This week I got an e-mail from Ken. He wants to harness the creek on his property to become more energy independent and lessen his personal impact on global climate change. I am going to examine the variables that will determine if Ken should go ahead with this project, and how much it might cost him.
Ken gave me his address so that I was able to examine his property’s topography on Google Earth. The main factor in this feasibility study is the elevation drop from the source of the water to the generator. The edge of his property is at 500 m elevation and he wants to locate the turbine/generator next to his house at 415 m elevation, with an elevation drop is 85 m (279 ft). By tracing the path of the creek I measured a total distance of 404 m (1328 ft). This represents a 21% slope (279′/1328′=21%, equal to 12 degrees).
A large-scale power project would involve building a large dam and harnessing the energy of the elevation drop directly at the dam. Since Ken does not have a few million dollars to spend and he wants to minimize his impact of the environment I would recommend capturing the water at his property line, using a small spring-dam, and piping it to the turbine at the house. For this purpose I would probably consider a flexible 2″ schedule-40 pipe because the terrain is so variable that laying a straight pipe would be difficult. This pipe comes in 50′ lengths that cost $106 ($2.12/foot) and he will need a coupling between sections for $0.95 each. The 1328′ distance will require 27 of these 50′ section for a total cost of around $2900.
The spring-dam can be constructed from locally available materials, salvaged materials, and/or some concrete (obtain proper permits and take all precautions when working in sensitive habitats such as creeks). The turbine can cost around $2000, and a properly-sized inverter will also be around $2000 for a total material cost of $6900.
Next we need to determine the potential energy of this system. Ken estimates a flow of 50 GPM (gallons per minute). The most basic calculation will determine the “head,” in Joules/second (Watts). The equation, m*g*h (mass x gravity x height), will tell us the potential energy in Joules. Since we know that we have 50 GPM, or 0.83 gallons per second, and we know that a gallon weighs 3.785 kg, we therefore know that we have 3.14 kg/second. The gravitation constant is 9.81 m/s^2 and the height is 85 m so we get 2,618 J (3.14 kg x 9.81 m/s^2 x 85). Since this is 2,618 J every second it is equivalent to 2.62 kW.
Since the pipe is quite long, we can expect a loss of 10 psi or more due to friction. Since the overall pressure with 279 feet of head would be around 120 psi in a vertical pipe, this 10 psi represents less than a 10% loss. This lowers the potential energy to 2.36 kW. Since turbines, generators, and inverters are not 100% efficient we will also need to take them into account. We will lose over 50% of our potential energy from the theoretical and practical limitations of our technology. This leaves around 1.18 kW of usable electrical energy.
Since Ken’s creek runs year-round, 24 hours per day, he can expect roughly 10,300 kWh (1.18 kW x 24 h x 365 days) out of this system. At electricity rates of $0.15/kWh this amounts to an annual savings of $1550. Since the entire system cost under $7000, Ken can expect a payback of 4-1/2 years ($7000/$1550), or a 22.2% Return on Investment (100%/4.5). Try to find that kind of investment on the stock market today!
*You should always consult a professional before investing in a project like this. The results derived above will vary widely depending on a large range of factors.*
Pablo P√§ster, MBA