Geothermal gradient

For other uses, see Geothermal (disambiguation).

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Earth cutaway from core to exosphere.

Geothermal gradient is the rate of increasing temperature with respect to increasing depth in the Earth's interior. Away from tectonic plate boundaries, it is 25–30°C per km of depth in most of the world. Strictly speaking, geo-thermal necessarily refers to the Earth but the concept may be applied to other planets. The Earth's internal heat comes from a combination of residual heat from planetary accretion (about 20%) and heat produced through radioactive decay (80%). The major heat-producing isotopes in the Earth are potassium-40, uranium-238, uranium-235, and thorium-232. At the center of the planet, the temperature may be up to 7,000 K and the pressure could reach 360 GPa. Because much of the heat is provided by radioactive decay, scientists believe that early in Earth history, before isotopes with short half-lives had been depleted, Earth's heat production would have been much higher. This extra heat production, which was twice that of present-day at approximately 3 billion years ago, would have increased temperature gradients within the Earth, increasing the rates of mantle convection and plate tectonics, and allowing the production of igneous rocks such as komatiites that are not formed today.

Heat sources

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Geothermal drill machine in Wisconsin, USA

Temperature within the Earth increases with depth. Highly viscous or partially molten rock at temperatures between 650 to 1,200 °C (1,202 to 2,190 °F) is postulated to exist everywhere beneath the Earth's surface at depths of 50 to 60 miles (80 to 100 kilometers)^{[citation needed]}, and the temperature at the Earth's center, nearly 4,000 miles (6,400 km) deep, is estimated to be 5650 ± 600 kelvins. The heat content of the earth is 10³¹ joules.

• Much of the heat is believed to be created by decay of naturally radioactive elements. An estimated 45 to 90 percent of the heat escaping from the Earth originates from radioactive decay of elements within the mantle.
• Heat of impact and compression released during the original formation of the Earth by accretion of in-falling meteorites.
• Heat released as abundant heavy metals (iron, nickel, copper) descended to the Earth's core.
• There is no reputable science to suggest that any significant heat may be created by electromagnetic effects of the magnetic fields involved in Earth's magnetic field, as suggested by some contemporary folk theories.
• Heat may be generated by tidal force on the Earth as it rotates; since land cannot flow like water it compresses and distorts, generating heat.

Present-day major heat-producing isotopes

Isotope	Heat release [W/kg isotope]	Half-life [years]	Mean mantle concentration [kg isotope/kg mantle]	Heat release [W/kg mantle]
238U	9.46 × 10-5	4.47 × 109	30.8 × 10-9	2.91 × 10-12
235U	5.69 × 10-4	7.04 × 108	0.22 × 10-9	1.25 × 10-13
232Th	2.64 × 10-5	1.40 × 1010	124 × 10-9	3.27 × 10-12
40K	2.92 × 10-5	1.25 × 109	36.9 × 10-9	1.08 × 10-12

In Earth's continental crust, the decay of natural radioactive isotopes has had significant involvement in the origin of geothermal heat. The continental crust is abundant in lower density minerals that are composed of relatively large atoms. Because of this, it holds the largest global reservoir of radioactive elements found in the Earth. Especially in layers closer to Earth's surface, naturally-occurring isotopes are enriched in the granite and basaltic rocks. These high levels of radioactive elements are present because they cannot be readily accommodated by the Earth's mantle due to the high pressures that are present. The mantle is mostly made up of high density minerals with high contents of atoms and relatively small atomic radii such as magnesium (Mg), titanium (Ti), and calcium (Ca).

Heat flow

Heat flows constantly from its sources within the Earth to the surface. Total heat loss from the earth is 44.2 TW (4.42 × 10¹³ watts). Mean heat flow is 65 mW/m² over continental crust and 101 mW/m² over oceanic crust. This is approximately 1/10 watt/square meter on average, (about 1/10,000 of solar irradiation,) but is much more concentrated in areas where thermal energy is transported toward the crust by convection such as along mid-ocean ridges and mantle plumes. The Earth's crust effectively acts as a thick insulating blanket which must be pierced by fluid conduits (of magma, water or other) in order to release the heat underneath. More of the heat in the Earth is lost through plate tectonics, by mantle upwelling associated with mid-ocean ridges. The final major mode of heat loss is by conduction through the lithosphere, the majority of which occurs in the oceans due to the crust there being much thinner and younger than under the continents.

The heat of the earth is replenished by radioactive decay at a rate of 30 TW. The global geothermal flow rates are more than twice the rate of human energy consumption from all primary sources.

