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By Charles Rhodes, P.Eng., Ph.D.

This web page identifies the minimum natural ventilation requirements required for storing spent CANDU fuel in a practical Deep Geological Repository (DGR).


The venting calculation methodology is similar to that for a natural draft high efficiency boiler. The warm gas in the exhaust vent acts as a hot air balloon and develops a buoyancy force. The buoyancy force multiplied by the exhaust gas axial velocity is the buoyancy power. This buoyancy power is dissipated by discharged kinetic energy in the exhaust gas and in the intake gas and by viscous drag in the intake and exhaust vents. In the case of straight large diameter ducts the viscous drag is negligible, which simplifies the calculation.

The calculation is further simplified by initially assuming that the intake duct and the exhaust duct are of equal cross sectional area. For the case of the DGR the duct diameter is chosen to be 6 m because the mining, railway and hydroelectric power industries have extensive practical experience forming 6 m diameter tunnels (drifts) and shafts.

1. CANDU spent fuel bundles are to be kept on nuclear generating station sites in dry cask storage until the thermal output per spent fuel bundle falls to under 10 W. This thermal emission level is projected to occur after about 50 years in storage, at which time most of the fuel bundle thermal output is due to actinide decay. After 50 years in storage the thermal emission due to actinide decay continues with little change for thousands of years.

2. The top of the DGR vault is 400 m below grade level to provide fuel container protection against up to 40 successive glaciations.

3. The warm air discharge is close to a mountain top at an altitude of 1900 m Above Sea Level (ASL).

4. The fresh air intake is at an altitude of 1500 m ASL. This elevation provides both 400 m of overhead rock to protect against glaciations and 300 m of underneath rock to ensure that the storage vault remains high above the local water table.

5. The exhaust air discharge duct is a round smooth wall vertical duct with an inside diameter of 6 m. This duct is formed from the inside of the vault using equipment that has been developed for this purpose by the mining industry. The advantqge of this arrangement is that the cut rock falls down where it is easily removed by truck via one of the horizontal tunnels.

6. The fresh air intake duct is a round smooth wall nearly horizontal duct with an inside diameter of 6 m. This duct also serves as a truck tunnel.

7. The intake air kinetic energy is dissipated as heat in the vault during the process of transferring heat from the fuel bundle containers to the vault exhaust air.

8. The exhaust air temperature is chosen to be 20 degrees K higher than the intake air temperature. This choice is a tradeoff between cost, intake air velocity and a tolerable working temperature. When the outside air temperature is 30 degrees C the highest space temperature in the vault will be 50 degrees C and productive work in the vault will be difficult. However, for much of the year when the outside air temperature is less than 10 degrees C the maximum vault space temperature will be less than 30 degrees C and productive work in the vault will be practical.

9. Density of air = 1.00 kg / m^3 at an altitude of 1500 m.

10. Specific heat capacity of air = 1.005 kJ / kg-degree K.

11. Assume steady state heat exchange to exhaust duct walls is negligible

Intake and exhaust duct walls are sufficiently straight and smooth and the duct air axial velocity is sufficiently small that viscosity effects can be neglected. This assumption leads to a minimum ventilation calculation. The actual required ventilation system will be slightly larger due to real life viscosity effects.

Vi = Axial velocity of intake air
Ve = axial velocity of exhaust air
Ai = cross sectional area of intake air duct
Ae = cross sectional area of exhaust air duct
Le = length of vertical exhaust duct
Li = length of intake air duct
g = acceleration of gravity
H = heat capacity of air per kg-degree K
Pt = thermal power output from stored CANDU fuel bundles
Rhoi = density of intake air at intake to vault
Rhoe = density of exhaust air at discharge from vault
Te = absolute temperature of exhaust air measured at vault discharge
Ti = absolute temperature of intake air measured at vault intake

1) Air mass flow conservation requires that:
Rhoi Ai Vi = Rhoe Ae Ve
2) Buoyancy Force = (Rhoi - Rhoe) Le Ae g
3) Buoyancy Power = (Rhoi - Rhoe) Le Ae g Ve
4) Exhaust air kinetic flow power = (Rhoe Ae Ve) (Ve^2 / 2)
5) Intake air kinetic flow power = (Rhoi Ai Vi) (Vi^2 / 2)
6) Choose Ai = 2 Ae to limit intake air velocity

Absent viscous forces conservation of energy requires that:
Buoyancy power = exhaust air kinetic power + intake air kinetic flow power
(Rhoi - Rhoe) Le Ae g ve = (Rhoe Ae Ve) (Ve^2 / 2) + (Rhoi As Vi) (Vi^2 / 2)
2 (Rhoi - Rhoe) Le Ae g ve = (Rhoe Ae Ve^3) + (Rhoi As Vi^3)

Ideal gas formula gives:
(Rhoe / Rhoi) = (Ti / Te)

From air flow mass conservation:
Vi = (Rhoe / Rhoi) (Ae / Ai) Ve
= (Ti / Te) (Ae / Ai) Ve

