Towards the enhancement of nuclear reactor
safety: physical phenomena involved in the
measurement accuracy of boron concentration
online monitoring systems

Nouhaila Tabti, Adrien Sari, and Dominique Tromson

Université Paris-Saclay, CEA, List, F-91120 Palaiseau, France

nouhaila.tabti@cea.fr

***Abstract***— In Pressurized Water Reactors (PWRs), boron-10 (¹⁰B) is added to the primary fluid as boric acid to regulate criticality and power distribution within the core. Indeed, ¹⁰B possesses a significant neutron absorption cross-section of approximately 3845 barns for thermal neutron energy (around 25.3 meV). Thus, under certain circumstances, even a slight variation in boron concentration could lead to criticality issues. This paper addresses the problems regarding the accuracy and real-time measurement of Boron Concentration Online Monitoring Systems (BCOMS) in PWRs. First, the paper focuses on presenting BCOMS's key performance and qualification criteria to ensure a real-time, accurate response during normal operation, operational transients, and accidental events. Then, we evaluate the influence of different dimensioning parameters on the overall measuring performance through Monte Carlo simulations using the MCNP6.2 code. Finally, we investigate, combining theoretical knowledge and simulation results, the physical phenomena involved in the measurement accuracy of BCOMS. This analytical approach not only fosters a deeper comprehension of the underlying phenomena but also facilitates the identification of potential areas for improving measurement accuracy, thereby enhancing the safety of nuclear reactors.

***Keywords*** —Pressurized Water Reactor (PWR), nuclear safety, primary fluid, boron, online monitoring, neutron absorption, Monte Carlo simulation.

# I. INTRODUCTION

BORON is added to the primary fluid of Pressurized Water Reactors (PWRs) as boric acid ($H_3BO_3$) to adjust reactivity and power distribution within the core. Indeed, boron-10 (¹⁰B) has a significant neutron absorption cross section following the ¹⁰B(n, α)⁷Li reaction, of approximately 3845 barns for a thermal neutron energy of 25.3 meV. During both normal operation and operational transients, boron is introduced into the primary fluid to offset fuel burnup and xenon oscillations. Moreover, the addition of boron becomes essential in the event of specific faults that might lead to a reactivity excursion in the core, in order to prevent criticality issues.

Therefore, it is of paramount importance to maintain the appropriate level of boron concentration to avoid any unintended criticality and ensure safe and reliable operation throughout the reactor's operational lifecycle. The implementation of robust monitoring and control measures for boron levels is crucial to effectively mitigate the potential hazards associated with boron dilution events. These measures play a crucial role in safeguarding the reactor's integrity and ensuring the safety of personnel and the surrounding environment.

There are different methods used to measure boron concentration [1], amongst which two ways are commonly used in nuclear reactors industry: periodic chemical sampling and Boron Concentration Measuring Systems (BCMS), also referred to as the "boron meters". It is well known that chemical sampling provides highly precise measurements, but it produces radioactive waste and necessitates a considerable turnaround time. Conversely, BCMS enables continuous measurement of boron concentration; however, its margin of error is higher than that of chemical titration. BCMS can be categorized into different types based on their operational mode and level of intrusiveness. They can be classified as either online or offline, referring to whether the measurement is performed in real-time or at discrete intervals, respectively. Additionally, boron meters can be further classified as either intrusive [2-7] or non-intrusive [8-12], depending on whether they require direct physical contact with the primary fluid or operate through non-contact methods.

This paper focuses on non-intrusive Boron Concentration Online Monitoring Systems (BCOMS) mounted on the Chemical and Volume Control System's discharge line (CVCS), since they can easily equip the actual operating reactors without a significant material modification in the design basis of the circuit. First, we highlight the essential performance and qualification criteria relative to boron meters. Second, we provide a description of the evolution of the overall performance following the variation of certain dimensioning parameters. This study is carried out by Monte Carlo simulation using the MCNP6.2 code [13]. Finally, we discuss results combining theoretical knowledge and some analytical
calculations in order to gain deeper insights into the physical phenomena that affect the measuring accuracy of BCOMS. This comprehensive and analytical approach aims to enhance our understanding of boron meter current performance and contributes to the advancement of their design and application in nuclear reactors.

