Heat Flow
From Geophysics 300
The Heat flow wiki
Contents |
History
History of the Earth
It is a generally accepted theory that the earth is cooling, and as a planet cools it goes through stages. In the beginning the earth would have been so hot that its surface would be only an ocean of magma. As it cooled progressively over time a crust began to form like lily pads on a pond, with magma separating the crustal islands. As the entire surface cooled enough for crust to form, the current tectonic plate regime came about. Heat convection in the interior of the earth still drives plate movement, but the cool crust seals itself at spreading and converging ridges. As the earth slowly continues to lose heat, the convection currents within the earth’s interior will no longer be sufficient to drive the movement of tectonic plates and the crust will cool to a hard shell.
Important People in Heat Flow History
Lord Kelvin (William Thomson, 1862) assumed the Earth was cooling with no new heat source. With these assumptions Kelvin found the earth to be 200 million years old if the initial temperature was 5440 degrees Celsius or 98 million years old if temperature was 3870 degrees Celsius. Thomson’s calculated error for these measurements was 20-400 million years.
Rutherford (1904) found Kelvin’s flaw, he gave a talk that Kelvin attended to the Royal Society of London on radioactive decay and proposed a much older Earth. Since then, multiple papers have been written to conclude what we now accept as the Earth’s age at approximately 4.55 billion years ago.
Other Important People in Heat Flow History
Georgius Agricola (1530) noted warmer conditions in mines.
Galileo Galilei (1564-1642) invented the first Thermoscope.
Other important temperature scientists are Fahrenheit, Ferchaut de Reaumur, and Anders Celsius.
James Joule (1840) invented the joule, his idea was to turn mechanical energy into heat.
John Clerk Maxwell (1831-1879) for Maxwell’s Thermodynamic equations.
Jean Baptiste Joseph Fourier (1822) for the theory of heat conduction.
Theory
Heat Transfer
Heat escapes from the earth’s interior through the crust mainly by conduction. The energy is transferred as vibrations in the crystal lattices of the rocks that make up the crust and then it is radiated out into the atmosphere. Alternative, but less significant pathways to the atmosphere include: dikes, volcanoes, and hydrothermal activity. Crustal structures which have angles less than normal(ie. perpendicular) to the Earth's surface divert heat and siphon the heat away from the normal vertical path. Heat, because of Fermat's Principle also prefers to travel to areas of exposed basement rock instead of areas of thicker sedimentation. Heat is also deflected from its vertical path by hydrothermal fluids and the genesis and flow of hydrocarbons.
Surface heat flow (geothermal) map of the U.S. from the Department of Energy
Surface Heat Flow: Q = q + AD This is the surface heat flow equation. Where Q is the surface heat flow, q is the heat from the mantle, A is the surface heat generation (Sun, chemical reactions, and other heat sources), and D is Depth in Kilometers. Since we humans live on the surface of our planet it is the easiest direct method we have for measuring heat flow.
Conduction Equation: Q / t = [kA(T1 − T2)] / d This is a rate equation from which we get heat Q transferred over an amount of time t. from the parameters: (k) the thermal conductivity of the barrier (earth’s crust); (A) area; (T1) temperature at the moho; (T2) surface temperature; (d) the thickness of the crust.
Thermal conductivity is noted as Lamda. Conduction is a temperature dependent value. It has a direct relationship between conduction and temperature. In heat flow the major method of heat propagation is through Phonon conduction. Phonon conduction is dependent on the crystal lattice structures. A thought exersize to emphasize this is to think of a jump rope with balls fastened to the rope at regular intervals. Fixing one end of the rope to a fixed location move the other end up and down at a constant distance and speed. Through this exercise one observes two things. First, the energy transfer from one vibrating atom to the next. Second, by choosing to have an end fixed to represent the surface the loss of energy as it nears the fixed end shows the diffusion of the heat as it travels towards the crust in a positive z or surface oriented direction. However, it should be noted that this process is not one dimensional or two dimensional but three dimensional.
The geomagnetic field and the movement of the tectonic plates are products of heat flow in the earth.
Understanding the Earth's Heat in Relation to Temperature
The biggest problem with our understanding of the temperatures of the earth's interior is its utter inaccessibilty. We can derive velocities through the earth, estimate material properties and the composition of its layers. However, without any way to directly measure temperature, we still have little understanding of how hot it actually is. In the crust average temperature increase with depth is 30K per Km. If this rate of increase continued to the core it would mean that the temperature at the center of the earth is hotter than the surface of the sun. This extrapolation is way too high. So we get our limited understanding from phase transitions in minerals. For example, we can estimate pressure and know that certain minerals like perovskite and spinel only form at high temperatures and pressures. So from laboratory experiments at the surface we can determine empirically at what depth spinel would begin to form perovskite.
