deletions | additions       diff --git a/discussion_thermal constraints.tex b/discussion_thermal constraints.tex  index e13bc50..818ab95 100644  --- a/discussion_thermal constraints.tex  +++ b/discussion_thermal constraints.tex 
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\[t = \frac{{\pi \cdot \left( {3.3 \times {{10}^{ - 4}} \cdot V - 0.5} \right)^2}}{{1 \times {{10}^{ - 6}}}}\]  Table 2 lists values of t for different values of V. The values of V were chosen corresponding to the volumes of fluid expelled from an overpressured 40km x 1000m 2kmm  thick sediment sequence at depth with incremental changes in porosity of 0.1, 1 and 10\% on dewatering. These approximate to the dimensions width and thickness  of shale in  the Carboniferous Edale basin to the north-east of the Derbyshire platform. The porosity changes range from the smallest incremental changes calculated for individual dewatering pulses of overpressured sediments to the integrated maximum volume of fluid that might be expelled \citep{Cathles:1983tj}. The corresponding values of t are 16, 1723 and 173500 years respectively. These correspond to mean fluxes of 285, 26.5 and 0.26 litres.m^{-1}.hr^{-1}. Such flow rates are not geologically unrealistic. The highest rates associated with the smallest fluid pulses are on the order of the rates of effusion from springs that have been monitored for periods of several years following moderate earthquakes e.g (add refs by Nur and Tsuneishi et al., 1970). One can legitimately question the model details and parameter estimates but the point of this somewhat heuristic approach is not to be an accurate model. Rather, it is to give an indication of the flow rates that are needed to sustain the maximum observed thermal anomaly within the Dirtlow Rake assuming a physical system that couples fluid overpressure and flow. That the model may only be accurate to within a factor of 5 to 10 does not invalidate the central result that if fluid release occurs in a pulsed and episodic manner then each event must be of short duration to sustain the necessary thermal anomaly.