Deck 15: Geothermal Energy

Question 1

Assume that geothermal heat transfer (at least near the surface of the earth)

Answer 1

Equation (8.4) gives

Question 2

A geothermal generating facility operates at the ideal Carnot efficiency and
utilizes a pressurized hot water resource at 240°C.
(a) Calculate the Carnot efficiency as a function of the temperature of the cold reservoir
from 40°C to 90°C.
(b) The waste heat from electricity generation may be utilized for space heating, and the
facility may, therefore, supply a community with both electricity and heat. This approach
is referred to as cogeneration and is discussed in more detail in Chapter 17. Using the
relative proportions (averaged over the year) for residential electricity and heat
requirements as presented in Chapter 2, is there an approach to regulating the cold
reservoir temperature that would make the best use of the geothermal resources?

Answer 2

(a) The Carnot efficiency is

Question 3

Heat is extracted from hot rock at a temperature of 250°C and used to

Answer 3

From equation (8.11), the heat extracted from rock is

Question 4

For a cold reservoir temperature of plot the Carnot efficiency of a

Question 5

It is clear that geothermal generating stations extract energy from a resource
more rapidly than it is replenished from the interior of the earth. Assume that a resource
has 10 EJ of energy that can be extracted economically. If this resource is used to generate
250 MWe of electricity, how long will the resource last? It is necessary to know the
efficiency of electric generation. Assume an efficiency of one-third the ideal Carnot
efficiency (Example 15.2). This is typical of the actual average operational efficiency of a
geothermal generating station.

Question 6

A geothermal electrical generating station has an actual efficiency of one-

Question 7

A geothermal resource has a life expectancy of 100 years if an average
power of 50 MWe is generated at two-thirds of the ideal Carnot efficiency. If the reservoir
temperature is pressurized water at 300°C and the cold reservoir temperature is 75°C, what
is the total energy available in the reservoir?

Question 8

Consider the total energy use for a typical North American single-family
home, as discussed in Chapter 2. If the house has a footprint of what fraction of its
energy needs could be met by the average geothermal heat flow from the earth's interior?

Question 9

If the average geothermal electricity generation in the United States

Question 10

Assuming that the geothermal heat flux in the United States is (on average)
typical of that which occurs worldwide, calculate the fraction of total U.S. primary energy
use that could be provided by geothermal energy if this energy could be utilized in its
entirety.

Question 11

Consider the possibility of extracting power from a flow of water of 1000

Question 12

In recent years, annual geothermal electricity generation in the United

Question 13

Assuming an average geothermal heat flux of

Question 14

Consider a geopressurized deposit with water at a temperature of 200°C
and dissolved methane with a molar fraction of 10-5. The heat content of the water is used
to generate electricity in a heat engine with one-half of the Carnot efficiency and a cold
reservoir of 50°C, and the chemical energy content of the methane is used by burning the
methane and generating electricity with a heat engine with an overall efficiency of 25%.
What is the energy produced by m3 of resource by each of these methods?

Question 15

If a typical home uses 8 × 1010 J of heat per year, how many homes could

Question 16

Calculate the ideal Carnot efficiency for a turbine operating with a hot

Question 17

Heat is extracted from geothermal pressurized water at a temperature of

Question 18

(a) Granite has a typical thermal conductivity of 1.

Question 19

As indicated in the chapter, geothermal heat comes primarily from the

Question 20

Estimate the world geothermal power production for the year 2025