One explanation for the earth's heat is the residual heat from the earth’s formation. Also, the radioactive decay of isotopes produce heat. Heat lost from the earth’s interior accounts for the biggest loss of energy from the earth itself. Other energy sinks are tidal friction, energy released from earthquakes, and reflected and re-radiated solar energy. The table below relates the factors for the earth in total.
Sources of heat within the earth are derived from the following sources: radioactive isotopic decay, friction in plates and their movement, and processes of diagenesis and metamorphism. While all of the processes are important to heat flow it is mainly due to radioactive decay processes. Areas on our planet where heat flow values are measured, noticeably different, and constant are known as heat flow provinces.
The thermal gradient is a measure of the change in temperature in three directions. However, since we live on the surface of this world we usually measure the changes in temperature vertically. From the human perspective on the planet Earth we can directly measure Heat flow within the crust. This direct measurement is accomplished using sensitive instruments in a drilled well and is the most accurate way of measuring the thermal gradient.
The cutaway graphic above of a Bullard-type heat flow probe is one of the many types of probes used to measure temperature. This highly sensitive instrument takes a direct measurement that allows the formulation of Thermal Gradient (Change in Temperature divided by change in depth). A Bullard plot measures temperature versus thermal resistance. In steady state the graph is linear; when it is not linear in steady state the graph contains errors that may occur from the assumptions made or exist within the data. The figure below is an example of a Bullard plot with the data taken from the sedimentary section.
Applications
Mineralogy
Heat flow, and the thermal gradient it establishes, are important variables in mineral formation because they determine which minerals are formed. Additionally, the rate of change in heat flow is important because the formation of many minerals depends on cooling rates. If rock is cooled quickly, such as in abrupt tectonic uplift, it is essentially frozen and the mineral assemblage is representative of the conditions under which it formed. If rock is cooled slowly, such as in gradual uplift, the mineral assemblage can undergo phase changes as pressure and temperature conditions change. In this way, studying the mineral assemblages present in a rock allows you to infer the pressure temperature conditions under which it formed, as well as how quickly it was cooled. This approach can be used to estimate where a rock was in the crust before it was uplifted. In igneous rocks, the cooling rate affects the type and size of crystals formed. In metamorphic rocks, the temperatures reached determines whether metamorphism occurs and the type of minerals produced. Heat flow equations can be applied to establish the geothermal gradient which governs mineralogical analysis. A phase diagram showing the different mineral forms for quartz is shown on the right.
There are many different types of measurements for thermal maturity. Thermal maturity is a measurement that measures the highest temperature a mineral is exposed to. These conditions are sometimes based on organic and inorganic indicators within the rock. Some of these indicators are Vitrinite reflectance (VR), Flourescence Alteration of Multiple Macerals (FAMM), the changes in liptinite and conodonts are given by the thermal alteration index (TAI), and conodont alteration index (CAI).
Sea Floor Subsidence
Seafloor subsidence is studied because it determines ocean depth and subduction zone mechanics. Sea floor subsidence rates are directly affected by heat flow through the mantle and the oceanic lithosphere. Subsidence occurs as the ocean floor cools and becomes more dense. Greater heat flow from the mantle would decrease cooling rates and inhibit sea floor subsidence. Decreased heat flow would lead to higher cooling rates and faster subsidence. When studying sea floor subsidence it is important to understand how heat flows through the oceanic lithosphere.
Geothermal Power
Natural geothermal resources can be utilized for power generation. Hot water is pumped from the ground into a heat exchanger which vaporizes a liquid. The expansion of this gas is utilized to turn a turbine and generate electricity. The liquid is allowed to cool and then pumped back into the heat exchanger to be vaporized again. The cooled geothermal water is either re-injected into a recharge well, or discharged on the surface.
In the past, the cost of building a power plant and drilling wells to reach geothermal resources has generally been considered too expensive to be worthwhile. However, because electricity has increased in demand and become more expensive, geothermal power is once again being considered as a viable alternative energy source. Once the wells have been drilled and the generators built, it offers relatively cheap, renewable, and environmentally friendly energy.
Current geothermal power technology requires naturally occurring geothermal resources. This limits geothermal use to areas where these resources are already available. Additionally, because heat flow is relatively low through rock, heat is extracted at a greater rate than it is replenished. This limits the lifetime of geothermal resources.
