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Table 2 Review of the constitutive equations of the brine properties and values of empirical coefficients

From: THM modeling of hydrothermal circulation at Rittershoffen geothermal site, France

Parameter Expression Coefficients
Density, \(\rho ^0_{w}\) (kg m\(^{-3}\)) 1070
Bulk modulus, \(K_{w}\) (GPa) 2.2
Dynamic viscosity, \(\mu _{w}\) (Pa s) \(\mu _w^\infty + \Delta \upmu _w^\infty \exp (\beta (T - T_{\text{ref}}))\) \(\mu _w^\infty = 1.9\times 10^{-4}\) (Pa s)
   \(\Delta \mu _w^\infty = 6.2\times 10^{-6}\) (Pa s)
   \(\beta = -\,0.02\,{\text {K}}^{-1}\)
   \(\hbox {T}_{ref} = 406.4\,{\text {K}}^{-1}\)
Heat capacity, \(c^p_{w}\) (\(\hbox {J kg}^{-1}{\text {K}}^{-1}\)) \(a_{c^{p}_{w}} + b_{c^{p}_{w}}(T - T^1) + c_{c^{p}_{w}}(T - T^1)^2\) \(a_{c^{p}_{w}}\) = 3.7 (\(\hbox {J kg}^{-1}{\text {K}}^{-1}\))
   \(b_{c^{p}_{w}}\) = 0.4 (\(\hbox {J kg}^{-1}{\text {K}}^{-2}\))
   \(c_{c^{p}_{w}} = 4.6\times 10^{-3}\) (\(\hbox {J kg}^{-1}K^{-3}\))
   \(T^1\) = 273.15 K
Thermal dilation, \(\alpha _{w}\) (\(K^1\)) \(a_{\alpha _w} + 2b_{\alpha _w}(T - T^0) + 3c_{\alpha _w}(T - T^0)^2\) \(a_{\alpha _w}=1.3\times 10^{-4}\) \({\text {K}}^{1}\)
   \(b_{\alpha _w}=4.3\times 10^{-7}\) \({\text {K}}^{2}\)
   \(c_{\alpha _w}=2.5\times 10^{-10}\) \({\text {K}}^{3}\)
   T\(^\circ\) = 293.0 K
Thermal conductivity, \(\lambda _{w}\) (\(W m^{-1}K^{-1}\)) \(a_{\lambda _w}\left[ 1 - b_{\lambda _w} \exp (-c_{\lambda _w}(T - T^1)\right]\) \(a_{\lambda _w}\) = 0.7 (\(\text{W}\,\text{m}^{-1}\text{K}^{-1}\))
   \(b_{\lambda _w} = 0.2\)
   \(c_{\lambda _w} = 0.02\,\text{K}^{-1}\)