Co-Generation Fission Power Plant

• Co-generation fission power plants are nuclear facilities that harness fission reactions to concurrently generate electricity and heat for secondary applications.
• They employ advanced multiphysics modeling and simulation techniques to accurately predict neutron transport, thermal feedback, and core responses.
• Rigorous benchmarking and validation through experiments and Monte Carlo simulations ensure reliable reactivity calibration and operational safety.

A co-generation fission power plant uses controlled nuclear fission reactions to simultaneously generate electrical power and utilize the resulting waste heat for secondary applications. Critical to its operation is the accurate simulation and benchmarking of the reactor’s core neutronics and thermal behaviors, which underpins design, safety, and deployment of combined energy production systems. The detailed modeling approaches and validation strategies established for research reactors offer essential frameworks for future co-generation plant designs and benchmarking.

1. Steady-State Neutron Transport and k-Eigenvalue Formulation

The operational basis of a co-generation fission power plant is the controlled maintenance of a neutron-induced fission chain reaction within a reactor core. The steady-state neutron transport equation in k-eigenvalue form governs the neutron population behavior:

$$\boldsymbol{\Omega}\!\cdot\!\nabla \,\psi(\mathbf{r},\boldsymbol{\Omega},E) + \Sigma_t(\mathbf{r},E)\,\psi(\mathbf{r},\boldsymbol{\Omega},E) = \int_0^\infty \!dE'\!\int_{4\pi}\!d\boldsymbol{\Omega}'\;\Sigma_s(\mathbf{r},E'\to E,\boldsymbol{\Omega}'\!\to\!\boldsymbol{\Omega})\,\psi(\mathbf{r},\boldsymbol{\Omega}',E') + \frac{1}{k_{\rm eff}} \int_0^\infty \!dE'\,\chi(E)\,\nu\Sigma_f(\mathbf{r},E')\, \int_{4\pi}\!d\boldsymbol{\Omega}'\,\psi(\mathbf{r},\boldsymbol{\Omega}',E')$$

where $\psi$ is the angular neutron flux, $\Sigma_t$ the total macroscopic cross section, $\Sigma_s$ the scattering kernel, $\nu \Sigma_f$ the fission production term, and $\chi$ the fission neutron energy spectrum. The effective multiplication factor, $k_{\rm eff}$, is defined as:

$$k_{\rm eff} = \frac{\text{neutrons produced by fission per generation}}{\text{neutrons lost by absorption + leakage per generation}},$$

and determines core criticality. The operational margin from criticality is quantified as reactivity $\rho = (k_{\rm eff}-1)/k_{\rm eff}$, with changes linked to control mechanisms and safety protocols. One dollar ($1\,\$$) is standardized to the effective delayed-neutron fraction$\beta_{\rm eff}$, relevant for transient and power ramping analyses (Castagna et al., 2017).

2. Core Geometry, Material Representation and Control Systems

Reactor cores are modeled using constructive solid geometry (CSG) with hierarchical elements: cells, surfaces, and universes. A typical research-reactor-derived configuration employs a circular lattice comprising a cluster array—such as the 91-position, five-ring array seen in the TRIGA Mark II reactor. Each fuel element’s individualized universe enables specific assignment of material composition and burnable poison loading, which is vital for co-generation plants using advanced fuel cycles or heterogeneous loading.

Key geometric features include:

• Fuel active zones (e.g., ZrH–UO₂ mixtures enlarged for enhanced moderation or poisoning),
• Control rods with parametrized insertion along the core axis,
• 30-cm thick graphite reflectors including radial and tangential irradiation channels,
• Water pool boundary for moderation and shielding.

Such configurations are preserved for rigorous benchmarking and are extendable to the more complex core-lattice structures envisaged for co-generation platforms (Castagna et al., 2017).

