Geothermal Heat Flow Calculator
Calculate geothermal heat flow using thermal conductivity and temperature gradient. Estimate subsurface temperatures and geothermal energy potential.
Geothermal Heat Flow Calculator
Calculator
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Formula: q = k x (dT/dz)
Worked example โ Heat flow: 90 mW/m^2 (Elevated) | Temp at 4 km: 132 C
Formula
q = k x (dT/dz)
Heat flow (q) in mW/m^2 equals the thermal conductivity (k) in W/(m*K) multiplied by the geothermal temperature gradient (dT/dz) in C/km. This is derived from Fourier's Law of heat conduction applied to vertical heat transfer through the Earth's crust.
Worked Examples
Example 1: Continental Heat Flow Calculation
Problem:A borehole shows a gradient of 30 C/km through granite with thermal conductivity of 3.0 W/(m*K). Calculate heat flow and temperature at 4 km depth (surface temp 12 C).
Solution:Heat flow q = k x gradient = 3.0 x 30 = 90 mW/m^2 Temperature at 4 km = 12 + (30 x 4) = 132 C Classification: Elevated heat flow (thinned crust zone) This gradient and temperature are suitable for geothermal exploration
Result:Heat flow: 90 mW/m^2 (Elevated) | Temp at 4 km: 132 C
Example 2: Geothermal Resource Assessment
Problem:An area of 500 km^2 has 100 mW/m^2 heat flow, gradient 40 C/km, conductivity 2.5 W/(m*K), surface temp 10 C at 5 km depth.
Solution:Temperature at 5 km = 10 + (40 x 5) = 210 C Total heat = (100/1000) x (500 x 10^6) = 50,000 kW = 50 MW thermal Recoverable heat = rock density x specific heat x volume x deltaT x 2% = 2700 x 900 x (500e6 x 5000) x 200 x 0.02 = very large Electric potential at 10% efficiency = 5 MW
Result:210 C at depth | 50 MW thermal | Significant geothermal potential
Frequently Asked Questions
What is geothermal heat flow?
Geothermal heat flow is the rate at which thermal energy from Earth's interior is transferred to the surface through conduction, convection, and radiation. It is measured in milliwatts per square meter and represents the outward flux of heat through the crust. The global average heat flow is approximately 87 milliwatts per square meter on continents and about 101 milliwatts per square meter through oceanic crust. This heat originates primarily from the radioactive decay of uranium, thorium, and potassium isotopes in the crust and mantle, along with residual heat from planetary formation. Heat flow measurements are fundamental to understanding crustal thermal structure, tectonic processes, volcanic activity, and assessing the viability of geothermal energy resources for power generation.
How is geothermal heat flow measured?
Geothermal heat flow is measured using Fourier's Law of heat conduction, which states that heat flux equals the product of the thermal conductivity of the rock and the geothermal temperature gradient. In practice, this requires two separate measurements. First, the temperature gradient is measured by lowering precision temperature sensors into boreholes and recording temperatures at multiple depths, typically at intervals of 10 to 50 meters. Second, rock core samples are collected from the same borehole, and their thermal conductivity is measured in a laboratory using a divided bar apparatus or needle probe method. The heat flow value is then calculated by multiplying these two quantities. Shallow measurements within 200 meters can be affected by groundwater flow, seasonal temperature variations, and topographic effects, requiring corrections.
What factors affect the geothermal temperature gradient?
The geothermal temperature gradient, which describes how quickly temperature increases with depth, is influenced by several geological factors. The average gradient is roughly 25 to 30 degrees Celsius per kilometer, but it varies enormously from less than 10 to over 100 degrees per kilometer. The primary controlling factor is heat flow from below, which is highest in tectonically active regions near plate boundaries, mid-ocean ridges, and volcanic hotspots. The thermal conductivity of the overlying rock matters greatly because insulating sedimentary rocks with low conductivity create steeper gradients than highly conductive crystalline basement rocks. The concentration of radioactive heat-producing elements in crustal rocks contributes additional heat from above. Groundwater circulation can redistribute heat, creating anomalously high or low gradients depending on flow direction.
What are the different types of geothermal energy resources?
Geothermal energy resources are classified into several categories based on temperature and geological setting. Hydrothermal resources are the most commonly exploited type, consisting of hot water or steam trapped in permeable rock formations at temperatures above 150 degrees Celsius, suitable for direct electricity generation. Enhanced Geothermal Systems involve engineering artificial reservoirs in hot dry rock by hydraulic fracturing to circulate water through naturally hot formations. Low-temperature geothermal resources below 90 degrees Celsius are used for direct heating applications including district heating, greenhouse agriculture, aquaculture, and industrial processes. Geopressured resources combine thermal energy with dissolved methane and hydraulic pressure in deep sedimentary basins. Ground-source heat pumps utilize the nearly constant shallow ground temperature for building heating and cooling without requiring high-temperature resources.
