Conditions for criticality by uranium deposition in water-saturated geological formations

Figures & data

Figure 1. Three geometries for the MCNP simulations: (1) fractured system I, (2) fractured system II, and (3) homogeneous system.

Table 1. Heavy metal compositions at the time of the accident.

Uranium	Isotopic weight	Plutonium	Isotopic weight
isotopes	fraction (%)	isotopes	fraction (%)
U-235	1.81	Pu-238	1.25
U-236	0.33	Pu-239	61.97
U-238	97.86	Pu-240	21.18
		Pu-241	3.93
		Pu-242	11.67
Total mass	248.88	Total mass	1.84
Metric tons of heavy metal (MTHM)		(MTHM)

Table 2. Heavy metal compositions after 200,000 years of decay.

Uranium	Isotopic weight	Plutonium	Isotopic weight
isotopes	fraction (%)	isotopes	fraction (%)
U-235	2.25	Pu-239	6.78
U-236	0.48	Pu-242	93.22
U-238	97.25
Total mass	250.46	Total mass	0.054
(MTHM)		(MTHM)

Table 3. Host rock compositions.

Sandstone		Iron-rich rock: magnetite–hematite-bearing pelitic gneiss
Composition	Weight fraction (%)	Composition	Weight fraction (%)
SiO2	78.7	SiO2	44.09
TiO2	0.25	TiO2	1.69
Al2O3	4.8	Al2O3	23.64
Fe2O3	1.1	Fe2O3	12.01
FeO	0.3	FeO	3.66
MnO	0.03	MnO	0.37
MgO	1.2	MgO	2.61
CaO	5.5	CaO	0.85
Na2O	0.45	Na2O	2.03
K2O	1.3	K2O	6.01
H2O	1.3	H2O	3.22
P2O5	0.08	P2O5	0.15
CO2	5.0
Grain density (g/cm^3)	2.71	Grain density (g/cm^3)	3.09

Figure 2. (a) k_eff contour plot for fractured sandstone with fractured geometry I. (b) k_eff contour plot for iron-rich rock with fractured geometry I.

Figure 3. Minimum VVF for k_eff > 0.98 for different rocks and geometries, assuming all 250 MT of uranium is deposited.

Figure 4. k_eff for different rock types and heterogeneous geometries with different fracture apertures.

Figure 5. (a) Critical mass contour plot for fractured sandstone. The values in the figure and in the side-bar scale are logarithm of MT of uranium included in the system. (b) Critical mass contour plot for homogeneous sandstone. The values in the figure and in the side-bar scale are logarithm of MT of uranium included in the system.

Table 4. Minimum critical void volume fractions (VVF) for various combinations of geometries and uranium deposition masses.

		Mass of uranium deposition (MTU)
		250	100	10	1
Rock type	Geometry	Minimum critical VVF
Sandstone	Fractured geometry I	0.094	0.104	0.133	0.260
Sandstone	Homogeneous	0.169	0.179	0.209	>0.300
Iron-rich rock	Fractured geometry I	0.265	0.273	>0.300	>0.300

Figure 6. Thermal disadvantage factor, fast fission factor, and thermal reproduction factor for different fracture apertures for fractured system I.