Course:PHYS100/Using Geothermal Energy in Building Design

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by Erin S., Azin J., Yasmin A., Jeff M., Presty W.

What is Geothermal Energy?

Geothermal energy is the heat from the earth which increases as we go deeper down into the earth. The resources of this energy range from the ground just beneath the earth to the higher temperature molten rocks called magma which is 4000 miles from the surface. The shallow ground normally has the temperature between 10-16°C. Ancient people use this energy to provide hot water for living and bathing .Later in 20th century it was found that geothermal energy is a efficient way to provide heat and electricity for houses for so many reasons. First, geothermal energy is renewable which means that the heat is continuously produced deep down in the earth so it’s a source of energy that never ends. Second, this energy does not damage the environment because there is no need to burn the fuel.

Geothermal energy can be divided into high temperature over (150C), which is normally used to provide electricity, and low temperature under (150C) which is used as source of heat for houses and commercial buildings. The energy exchange between the ground and the building is provided by pumping water or heat transfer fluid to absorb the heat from the earth then circulating in the building.

Relevant Physics and Assumptions

Relevant Physics

Heat transfer through walls (concrete). Q = (k * A * (Th-Tc))/L Thermal dynamics energy is not destroyed it is only converted from one form to another


A 30 000 square foot commercial building, with an open layout, so heat transfer through interior walls is negligible. A 5 degree Celsius temperature throughout the building, consistent with the outdoor temperature, with a target temperature of 20 degree Celsius. Recirculating air throughout the building, without air intake from outdoors. The comparison of geothermal, electric and gas energy will be for identical buildings, with no windows, and walls made of concrete, which has a k value of 0.80. Assume equal energy transfer with gas, electric and geothermal energy, as well as no additional heat sources in building, ie. people. Thickness of the concrete walls is 0.3 metres. No heat is lost through the ceiling or floor of building. Assume equal heat loss from all 3 buildings (gas, electric and geothermal).

Geothermal Heating

Geothermal heating systems typically can be installed in an open or closed loop system. Since this is a commercial building I have chosen a closed loop system with vertically installed pipes, circulating a water/antifreeze combination liquid down into the earth and the heated liquid back to the surface where heat Is extracted by electrical heat pumps. For a 30 000 square foot commercial building the standard requirements say we would need 50 vertical bore holes at 300ft in depth. The requirement for out 30000 square foot building is a 27 ton system, and the average cost for geothermal systems is 2,500$ per ton of capacity resulting in an instillation cost of 67,500$ instillation costs. The Heat pumps which operate the system typically work on a coefficient of 1kw energy required produces about 6kw of energy is pulled from the earth. So for our energy requirements of the system:

P= kA(Th-Tc)/L

2787m2 * 0.8 W/m*k = 2229.6 W*m/k

2229.6 W*m/k / 0.30m = 7314.96063W/k

7314.96063W/k * 15 degrees C = 109724.4094 Watts or 109.7299921 Kw

So for the 110Kw of energy required to heat the building we can find the energy requirement is 1/6 for Geothermal heating

110 Kw * 1Kwi/6Kwa = 18Kw actual electrical requirement

30 day month assuming 24h heating

18 Kw * 720h = 12960Kw/h

As per our other models we have used an value of 6 cents per Kw/h

12960Kw/h *6 cents = 77760 cents or 777.60$

Compared to 4,416.96$ required for conventional electrical heating, geothermal is 82.4 % more efficient.

Saving roughly 4,000$ a month the geothermal heating system will start showing profit in 17 months.

Electric Heating

- First, an overview of what electrical energy is. Electric energy is energy that results from the interaction of subatomic particles that have electromagnetic force. The charge created from this interaction can be transferred though a medium by direct contact, for instance, through a metallic wire. Throughout British Columbia home heating( which is a secondary energy source) is obtained by means of hydroelectricity. Hydroelectricity creates electricity from the mechanical falling action of water spinning turbines which are connected to electric generators. In other words, mechanical energy is being converted into electrical energy that we can use to power our homes.

- Costs of installing a forced air electric furnace is an estimated 40,000 $. Typically these costs are higher than those of gas furnace installation costs.

- In order to calculate the monthly costs for heating a 30,000ft2 commercial building we need to consider how many kilowatt hours are needed to heat this space from 5 degrees Celsius to a desired 20 degrees Celsius.

