Thermodynamic Properties of Supercritical CO₂/CH₄ Mixtures from the Virial Equation of State

Abstract

Mixture virial coefficients to seventh order are presented for the system CO 2 /CH 4 at four supercritical temperatures: 323.15, 373.15, 473.15, and 573.15 K. Values are evaluated via the Mayer sampling Monte Carlo method using a three-site TraPPE model for CO 2 and a one-site model for CH 4 . The coefficients are used to compute seven thermodynamic properties (viz., compressibility factor, isothermal compressibility, volume expansivity, isochoric and isobaric heat capacities, Joule−Thomson coefficient, and speed of sound) as a function of mole fraction and density for these temperatures. Comparison is made with corresponding data in the literature as obtained by molecular dynamics simulation, covering densities up to about twice the critical density. Key conclusions are as follows, noting that some exceptions are observed in each case: (a) The virial equation of state (VEOS) to fourth or fifth order describes all properties to within the simulation uncertainty for densities up to at least the critical density, and the addition of terms up to seventh order extends this range considerably. (b) The accuracy of the VEOS is severely diminished for conditions approaching the critical point (the present work extends down to a reduced temperature of 1.06 for CO 2 ), and the study of the pure component behavior suggests the critical singularity blocks convergence for conditions at considerably higher temperatures, albeit at correspondingly higher pressures. (c) Comparison of the VEOS at different orders provides a reliable guide to its accuracy at a given order, so the VEOS can provide a self-assessment of its accuracy when independent data for comparison are unavailable. (d) The VEOS provides a good description of the Joule−Thomson coefficient, including the inversion point in particular. The third-order series is needed to obtain behavior that is qualitatively correct, and the addition of higher-order terms steadily improves the accuracy quantitatively. (e) Under conditions where the seventh-order series is converged, properties can be computed to a given precision with VEOS using much less computational effort in comparison to molecular simulation.

Properties of supercritical N2, O2, CO2, and NH3 mixtures from the virial equation of state

“…In most such cases, the properties can be obtained by the VEOS with much less computational effort, as well. 6 The positive features of the VEOS are particularly relevant when (such as we did for helium 7 ), but rather to generate a good, wellfounded model for a multicomponent mixture. We take the N 2 /O 2 / CO 2 /NH 3 system as a prototype because (a) these compounds are relevant practically; (b) a TraPPE model has been developed for each; and (c) experimental data are available for the pure components and some mixtures, for comparison to the VEOS-based calculations.…”

Theoretical modeling of the effect of temperature on CO2 injectivity in deep saline formations

“…Although most of these analytical models have been developed for production of oil and gas, they can be adapted to investigate the thermal behavior of injection fluids. Several correlations have also been developed to predict CO 2 properties under different temperature and pressure conditions . If the temperature distribution of injected CO 2 from the wellhead to the reservoir is properly modeled, the effect of temperature changes around the wellbore injection inlet on CO 2 injectivity can be investigated.…”

“…Several correlations have also been developed to predict CO 2 properties under different temperature and pressure conditions. [38][39][40] If the temperature distribution of injected CO 2 from the wellhead to the reservoir is properly modeled, the effect of temperature changes around the wellbore injection inlet on CO 2 injectivity can be investigated.…”

Direct orientation sampling of diatomic molecules for path integral Monte Carlo calculation of fully quantum virial coefficients

“…Through this formula, the temperature-dependent virial coefficients, B n (T ), can be used to estimate a variety of physical properties in addition to the pressure, such as the Joule-Thomson coefficient, critical properties, 1,2 and others. 3 The unique feature of the virial equation of state, in comparison to other thermodynamic models, is that it represents rigorously the effect of interactions among N molecules, such that if given a molecular model, the virial coefficients for its equation of state can be determined without approximation. This can be clearly seen from the analytic expressions for the virial coefficients in terms of N-body configurational integrals 4 which depend only on the interaction potential between N molecules as…”

“…14,15 Since there are many MC algorithms to compute virial coefficients and many possible algorithms for sampling the configuration space within each MC simulation, there exist a variety of implementations of the general PIMC method. For instance, PIMC with quadrature has been used to compute virial coefficients of 3 He, 4 He, H 2 , and H 2 O, 8,10,[16][17][18][19] while PIMC with Mayer Sampling Monte Carlo 20 (MSMC) has been used to compute virial coefficients of 4 He. 7 Sampling of configurations in PIMC is made difficult by the different ranges of motions needed for rearrangements of the ring of beads versus its translation as a whole.…”