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The quadratic relationship between the mean production temperature and the aperture standard deviation is also expected owing to the fact that (bar{Theta }_1) must be zero based on linearity.
Besides, the mean production life decreases with greater aperture standard deviation only when the correlation length is relatively long.
As (sigma _h/leftlangle w rightrangle) increases, the mean production temperature decreases quadratically and the standard deviation increases linearly.
The use of statistical values of an ensemble of realizations including the mean and standard deviation of production temperatures will offer a better and more practical understanding of the effects fracture surface variations have on discretely fractured geothermal reservoirs.
Additionally, our use of statistical values for an ensemble of realizations, including the mean and standard deviation of production temperatures, offers a better and more practical understanding of the effects fracture aperture variations have on discretely fractured geothermal reservoirs.
Figures 3 and 4 show how the strength of aperture variations affects the mean and standard deviation of the production temperature.
As discussed earlier, the mean and standard deviation of the production temperature distribution have a quadratic and a linear behavior, respectively: begin{aligned} Theta _{p,0} - bar{Theta }_p = C_1 left( frac{sigma _h}{leftlangle w rightrangle }right) ^2, end{aligned} (18 and begin{aligned} sigma _{Theta } = C_2 left( frac{sigma _h}{leftlangle w rightrangle }right).
We assess the mean, standard deviation, skewness and kurtosis ('Methods'Methods
mean signed deviation.
mean squared deviation.
root mean square deviation.
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