For how many years can this plant be operated?

Question

A pilot geothermal plant is installed over a basin with an estimated stored heat energy capacity of 88 TJ. The geothermal plant has an average capacity of 230 kW. For how many years can this plant be operated?

Answer 1

The capacity of the plant is an average power output, expressed in kW. Power is a rate, which describes how much energy is used over time. As an equation: P = E/t. In this case P=230 kW is equivalent to 230 kJ/s. In scientific notation: 2.3*10⁵ J/s.

 

The energy stored in the basin is E=88 TJ, or terajoules. In scientific notation, this is 8.8*10¹³ J.

 

To solve for time (in seconds), divide the energy by the power:

t = E/P = 8.8*10¹³ J / (2.3*10⁵ J/s) = 3.85*10⁸ seconds.

 

This is somewhat unwieldy. A quick calculation shows that 60 s/min *60 min/hr *24 hr/ day *365 day/yr = 3.15*10⁷ seconds in a year. So the plant can run for about 12.13 years!