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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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Fig. 1. Sample Subsurface Temperature Profile around a height lateral flow at depth with temperature | Fig. 2. Sample Subsurface Temperature Profile around two lateral flows with temperature LaTeX Math Inline |
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| Subsurface temperature distribution |
Inputs
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Equations
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Driving equation | Initial conditions | Boundary conditions |
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| \frac{\partial T_e}{\partial t} = a^2a_e^2 \, \Delta T_e = a^2a_e^2 \, \frac{\partial^2 T_e}{\partial z^2} |
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| T_e(t=0, z) = T_G(z) |
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| T_e(t, z_f \leq z \leq z_f + h_f) = T_f = {\rm const} |
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| T_e(t, z \rightarrow \infty) = T_G(z) |
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| \mbox{if} \, z < z_f \; \Longrightarrow \;T_e(t,z) = T_f + (T_G(z) - T_f) \cdot \mbox{erf} \left( \frac{z_f-z}{\sqrt{4at4 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{4at4 a_e t}} \right) |
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where
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