Burnable absorbers

Hana opens the loading report for the next reload. Of the 72 fresh assemblies, most contain integral fuel burnable absorber rods and some contain gadolinia rods. "A reload puts a third of a core of fresh fuel in at once," Teodora says. "That fuel has far more reactivity than the core needs at the start of the cycle. Without burnable absorbers, we would need so much boron that the moderator temperature coefficient could turn positive, and the hot fresh assemblies would peak too high. Burnable absorbers solve both problems."

Why burnable absorbers are needed

A batch-loaded reactor starts each cycle with enough reactivity to last until the end of the cycle. At the start, the fresh fuel has its highest reactivity, so the core carries a large excess that must be held down. Three tools are available: control rods, soluble boron in the coolant and burnable absorbers in the fuel. Control rods are needed for control and shutdown and should not be deeply inserted during normal operation, because they distort the power distribution. Soluble boron is uniform and flexible, but too much of it causes a problem: boron is removed from the core when the moderator heats and expands, so a high boron concentration makes the moderator temperature coefficient less negative and could make it positive at the start of a cycle.

A burnable absorber is a neutron absorber placed in or near the fuel that is gradually consumed by neutron absorption. Ideally, it holds down excess reactivity early in the cycle and burns away as the fuel itself loses reactivity, so that the net reactivity stays nearly flat. It can also be placed selectively to flatten the power distribution by suppressing the hottest fresh assemblies.

Self-shielding and the burnout curve

The way a burnable absorber loses its worth depends on how strongly it shields itself. Gadolinium-155 and -157 have thermal absorption cross sections of tens to hundreds of thousands of barns. A gadolinia pellet is so black to thermal neutrons that the interior is almost completely shielded at first. Absorption happens in a thin outer layer, and the absorber burns away from the outside inward, like the layers of an onion. The worth of the pin therefore falls slowly at first and then quickly as the last of the gadolinium is consumed. After burnout, the pin behaves like ordinary fuel with slightly lower uranium content.

A boron coating, by contrast, is thin and only weakly self-shielded. Every boron-10 atom sees nearly the same flux, so the coating burns out almost exponentially, losing a constant fraction of its remaining atoms per unit burnup. The two absorbers therefore have different shapes of reactivity curve, and designers often combine them to shape the core reactivity through the cycle.

The program below models both behaviors with an escape factor that depends on the optical thickness of the absorber, and applies their worths to an assembly whose reactivity falls linearly with burnup.

# Burnable absorbers: how a gadolinia pin and an IFBA-coated pin lose their worth.
# Self-shielding is modeled by an escape factor g(x) = (1 - e^-x)/x, where x is the
# optical thickness of the absorber, which shrinks as it burns. Values are illustrative.
import math
def g(x): return 1.0 if x < 1e-9 else (1 - math.exp(-x)) / x
def burn(x0, sigma_phi_per_mwd, steps, dbu):
    """Return remaining absorber fraction at each burnup step (MWd/kgU)."""
    n, out = 1.0, []
    for i in range(steps + 1):
        out.append((i * dbu, n))
        rate = sigma_phi_per_mwd * g(x0 * n)
        n = max(0.0, n * math.exp(-rate * dbu))
    return out
# gadolinia: very black (x0 large), so it burns slowly at first, then quickly
gad = burn(x0=25.0, sigma_phi_per_mwd=2.2, steps=20, dbu=1.0)
# IFBA: thin boride coating, nearly unshielded, burns roughly exponentially
ifba = burn(x0=0.8, sigma_phi_per_mwd=0.17, steps=20, dbu=1.0)
worth_gad0, worth_ifba0 = 0.060, 0.045         # initial assembly hold-down (delta k)
k_fresh = 1.30
print(" burnup | Gd left | IFBA left | k_inf no BA | with Gd | with IFBA")
for (bu, ng), (_, ni) in zip(gad, ifba):
    if bu % 2: continue
    k0 = k_fresh - 0.0105 * bu                  # linear reactivity loss with burnup
    print(f"{bu:7.0f} | {ng:7.2f} | {ni:9.2f} | {k0:11.3f} | {k0 - worth_gad0*ng:7.3f} | {k0 - worth_ifba0*ni:9.3f}")

