We have used in this work the crossover soft-SAFT equation of state to model nitrogen dioxide/dinitrogen tetraoxide (NO 2 /N 2 O 4 ), carbon dioxide (CO 2 ) and their mixtures. The prediction of the vapor -liquid equilibrium of this mixture is of utmost importance to correctly assess the NO 2 monomer amount that is the oxidizing agent of vegetal macromolecules in the CO 2 + NO 2 / N 2 O 4 reacting medium under supercritical conditions. The quadrupolar effect was explicitly considered when modeling carbon dioxide, enabling to obtain an excellent description of the vapor-liquid equilibria diagrams. NO 2 was modeled as a self associating molecule with a single association site to account for the strong associating character of the NO 2 molecule. Again, the vaporliquid equilibrium of NO 2 was correctly modeled. The molecular parameters were tested by accurately predicting the very few available experimental data outside the phase equilibrium. Soft-SAFT was also able to predict the degree of dimerization of NO 2 (mimicking the real NO 2 /N 2 O 4 situation), in good agreement with experimental data.Finally, CO 2 and NO 2 pure compound parameters were used to predict the vaporliquid coexistence of the CO 2 + NO 2 / N 2 O 4 mixture at different temperatures.Experimental pressure -CO 2 mass fraction isotherms recently measured were well described using a unique binary parameter, independent of the temperature, proving that the soft-SAFT model is able to capture the non-ideal behavior of the mixture.

Flash calculation is the most time consuming part in compositional reservoir simulations and several approaches have been proposed to speed it up. Two recent approaches proposed in the literature are the shadow region method and the Compositional Space Adaptive Tabulation (CSAT) method. The shadow region method reduces the computation time mainly by skipping stability analysis for a large portion of compositions in the single phase region. In the two-phase region, a highly efficient Newton-Raphson algorithm can be employed with initial estimates from the previous step. The CSAT method saves computation time by replacing some of the phase split calculation in the two-phase region with pre-stored flash calculation results. The stored results can be used when the new feed composition is on one of the stored tie lines within a certain tolerance. The number of tie lines stored for comparison and the tolerance set for accepting the feed composition are the key parameters in this method since they will influence the simulation speed and the accuracy of simulation results. Inspired by CSAT, we proposed a Tieline Distance Based Approximation (TDBA) method to get approximate flash results in the two-phase region. The method uses the distance to a previous tieline in the same gridblock to decide whether the approximation should be made. Comparison between the shadow region approach and the approximation approach, including CSAT and TDBA, has been made by using a slimtube simulator where the simulation temperature and the simulation pressure are set constant. It is shown that TDBA can significantly improve the flash calculations in the two-phase region.

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Compositional reservoir simulations are widely used to simulate reservoir processes with strong compositional effects, such as gas injection. The equations of state (EoS) based phase equilibrium calculation is a time consuming part in this type of simulations. The phase equilibrium problem can be either decoupled from or coupled with the transport problem. In the former case, flash calculation is required, which consists of stability analysis and subsequent phase split calculation; in the latter case, no explicit phase split calculation is required but efficient stability analysis and optimized coding of the basic thermodynamic subroutines are still crucial to the overall speed. This work tries to provide a comprehensive strategy to increase the speed for compositional simulation. This strategy begins with the coding of the basic thermodynamic properties, including the derivatives of fugacities with respect to molar numbers. Then, in the algorithms for stability analysis and phase split calculation, successive substitution with acceleration and minimization-based second-order methods are combined to gain both robustness and efficiency. For compositional simulations, the results from previous simulation steps provide the possibility to skip stability analysis by the shadow region method in the single phase regions. The approach was implemented in the general purpose research simulator (GPRS) developed by Stanford University. GPRS is a modular, state of the art reservoir simulation and its architecture makes the implementation and evaluation of new ideas and concepts easy. Tests on several 2-D and 3-D gas injection examples indicate that with an efficient implementation of the thermodynamic package and the conventional stability analysis algorithm, the speed can be increased by several folds. Application of the shadow region method to skip stability analysis can further cut the phase equilibrium calculation time.

Flash calculation can be a time-consuming part in compositional reservoir simulations, and several approaches have been proposed to speed it up. One recent approach is the shadow-region method that reduces the computation time mainly by skipping stability analysis for a large portion of the compositions in the single-phase region. In the two-phase region, a highly efficient Newton-Raphson algorithm can be used with the initial estimates from the previous step. Another approach is the compositional-space adaptivetabulation (CSAT) approach, which is based on tie-line table look-up (TTL). It saves computation time by replacing rigorous phase-equilibrium calculations with the stored results in a tie-line table whenever the new feed composition is on one of the stored tie-lines within a certain tolerance. In this study, a modified version of CSAT, named the TTL method, has been proposed to investigate if approximation by looking up a tie-line table can save flash-computation time in the two-phase region. The number of tie-lines stored for comparison and the tolerance set for accepting the feed composition are the key parameters in this method because they will influence the simulation speed and the accuracy of simulation results. We also proposed the tie-line distance-based approximation (TDBA) method, an alternative method to TTL, to obtain approximate flash results in the two-phase region. The method uses the distance to a previous tie-line in the same gridblock to determine whether the approximation should be made. Comparison between the shadow-region approach and the approximation approach, including TTL and TDBA, has been made with a slimtube simulator by which the simulation temperature and the simulation pressure are set constant. It is shown that TDBA can significantly improve the speed in the two-phase region. In contrast, TTL, even with a precalculated tie-line table, is not so advantageous compared with an efficient implementation of rigorous flash. Furthermore, we implemented TDBA in a compositional streamline simulator to apply TDBA to scenarios with pressure variation across the reservoir. We also discussed how to extend TDBA to the general situation in which pressures in gridblocks are updated dynamically.

First-principles full-potential linearized augmented plane-wave method based on density functional theory is used to investigate the structural, electronic and magnetic properties of KX ([Formula: see text], Se and Te) binary alkali–metal chalcogenides compounds. These compounds in different crystalline phases, NaCl (B1), CsCl (B2), ZB (B3), NiAs (B8[Formula: see text], WZ (B4) and Pnma, were calculated within the generalized gradient approximation (GGA-PBE) and the modified Becke–Johnson approach (mBJ-GGA-PBE) for the exchange–correlation energy and potential. We found that the most stable phase for the KX binary compounds is the nonmagnetic Pnma phase. The calculated lattice parameters, bulk moduli, their first-pressure derivatives and internal parameters are in good agreement with the other theoretical data. The electronic band structure and density of states show that half-metallic and magnetic character arises, which can be attributed to the presence of spin-polarized [Formula: see text] orbitals in the group VI elements. KX ([Formula: see text], Se and Te) compounds, except for KSe and KTe in the CsCl and NiAs phases, show HM character in all phases, with an integer magnetic moment of 1[Formula: see text][Formula: see text] per formula unit and HM gaps.