this is for holding javascript data
Paul Dennis edited discussion_fluids.tex
over 8 years ago
Commit id: 103a3d6b031d4de6910cbc36e03c2e33725e08b7
deletions | additions
diff --git a/discussion_fluids.tex b/discussion_fluids.tex
index e69de29..33258da 100644
--- a/discussion_fluids.tex
+++ b/discussion_fluids.tex
...
\subsection{Thermal constraints on fluid flux}
To a first approximation we can use the estimated temperatures of the fluid end members to constrain the flux of fluid needed to develop a thermal anomaly similar to that observed at Dirtlow Rake. The question is how much fluid and how fast does it have to flow along the fault to (i) heat the rock in the fault zone and (ii) prevent significant heat loss via conduction through the walls of the fault? The problem is illustrated in Figure 8. Hydrothermal fluid at an initial temperature $\Theta$_{i} enters the fault at depth \textit{x}_{1} and flows up along the fault to a depth of \textit{x}_{2} where it has cooled to a temperature $\Theta$_{1}. We assume that the heat lost from the fluid (i) heats the immediate fault zone to the temperature of the fluid ($\Theta$_1) and; (ii) is lost through thermal diffusion perpendicular to the fault walls. For a parallel plate slab we can express this energy balance per metre length of fault as:
\[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]
where V is the volume of fluid expelled along the fault, h is the effective width of the fault, C_{p}^{w} and 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:
\[t = \frac{{\pi \cdot \left( {3.3 \times {{10}^{ - 4}} \cdot V - 0.5} \right)^2}}{{1 \times {{10}^{ - 6}}}}\]
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 thick sediment sequence at depth with incremental changes in porosity of 0.1, 1 and 10\% on dewatering. These approximate to the dimensions of 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. It is to give an indication of the flow rates that are needed to sustain the maximum observed thermal anomaly within the Dirtlow Rake and Castleton fault assuming a physical system that couples fluid overpressure and faulting. That the model may only be accurate to within a factor of 5 to 10 does not invalidate the central result that the fluid release must occur as pulses of short duration to sustain the thermal anomaly.
A corollary of the pulsed nature of fluid release is that mineralization is episodic with separate events spanning limited periods up to several thousand to several ten thousand years separated by periods of stasis. This observation is convergent with recent data on the Zn content of mineralizing fluids determined from fluid inclusions in several MVT provinces that suggests mineralization events could be of durations as short as 10,000 years \citep{Bodnar:2009hc, Wilkinson06022009}.
