An efficient modelling technique based on the representation of the precipitated asphaltene as a pure dense phase is presented. The success of the approach is based on the division of the heaviest component in the oil into a nonprecipitating and a precipitating component.The characterization of these components is discussed. This model was able to make quantitative predictions of experimental data from the literature as well as additional data from industry. This was achieved with only a small number of adjustable parameters (two or three). The mechanistic aspect of the model with regards to colloidal nature of asphaltene/resin micelles is also discussed. An algorithm for three-phase flash calculations with asphaltene precipitation is described.

An efficient modelling technique based on the representation of the precipitated asphaltene as a pure dense phase is presented. The success of the approach is based on the division of the heaviest component in the oil into a nonprecipitating and a precipitating component.The characterization of these components is discussed. This model was able to make quantitative predictions of experimental data from the literature as well as additional data from industry. This was achieved with only a small number of adjustable parameters (two or three). The mechanistic aspect of the model with regards to colloidal nature of asphaltene/resin micelles is also discussed. An algorithm for three-phase flash calculations with asphaltene precipitation is described.

Two cubic equations of state (EOS) have been adopted to compute multicomponent two-phase compressibility, CO 2 /water and hydrocarbon/water phase behavior, and gas-and liquid-phase densities. The equations used in this paper are the Schmidt-Wenzel (SW) EOS and the Peng-Robinson (PR) EOS. While these cubic equations have the same form, the SW is reported to be more accurate for predicting hydrocarbon gas-and liquid-phase densities. Density predictions are compared with experimental data to confirm the superiority of the SW EOS.The use of EOS to predict equilibrium phase compositions of water/hydrocarbon and water/C0 2 systems is discussed. For the water/hydrocarbon systems, the aqueous-phase interaction coefficient between water and the dissolved component shows a strong temperature dependency, while in the gas phases, a constant value of interaction coefficient is adequate. In the case of the CO 2 /water systems, the interaction coefficients for both the aqueous and gas phases show temperature dependency.A scheme to compute the two-phase compressibility of multicomponent reservoir fluid systems is also introduced. Our results show the expected sharp change in the compressibility during phase change. Such computations are required in some reservoir simulators.

Optimum binary interaction parameters and volume translation factors for a number of paraffinic, naphthenic and aromatic compounds for the Schmidt-Wenzel and the Peng-Robinson equations of state have been determined. Summary In this work, optimum binary interaction parameters for a number of paraffinic, naphthenic and aromatic hydrocarbon compounds and CO2 for the Peng-Robinson and the Schmidt-Wenzel equations of state have been determined and trends with respect to temperature, and molecular size and type have been examined. The capability of the two equations of state for liquid density predictions has been assessed and a volume translation approach to improve density predictions has been evaluated. predictions has been evaluated Introduction Design of separation processes using supercritical CO2 and numerical simulation of CO2 enhanced oil recovery (EOR) processes require the calculation of phase equilibria for mixtures of CO2 and various hydrocarbon components of interest. Generalized cubic equations of state (EOS) like the Redlich-Kwong-Soave (RKS) Peng-Robinson (PR) have been used extensively for modeling Peng-Robinson (PR) have been used extensively for modeling CO2-hydrocarbon systems. The Schmidt-Wenzel (SW) EOS, a more general cubic equation of state was developed to improve liquid density predictions compared to the PR and the RKS equations, while giving virtually the same equilibrium compositions. Each of the equations of state predicts phase behavior of pure components given only the critical properties of the component and its acentric factor. For the accurate prediction of properties of mixtures, binary interaction parameters are also required. A number of studies of the interaction parameter for the RKS and the PREOS have been reported in the literature. Kato et al. formulated a correlation for the interaction parameter in the PREOS in terms of temperature and the acentric factor of the hydrocarbon component after studying CO2-n-alkane binary systems. Turek et al., reported interaction parameters for the RKSEOS for a number of binary CO2-paraffin systems and few aromatic systems and attempted to correlate them using acentric factors for the hydrocarbon component. Lin studied the binary interaction parameters in the PREOS for a number of CO2-hydrocarbon systems parameters in the PREOS for a number of CO2-hydrocarbon systems (predominantly n-alkanes with a few naphthenic and aromatic compounds), and concluded that an interaction parameter of 0.125 was better for all chemical types than using any of the correlations that had been reported. Nishiumi et al. correlated the binary interaction parameters for the PREOS between various groups such as the hydrocarbons, CO2, hydrogen sulfide, nitrogen etc. in terms of the absolute difference between the acentric factors of each component and the ratio of the critical molar volumes of the two components. Valderrama et al. determined the interaction parameters for five EOS for a limited number of CO2-n-alkane systems and correlated them either as a function of temperature or in terms of the acentric factor of the hydrocarbon component and temperature. Even though the phase compositions can be predicted accurately by using the proper interaction parameters, this does not ensure the matching of liquid phase molar volumes or densities. In fact, it has been well documented that the cubic equations of state do not predict accurately the densities of the liquid phases. Volume translation approaches have been used to correct for the phase densities while keeping the compositions unchanged. In the context of CO2-hydrocarbon phase behavior, most of the work reported so far deals with n-alkane systems and a very limited number of naphthenic or aromatic systems. The behavior of heavier n-alkanes has not been studied carefully. In this work, we report optimal binary interaction parameters for an extensive number of systems, n-alkanes (ranging from C1 - C32), naphthenic compounds and aromatic compounds for the SWEOS and the PREOS. These optimal values were obtained by using a nonlinear PREOS. These optimal values were obtained by using a nonlinear least squares algorithm on a specific predetermined criterion. When the liquid phase densities calculated from the equations of state were not adequately close to the experimental densities, volume translations for either only the CO2 component or both the CO2 and the hydrocarbon component were used to match the experimental and the predicted densities. The performance of the two equations of state in matching both the phase compositions and phase densities is compared in the subsections that follow. Theory Cubic equations of state are normally used in vapor-liquid equilibrium calculations for mixtures of non-polar and slightly polar components. In a recent article, the state of VLE polar components. In a recent article, the state of VLE computations using EOS has been reviewed. The RKSEOS and the PREOS are the most commonly used cubic equations of state. PREOS are the most commonly used cubic equations of state. In view of the fact that the SWEOS proved superior to the PREOS for predictions of hydrocarbon liquid-phase densities, it was used in this work and the PREOS was used for comparison purposes. The SWEOS is a more generalized form of a cubic EOS. However, data requirements for the three EOS are the same (critical pressure and temperature and the acentric factor), but the SWEOS pressure and temperature and the acentric factor), but the SWEOS gives component dependent critical compressibility factors. Details about the PR and SW EOS (the equations, the mixing rules and all the relevant parameters) can be found in the original references and are not reproduced here. The detailed phase equilibria calculations are described elsewhere. The most frequently used equations of state, the SRKEOS and the PREOS usually predict the vapor phase density of hydrocarbon mixtures well, but do not predict the liquid phase density adequately.

