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

Normally most of the reactor waste heat output from electricity generation is dumped to a water based district heating system. The discharge temperature of this water ranges from 80 degrees C in the summer to 120 degrees C in the winter. If the district heating load is larger than can be met with waste heat from enabled electricity generation the electricity generators can be additionally loaded by electric boilers at consumer sites that further heat the district heating water. If the district heating load is smaller than the waste heat from electricity generation the surplus heat is rejected via roof top fan coil units installed at the remote load locations. These remote fan coil units are powered via dedicated circuits that run along side the district heating pipes from the reactor location. Thus the remote building owner is not responsible for the electricity load imposed by remote fan coil units that are operated for the benefit of the reactor owner rather than for the benefit of the building owner.

However, in the event of a loss of power at the reactor location this remote heat disposal methodology will cease operating because both the fans of the fan coil units and the circulation pumps of the district heating system will not operate. In these circumstances the reactor must be able to reject fission product decay heat at the reactor location using on-site natural draft cooling towers.

At the reactor site there must be two to four independent natural draft dry cooling towers. Each such cooling tower must be sized and piped to safely reject all of the fission product decay heat by natural circulation even if the other cooling towers are out of service. Assuming that more than one cooling tower remains in service the additional heat rejection capacity will enable system black start which will include energizing the district heating system circulating pumps and the remote fan coil units. Once there is remote heat rejection capacity the reactor power can be increased.

The minimum required cooling capacity per cooling tower for rejecting fission product decay heat is:
(0.08) X 875 MWt = 70 MWt / tower.

It is prudent to have a certain source of water sufficient to remove fission product decay heat by evaporation in emergency circumstances when the normal heat sink such as an air cooled cooling tower is unavailable. This source of water might take the form of a large swimming pool, a large decorative pond, or the like. Reserve water storage pools can potentially be located underneath each cooling tower.

Assume that emergency cooling water is stored in four on-site below grade cylindrical tanks, each 20 m high by 25 m diameter, located below the cooling towers. Then the volume of water immediately available on-site for emergency cooling is:
4 X Pi (25 m / 2)^2 20 m
= 39, 269 m^3
= 39.269 X 10^6 kg


The latent heat of vaporization of water is:
22.6 X 10^5 J / kg

Hence evaporation of this stored water requires: 22.6 X 10^5 J / kg X 39.269 X 10^6 kg
= 887.48 X 10^11 J

Without any use of the cooling tower dry cooling capacity that amount of water is sufficient to remove maximum fission product decay heat of:
0.08 X 875 MWt = 70 MWt for:
887.48 X 10^11 J / (70 X 10^6 J / s)
= 12.678 X 10^5 s
= 12.678 X 10^5 s / (3600 s / h)
= 352.17 hours.

Hence no matter what the disaster, it is essential to either replenish the stored emergency cooling water or restore 50% operation of at least one of the four cooling towers within 2 weeks of the disaster.

The required rate of water evaporation to reject the fission product decay heat is:
70 MWt X (10^6 Wt / MWt) X (1 J / s-Wt) X (1 kg H2O / 22.6 X 10^5 J)
= 30.973 kg / s

A cylindrical cooling tower 25 m in diameter has a cross sectional area A of:
A = Pi X (25 m / 2)^2 = 490.87 m^2

The heat capacity of air is:BR> Cp = 1.00 kJ / kg deg C

The density of air is about:
Rhoa = 1.225 kg / m^3

Assume an exhaust air velocity of V = 8 m / s

Assume an temperature rise of dT = 30 degrees C

Then the thermal power removed by the exhaust is:
A V Rhoa Cp dT
= 490.87 m^2 X 8 m / s X 1.225 kg / m^3 X 1.00 kJ / kg deg C X 30 deg C
= 144,318kJ / s
= 144.318 MWt

The cooling tower should be tall enough that the required axial flow velocity is developed by buoyancy.

The gas kinetic flow power is:
(mass / s) (V^2 / 2) = (Rhoa A V) V^2 / 2

The driving power = dP A V

Conservation of energy gives:
dP A V = (Rhoa A V) V^2 / 2
dP = (Rhoa) V^2 / 2

dP = (dRhoa) H g
where H = height of cooling tower.

(dRhoa) H g = (Rhoa) V^2 / 2
H = (Rhoa) V^2 / [2 (dRhoa) g]

Rhoa = 1.225 kg / m^3

dRhoa = 0.1125 kg / m^3

H = (Rhoa) V^2 / [2 (dRhoa) g]
= 10 (8 m / s)^2 / [2 (9.8 m / s^2]
= 32.65 m

Thus this is the theoretical minimum height for one 25 m diameter tower to remove 144.3 MWt by dry cooling. This dry cooling involves raising the ambient air temperature by 30 degrees C which probably means circulating 80 deg C to 100 deg C condenser water through the cooling tower coils. This condenser water temperature is very high for efficient electricity generation. The electrical generation efficiency can be improved by use of remote cooling on the district heating loops to lower the turbine condenser water temperature.

The required ground clearance is given by:
Pi (25 m / 2)^2 = Pi (25 m) (ground clearance)
(ground clearance) = Pi (25 m / 2)^2 / Pi (25 m) = (25 m / 4) = 6.25 m

It appears that including ground clearance the dry cooling towers should extend 40 m to 50 m above grade. The extra height is required due to the air flow resistance caused by the condenser cooling water heat exchange coils located at the bottom of the cooling tower.

In order to be certain about fission product decay heat removal, no matter what the disaster, it is essential to either replenish the stored emergency cooling water or restore 50% operation of at least one of the four cooling towers within 2 weeks of the disaster.

The primary sodium pool enclosure is a square 28 m / side. Along each 28 m face are two heat exchange galleries, each with external dimensions 13.5 m long X 10.0 m wide. The four 10.0 m X 10.0 m corner squares are reserved for argon bladder silos.

Along each heat exchange gallery face is a 10 m wide laneway allowance for heavy equipment delivery and removal, so before considering the turbine halls, cooling towers, electrical switch gear, water reservoirs, parking requirements, perimeter driveway and laneway space for trucks approaching air locks the minimum required land area is a square 68 m X 68 m.

Thus it is reasonable to contemplate a total FNR land area requirement of 113 m X 113 m, which is approximately one city block. That space allows for up to 8 turbine halls, each with outside dimensions of 26.5 m X 22.5 m and four 50 m tall cooling towers, each with outside dimensions 25 m X 25 m. The emergency cooling water tanks are located directly under the cooling towers. The system electricity generation efficiency can be improved if the condenser cooling water temperature can be reduced via the use of remote cooling towers or remote fan coil units.

This web page last updated May 7, 2020

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