## II. BCOMS PERFORMANCE AND QUALIFICATION CRITERIA

To establish accurate real-time measurements of boron concentration, a comprehensive examination of design and safety requirements is essential in determining performance and qualification criteria for BCOMS. Nuclear Power Plants (NPPs) are complex systems with intricate interconnections between different phenomena, such as neutronics, thermal hydraulics, mechanics, and thermomechanics. By studying these diverse phenomena, a set of crucial criteria can be formulated to assess the overall efficiency of the system. We divide the selected criteria into two categories: performance criteria, which directly assess accuracy and response time, and qualification criteria, which are essential to ensure compliance with safety measures. By categorizing the criteria in this manner, we can effectively evaluate both the operational effectiveness and the adherence to safety standards required for nuclear reactors systems.

We have identified three main performance criteria: counting rate (CR), measuring resolution (R), and neutron sensitivity ($S_n$) compared to thermal sensitivity ($S_T$). The counting rate (CR) criterion reflects the measurement statistics, thus influencing the system's response time. Measuring resolution, as described in (1), quantifies the variation in CR relative to a reference value ($CR_{ref}$). It serves as a crucial metric for evaluating the system's ability to discern and resolve minute differences in boron concentration ($C_B$). By assessing measuring resolution, we can effectively gauge the system's precision in distinguishing subtle variations in $C_B$. The comparison between neutron and thermal sensitivities, described as in (2) and (3), is to ensure that $S_n$ is greater than $S_T$ by at least one order of magnitude. This criterion ensures that the BCOMS provides a relatively stable response across temperature variation.

$$R \stackrel{\text{def}}{=} \frac{\Delta CR}{CR_{\text{ref}}} \quad (\%) \quad (1)$$

$$S_n \stackrel{\text{def}}{=} \frac{\Delta CR}{\Delta C_B} \quad (\text{cps/ppm}) \quad (2)$$

$$S_T \stackrel{\text{def}}{=} \frac{\Delta CR}{\Delta T} \quad (\text{cps}/^{\circ}\text{C}) \quad (3)$$

Additionally, to ensure the safety and reliability of BCOMS, three key qualification criteria have been established: radiation protection, mechanical qualification and redundancy. Boron meters are equipped with a neutron source, it is therefore necessary to mitigate radiation exposure to system operators and surrounding environments. The mechanical qualification criterion assesses the structural integrity and durability of the system under various operational conditions and accidental situations, ensuring its stability and longevity. Lastly, as per the redundancy criterion, it is imperative to implement a dual-channel acquisition line spanning from the neutron detector to the processing unit. This redundancy measure ensures system

integrity by providing redundant data pathways, enhancing reliability and safeguarding against potential failures along the entire acquisition and processing chain. In this paper, we focus our study on evaluating the performance of BCOMS based exclusively on the criteria of CR and measuring resolution (R) in a redundant non-intrusive BCOMS.

## III. DESIGN OF A NON-INTRUSIVE BCOMS

Prior to conducting the performance assessment of BCOMS, this section provides a comprehensive review of the measuring principle and key characteristics associated with these systems.

### A. Measuring principle

The measuring principle of boron meters, depicted in Fig. 1, remains consistent, irrespective of whether they are intrusive or not. It revolves around quantifying the attenuation and absorption of a neutron flux. Neutrons, suitably slowed down by a neutron moderator, undergo capture within the primary fluid through the (n, α) reaction. Subsequently, the remaining neutrons are detected by a dedicated neutron counter, establishing an anticorrelation between the detector count and boron concentration. This anticorrelation is determined through calibration techniques, which involve finding a fitting function capable of converting the measured CR (in cps) to $C_B$ (in ppm). Multiple studies have put forth various solutions aiming at improving calibration accuracy regarding fitting functions [2, 4, 7, 11].