 burnup | Gd left | IFBA left | k_inf no BA | with Gd | with IFBA
      0 |    1.00 |      1.00 |       1.300 |   1.240 |     1.255
      2 |    0.83 |      0.79 |       1.279 |   1.229 |     1.244
      4 |    0.67 |      0.61 |       1.258 |   1.218 |     1.231
      6 |    0.50 |      0.46 |       1.237 |   1.207 |     1.216
      8 |    0.34 |      0.35 |       1.216 |   1.196 |     1.200
     10 |    0.19 |      0.26 |       1.195 |   1.184 |     1.183
     12 |    0.06 |      0.19 |       1.174 |   1.170 |     1.165
     14 |    0.00 |      0.14 |       1.153 |   1.153 |     1.147
     16 |    0.00 |      0.10 |       1.132 |   1.132 |     1.128
     18 |    0.00 |      0.07 |       1.111 |   1.111 |     1.108
     20 |    0.00 |      0.05 |       1.090 |   1.090 |     1.088

The gadolinia case shows the characteristic plateau: k_inf falls slowly over the first 10 MWd/kgU because the absorber is burning away as fast as the fuel loses reactivity, then the two curves join once the gadolinium is gone. The IFBA case starts with less hold-down but burns out gradually, leaving a small residual. A real design avoids a large residual at the end of the cycle, because any absorber left over is lost reactivity that shortens the cycle.

Using burnable absorbers to shape power

Burnable absorbers also control where power is produced. Fresh assemblies have the highest reactivity in the core and tend to run at the highest power. Placing absorber pins in them lowers their power during the early part of the cycle, when the risk of exceeding a peaking limit is greatest. Designers choose the number of absorber pins per assembly, the gadolinia content and the axial extent of the absorber to tailor the power distribution. Axial blankets of natural or lightly enriched uranium at the ends of each rod, and cutbacks of absorber near the top and bottom, help shape the axial power profile.

Gadolinia pins have drawbacks that must be managed. Gadolinia lowers the thermal conductivity of the pellet and the melting point, and the pins usually have lower uranium-235 enrichment to compensate. Because their power is low early and high later, their peak conditions may come late in life. Lattice codes model gadolinia pins with many radial rings to follow the onion-skin burnout correctly, and the depletion steps must be small while the gadolinium is burning.

Burnable absorbers in BWR and PWR reloads

In TVA's pressurized water reactors, most fresh assemblies carry integral fuel burnable absorber rods, and some carry gadolinia rods for stronger, longer hold-down where needed. The reload designer chooses how many absorber rods each fresh assembly carries and where those assemblies sit, so that the critical boron starts at an acceptable level and the peaking factors stay within limits. In boiling water reactors such as the BWRX-300, gadolinia is the main burnable absorber, and its distribution in each assembly is designed together with the control blade pattern.

Designing the burnout to match the cycle

The ideal burnable absorber disappears exactly when it is no longer needed. If it burns out too early, the core has excess reactivity left late in the cycle that must be held down by boron. If it burns out too late, the residual absorber steals reactivity at the end of the cycle and shortens the cycle. For an 18-month cycle, gadolinia contents are chosen so that most of the gadolinium has burned out by roughly the middle of the cycle, while IFBA coatings decline steadily. For 24-month cycles, which require higher-enrichment fuel and more hold-down, designers use more absorber pins and higher gadolinia concentrations, or slower-burning absorbers such as erbia.

Burnable absorber modeling in lattice and core codes

Burnable absorbers are among the hardest features to model accurately, because they combine strong self-shielding with fast depletion. A lattice code divides each gadolinia pellet into many thin radial rings, often ten or more, so that the onion-skin burnout is followed ring by ring. It also uses shorter depletion steps while the gadolinium is burning, because the absorption rate in the rings changes quickly. The core simulator receives the result as part of the cross section tables: the assembly's few-group constants are tabulated against burnup, and the burnout appears as a change in those constants. Errors in burnable absorber modeling show up in the plant as differences between predicted and measured critical boron early and in the middle of the cycle, which is one of the first things core designers check after start-up.

Burnable absorber design is closely tied to fuel fabrication and inspection. Gadolinia pellets have a lower thermal conductivity and a lower melting point than ordinary uranium dioxide pellets, so the gadolinia-bearing rods usually contain uranium of lower enrichment to keep their power and temperature lower. Coated pellets must have a uniform coating thickness, checked during manufacture, so that the boron loading matches the design. Each design choice, from the number of absorber pins to their positions and concentrations, is evaluated by the lattice code and confirmed by the core simulator before the fuel is ordered, often more than a year before it enters the core.