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Chapter 17 Geothermics. The earth is hot in the middle (>4000° C) and cold at its surface (19 ° C) and very cold outside its atmosphere in space (-270 ° C).
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Chapter 17 Geothermics The earth is hot in the middle (>4000° C) and cold at its surface (19 ° C) and very cold outside its atmosphere in space (-270 ° C). Anytime there is a temperature difference, heat MUST flow from the hot to the cold regions: this heat flow cools the hotter regions and warms the cooler region. This heat-flow MUST happen because the earth is out of thermal equilibrium with its surroundings (space). This heat-flow out of the earth and into space will slowly cool the earth until it reaches thermal equilibrium with space in >10 Ga. In other words, the Earth is cooling very very slowly. In the last 4 Ga, the cooling has been about 100 ° C per Ga. There are three ways to move heat from point A to B: Conduction: heat moves (diffuses) via crystal lattice vibrations. Conduction can never be stopped if a temperature difference exists between two regions. Examples? Convection: heat moves by light and dense parcel going up and down in the earth’s gravity field and advecting (moving via flow of parcels) heat. This only occurs if the parcel buoyancy forces are large with respect to the strength (viscosity) of the mantle. Examples? Radiation: heat moves in the energy of infared frequency electromagnetic waves at speed of light. Examples?
Geologic phenomena and heat flow • Yellowstone hydrothermal geyser fields • Oil/gas maturation • Volcanoes • Earthquakes • Hydrothermal mineralization • Plate tectonics • Geothermal power production • Mid-ocean ridges • Subducting slabs • Metamorphism of rocks
What is heat: Q(Joules)= Heat-capacity *Temperature1 Joule = 4.1 calories
Heat always flows from hot to cold as long as there is a temperature contrast WHY? All forms of energy (e.g., heat), are relentlessly driven to spread out (disperse) their energy into larger volumes over time. This energy spreading out drives a system toward thermal equilibrium. This relentless ‘force’ is called the second law of thermodynamics which ALWAYS forces a system to increase its entropy in time.
Conductive heat transport in lithosphere and convective heat transport along mantle adiabat The lithosphere is strong and hence translates over the asthenosphere, therefore heat cannot be convected across the lithosphere and instead heat is conducted across the lithosphere. Note the lithosphere DOES only deforms via flow where mountain roots are made. The mantle (parcels) are moving heat via convection, although heat conduction is always occurring. But the 1-10 cm/yr flow moves (advects) the heat much much faster than heat conduction! The temperature in the lithosphere is near a straight line which is called the conductive geotherm: dT/dz = 30°C/km. The lithosphere geotherm will curve when there is heat production (e.g., in continental crust). The adiabatgeotherm is about dT/dz = 0.5°C/km; this temperature rise with depth is because the each parcel of heat is being compressed into a smaller volume due to the pressure increase with depth.
Heat flux and amount of heat Heat flux: W/m2 Energy per area Heat: W Energy per sec dT dz dz
Measuring thermal conductivity Because it is very hard to measure mW scale heat fluxes, a tactic is to measure the temperature gradient in a borehole (or otherwise) and the thermal conductivity of the rocks in the borehole. The heat flux is calculated: q= k*dT/dz The thermal conductivity of a rock can be measured by heating (heat source) one side of the metal rod and cooling the other side (heat sink) and measuring the thermal gradients in the metal and rock-sample regions. Using the known conductivity of the metal, the heat flux is calculated. Thus, the conductivity of the rock is q/(dT/dz). Backwards! q
Heat flow with oceanic plate age The heat flux is high at mid-ocean ridge where heat is being convected to 20 km depth. Then the plate moves horizontally and cools over 150 ma in a systematic way. This cooling is manifest as the lithosphere getting thicker with time.
Heat production: heat flux increases in direction of heat flow Note that the heat flux vectors get longer towards the cooler side of the column. This is because a constant heat production (μW/m3 ) throughout the 3 m column is assumed. Thus, this creation of heat increase the heat flow and the thermal gradient towards the cooler end (i.e., the earth’s surface). Thus, the distribution of heat production in the crust changes the geotherm.
Heat productivity vs. heat flux relationship The crust is highly concentrated in radioactive elements such as Uranium. As Uranium decays it makes heat which is term the heat productivity in micro-Watts per unit volume units. By measuring the surface rock heat productivity, a linear relation between heat productivity and heat flux is often found. This mean the upper crustal rocks heat production controls the heat flux. The y-intercept value is the reduced heat flow (qr ) which is from the mantle.
Radioactive heat generation Note that 40% of the Earth’s total heat flow comes from radioactive heat generation! The other 60% comes from ‘secular cooling’ of the original accretional heat 4.5 Ga ago. Also, note that 10% comes from continental crust, but only 0.15% from ocean crust. Finally, in general there is a decrease in heat flow with the age of continents. Why ?
The primary contributions to observed total surface heat flow (46 +/- 3 TW) are shown here. Radiogenic heat production, mantle cooling and heat flow from the core dominate the mantle energy budget, but there are substantial uncertainties in the latter two contributions. Improved constraints on any component will also constrain the balance of the other components. Early estimates of heat flow from the core of 3–4 TW are now being challenged by higher estimates of 5–15 TW, which can bring the sum of heat sources into agreement with the observed heat flow without requiring exceptionally large mantle cooling or non-chondritic radiogenic heat production.
Oceanic and continental heat flux and geotherms The geotherm in the lithosphere is conductive and the geotherm in the convecting mantle is the adiabat. Note that the conductive heat flux in the oceans is constant and hence the geotherm is a straight line. Why? But, the conductive heat flux in the continent increase towards the surface and the geotherm is a curved line. Why? The base of the lithosphere has the same temperature at all three places of about 1300°C.
Seismic velocity mapped to temperature for Oceanic lithosphere
Temperature re-equilibration So far, we have been assuming that the temperature does NOT vary in time. This is called thermal steady-state or equilibrium. So, what if the temperature structure changes in time due to basins filling or tectonic overthrusts? Adding sediments quickly to the top of the crust, causes a thermal disequilibrium that will be brought to equilibrium over Ma time-scales. Thrusting 20 km of the upper crust over the surrounding surface quickly, creates a disequilibrium that takes greater than 50 Ma to reach equilibrium.
Geothermal heat extraction and energy production Where high temperature rock is near the surface, the heat contained in the hot-rock can be mined to drive steam-turbines to make electricity. This is done by pumping water down the injection well where it flows through the cracks in the rocks and heats up and corresponding cools-down the rocks over time. The hot water is then extracted via a production well. Note: this is not a renewable resource as the water circulation extracts the heat much much faster than the earth mW scale heat flux can replace the mined heat (energy).
Atmospheric temperature changes effects on shallow geotherms Periodic (daily, seasonal) changes in atmospheric temperature can ‘temperature waves’ to propagate downward into the crust, but the attenenuate exponentially! A recent 2 ° C increase in surface temperature between 1900-2000 can be measured in the borehole temperature profile and well modeled using the heat flow equations.
Heat flow: Red (high) Blue (low
Thermal boundary layer and at core-mantle boundary and heat exchange