<figure><img src="image_1.png" /><figcaption>Fig. 1. Boron meter measuring principle.</figcaption></figure>

### B. Neutron source

The borated water is interrogated by neutrons emitted from a neutron source such as Am-Be or $^{252}$Cf. In the frame of this work, we study the performance of a BCOMS equipped with an Am-Be neutron source, since this latter is characterized with a long half-life, of roughly 432 years, which alleviates the need for frequent recalibration. Indeed, $^{241}$Am decays via α emission to $^{237}$Np. Neutrons are then generated through the reaction $^{9}$Be(α, n)$^{12}$C.

### C. Neutron counter

Based on specific properties regarding neutron sensitivity to thermal neutrons and sensitive length, we select a CPNB48 boron-lined proportional counter [14], manufactured by PHOTONIS. Neutrons interact with the boron coating on the inside wall of the tube following the $^{10}$B(n, α)$^{7}$Li reaction. Since reaction products (i.e., $^{7}$Li and α particles) are oppositely directed, only one reaction product ionize the gas per (n, α) reaction. The ionized particles are then converted to a signal by the applied voltage, inducing the gas multiplication process of
electrons near the anode wire.

### D. Neutron moderator

Efficient neutron moderation is crucial to enhance the sensitivity of neutron detectors towards thermal neutrons. This moderation process primarily involves elastic and inelastic scattering. In this study, we compare the measuring performance of three commonly used neutron moderators: high-density polyethylene (HDPE), graphite and amorphous carbon.

## IV. PERFORMANCE ASSESSMENT

In this section, we examine the impact of various dimensioning parameters on the selected performance criteria by Monte Carlo simulation using the MCNP6.2 code. This rigorous analysis allows us to gain insights into how different parameter configurations affect the identified performance metrics. By elucidating these relationships, we can enhance our understanding of the system's behavior and inform effective design and optimization strategies.

Fig. 2 presents the MCNP6.2 model depicting the preliminary design of a non-intrusive BCOMS. In this work, we investigate the influence of the detector position, spacing and moderator material. Note that the study of the detector position and spacing was performed in the case of the use of HDPE as an external neutron moderator, with a radius of 20 cm and a height of 50 cm.

<figure><img src="image_2.png" /><figcaption>Fig. 2. 3-D visualization of the MCNP6.2 model of a non-intrusive BCOMS mounted around the CVCS pipeline.</figcaption></figure>

### A. Detector position

In order to assess the impact of detector position relative to the neutron source, we conducted an evaluation around the CVCS pipeline, as depicted in Fig. 3. The objective was to compare two configurations: direct attenuation (on the left) and backscatter geometry (on the right). Various angular distributions of detectors were simulated around the pipeline, ranging from 30° (for direct attenuation) to 330° (for backscattering).

<figure><img src="image_3.png" /><figcaption>Fig. 3. 2-D view of the simulated detector position configurations.</figcaption></figure>

Fig. 4 presents the plotted evolution of CR (at 0 ppm) and measuring resolution. It is important to note that CR correlates with the (n, α) reaction rate occurring in the boron deposition

layer of the counter tube. The (n, α) reaction rate was calculated using the F4 tally to estimate the detection efficiency.

<figure><img src="image_4.png" /><figcaption>Fig. 4. Impact of detector position, MCNP6.2 simulation results.</figcaption></figure>

Observations indicate that as the system transitions towards a backscatter geometry, there is a notable increase in measuring statistics while encountering a decrease in measuring resolution. In this context, selecting a high sensitivity detector helps minimize constraints related to CR, making resolution a more crucial performance criterion.

Based on this analysis, a direct attenuation measuring configuration is chosen, enabling the best measuring resolution of approximately 35% while maintaining a sufficiently fast response time. This decision is made considering the intensity of the neutron source emitting approximately $10^6-10^7$ n.s$^{-1}$ in $4\pi$ sr.

