How to Calculate Total Thermal Power in Nuclear Reactors?

[emilmammadzada]

TL;DR

How to Calculate Total Thermal Power in Nuclear Reactors?

Hello Dear Experts.
I need help with the calculation of total thermal power in nuclear reactors. Can someone explain the general mathematical approach or provide useful formulas for this calculation?

Thanks!

 

[Alex A]

From what information? A reactor will try to run at whatever power it's told to. You can run a 1GW reactor at 100MW, you can run it at 10GW, briefly, and what stops it working for longer won't be fundamental physics. Limits on the design will prevent heat being removed fast enough. Higher temperatures will cause failure of parts. That is a factor of design, coolant, mass flow through pumps...

Fission rate * Energy per fission = Reactor power

But it's not that helpful. Try reading this thread.

 

[emilmammadzada]

From what information? A reactor will try to run at whatever power it's told to. You can run a 1GW reactor at 100MW, you can run it at 10GW, briefly, and what stops it working for longer won't be fundamental physics. Limits on the design will prevent heat being removed fast enough. Higher temperatures will cause failure of parts. That is a factor of design, coolant, mass flow through pumps...

Fission rate * Energy per fission = Reactor power

But it's not that helpful. Try reading this thread

So what I want to understand here is how to calculate the total thermal power for a SMR and a normal reactor. How does the number of fuel pins or fuel volume affect it?

 

[Astronuc]

How does the number of fuel pins or fuel volume affect it?

One has to define a set of technical limits for the fuel, usually set by the peak power location, the peak channel enthalpy gain/rise, fuel rod (or particle) internal pressure, peak fuel temperature (one has to retain some margin to melting), peak cladding temperature (determined by limiting creep and/or corrosion/material loss), limiting heat flux, . . . , and dimensional stability (addressing creep, swelling, and physical distortion of the fuel elements and structure). Translating that into.a core design comes from experience. One has to similate normal operation, anticipated operational occurrences (AOOs), and a variety of transiens, and beyond design basis events (severe accidents). The fuel should retain fission products to the extent possible, the core must remain coolable (mostly to removed decay heat), and the reactor must be able to shutdown in a subcritical configuration upon demand (i.e., the fission process (chain reaction) ceases).

Like large commercial nuclear reactors, SMRs could be smaller LWRs (based on PWR or BWR technology), graphite moderated (gas, liquid metal, or molten salt cooled), molten salt fueled (MSRs), or liquid metal fast reactors.

I did a compact 300 MW fast reactor design that used (U,Pu)N cladding in a W-Mo-Re alloy, with a core exit temperature of 1300°C. The core was cooled by liquid Li. The core size was on the order of 1 m height and slightly more than 1 m in diameter. I did a similar design recently, but using liquid Pb, or Pb-Bi, but more conventional core design.

Fuel cycle management (batch sizes, enrichments and enrichment distributions), cycle length (annual, 18-month, 24 month, . . . ), maximum burnup of the fuel assembly and peak rod (or pellet), and how many times an assembly (or fuel element) will be returned to the core.

Small cores generally have a higher fraction of neutron leakage from the core compared to large cores. One can somewhat mitigate neutron leakage with an appropriate 'reflector', e.g., low enriched, or natural, or even depleted U) fuel.

 

[Astronuc]

You can run a 1GW reactor at 100MW, you can run it at 10GW, briefly, and what stops it working for longer won't be fundamental physics.

If one runs a reactor designed for 1 GW at 10 GW, then one would likely melt the core. The heat would not transfer fast enough, and very likely thermal expansion (and possibly gaseous swelling, which is dependent on burnup) of the fuel would cause the coolant channels to close. Certainly, one would be boiling water or sodium, or in the case of a gas, although thermal conductivity increases with temperature, the density decreases with temperature meaning it is more difficult to compress, i.e., one has to compress more to obtain a given density. The pressure would increase putting more stress on the pressure vessel containing the core. Increase coolant flow rates would likely lead to flow-induced vibrations in the core, or even lift fuel assemblies/fuel elements.

As temperature rises, thermal neutron cross section in the fuel decreases and resonance absorption increases; the 'Doppler resonance' absorption is a limiting effect in overpower transients.

