Three-Parameter Modification of the Peng-Robinson Equation of State To Peng-Robinson Equation of State To Improve Volumetric Predictions Summary. The Peneloux-Rauzy-Freze (PRF) method of improving volumetric predictions by introducing a third parameter into a two-parameter equation predictions by introducing a third parameter into a two-parameter equation of state (EOS) is applied to the Peng-Robinson EOS (PR-EOS). The modified PR-EOS is evaluated for application to hydrocarbon fluids. A method is PR-EOS is evaluated for application to hydrocarbon fluids. A method is developed for characterizing the third parameter for the heptanes-plus fractions. The usefulness of the modified PR-EOS in improving volumetric predictions is illustrated by applying the equation to several crude-oil predictions is illustrated by applying the equation to several crude-oil and gas-condensate systems from the literature. Introduction In recent years, two-parameter cubic EOS's--e.g., the PR-EOS and the Soave-Redlich-Kwong EOS (SRK-EOS)-have been commonly used by the petroleum industry for predicting the phase behavior and volumetric properties of hydrocarbon fluid mixtures. Once the heptane-plus fraction of the hydrocarbon fluid is properly characterized into a mixture of pseudocomponents, these equations predict the vapor/liquid equilibrium conditions with a reasonable accuracy. However, the volumetric estimates obtained through these two-parameter EOS's are not as accurate. In our experience with the application of the PR-EOS to reservoir fluids, we found that the error in the prediction of gas-phase z factors ranged from 3 to 5 % and the error in the liquid density predictions ranged from 6 to 12 %. Recently, Peneloux et al. developed a method of improving the volumetric predictions by introducing a third parameter into a two-parameter cubic EOS. This method is particularly attractive because the third parameter does not change the vapor/liquid equilibrium conditions determined by the unmodified, two-parameter equation, but modifies the phase volumes by effecting certain translations along the volume axis. Thus, if a given reservoir fluid is already characterized for use in some two-parameter EOS, the application of the PRF method to this fluid requires characterization of only the third parameter. In this work, we apply the PRF method to the PR-EOS. Some background material on the PRF method is given in the next section. For the modified three-parameter PR-EOS, the section Third- Parameter Characterizations for the PR-EOS presents the Parameter Characterizations for the PR-EOS presents the third-parameter values for some lighter hydrocarbons and develops a correlation for characterizing the third parameter for the heptane-plus fractions of reservoir fluids. To apply the modified, three-parameter PR-EOS to calculate the phase and volumetric behavior of reservoir fluids, PR-EOS to calculate the phase and volumetric behavior of reservoir fluids, the section on Applications develops a novel, two-step procedure for characterizing all three parameters for the procedure for characterizing all three parameters for the heptane-plus fractions. The first step characterizes the two parameters of the unmodified PR-EOS with the phase-behavior data derived from the analysis of conventional laboratory experiments. The second step adjusts the correlation coefficients of the third-parameter correlation mentioned earlier, using the heptane-plus density data a standard conditions. Also presented in this section is the application of the modified PR-EOS to several crude-oil and gas-condensate systems. PRF Method PRF Method Consider one mole of a mixture of n components of composition zi, at temperature T and pressure p, obeying an EOS of the formwhere V is the molar volume. Assuming that at the thermodynamic equilibrium, the mixture may split at most into two distinct phases, we can determine the phase properties by solving the following wellposed system of (2n + 3) equations in (2n + 3) unknowns. The equations areandwhere the unknowns are fL, xi, yi, V, and Vg. Here fL denotes the mole fraction of liquid phase. (xi, V ) and yi, Vg) denote the composition and the molar volume of the liquid and gas phases, respectively. Eqs. 2 and 4 apply to each Component i and thus pose 2n equations in total. Subscripts and superscriptsand g denote the liquid and gas phases, respectively. Eq. 4 is the thermodynainic-equilibrium condition for each Component i and equates the fugacity of each component in equilibrium phases. Phi i is the fugacity coefficient for Component i and can be evaluated from the functional form of the Eq. 1 EOS. Eq. 2 is the material-balance equation for each component, while Eq. 3 represents the overall material balance. Eqs. 5 and 6 related the molar volume of each equilibrium phase to its composition, temperature, and pressure through the Eq. 1 EOS. pressure through the Eq. 1 EOS. Two-parameter cubic EOS's mentioned earlier form Eq. 1 as a third-degree polynomial in molar volume V and have two mixture parameters, a and b, related to the component parameters, ai and bi, parameters, a and b, related to the component parameters, ai and bi, through the following mixing rules:andSPERE P. 1033