### B. Detector spacing

Building upon the previously selected direct attenuation configuration, we proceed to evaluate the impact of detector spacing. In this assessment, we examine the evolution of CR and $\mathcal{R}$ across a range of spacing options between the two measuring channels, spanning from 1 to 30 cm, as illustrated in Fig. 5.

<figure><img src="image_5.png" /><figcaption>Fig. 5. 2-D view of the simulated detector spacing configurations.</figcaption></figure>

Simulation results are presented in Fig. 6, revealing important insights into the influence of detector spacing. A notable observation is that at a detector spacing of approximately 4 cm, there is a slight increase in CR. However, this increase comes at the expense of a 10% decrease in $\mathcal{R}$; when compared to the minimum detector spacing that yields the highest resolution, approaching 35%. Based on these findings, we confidently select the measuring configuration with the minimum detector spacing, ensuring optimal measuring resolution.
<figure><img src="image_6.png" /><figcaption>Fig. 6. Impact of detector spacing, MCNP6.2 simulation results.</figcaption></figure>

### C. Neutron moderator material

In the final phase of our analysis, we conducted a comprehensive comparison of neutron moderator materials, specifically HDPE, graphite and amorphous carbon. The simulation results, depicted in Fig. 7 and summarized in Table 1, underscore the profound influence of the neutron moderator on overall performance. In fact, carbon-based moderators, such as graphite and amorphous carbon, exhibit a remarkable enhancement in measuring resolution, reaching nearly 60% compared to the 35% achieved by HDPE. This notable improvement enables better discrimination of $C_B$, particularly for higher values where we observe a drastic decrease $\mathcal{R}$. Furthermore, it is noteworthy that the higher density assigned to amorphous carbon contributes to a simultaneous increase of 34% in CR, while graphite exhibits a 16% decrease, compared to HDPE.

<figure><img src="image_7.png" /><figcaption>Fig. 7. Influence of neutron moderator material, MCNP6.2 simulation results.</figcaption></figure>

<table><caption>TABLE I
COMPARISON OF CR AND MEASURING RESOLUTION AMONG HDPE, GRAPHITE, AND AMORPHOUS CARBON</caption><thead><tr><th></th><th>HDPE</th><th>Graphite</th><th>Amorphous carbon</th></tr></thead><tbody><tr><td>ΔCR/HDPE (0 ppm)</td><td>-</td><td>- 16%</td><td>+ 34%</td></tr><tr><td>Global resolution (R)</td><td>35%</td><td>61%</td><td>58%</td></tr><tr><td>R<sub>[0-1250] ppm</sub></td><td>21%</td><td>35%</td><td>33%</td></tr><tr><td>R<sub>[1250-2500] ppm</sub></td><td>9%</td><td>21%</td><td>19%</td></tr><tr><td>R<sub>[2500-5000] ppm</sub></td><td>9%</td><td>24%</td><td>21%</td></tr></tbody></table>

## V. PHYSICAL PHENOMENA

The primary focus of this section is to gain insights into neutron-induced phenomena that affect the overall performance of the studied BCOMS. Specifically, our aim is to understand the

underlying physical mechanisms contributing to the decrease in measuring resolution, clearly observed in Table 1, as boron concentration increases. Furthermore, we seek to explore the influence of different materials on the performance criteria, unraveling the intricate relationship between neutron moderator properties and system performance.

The behavior of neutron population is governed by the Boltzmann transport equation establishing a delicate balance between mechanisms that generate and deplete neutron population [15]. Solving the Boltzmann equation presents substantial challenges due to its reliance on seven independent variables (three in space, two in direction, energy and time). In response to this complexity, two main approaches have been developed. On the one hand, various numerical methods, such as deterministic methods and the Monte Carlo method, have been utilized [16]. On the other hand, the diffusion theory approximation offers a practical and efficient solution, providing an analytical approach under specific assumptions regarding the system's geometry and neutronics. This approximation has garnered recognition for its effectiveness in addressing a wide range of challenges encountered in reactor design. By simplifying the complex Boltzmann equation, the diffusion approximation presents a more manageable formulation, as in (6), where “Δ” is the Laplacian operator, parameter K combines the macroscopic transport ($\Sigma_{tr}$) and absorption ($\Sigma_a$) cross-sections, and D denotes the diffusion coefficient.