Couyt.gnl 1987 Soc,ely of Pwfoloum EngmeefsTh,s paper was p!cparcw Iof prescmlabon a! !hc? timth SPE Sympcmum on Reswvo,r S,mu$alml hcl~m San Anlomo. Texas. February 1-4. 1987 Th,s P3PIY was selected 10, prwcn!alron by an SPE Program Comm,ltee fol10wIn9 rewew Of mfo,mahon contained m an abSIfaCt submitted by !De aulhOr(S) Contents ot me paper as presente' have not been rewewed by the SOc,e!y of Petroleum Engineers and are Sublecl 10 UJrfeC!lOn by Ihe i3tilh0 r(S) Tho mater.,1 as presenleci does not necessaf!ly IefleC! any posmon of lhe SOcfety of Pelroleum Engineers. IIS Otficers 01 members Papers p,esen!ed al SPE meetings are subject to pvbhcat:on rewew by Ed,lo,:al Comm,llees of Ihe Society of Petroleum Engmeets Permmon to copy IS ,eslt,c led 10 an abS1,W1 01 cot more man 30+3 woms Hlusl, atrons may nol be co!3:ed The absrracl should contain cons~,cuoua acknowledgment Of where and by wnom me paper ,s presented Wie Publications Manager SPE. P O Box 833836. R,chatclson. TX 75083-3836 Telex. 730989 SPFDAL ABSTRACTThis paper examines the iela:ive strengths and weaknesses of solving a fully compositional isothermal three phase numerical simulotor by two fundamentally different approaches. One of [hc me[hods considered is based on the standard Newton-R:iphson Froccdure where the partial derivatives for all the pertinent equa[ions are written wi[h respect to a selected set of primary variitbles in a Jacobian mm-ix. This model can be solved fully implicitly as CXNS did, or implicidy for pressure and explicitly for saturation and composition (IMPEM) m Fussull and Fussell or Young and Stephenson did. The altr.mative method, first proposed by Acs et al., is based on a volume balimce where in each simulator block, the pore volumes arc equaled with the fluid volumes. AS Originally prcsposcd, [his method was also an IMPEM one, but Waus later extended it 10 include a sequential step implicit in saturation. As yet, no computational results have been published for this volume balimce method.The Young and Stephenson model is compared with the l\lPEM method of Acs et al. as well as the sequential method of Watts. The main area rsf comparison is the relative ease or difficulty with which each simulator handles v@ous compositional problems. The advantages and disadvantages of usink either method under differen: circumstances are discussed. A: WCII, the performance of these simulators in their corresponding black oil forms is compared.Both mode!s can be run using either the Peng Robinson, So~ve-Rcdlich-Kwong, or Schmidt-Wenzel equations of state. All the derivatives needed in both mwtels can b-e solved explicitly from analytical expressions that have been derived from these equa[ions of state.