The thermal power Pt emitted by the stored fuel bundles that is exhausted by the assumed ventilation system is:
Pt = Rhoe Ae Ve H (Te - Ti)
= (Ti / Te) Rhoi Ae Ve H (Te - Ti)

Recall that from the buoyancy power balance:
2 (Rhoi - Rhoe) Le Ae g ve = (Rhoe Ae Ve^3) + (Rhoi Ai Vi^3)
= (Rhoe Ae Ve^3) + (Rhoi Ai [(Ti / Te) (Ae / Ai) Ve]^3)

2 (Rhoi - Rhoe) Le Ae g = (Rhoe Ae Ve^2) + (Rhoi Ai (Ti / Te)^3 (Ae / Ai)^3 Ve^2)
2 [Rhoi - (Ti / Te) Rhoi] Le Ae g = ((Ti / Te) Rhoi Ae Ve^2) + (Rhoi Ai (Ti / Te)^3 (Ae / Ai)^3 Ve^2)
2 [1 - (Ti / Te)] Rhoi Le Ae g = Ve^2 Rhoi[((Ti / Te) Ae) + (Ai (Ti / Te)^3 (Ae / Ai)^2)]
= Ve^2[((Ti / Te) Rhoi Ae)[1 + ((Ti / Te)^2 (Ae / Ai))]
Ve^2 = {2 [1 - (Ti / Te)] Rhoi Le Ae g} / [((Ti / Te) Rhoi Ae)[1 + ((Ti / Te)^2 (Ae / Ai))]
= 2 (1 - (Ti / Te)) Le g / [(Ti / Te)[1 + ((Ti / Te)^2 (Ae / Ai))]]

Pt = (Ti / Te) Rhoi Ae Ve H (Te - Ti)
= (Ti / Te) Rhoi Ae H (Te - Ti)
X {2 (1 - (Ti / Te)) Le g / [((Ti / Te))[1 + ((Ti / Te)^2 (Ae / Ai))]}^0.5

This formula gives the amount of thermal power that the assumed duct arrangement can remove via natural ventilation at the assumed air temperatures.

Ai = Ae = Pi (3 m)^2 = 28.26 m^2
g = 9.8 m / s^2
Rhoi = 1.00 kg / m^2 at altitude of 1500 m.
(Te - Ti) = 20 degrees K
Ti = 288 deg K
H = 1.005 kJ / kg-deg K

Pt = (Ti / Te) Rhoi Ae H (Te - Ti)
X {2 (1 - (Ti / Te))] Le g / [((Ti / Te))[1 + ((Ti / Te)^2 (Ae / Ai))]}^0.5
= (288 / 308) (1 kg / m^3) (28.26 m^2) (1.005 kJ / kg deg K) (20 deg K)
X {2 (20 / 308) (400 m) (9.8 m /s ^2) / [(288 / 308) [1 + ((288 / 308)^2 (1)]}^0.5
= 554.92 kJ/ m X {509.09 m^2 / s^2 / [.935 [1 + .874]}^0.5
= 554.92 X 17.045 kJ / s
= 9.458 MW


A practical issue is the axial air velocity Vi in the intake air shaft which also serves as a truck tunnel. If the air velocity is too high it may be necessary to change assumed parameters to reduce the intake air velocity Vi. For example, the ratio (Ai / Ae) can be increased from 1 to 2 by doubling the number of intake air tunnels.

Recall that:
Vi = (Ti / Te) (Ae / Ai) Ve
= (Ti / Te) (Ae / Ai){2 (1 - (Ti / Te)) Le g / [(Ti / Te)[1 + ((Ti / Te)^2 (Ae / Ai))]]}^0.5
= (288 / 308)(1) {2 (1 - (288 / 308)) (400 m) (9.8 m / s^2) / [(288 / 308) [1 + (288/ 308)^2 (1)]}^0.5
= (.935){509.09 (m^2 / s^2)/ ,935 [1 + .874]}^0.5
= 15.9 m / s

= 15.9 m / s X (1 km / 1000 m) X (3600 s / hr) = 57.3 km / hr

This is a high air velocity in which to drive a vehicle or to do work, because construction debris can become dangerous projectiles. However, significantly reducing this air velocxity substantially increases the overall DGR cost.

The number of 6 m diameter vertical exhaust shafts required to remove decay heat from 3,000,000 CANDU fuel bundles at 5 W per bundle is:
15 MW / (9.458 MW / ventilation shaft) = 1.6 ventilation shafts. After making allowance for viscous effects, 2 such shafts are required. These exhaust shafts must be complemented by comparable intake air shafts that run nearly horizontally at vault level.

There is nothing in the NWMO publications that contemplates this much ongoing natural ventilation or that contemplates DGR installation within a mountain to provide the 400 m elevation difference between the ventilation air intake and the ventilation exhaust air discharge.

This web page last updated April 10, 2014

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