3.1. A Simplified Model Calculation
A rough estimation of the effect of the radiolysis of the target’s cooling water due to its interaction with neutron and gamma radiation was performed (refer to
Figure 3) which represents the steady-state situation of the rotating target.
The radiolysis process is described by:
The radiation field during plant operation is typically determined by (1) neutron field composed of two components: the “direct” beam due to the neutrons emitted by the “hot spot” area and by the diffuse component due to the neutrons which, scattered from all structural materials and from bioshielding materials enter into the volume where the cooling water is contained; (2) gamma radiation field due to both “prompt” processes and those due to the activation of materials following neutron irradiation. Together with these “beam on” processes, gamma radiation is also present during “beam off” for a time interval depending on the half lives of the radionuclides generated by neutron irradiation and with an intensity determined by the overall activation of the materials. A quantitative estimate of the neutron and gamma fields in the evaporator component of the target can only be obtained with a numerical calculation which, however, requires definitive geometry and materials that constitute the neutron source and the bioshielding that are under definition at present. A first rough estimate can be made, taking as input data derived from a study performed to calculate the effect of the radiolysis of the water in the cooling system of the integrated first wall blanket edge localized mode and vertical stabilization coil divertor primary heat transport system (IBED-PHTS) [
6]. A simplified model is schematically represented in
Figure 4.
Figure 5 describes the kinetics of the molar concentration (mol L
) production of the various species generated as a function of time due to radiolysis induced by neutron and gamma fields interacting with the cooling water, which is at an average temperature of about 98
C during the operation. The concentration of the species generated by radiolysis depends on the energy deposited by the neutron and gamma flux which at the first ITER wall is expected to be 10
cm
s
.
If we consider the operating conditions of SORGENTINA, which provide for a neutron emission rate Y = 5–7 × 10
s
, and referring to
Figure 3, where the quantity of water is of the order of ten (or a few tens) of liters, the molar concentration of H
and other species can be scaled in a very first approximation with the expected flux in the evaporator volume where cooling water circulates in operation conditions. Considering for simplicity the area below the hot spot (with a diameter of 10–12 cm) and a height of 10 cm, the volume of water is in the order of 1 L. Considering a maximum neutron flux in the order of 10
cm
s
to maximize the effect), the concentration of H
, for example, is of the order of 10
M (referring to the graph in
Figure 5) at the steady state. In this hyper-simplified treatment of the problem, the differences due to the thermodynamic conditions of the water were not taken into account in the case that IBED-PHTS water is at a temperature of 70
C and at a pressure of 4 MPa at the inlet to the various modules (average T operating temperature: 98
C), while under the hot spot of
Figure 3 there is a phase transition that occurs below 100
C considering that the average operating pressure is of the order of 0.3 bar in operation conditions. If we consider that the effect of p and T does not cause a variation of the order of magnitude, the estimate of 10
M can be considered as reasonable, within the approximations used. The volume occupied in the thermodynamic operating conditions of SORGENTINA are of the order of 2
L and are therefore absolutely negligible at steady state, as compared to the volume of the rotating target. This should not affect its operation based on the continuous circulation of the steam generated in the phase transition due to the absorption of the thermal power due to the ion beam impinging on the rotating target. It is worth highlighting that in this very simplified and conservative calculation, the radiolysis products scale with the neutron flux (assuming that also the gamma radiation is proportional to the neutron field intensity) and the chemical properties of the SORGENTINA’s cooling water are supposed to be similar to those of the IBED-PHTS system.
3.2. Refined Model Numerical Simulations
Numerical integration of differential kinetic equations (Equation (
3)) provides the time-dependent profiles describing how concentrations of the radiolysis products vary with the exposure time approaching equilibrium. Although the method was successfully developed and validated by Bartels et al. [
16], and G-values, reactions, and their rate constants have been well established by many researchers, we further verified the validity of the calculation model by comparing the simulation result with the experimental data of Yakabuskie et al. [
17], as shown in
Figure 6.
To better understand how possible pH alteration could affect the different equilibria involving the radiolysis products, the same simulations were carried out by changing the starting pH value from 6.5 to 7.5.
The concentrations of main radicals and stable species for water with an initial pH of 6.5 are shown in
Figure 7. Note that a solution with a pH of 6.5 is slightly acid at room temperature, but at 60 °C this value corresponds to the neutral pH
.
It is possible to see how the steady-state concentration is reached at about 10 s, and H
and H
O
are in larger excess (∼0.3 µM), compared to the other radiolysis products, by at least two orders of magnitude. The concentrations of HO
and HO
radicals are negligible throughout the simulation time, while the pH of water increases by about 0.2 units (
Table 4). The OH· radicals produced mainly in reactions (11) and (18) (
Table 1) are consumed almost equally in both reactions (1) and (3) due to their similar rate constants. This results in nearly equal concentrations of generated H
and H
O
. The steady-state concentrations of the main radiolysis products are summarized in
Table 4.
