deletions | additions       diff --git a/discussion_thermal constraints.tex b/discussion_thermal constraints.tex  index 1dcf8af..b54bd86 100644  --- a/discussion_thermal constraints.tex  +++ b/discussion_thermal constraints.tex 
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\[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]  where V is the volume of fluid expelled along the fault, h is the effective width of the fault, C_{p}^{w} C$_{p}^{w}$  and C_{p}^{r} C$_{p}^{r}$  are the specific heat capacities of water and rock respectively, $\rho_{w}$ and $\rho_{r}$ the densities of water and rock, and $\textit{k}$ the thermal diffusivity of rock. Noting that $C_{p}^{w}$ $\cdot$ $\rho_{w}$ $\approx$ 2 $\cdot$ $C_{p}^{r}$ $\cdot$ $\rho_{r}$ and selecting values of 120$^{\circ}$, 100$^{\circ}$ and 40$^{\circ}$C respectively for $\Theta_{i}$, $\Theta_{1}$ and $\Theta_{2}$, 3000m for $\textit{x}_{1}$, 1000m for $\textit{x}_{2}$ and an effective fault width of 1m we find that the maximum duration (s) for an individual fluid pulse is: \[t = \frac{{\pi \cdot \left( {3.3 \times {{10}^{ - 4}} \cdot V - 0.5} \right)^2}}{{1 \times {{10}^{ - 6}}}}\]