Table 2 Review of the constitutive equations of the brine properties and values of empirical 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 (\(\text{W}\,\text{m}^{-1}\text{K}^{-1}\))

\(b_{\lambda _w} = 0.2\)

\(c_{\lambda _w} = 0.02\,\text{K}^{-1}\)