-core model is also employed in SIMMER to assess the differences, with respect to FRENETIC, induced by the adoption of a Cartesian mesh and of the discrete ordinates method. The full input data consistency is ensured providing the same set of few-group material constants, generated with the Monte Carlo code Serpent 2. Finally, the W-ε scheme is applied to accelerate the angular and spatial convergence of the keff sequences computed by SIMMER in order to estimate the asymptotic errors with respect to the reference Serpent calculation.

Spent fuel characterization analysis using various nuclear data libraries

Experience shows that the solution to waste management in any national programme is lengthy and burdened with uncertainties. There are several uncertainties that contribute to the costs associated with spent fuel management. In this work, we have analysed the impact of the current nuclear data on the isotopic composition of the spent fuel and consequently their influence on the main spent fuel observables such as decay heat, activity, neutron multiplication factor, and neutron and photon source terms. Nuclear libraries based on the most general nuclear data ENDF/B-VII.0, ENDF/B-VII.1, ENDF/B-VIII.0 and JEFF-3.3 are considered. A typical NPP Krško fuel assembly is analysed using the Monte Carlo code Serpent 2. The analysis considers burnup of up to 60 GWd/tU and cooling times of up to 100 years. The comparison of results showed significant differences, which should be taken into account when selecting the library and evaluating the uncertainty in determining the characteristics of the spent fuel.

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

The Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance–covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U-238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance–covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

Validating the serpent-ants Calculation Chain Using BEAVRS Fresh Core Hot Zero Power Data

Abstract The serpent Monte Carlo code and the serpent-ants two-step calculation chain are used to model the hot zero power physics tests described in the BEAVRS benchmark. The predicted critical boron concentrations, control rod group worths, and isothermal temperature coefficients are compared between serpent and serpent-ants as well as against the experimental measurements. Furthermore, radial power distributions in the unrodded and rodded core configurations are compared between serpent and serpent-ants. In addition to providing results using a best practices calculation chain, the effects of several simplifications or omissions in the group constant generation process on the results are estimated. Both the direct and two-step neutronics solutions provide results close to the measured values. Comparison between the measured data and the direct serpent Monte Carlo solution yields root-mean-square (RMS) differences of 12.1 mg/kg, 25.1×10−5 and 0.67×10−5 K−1 for boron, control rod worths and temperature coefficients, respectively. The two-step serpent-ants solution reaches a similar level of accuracy with RMS differences of 17.4 mg/kg, 23.6×10−5 and 0.29×10−5 K−1. The match in the radial power distribution between serpent and serpent-ants was very good with the RMS and MAXimum (MAX) for pin power errors being 1.31% and 4.99%, respectively, in the unrodded core and 1.67% (RMS) and 8.39% (MAX) in the rodded core.

Investigation of novel weight window methods in Serpent 2 for fusion neutronics applications

Released in 2009, the Serpent Monte Carlo code has established itself as a highly efficient and powerful simulation code for nuclear systems analysis. Originally developed for reactor physics applications, the scope of the code now extends to coupled multi-physics simulations and photon transport. The latter has allowed adoption of the code by the fusion neutronics community following developments of a coupled neutron-photon capability in 2014 and the ability to handle complex geometry types in 2016. The code is well validated for the energy regimes and geometry types one can expect in fission reactor analysis. Over the course of recent years a benchmarking effort has been undertaken for application of the code to nuclear fusion. Compared to nuclear fission, or accelerator based applications, the underlying particle interaction phenomena differ greatly at the energies expected in a fusion reactor as well as the specific responses that are of interest. In this paper, a novel weight window generation implementation in Serpent is investigated. The applicability of this method is demonstrated for the Frascati Neutron Generator (FNG) bulk blanket and shield experiment, part of the SINBAD database, and a DEMO helium cooled pebble bed (HCPB) computational model. A comparison is performed against MCNP using weight windows generated with ADVANTG. Excellent agreement is found for the specified tallies and the significant efficiency gain using weight windows generated using both methods is comparable. A robust variance reduction method implementation is fundamental to applications to fusion neutronics and as such, this work is an important step in deployment of Serpent for this type of analysis.

Rapid neutronic and thermal hydraulic analysis of LEU space reactor core

In order to minimise the mass of a 1MWe LEU space fission power system design, a rapid method of carrying out neutronic and thermal hydraulic analysis for the reactor is required. A two-stage deterministic analysis routine has been constructed using a core-plane method of characteristics calculation followed by a full-core SP3 calculation, within the ANSWERS© code WIMS11. This is compared to a faster route that skips the core-plane calculation and also the Monte Carlo code Serpent. Results suggest sufficiently-good agreement for the WIMS-based methods to be useful in a full system mass-minimising optimisation routine. The neutronics scheme is coupled with a simple sub-channel thermal hydraulics code with a finite-element heat conduction model for the fuel block.