In the end, fundamental physics of the materials limit how much power a core can produce and remain stable and intact.

For example, about 30% of fission products (and their daughter products) are isotopes of Xe and Kr. One has to consider both the Xe and Kr precursors and decay products; Te > I > Xe > Cs and Se > Br > Kr > Rb. The halides and alkali metals become volatile at moderate temperature and Te and Se will become volatile at somewhat higher temperatures, all of which would contribute to fuel swelling and increase internal pressure.

Edit/update - Walter A. Paulson and Roy H. Springborn
Estimation of fission-product gas pressure in uranium dioxide ceramic fuel elements
(NASA Lewis Research Center Cleveland, OH (now NASA Glenn Research Center)
https://ntrs.nasa.gov/citations/19690000885

The French CEA has observed volatile compounds of Te, I and Cs in nuclear fuel. Te decays to I, and I can form compounds with Zr, e.g., ZrI₄, which is volatile and attacks grain boundaries in Zr-alloys in a reverse van Arkel process. As I diffuses into the Zr-alloys, some will decay to Xe and Cs, futher undermining structural integrity of the alloy.

 

[Astronuc]

One can scale existing technology, which for PWR would be based on 17x17 fuel assemblies designed and manufactured by Framatome, KNF, Mitsubishi and Westinghouse. For example, the NuScale and mPower designs were reduced height 17x17 fuel with the same lattice and guide tubes for control rods. Whereas the large power reactors (3.6-3.7 GWt, 193 assemblies in the core) had 8 rows of fuel from center to core flats (or 15 rows of assemblies across the breadth of the core), the smaller reactors would have 4 rows (including the center assembly), or 7 assemblies across the core. Typically, one has an odd se of rows since the center assembly provides symmetry in the core. A typical full size (height 3.66 m, 12 ft) 17x17 fuel assembly produces an average power of 9 MW in a core of 193 fuel assemblies.

In hexagonal or triangular lattice, as in the VVER designs, there is a center assembly, which is surrounded by 5 assemblies (6 faces for each assembly), which are surrounded by 12 assemblies, with successive rings being multiples of 6 assemblies.

The new BWRX-300 reactor uses smaller fuel assemblies based on current technology. The core has 240 assemblies, much like the existing KKMühleberg reactor.

https://www.gevernova.com/nuclear/carbon-free-power/bwrx-300-small-modular-reactor

And apparently, Westinghosue has a smaller reactor design, AP300. The following is rather superficial and does not provide technical information on the core design.
https://www.nrc.gov/docs/ML2331/ML23310A144.pdf

 

[emilmammadzada]

One can scale existing technology, which for PWR would be based on 17x17 fuel assemblies designed and manufactured by Framatome, KNF, Mitsubishi and Westinghouse. For example, the NuScale and mPower designs were reduced height 17x17 fuel with the same lattice and guide tubes for control rods. Whereas the large power reactors (3.6-3.7 GWt, 193 assemblies in the core) had 8 rows of fuel from center to core flats (or 15 rows of assemblies across the breadth of the core), the smaller reactors would have 4 rows (including the center assembly), or 7 assemblies across the core. Typically, one has an odd se of rows since the center assembly provides symmetry in the core. A typical full size (height 3.66 m, 12 ft) 17x17 fuel assembly produces an average power of 9 MW in a core of 193 fuel assemblies.

In hexagonal or triangular lattice, as in the VVER designs, there is a center assembly, which is surrounded by 5 assemblies (6 faces for each assembly), which are surrounded by 12 assemblies, with successive rings being multiples of 6 assemblies.

The new BWRX-300 reactor uses smaller fuel assemblies based on current technology. The core has 240 assemblies, much like the existing KKMühleberg reactor.

https://www.gevernova.com/nuclear/carbon-free-power/bwrx-300-small-modular-reactor

And apparently, Westinghosue has a smaller reactor design, AP300. The following is rather superficial and does not provide technical information on the core design.
https://www.nrc.gov/docs/ML2331/ML23310A144.pdf

Dear expert, I am trying to design a hexagonal smr type reactor. My reactor k_eff starts to decrease rapidly after 20 days, for example from 1.2 to 0.8. What edits do you suggest to prevent this? I have attached the serpent input file below .How can I make appropriate optimizations for this reactor?