Fluids at crustal pressures and temperatures

Abstract

The pressure-volume-temperature data of several gases (H₂, O₂, CO, CH₄, N₂ and CO₂) have been used to obtain the following corresponding states equation (P>1 kbar; T>400 K): Z(±0.0878)=A+BP _r +CP ^/2 _r (21) where Z is the compressibility factor, P _r reduced pressure (P/critical P), T _r reduced temperature (T/critical T) and the coefficients are given by: A=1−0.5917 T ^/−2 _r B=0.09122 T ^/−1 _r C=1.4164×10⁻⁴ T ^/−2 _r −2.8349×10⁻⁶ ln T _r (P>1 kbar; T>400 K). At pressures below 1 kbar, Z is given by: Z(±0.0761)=1+BP _r +CP ^/2 _r (23) where B=0.09827 T ^/−1 _r −0.2709 T ^/−3 _r C=0.01472 T ^/−4 _r −0.00103 T ^/−1.5 _r . For water (P>1 kbar; T>400 K): Z(±0.0209)=A+BP+CP ² (22) where A=−0.7025+1.16×10⁻³ T+99.6799 T ⁻¹ B=0.2143 T ⁻¹−3.1423×10⁻¹⁴ T ³ C=−2.249×10⁻⁶ T ⁻¹−0.1459 T ⁻³+2.1690×10⁻¹⁵ T ². At pressure below 1 kbar, the equation is (P>100 bar; T >673 K): Z(±0.0601)=1+B′/V+C′/V ² (24) where B′=−2.20960 T^0.5+3.35460×10⁻⁸ T³ C′=3.4569×10⁻⁵T^2.5+64.9764 ln T Fugacities of the gases may be obtained by integrating the Z equations separately and combining the results as follows:

$$\int\limits_1^P {VdP = RT} {\text{ }}\left( {\int\limits_1^{1000} {Z_{23} /PdP + } \int\limits_{1000}^1 {Z_{21} /PdP} } \right)$$

((26))

The subscript in Z denotes the equation which is to be used for calculating Z.