Triangular Polynomial Expansion Nodal Method for VVER Core Analysis

Due to the low computational cost, nodal diffusion methods are still commonly used to simulate full-core reactor problems. This work represents the developmental effort to build an accurate nodal kernel to treat hexagonal geometry in the core simulator code PARCS. An innovative method called TriPEN-9 has been developed by splitting a hexagonal assembly into six triangular nodes and solved using cubic polynomial expansion for the scalar flux with nine-term expansion coefficients. The nodal diffusion calculation is further accelerated with the multilevel coarse-mesh finite difference method. The verification of the TriPEN-9 method on the VVER full-core problem is provided with the model based on the NURESIM (Nuclear Reactor Simulator)-SP1 V1000-2D-C1-tr benchmark problem. The Serpent Monte Carlo code is used as a reference solution for verification and to generate homogenized group-constants data for PARCS. Exact discontinuity factors were generated in GenPMAXS, a cross-section processing code, using a similar expansion method as the TriPEN-9 core solver method with the utilization of heterogeneous solutions from Serpent. Implementing the TriPEN-9 method in PARCS, this approach can exactly reproduce the solutions from the high-fidelity Serpent calculations.

Comparison of calculation methods for lead cooled fast reactor reactivity effects

This study analyzes three different reactivity feedback coefficients of the Advanced Lead-cooled Fast Reactor Demonstrator (ALFRED) reactor. During the evaluations, the central difference Direct Perturbation Method (DPM) and the Linear Perturbation Theory (LPT) were applied to determine the feedback coefficients and their uncertainties due to cross-section data. The continuous energy SERPENT Monte Carlo code, the multigroup TSUNAMI-3D sequence of the SCALE program package, and PARTISN discrete ordinate neutron transport code coupled with SEnTRi developed by the authors was applied, and the properties of these fundamentally different calculations are presented. In order to validate the methodologies, lead void coefficient calculations were performed for the Comet critical assembly, which confirmed that a good agreement could be reached between the different methods and measurement results. Besides the high-level transport approximation, the calculations indicated that the appropriate spatial resolution has outstanding importance in describing the high flux gradient.

Simulation-based studies on graphite absorption properties for ASTRA critical experiments

This work is focused on the improvement of the graphite impurity content characterization for the ASTRA critical facility. The equivalent boron content for the graphite reflectors of the ASTRA facility reported in the benchmark specifications was estimated using the results of the exponential experiments performed by graphite manufacturer. Because raw measured data are not available for these experiments, we tried to reassess the equivalent boron content for the ASTRA graphite reflectors using the results of analogous exponential experiments performed earlier on the empty RBMK critical facility at the National Research Center «Kurchatov Institute» and further simulation of the experiments utilizing the Monte Carlo code Serpent with ENDF/B-VII.0, ENDF/B-VII.1, and ENDF/B-VIII.0 cross-section libraries. The same grade graphite was used for manufacturing the graphite blocks for the RBMK critical facility and the ASTRA critical facility. The Monte Carlo simulations confirmed the accuracy of the exponential measurements performed for RBMK graphite characterization. It was also shown that the simulation must reproduce the graphite absorption cross-section estimated using the exponential experiments for the agreement between the measured and calculated distribution of thermal neutron flux. Therefore, the equivalent boron content should be assessed individually for each cross-section library used in the simulation. In case of the ASTRA facility the carbon capture cross section of 3.36mb at 0.0253 eV (ENDF/B-VII.0) was used to deduce the equivalent boron content of 1 ppmwt from the measured results. Thermal capture cross-section of carbon was significantly increased in the ENDF/B-VII.1 and other recent cross-section libraries. Therefore, when calculating the ASTRA benchmark with these cross-section libraries the equivalent boron content reported in the benchmark specification should be reassessed.

Application of Serpent Monte Carlo Code for Modeling of Non-destructive Systems Based on Backscattered X-Rays

Research of objects with unilateral access is a promising area for the development of non-destructive testing systems. To create a real system and determine its optimal parameters, it is important to conduct preliminary computer simulations. The paper is devoted to creating a model of a non-destructive system based on backscattered X-rays in the Serpent Monte Carlo code. There are no known studies of the use of Serpent software to build such models. The purpose of the study was to confirm the possibility of detecting a defect, i.e., a material of a different density than the test object, which was placed in this object. A model was created, the main components of which were the radiation source, the object under study, the defect, and the detector of backscattered radiation. Experiments were performed for several combinations of system parameters, in particular when changing the angle of illumination and the distance between the object and the detector. The energy of the radiation source used in the study was 100 keV. The test object of study was a steel plate, which contained a defect — a lead plate. Calculations were performed for six cases at illumination angles of 30 and 45 degrees (scattering angles of 120 and 135 degrees, respectively), and the distance between the object and the detector 1 and 5 cm. The detector was a plane that coincided with a NaI scintillation plate of 60 by 30 cm in size. It was conventionally divided into 1800 elements to detect the flux density of backscattered radiation. A qualitative and quantitative analysis of the results met theoretical expectations. In particular, the Compton equation was fulfilled, which states that as the cosine of the scattering angle \theta increases, the energy of scattered radiation also increases. In the case of θ = 1200, the average flux density of backscattered radiation recorded by the detector was 1.1*10-3 units per square centimeter per second, and in the case of θ = 1350, this value was 7.9*10-4. The results of the study can be used to build real non-destructive testing devices. These devices can be used in medicine, industry, and security systems. The model has some limitations. The radiation source in this model is monoenergetic, in contrast to classical X-ray systems, in which the radiation has a spectrum. Also, a defect is a plate of a large area, which is almost equal to the area of ​​the object under study. For practical use, the device must be capable to detect a defect many times smaller than the object under study, such as a void in the weld, a tumor in the human body, or smuggled substances. The model can be improved in the future.