Predicting the Phase Behavior of Nitrogen + n-Alkanes for Enhanced Oil Recovery from the SAFT-VR Approach:  Examining the Effect of the Quadrupole Moment

Abstract

The phase behavior of nitrogen + n-alkanes is studied within the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). The effect of the quadrupole moment of nitrogen on the phase behavior is considered through an extension of the SAFT-VR equation that includes an additional contribution to the Helmholtz free energy due to quadrupolar interactions. A significant improvement in the description of the phase diagram of the binary mixtures of nitrogen with different n-alkanes is obtained with the new approach when compared to predictions from the original SAFT-VR EOS (i.e., without the quadrupolar term). The experimental value for the quadrupole moment of nitrogen is used in the new equation; thus, no additional parameters are employed. Given the nonideal nature of the binary mixtures, a binary interaction parameter is needed to describe the full-phase diagram and high-pressure critical lines of these systems; however, this can be fitted to a single system and successfully used to predict the phase behavior of other binary mixtures without additional fitting. Furthermore, only a single, transferable, cross-energy parameter is required when the quadrupolar term is considered, whereas a cross-range parameter is also needed with the original SAFT-VR approach. The inclusion of the quadrupolar term in the equation of state therefore reduces the need to use effective parameters by explicitly including at the molecular level interactions due to the quadrupole moment.

Prediction of binary intermolecular potential parameters for use in modelling fluid mixtures

“…For this mixture, k ij = 0.15 with SAFT-VR was obtained by adjustment to experimental mixture data. (We note that the SW-potential parameters used in this work [62] to model N 2 were slightly different from those in Zhao et al [63], however the same values of k ij (to two significant figures) were calculated using the parameters of either model.) In Figure (5) we present SAFT-VR calculations of the absorption of N 2 in 111 kg mole −1 HDPE using k ij = 0, k ij = 0.11 (the predicted value) and k ij = 0.15 (the fitted value from Ref.…”

“…Zhao et al [63] have recently studied several such mixtures using SAFT-VR. Calculations using the Lorentz-Berthelot rules were adequate for mixtures of nitrogen with methane, n-butane and n-pentane, however it was pointed out that a (non-zero) binary-interaction parameter would be needed to capture the mixture data for nitrogen + n-heptane.…”

“…(We obtain these same values (to two significant figures) irrespective of whether we include the quadrupole of nitrogen (1.46 DÅ, the average of experimental values given in reference [64]) in our calculation, using equation (38), or neglect it, i.e., using equation (25); since nitrogen is a small molecule, we are able to calculate k ij using either equation.) Zhao et al [63] provided k ij values obtained by fitting to the critical lines for several other N 2 + n-alkane mixtures. For these cases, non-zero potential-range binary-interaction parameters, l ij , were also employed, hence we calculated k ij for these systems via SW ij evaluated using equation (23) rather than directly using equation (25), in which the arithmetic mean rule is assumed.…”

“…Table 1: Predicted binary square-well depth k ij parameter values for binary mixtures of n-alkanes from methane to n-octane Table 3: Predicted binary energy parameter k ij for nitrogen + n-alkane mixtures studied in reference [63] and those obtained by adjusting the theoretical description to experimental data; the subscript "crit" indicates that the SW parameters were rescaled to the critical point. l ij represents the adjustment to the arithmetic-mean combining rule for the binary range parameter λ ij used in reference [63].…”

“…Table 1: Predicted binary square-well depth k ij parameter values for binary mixtures of n-alkanes from methane to n-octane Table 3: Predicted binary energy parameter k ij for nitrogen + n-alkane mixtures studied in reference [63] and those obtained by adjusting the theoretical description to experimental data; the subscript "crit" indicates that the SW parameters were rescaled to the critical point. l ij represents the adjustment to the arithmetic-mean combining rule for the binary range parameter λ ij used in reference [63]. Table 5: SAFT-VR parameters (with the square-well potential) for Ne, Xe, H 2 S and CO. Model parameters for Ne and H 2 S were estimated during the course of this work; the parameters for Xe are taken from reference [74] and those for CO are taken from reference [79].…”