We will assume that we are considering a 30 day month and that the exterior walls of this building are made of concrete. Heat loss through the windows is negligible. Assume the rate is 6 cents/kwh. Also, the thickness (L) of the walls is 0.30 m.
First we will assume that the building is 200 ft by 150 ft by 10 ft 
  A= (200*10)2 + (10 * 150)2 = 7,000ft2
Now we need to convert 30,000ft2 into meters squared.
  7,000ft2 * 0.0929= 650.30 m2

**Rate of Conduction of Heat Across a temperature difference is expressed using the formula**
                                           P= kA(Th-Tc)/L
Then we multiply the thermal conductivity constant of concrete (0.8 W/m*k) by the total area of the building.
  650. 30 m2 * 0.8 W/m*k = 520.24 W*m/k
  520.24 W*m/k / 0.30m = 1734.13W/k
  1734.13 W/k * 15 degrees C = 26012.00 Watts or 26.012 Kw
We will assume that the building will consume 26.012Kwh for dt of 30 days(720hours).
  Therefore the Kilowatthours of power produced are:
     26.012Kw*720hrs= 18,728.64Kwh
The total cost of electricity will amount to:
  6 cents * 18,728.64 kwh =  112,371.84 cents or 1,123.72$

(Rate was rounded from 6.27 cents/Kwh to 6 cents/Kwh for simplicity)

Gas Heating

Heating a commercial building of 30 000 square feet with natural gas requires a furnace system to be in place. The type of furnace we are considering is a forced air furnace, fueled by natural gas. Heat is produced by burning natural gas and air is forced through a heat exchanger via electric fan. After the air is heated, it is distributed throughout the building through a system of ducting, and then returned to the furnace at a lower temperature until the return air has reached the desired temperature of 20 degrees Celsius.

To determine the size and number of furnaces required to heat a 30 000 square foot building, the BTU should be taken into account. One BTU is the amount of heat required to increase the temperature of 1 lb of water by 1 degree Fahrenheit. Also, 1 BTU is sufficient to heat 55 cubic feet of air by 1 degree Fahrenheit.

 30000 * 10= 300 000 cubic feet
 300000/55= 5 454
 20 degrees Celsius - 5 degrees Celsius = 27 degrees Fahrenheit
 5454 * 27= 147 258 BTU

To generate 147 258 BTU, more than 1 furnace will be needed, which is common in commercial building design. Two furnaces will be able to accommodate 73 629 BTU each, which is a more realistic number of BTU a furnace will be able to generate. A 100 000 BTU natural gas furnace with 95% efficiency costs roughly $2000. So, if we need 2 furnaces,as well as ducting and gas piping for the building which costs roughly $3000, the total cost of the equipment needed is $7000.

From the Terasen Gas website [1], current Lower Mainland charges are calculated in GJ.

 1 BTU is 1055 Joules, and 147258 BTU is 0.155 GJ. So, it takes 0.155 GJ to heat up the building once from 5 to 20 degrees Celsius.

Since the furnace only has to go from 5 to 20 degrees Celsius once, we need to find out how much it costs to maintain a temperature of 20 degrees Celsius for the rest of the month. If the furnace is set to turn on when the temperate of the return air is 18 degrees Celsius, then the furnace only needs to generate enough heat to increase the temperature by 2 degrees Celsius.

 300 000/55= 5454
 A difference of 2 degrees Celsius is equal to 4 degrees Fahrenheit. Since we have 2 furnaces, 10908 BTU need to be generated to reach 20 degrees Celsius. 
 5454 * 4= 21816/2= 10908
 21816 BTU= 0.0115 GJ

If we assume that the furnace will do this once an hour to maintain temperature, then excluding the 1st hour, we have 23 hours to maintain temperature.

 0.0115 * 23= 0.2645 GJ per day plus the 0.155GJ needed to heat the building up to 20 degrees Celsius from 5, is 0.4195 GJ for the first day. 

For remaining days of the month, the furnace just needs to maintain temperature. So,

 0.0115 * 24= 0.276 GJ per day. 
 So, multiply this by 29 days, which is 8.004 GJ. And then add the 0.4195 from the first day, which is 8.4235 GJ per month.

From the Terasen Website this building falls under Rate 2, which is for small commercial buildings with an annual consumption of 2000 GJ of natural gas or less, charges are as follows:

 Basic charge $24.84
 Delivery charge per GJ $2.604 = $21.93
 Midstream charge per GJ $1.628 = $13.71
 Cost of gas per GJ $4.976 = $41.92
 Total charges= $102.40 per month
 $7000 + $102.40= $7102.40 for cost of the furnaces and charges for the 1st month.

Geothermal, Electric and Gas Energy Models

IMG-1.jpg IMG_0002.jpg

Comparing Geothermal Energy to Gas and Electric Energy


(Comparison in terms of pollution and green house gas emissions)

Hydroelectricity is not exactly free of carbon emissions . To create these dam reservoirs trees may be burned down causing an increase in greenhouse gas emissions ( such as the release of methane and carbon dioxide). However, no fossil fuels are burned therefore a significant less amount of carbon dioxide will be released into the atmosphere.


Gas is one of the cleanest burning, most efficient fuels available. According to Terasen Gas, burning natural gas produces 48546 g/GJ of carbon dioxide, 2245 mg/GJ of volatile organic compounds, 776 mg/GJ of Particulate matter, 34286 mg/GJ carbon monoxide, 40816 mg/GJ oxides of nitrogen and 245 mg/GJ sulphur dioxide.


Once installed, geothermal produces virtually "free" energy up to 12-16 degrees Celsius. Compensating for the 4-8 degrees requires supplemental heating by either electric or gas energy. Based on previous calculations, in the long run, it would be recommended to use geothermal energy with supplemental gas energy.