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Geothermal gradient

Geothermal gradient

The geothermal gradient is the rate of increase in temperature per unit depth in the Earth. It 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.

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 0.01 K/m we get that q = 0.03 W/. This estimate, corroborated by thousands of observations of heat flow in boreholes all over the world, gives a global average of 3×10−2 W/m². Thus, if the geothermal heat flow rising through an acre of granite terrain could be efficiently captured, it would light two 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.

References

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