Starting with a pH
value of 7 (
Figure 7b), the concentration profiles change, resulting in an increase of H
and H
O
to 7.32 µM and 3.48 µM, respectively. Except for OH· and H· radicals, the other species show higher concentrations than those observed at pH
of 6.5, although HO
and HO
are, again, negligible (
Table 4). Unlike the previous simulation, the steady state is reached after a longer time (about 10
s), and the oxygen concentration grows by three orders of magnitude. Similar results were obtained in the simulation at pH
7.5, in which the same trend in the concentration profiles was observed (
Figure 7c). In this case also, the steady-state concentration is reached in about 10
s of irradiation, after which H
and H
O
further increase to 13.4 µM and 6.52 µM, respectively (
Table 4). As in the previous simulation, the oxygen reaches micromolar concentrations while the pH value increases by about 0.3 units. A comparison between the concentration profiles of different radiolysis products calculated in the three simulations is shown in
Figure 8a. It is even more evident how the transition time shifts towards longer values by increasing the pH value, and the final concentration of stable molecules and ions slightly increases while that of the radicals decreases; see
Figure 8b.
A slight change in the pH value during the exposure was observed in all three simulations, therefore consisting of a decrease in the H concentration and simultaneous increase in OH. By observing the concentration profiles at short times, it is possible to see how almost all species seem to reach the steady state within 10 s and at the same concentrations as at pH 6.5, but their profiles start to change again at a longer time.
Since it is common to inhibit the production of the main oxidizing species, such as O
, H
O
, and ·OH radicals, by adding an adequate amount of H
, further calculations simulating a flow of hydrogen were performed. This also allows to simulate possible H
production from aluminum-water reactions induced by
-radiation [
18,
19,
20].
Figure 9 refers to similar calculations in which a hydrogen flow at three different concentrations was simulated in water with pH
6.5, 7, and 7.5.
These simulations allow to better understand how the H
may affect the concentration of other radiolysis products, particularly the oxidizing species. In the presence of only 1 µM H
(∼2 ppb), the steady-state concentration of oxygen significantly decreases by two orders of magnitude and is reached within 5 s at pH 6.5, as shown in
Figure 9a. The decrease is also seen for all radiolysis species, except for the hydrogen radicals, which slightly increase due to the introduction of H
(
Table 5).
The same trend, although to differing degrees, occurs when 10 µM H is added. Again, the steady-state concentrations are reached in shorter times as hydrogen concentration enhances. Obviously, a higher addition of H can decrease the concentration of oxidants to lower levels. However, the efficiency of H injection for suppressing oxidant production declines as the amount injected increases.
Indeed, the addition of 100 µM H
no longer leads to a further decrease of H
O
(from 0.0736 µM to 0.0715 µM). Additionally, the oxygen suppression will become less significant in passing from 6.81 × 10
µM to 5.13 × 10
µM. The lowest H
concentration at which the production of radiolysis species changes from a continuous increase to a steady state is usually referred to as the threshold hydrogen concentration (THC) [
21]. In this regard, it is important to find the right compromise between suppressing the radiolysis process and limiting potential issues related to excessive H
concentration. Similar results were obtained at higher pH values, as shown in
Figure 9b,c. Despite the higher steady-state concentration of both H
O
and O
(at 0 µM H
), the addition of 1 µM of H
reduces their concentrations to levels comparable to those achieved at pH 6.5. This behavior is even more noticeable in
Figure 10a, where a comparison between the concentration trend of the main radiolytic products after 1 year of exposure at the three pH values and different [H
] addition is shown. The differences in the steady-state concentrations of some species, such as O
, O
, ·OH, and ·H, as a function of the pH are almost nullified by the hydrogen addition. Thus, the difference of more than three orders of magnitude in the oxygen concentration due to pH differences is no longer detected when an initial flow of hydrogen is employed. Interestingly, although higher pH values induce slower reaching of the steady state when no H
addition occurs, the addition of an appropriate amount of hydrogen instead promotes faster transition time (
Figure 9 and
Figure 10b).
By comparing the O concentration profiles at the three different pH values, it is possible to see how, although the steady state is reached within 5 s from the beginning of the irradiation, the transition time is even lower than the second at pH 7.5. This means that the THC shifts to lower values when the pH increases, as a higher H concentration is required to reach a stable concentration of oxygen at pH values of 6.5 and 7, within this time window (<1 s). In fact, the oxygen also seems to reach the steady state at pH below 7.5, but its profile starts to rise again at a longer time, before stabilizing at about 5 s. Note that all calculations were performed by enforcing a constant concentration of H, thus suggesting the need to modulate its addition during operations to maintain that condition. Interestingly, further simulations showed how this should not be necessary, since the initial amount of H does not undergo any significant changes (maximum of 1% of the initial concentration) even after a year of work; thus, only an appropriate initial injection could be sufficient.