Engineered Geothermal Power
Scientists at the Idaho National Experimental Laboratory (INEL) have been investigating the potential of engineered geothermal energy. They seek to develop a method for harnessing geothermal power, regardless of whether there is already hot water present. They propose that geothermal resources could be created by injecting water into hot dry crustal rock and pumping it back out to generate electricity with. This technique is know as heat mining. Engineered geothermal requires two wells, one for injection and one for extraction or production. The wells are drilled away from each other and then air is forced into one of the wells to fracture the rock between them. This creates the flow path. Water is injected into one of the wells, forced through the fractures, and extracted from the other well. Electricity is generated in the same way as in regular geothermal power. The illustration below shows a hypothetical engineered geothermal system:
Although this technique offers the potential to create geothermal resources at any location, it is limited by its cost. Not only must two wells be drilled, but they must be drilled down to rock of an appropriate temperature.
Parks & Recreation
One of the main attractions at Yellowstone National Park is its geothermal features. It contains one of the most diverse and intact collections of geysers, hotsprings, mudpots, and fumaroles. The park contains over 300 geysers, which make up about two thirds of the total geysers found on Earth. The national park is underlain by the Yellowstone Hotspot, which provides the heat gradient to produce such a geothermally active region. The Yellowstone Hotspot's path can be traced across the Snake River Plain of southern Idaho. The remnant heat from its passing is partially responsible for the relatively high subsurface temperatures throughout the region.
Aside from the aesthetic beauty of brilliantly colored geothermal areas, these resources are also utilized for recreational past times. Hot springs have been used throughout history for bathing. In ancient Rome and Japan, bath-houses were built around naturally occurring hot springs and they became important parts of their cultures.
References
History
Lowrie, William, "Fundamentals of Geophysics 2nd Edition," Cambridge University Press, C. 2007, p.220-252
Beardsmore, G.R. and Cull, J.P., "Crustal Heat Flow: A Guide to Measurement and Modeling." Cambridge University Press. C. 2001
Arianrhod, Robyn. "Einstein's Heroes: Imagining the World Through the Language of Mathematics." Oxford University Press, C. 2005
Theory
"Geomagnetic Field" Encyclopedia Brittanica.2008. Brittanica Online. 09 May, 2008. <http://www.britannica.com/eb/article-9036468/geomagnetic-field>
Maurer, Robert. "Tectonic Forces: The Origin and the Mechanics of the Forces Responsible for Tectonic Plate Movements Simplified Version" MSc. CEng. Online 14 July, 2003. <http://www.tectonic-forces.org/simplified.htm>
Picture- "Bullard-type Heat Flow Probe" Monash University Science. Updated 28 November 2007. 09 May, 2008. <http://www.geosci.monash.edu.au/assets/images/heatflow/fig3_4big.gif>
Anderson, Don L. "Energetics of the Earth and the Missing Heat Source Mystery" MantlePlumes.org 20 July, 2005 <http://www.mantleplumes.org/Energetics.html>
Nave, C.R. "Hyperphysics" C. 2005 Georgia State University <http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heatra.html>
Tony, "The Homely Scientist" Blog, April 2006. <http://www.homelyscientist.com/2006/04/>
Picture- "Bullard Plot" Monash University Science. Updated 28 November 2007. 09 May, 2008. <http://www.geosci.monash.edu.au/assets/images/heatflow/fig6_1big.gif>
Blackwell, David. et al. "2004 Surface Heat Flow Map" SMU Geothermal Lab <http://www.smu.edu/geothermal/heatflow/heatflow.htm>
Applications
Mineralogy - White, Craig. Earth Materials - class lectures. Boise State University, Fall 2007. Pressure-Temperature diagram courtesy University of Oregon: http://darkwing.uoregon.edu/~cashman/GEO311/311pages/L5_crystallization.htm
Seafloor Subsidence - Beardsmore, G.R. and Cull, J.P., "Crustal Heat Flow: A Guide to Measurement and Modeling." Cambridge University Press. C. 2001
Geothermal - Idaho National Engineering & Environmental Laboratory - http://geothermal.inel.gov/
Image and information from INEL's in-depth geothermal report: http://geothermal.inel.gov/publications/future_of_geothermal_energy.pdf
Parks & Rec. - http://www.nps.gov/yell/naturescience/geothermal.htm
Authors
Tim Brown, Mike Poulos, Andy Weigel