This paper describes the first comprehensive inter-well field trial of low-salinity EOR. The objective of the trial was to demonstrate that reduced-salinity waterflooding works as well at inter-well distances as it does in corefloods and single well tests. The trial was designed to evaluate two risks: 1) whether mixing or other mechanisms prevent achievement of reduced-salinity improved recovery in the reservoir and 2) whether the adverse mobility ratio between the injected water and the oil bank causes viscous fingering – resulting in mobilized oil being left behind. The demonstration was implemented in a single reservoir zone at the Endicott field (North Slope Alaska). The trial involves an injector and a producer 1040 feet apart. The producer was monitored for changes in watercut and ionic composition. In December 2007, produced saline water was injected to pre-flood the pattern until watercut was over 95%. Reduced-salinity water injection commenced June 2008. The associated EOR response was detected in the producer after three months. Data from a wellhead watercut meter and fluid samples from a test separator both revealed a clear drop in watercut, from 95% to 92%. The timing of the drop in watercut coincided with the breakthrough of reduced-salinity water at the producer. Incremental reduced-salinity EOR oil recovery timing and volume matched behaviors observed in corefloods and single well tests. By May 2009, 1.3 pore volumes of reduced-salinity water had been injected. The incremental oil recovery is equal to 10% of the total pore volume in the swept area. Initial oil saturation at Endicott is 95%. In the pilot area, tertiary reduced-salinity waterflooding is expected to drop residual oil saturation from 41% to 28%, a 13 unit drop in residual oil. The inter-well field trial demonstrates that the identified risks did not impact performance.

We treat the onset of convective motions for the case in which the base-state density profile is evolving in time. The formulation is in terms of random forcing which we take to be thermodynamic in origin, following our earlier work (see Jhaveri & Homsy 1980). Experimental evidence is reviewed which clearly demonstrates the need for such a stochastic formulation. The randomly forced initial-value problem is solved numerically at high Rayleigh numbers in the mean-field approximation for both a step change and linear temporal increase in surface temperature. The numerical results give both an expected value for the onset time for which convection is measurable and the variance of that expected value. The results are in good agreement with available experiments.

BP has developed a range of innovative techniques to maximize economic oil recovery from its global miscible gas floods and the results have been reported in a series of publications over the past three decades. The purpose of this paper is to provide an overview of BP's experience of establishing, managing and optimizing a miscible gas flood.Prudhoe Bay (Alaska) is the world's largest miscible gas project. Conventional and unconventional methods have been applied in a variety of different settings. An extensive surveillance program has facilitated a good understanding of the processes operating at field scale and surveillance data are used to optimize the flood. In 2000, a large-scale gas cap water injection project was implemented to slow the decline in field pressure. This project has made the vaporization process more efficient at higher pressure, resulting in additional recovery. Miscible gas injection has been extended to numerous other fields on the North Slope of Alaska.BP has two active miscible gas projects in the North Sea: Magnus and Ula. Tertiary miscible water-alternating-gas (WAG) flooding in Magnus field started in 2002 and its impact on reservoir performance is significant and well understood. Tertiary miscible WAG injection in Ula field started in 1998 and has played a key role in arresting production decline. The WAG scheme in Ula is currently being expanded. In addition to these projects, BP operates a CO 2 injection and storage project at In Salah, Algeria, where more than 3.2 million tonnes of CO 2 have been stored since 2004.Miscible gas injection has generated considerable benefits for BP over the past three decades and will continue to do so. The potential availability of large sources of CO 2 in the future, supplied by carbon capture, could help maintain a leading role for miscible gas injection for years to come. IntroductionMiscible flooding is a proven method for enhancing oil recovery. The principle is to reduce the interfacial tension between the displacing solvent and displaced oil and thereby achieve a significant reduction in the residual oil saturation compared to immiscible water flooding and primary depletion. Under ideal conditions, miscible flooding can recover almost 100% of the oil originally in place. Under field conditions, this limit is seldom achieved owing to imperfect volumetric sweep, incomplete displacement of oil in rock that is swept and inadequate capture of displaced oil (Stalkup, 1983). In addition, commercial factors may limit the amount of miscible gas that is available. Despite these limitations, there are many successful miscible gas projects around the world and the prospects for miscible flooding in the future look bright if new sources of CO 2 become available for enhanced oil recovery.