Direct application

Heat from Earth's interior can be used as an energy source, known as geothermal energy. The geothermal gradient has been used for space heating and bathing since ancient Roman times, and more recently for generating electricity. As the human population continues to grow, so does energy use and the correlating environmental impacts that are consistent with global primary sources of energy. This has caused a growing interest in finding sources of energy that are renewable and have reduced greenhouse gas emissions. In areas of high geothermal energy density, current technology allows for the generation of electrical power because of the corresponding high temperatures. Generating electrical power from geothermal resources requires no fuel while providing true baseload energy at a reliability rate that constantly exceeds 90%. In order to extract geothermal energy, it is necessary to efficiently transfer heat from a geothermal reservoir to a power plant, where electrical energy is converted from heat. On a worldwide scale, the heat stored in Earth's interior provides an energy that is still seen as an exotic source. About 10 GW of geothermal electric capacity is installed around the world as of 2007, generating 0.3% of global electricity demand. An additional 28 GW of direct geothermal heating capacity is installed for district heating, space heating, spas, industrial processes, desalination and agricultural applications. Because heat is flowing through every square meter of land, it can be used for a source of energy for heating, air conditioning (HVAC) and ventilating systems using ground source heat pumps. In areas where modest heat flow is present, geothermal energy can be used for industrial applications that presently rely on fossil fuels.

Variations

The geothermal gradient varies with location and is typically measured by determining the bottom open-hole temperature after borehole drilling. To achieve accuracy the drilling fluid needs time to reach the ambient temperature. This is not always achievable for practical reasons.

In stable tectonic areas in the tropics a temperature-depth plot will converge to the annual average surface temperature. However, in areas where deep permafrost developed during the Pleistocene a low temperature anomaly can be observed that persists down to several hundred metres. The Suwałki cold anomaly in Poland has led to the recognition that similar thermal disturbances related to Pleistocene-Holocene climatic changes are recorded in boreholes throughout Poland, as well as in Alaska, northern Canada, and Siberia.

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In areas of Holocene uplift and erosion (Fig. 1) the initial gradient will be higher than the average until it reaches an inflection point where it reaches the stabilized heat-flow regime. If the gradient of the stabilized regime is projected above the inflection point to its intersect with present-day annual average temperature, the height of this intersect above present-day surface level gives a measure of the extent of Holocene uplift and erosion. In areas of Holocene subsidence and deposition (Fig. 2) the initial gradient will be lower than the average until it reaches an inflection point where it joins the stabilized heat-flow regime.

In deep boreholes, the temperature of the rock below the inflection point generally increases with depth at rates of the order of 20 K/km or more.Fourier's law of heat flow applied to the Earth gives q = Mg where q is the heat flux at a point on the Earth's surface, M the thermal conductivity of the rocks there, and g the measured geothermal gradient. A representative value for the thermal conductivity of granitic rocks is M = 3.0 W/mK. Hence, using the global average geothermal conducting gradient of 0.02 K/m we get that q = 0.06 W/m². This estimate, corroborated by thousands of observations of heat flow in boreholes all over the world, gives a global average of 6×10⁻² W/m². Thus, if the geothermal heat flow rising through an acre of granite terrain could be efficiently captured, it would light four 60 watt light bulbs.

A variation in surface temperature induced by climate changes and the Milankovitch cycle can penetrate below the Earth's surface and produce an oscillation in the geothermal gradient with periods varying from daily to tens of thousands of years and an amplitude which decreases with depth and having a scale depth of several kilometers. Melt water from the polar ice caps flowing along ocean bottoms tends to maintain a constant geothermal gradient throughout the Earth's surface.

If that rate of temperature change were constant, temperatures deep in the Earth would soon reach the point where all known rocks would melt. We know, however, that the Earth's mantle is solid because it transmits S-waves. The temperature gradient dramatically decreases with depth for two reasons. First, radioactive heat production is concentrated within the crust of the Earth, and particularly within the upper part of the crust, as concentrations of uranium, thorium, and potassium are highest there: these three elements are the main producers of radioactive heat within the Earth. Second, the mechanism of thermal transport changes from conduction, as within the rigid tectonic plates, to convection, in the portion of Earth's mantle that convects. Despite its solidity, most of the Earth's mantle behaves over long time-scales as a fluid, and heat is transported by advection, or material transport. Thus, the geothermal gradient within the bulk of Earth's mantle is of the order of 0.3 kelvin per kilometer, and is determined by the adiabatic gradient associated with mantle material (peridotite in the upper mantle).

This heating up can be both beneficial or detrimental in terms of engineering: Geothermal energy can be used as a means for generating electricity, by using the heat of the surrounding layers of rock underground to heat water and then routing the steam from this process through a turbine connected to a generator.

On the other hand, drill bits have to be cooled not only because of the friction created by the process of drilling itself but also because of the heat of the surrounding rock at great depth. Very deep mines, like some gold mines in South Africa, need the air inside to be cooled and circulated to allow miners to work at such great depth.

See also

• Geothermal power
• Hydrothermal circulation

References

"Geothermal Resources". DOE/EIA-0603(95) Background Information and 1990 Baseline Data Initially Published in the Renewable Energy Annual 1995. http://www.eia.doe.gov/cneaf/solar.renewables/renewable.energy.annual/backgrnd/chap9b.htm. Retrieved May 4, 2005.

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