How does thermal conductivity vary among different rock types?
Thermal conductivity varies significantly among rock types and is a critical parameter in heat flow calculations. Quartzite and sandstone rich in quartz have the highest conductivities among common rocks, typically 4 to 7 watts per meter per kelvin, because quartz itself has a high conductivity of about 7.7 watts per meter per kelvin. Granite and other crystalline igneous rocks typically range from 2.5 to 3.5 watts per meter per kelvin. Limestone and dolostone fall in the range of 2 to 3.5 watts per meter per kelvin. Shale and mudstone have among the lowest conductivities at 1.0 to 2.5 watts per meter per kelvin due to their fine-grained clay mineral composition. Water-saturated porous rocks generally have higher conductivity than dry ones. Temperature also affects conductivity, with most rocks showing decreasing conductivity at higher temperatures.
What does thermal resistance tell me, and how do I use it with layered rock?
Thermal resistance is depth divided by conductivity, in units of m2 K/W, and it is the quantity that converts a heat flux into a temperature rise: delta T equals q times R. For 3,000 m of rock at 3.0 W/(m K) the resistance is 1,000 m2 K/W, and a flux of 90 mW/m2, or 0.09 W/m2, gives 90 degrees of warming, exactly matching a 30 degrees C/km gradient over 3 km. The real value of the concept is in layered sections: resistances add, so summing each layer's thickness divided by its own conductivity and multiplying by the constant heat flow predicts bottom-hole temperature far better than applying one average gradient through shale, salt and basement alike.
Why is oceanic heat flow higher than continental heat flow if the crust holds fewer radioactive elements?
Because ocean floor is young and still cooling. Lithosphere created at a spreading ridge loses heat to seawater as it ages, and the half-space cooling model predicts that conductive heat flow falls off in proportion to one over the square root of crustal age, which is why fluxes of several hundred mW/m2 near a ridge crest decline to 50 mW/m2 or less on 100-million-year-old seafloor. Continental heat flow, by contrast, is dominated by radiogenic decay of uranium, thorium and potassium in thick granitic crust, which is a steadier but smaller source. Measured near-ridge values also run below the model prediction because hydrothermal circulation carries heat away advectively rather than by conduction.
What is radiogenic heat production and how does it separate from mantle heat flow?
Radiogenic heat production A, in microwatts per cubic metre, is the heat released by decay of uranium-238, thorium-232 and potassium-40 in the rock itself, and it is measured by gamma spectrometry on core or from a spectral gamma log. Because granite concentrates these elements, the heat entering a borehole from below is less than the heat leaving the surface above it. Within a single geological province, surface heat flow plots as a straight line against near-surface heat production, with an intercept giving the reduced heat flow arriving from the mantle and a slope with the dimensions of a depth, typically around 10 km, interpreted as the thickness of the enriched layer. Separating the two is essential before treating a high heat flow as evidence of a mantle anomaly.
Which corrections does a shallow heat flow determination need?
Three systematic effects contaminate the top few hundred metres. Paleoclimate is the largest: surface temperatures rose by several degrees after the last glaciation, and that step is still diffusing downward, depressing the apparent gradient in the shallowest section and inflating it slightly deeper. Topography refracts the heat field, concentrating flux under valleys and dispersing it under ridges, which needs a terrain correction from a digital elevation model. Rapid sedimentation buries cool material and suppresses gradients in young basins, while erosion does the opposite. Groundwater advection is the wildcard, since it can either mask or mimic all of these. This is why continental determinations are normally based on logs deeper than 200 to 300 m.
Does the total heat output over the survey area represent extractable power?
No, and conflating the two is the most common error in resource screening. Multiplying heat flow by area gives the natural conductive throughput, so 100 mW/m2 across 500 km2 is 50 MW of thermal energy crossing that ground continuously. Capturing it would mean intercepting every joule the Earth delivers over an area larger than many cities. Practical projects instead mine stored heat from a finite rock volume, which the recoverable estimate approximates as rock density times specific heat times volume times the temperature drop, multiplied by a recovery factor of only a few percent because most of the heat sits in rock that no fluid ever contacts. That stock depletes over decades, so heat flow governs how fast the reservoir recharges, not how much power a plant can produce.
References
Background & Theory
History
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer ยท Editorial policy
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