Motivation
The Temperature Flat Source Solution @model is one of the fundamental solutions of temperature diffusion equations modelling the temperature conduction in linear direction (see Fig. 1).
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Subsurface Temperature Profile around Lateral Flow makes adjustments to Geothermal Temperature Profile
to account for the lateral reservoir flow with a constant temperature (see Fig. 1 and Fig. 2).
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Image Removed 1 around Lateral Flow around two lateral flows with temperature | LaTeX Math Inline |
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and | LaTeX Math Inline |
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| body | --uriencoded--T_%7Bf2%7D |
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Outputs
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| Temperature Subsurface temperature distribution |
Inputs
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| Time lapse after the temperature step from |
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| Spatial coordinate along the transversal direction to constant temperature |
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Equations
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| Driving equation | Initial conditions | Boundary conditions |
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| \frac{\partial T_be}{\partial t} = a^2 a_e^2 \, \Delta T_be = a^2a_e^2 \, \frac{\partial^2 T_be}{\partial z^2} |
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| T_be(t=0, z) = T_G(z) |
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| T_be(t, z=0 z_f \leq z \leq z_f + h_f) = T_f = {\rm const} |
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| T_be(t, z \rightarrow \infty) = T_G(z) |
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| \mbox{if} \, z < z_f \; \Longrightarrow \;T_be(t,z) = T_f + (T_G(z) - T_f) \cdot \mbox{erf} \left( \frac{2z_f-z}{\sqrt{\pi}} \int_0^{z/\sqrt{4at}} e^{-\xi^2} d\xi4 a_e t}} \right) |
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| \mbox{if} \, z_f \leq z \leq z_f + h_f \; \Longrightarrow \; T_e(t,z) = T_f |
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| \mbox{if} \, z > z_f + h_f \; \Longrightarrow \; T_e(t,z) = T_f + (T_G(z) - T_f) \cdot \mbox{erf} \left( \frac{z-z_f-h_f}{\sqrt{4 a_e t}} \right) |
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where
See Also
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Geology / Geothermal Temperature Field / Geothermal Temperature Profile
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