$$ \Delta\phi - K^2\phi = 0; \quad K^2 = \frac{\Sigma_a}{D} = 3\Sigma_a\Sigma_{tr} \quad (6) $$

This study endeavors to attain a deep comprehension of the fundamental physical phenomena contributing to the observed decline in measuring resolution within the BCOMS. Hence and to simplify the analysis, we adopt a one-dimensional Cartesian coordinate system to solve (6) in both the borated water region and the neutron moderator (graphite) region, while incorporating appropriate boundary conditions. Then, we compare the analytical solution with the MCNP6.2 calculations. Results are presented in Fig. 8, where we observe a coherence in the behavior of the two curves. However, there are discrepancies between them, which can be attributed to the geometric and neutronic assumptions and simplifications made within the diffusion theory approximation.

<figure><img src="image_8.png" /><figcaption>Fig. 8. Comparison between the analytical solution and the MCNP6.2 calculation of the neutron flux distribution in the detector region.</figcaption></figure>
Remarkably, the analytical solution of the neutron flux distribution ($\phi_n$) offers an insightful explanation for the decrease in measuring resolution, which is observed through the flattening tendency in calibration curves as the $C_B$ increases. The solution of (6) in a Cartesian coordinate system involves a combination of exponential functions that yield an exponential-like shape to the neutron flux distribution. Specifically, the solution includes exponential functions with arguments of $Kx$ and $-Kx$, where $x$ represents the distance traveled along the considered axis.

Additionally, the neutronic characteristics of the moderator play a crucial role in shaping the neutron flux population and energy distribution within both the borated water and the detector region. Notably, HDPE demonstrates significantly greater absorption rates compared to graphite and amorphous carbon, thus exerting a substantial impact on the neutron flux population. Furthermore, HDPE exhibits a higher macroscopic scattering cross-section than amorphous carbon and graphite, thereby influencing the energy distribution of neutrons. These contrasting properties contribute to the observed disparities in terms of CR and $\mathcal{R}$.

## VI. CONCLUSIONS AND OUTLOOK

This study presents a comprehensive performance analysis of non-intrusive Boron Concentration Online Monitoring Systems (BCOMS) installed around the CVCS pipeline of a PWR. We evaluate, using the MCNP6.2 code, the impact of three critical dimensioning parameters on the counting rate and measuring resolution. The results indicate that a direct attenuation configuration with minimized detector spacing yields improved accuracy. Furthermore, our investigation into the influence of external neutron moderators reveals that carbon-based materials such as graphite and amorphous carbon exhibit a significant increase in measuring resolution compared to HDPE.

However, it is worth noting that a substantial decrease in resolution occurs as boron concentration increases across the various configurations. This intriguing phenomenon motivates our focus on understanding the underlying physical mechanisms responsible for the observed flattening behavior in calibration curves. Through an analytical study employing the diffusion theory approximation, we establish a correlation between the neutron's behavior within the boron meter and the observed resolution. This finding aligns with the results obtained from MCNP6.2 calculations. Our conclusion is that the flattening behavior is an intrinsic phenomenon inherent to borated water and cannot be eliminated. Consequently, the best approach is to identify an appropriate external neutron moderator that offers optimal measuring resolution. Currently, carbon-based moderators exhibit the most favorable performance, with a resolution of nearly 60%. However, the selection of the neutron moderator is still under investigation, as it is crucial to consider other design and safety requirements.

Moreover, we aim to enhance the analytical calculations by solving the equation (6) in a three-dimensional coordinate system, enabling the derivation of a formula that links resolution to the moderator's properties. In addition, an

expanded study of various advanced moderators is planned. Ultimately, our objectives include manufacturing an optimized prototype of BCOMS to experimentally calibrate the device and assess overall performance, including thermal stability.

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