Calculations for propane usage in folk festival shower cubicles.

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The Portakabin shower cubicles at the first Shrewsbury folk festival were a delight - except that they were out of use for much of the time!

However, had they worked, they would have been used intensively. So how long would the gas cylinders have lasted? The following calculations are believed to be realistic (but you may know better!)

The shower block contained about 6 shower cubicles (I forgot to count them!) and each would have required about 10 kW of power to heat water from cold. The water flow rates were quite generous, so 10 kW may be an underestimate. A total loading of 60 kW is assumed. With a gas boiler efficiency of (say) 75% the input power requirement would be 80 kW. However, because of the time taken for people to dry themselves (at least as long as taking a shower) the average loading would drop to maybe 30 kW. The boilers would still need to be rated at 80 kW because there would be periods when all the showers were in use at the same time. The average power demand for 6 cubicles in this block, even with a queue of folkies waiting to shower, would probably not be more than 30 kW.Each propane cylinder shown in the photograph contained 47 kg of gas, a total of 188 kg.

The base figure required is the gross calorific value for propane gas. This is 94 MJ/m3 at 15C. However, Calor gas is sold by mass, often termed weight, except for bulk supply where (liquid) litres may be used.

More useful is the heat of combustion, and is given in the Handbook of Chemistry and Physics as 530.57 kg calories per gram molecular weight. Using the conversion of 4.184 J = 1 cal, this equates to 2219.9 kJ per 44.1 g of propane where 44.1 is the molecular weight. The gross calorific value is therefore 2220/44.1 = 50.3 MJ/kg. A search of the Internet yields a figure of 49.93 MJ/kg, close enough! These figures convert to 13.9 kWh/kg, so each gas cylinder contains potentially about 650 kWh of energy.

If you are a pedant, this can be checked from individual heats of formation of compounds as follows. The combustion equation for propane gas (C3H8) is:

C3H8 + 5O2 = 3CO2 + 4H2O (where masses are 36 + 8 + 160 = 3(44) + 4(18)).

Individual reactions for carbon dioxide and water are, from thermochemical tables,

C + O2 = CO2 - 393.51 kJ/mol and

H2 +0.5(O2) = H2O - 285.83 kJ/mol

where the heats given are incremental standard heats of formation of the compounds. The negative sign indicates that heat is evolved.

Also from thermochemical tables, the heat of formation of propane from elements is -103.84 kJ/mol. The negative sign indicates that (like water and carbon dioxide) propane is a stable molecule, unlike acetylene, for example.

This means that in burning propane, heat is evolved owing to formation of carbon dioxide and water but a little is used to break up the propane molecules into individual C and H atoms. (In contrast molecules of acetylene are unstable and emit heat in addition to the heat of combustion of the C and H atoms. This is one reason why acetylene burns with such a high temperature flame.)

Thus, for propane, the heat of combustion per mole is:

3(393.51) = -1180.53 (evolved), 4(285.83) = -1143.32 (evolved) + 103.84 (utilised)
Total:  -2220.01 kJ/mol (evolved).

This is very close to the value of 2219.90 given above.

Thus, for every 44.1 g of propane that are burnt 2220 kJ of heat are liberated, expressed as gross calorific value (which means that the water produced is assumed to condense to liquid and release its latent heat of vapourisation). Once again, the calorific value is 2220/44.1 = 50.3 MJ/kg.

If it is wished to calculate the net calorific value (which is often the more useful figure especially for fuels that have a high H:C ratio such as methane), then for every 44.1 g of propane burnt, 72 g of water are produced. The heat of vapourisation of water at 100 C is 2257 J/g, or 162.5 kJ per mole of propane. Thus the net calorific value is 2220 - 162.5 = 2057.5 kJ/mol.

The difference is some measure of the extra heat that may be obtained in a condensing boiler. However, much of the efficiency benefit arises from the bigger heat exchanger, rather than from condensation per se.

Alternatively, if it is assumed that propane is a 'perfect gas' around STP then 44.1 g will occupy 22.4 litres (a matter of O level chemistry). At 15 C it will occupy 22.4 x (288/273) or 23.6 litres. Thus a cubic metre of gas at 15 C will have mass of 44.1/23.6 = 1.87 kg.

According to Tables in Kaye and Laby (a standard reference book), the gross calorific value of propane is 94 MJ/m3 at 15 C and normal atmospheric pressure, which yields a result of 94/1.87 = 50.27 MJ/kg. This is acceptably close to 50.3 MJ/kg!

Hence, from several routes we arrive at a gross calorific value for propane of 50.3 MJ/kg. A 47 kg cylinder will 'contain' 47 x 50.3 MJ or 656.7 kWh of energy, there being 3.6 MJ in one kWh -  assuming that all the water formed upon combustion is liberated in the liquid phase (this would only happen in a perfect condensing boiler).

Now for the interesting bit!

Four 47 kg cylinders contain 188 kg of gas, equivalent to 188 x 50.3 MJ or 9456 MJ or 2627 kWh. Demand has been estimated at 30 kW with a queue of people, so the cylinders would last 87.6 hours or 3.65 days - 24 hours per day. A more realistic estimate is that the gas might last as long as 10 days, simply because high usage would not be maintained 24 hours per day.

To cross check the calculation, assume that each shower consumed 40 litres of water heated through 30 K (10 to 40 C). The net heat requirement would be 5 MJ and the gross equivalent 6.66 MJ. The 4 cylinders contained 9456 MJ, enough for 1420 showers. Assuming 6 showers in the block and 20 minutes in total per shower (including drying time), you could squeeze in 18 showers per hour (or maybe 36 folkies per hour if they went in two by two.....).

Divide 1420 by 18 and you get about 80 hours, and based on a 8 hours per day of continuous usage you again arrive at about a 10 day capability.

A rule of thumb would be that each 47 kg propane cylinder should provide 350 showers, but if you worked on the basis of 250 to 300 showers per cylinder, you should have some reserve capacity.

If the entire showering capability for 2500 people was to be provided for a 4 day festival, and assuming one shower per person per day (=10,000 showers) you would need around 30 gas cylinders. More to the point, if showers were taken over an 8 to 12 hour period each day you would need 12 to 18 shower blocks. At Shrewsbury, it might be cheaper to get the showers in the pavilion working properly!However, to provide an adequate capability not only the boiler but any heat transfer system would need to have a power rating of at least 80 kW - and maybe as high as 120 kW because there are at least 12 showers in total. Few folk festival venues probably provide such power capabilities so either folkies shower under tepid water or maybe they do it less often (or with less water) than has been assumed in these calculations?! The photo shows some of the showers on the ground floor at Shrewsbury County Ground. Four or five modular in-line boilers supplied by natural gas might be the answer. Or some large 3-phase immersion heaters!

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