3. Nuclear Data, Thermal Feedback, and Multiphysics Coupling

Continuous-energy nuclear data (e.g., JEFF-3.1) are standard for all nuclides, with detailed thermal scattering law $S(\alpha,\beta)$ treatments for ZrH and H₂O, capturing fine-grained moderation phenomena. Doppler broadening for uranium isotopes is accounted for with library interpolation at ≤10 K intervals across the range 300 K–1200 K, ensuring fidelity in modeling power operation regimes.

In power operation (e.g., at 250 kW), temperature-dependent cross sections are selected for each core region, with fuel discretized both axially (five zones per pin) and radially by core ring. Negative reactivity feedback mechanisms are modeled via:

• $$\alpha_{\rm mod} \simeq \partial\rho/\partial T_{\text{fuel}}$$ due to zirconium hydride moderation,
• Doppler broadening coefficient $$\alpha_D = (1/k)(\partial k/\partial T_{\text{fuel}})$$.

Moderator and reflector zones are isothermal in first approximation. This stratified temperature mapping establishes the basis for multiphysics coupling—crucial for co-generation plants where heat extraction impacts reactivity and safety margins (Castagna et al., 2017).

Fuel Section (Axial)	Core Rings B	C	D	E	F
1	430	420	410	390	380
2	490	480	460	430	400
3	500	500	480	430	400
4	480	460	440	400	370
5	370	360	350	360	330

Table: Full-power (250 kW) segment temperatures (K) for a 5x5 discretization.

4. Benchmarking Methodologies and Reactivity Worth Calibration

Operation and licensing of co-generation fission plants require validated criticality benchmarks. Methodologies draw from experimental critical configurations, such as the 26 low-power (10 W) TRIGA Mark II benchmarks, with rod positions precisely modeled and control-rod reactivity measured by stable-period (inhour) methods. Serpent Monte Carlo simulations set all configurations and control states, computing $k_{\rm eff}$ and $\rho$ for direct comparison to experimental criticality.

Measured biases average $(0.08 \pm 0.02)\$$, with standard deviations$\sim0.10\$, originating primarily from geometric and control-rod modeling uncertainties. Validation against established simulation codes (e.g., MCNP) demonstrates inter-code agreement within $\sim0.06\$, and both codes reproduce zero reactivity in critical conditions within experimental uncertainty bounds (Castagna et al., 2017).

5. Monte Carlo Simulation Settings and Computational Considerations

For robust uncertainty quantification and benchmarking, typical Monte Carlo settings include:

• 50 inactive cycles to establish equilibrium source distribution,
• 500 active cycles with $4 \times 10^5$ neutrons per cycle (total $\approx 2 \times 10^8$ histories),
• Monitoring of $k_{\rm eff}$ convergence with target relative standard deviation $\leq10^{-4}$,
• Direct one-sigma uncertainty propagation for critical parameters ($\sigma_\rho = \sigma_k/k_{\rm eff}^2$).

Parallelization via OpenMP threading achieves near-linear scaling up to $\sim$16 threads, with $\sim$3 hours runtime for full-core keff studies on eight cores. These scalable high-fidelity calculations are foundational for the core neutronics design, safety, and operational flexibility required in co-generation plants (Castagna et al., 2017).

6. Practical Recommendations and Significance

Key procedural recommendations for high-fidelity reactor simulation and co-generation design include:

• Employing individualized (per-pin) universes for unique burnable poison loading and temperature assignments,
• Pre-processing nuclear cross sections at fine temperature intervals for accurate feedback modeling,
• Utilizing built-in reactivity-worth and buckling search routines for rapid analysis,
• Independent validation of control-rod modeling via small-step calculations prior to full-core studies.

Such rigorous practices enable detailed multiphysics assessments essential for co-generation fission power plants, supporting integration with secondary energy utilization systems, enhanced safety, and compliance with operational benchmarks. The techniques demonstrated ensure that the complex coupling of neutronic behavior, heat management, and core control is accurately represented and benchmarked against both experimental data and cross-code validation references (Castagna et al., 2017).