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

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 ($$\text{W}\,\text{m}^{-1}\text{K}^{-1}$$)
$$b_{\lambda _w} = 0.2$$
$$c_{\lambda _w} = 0.02\,\text{K}^{-1}$$