Associating fluids predictions

The geochemical interactions possible between an injected waste and the reservoir rock and its associated fluids can be quite complex. Thus a combination of computer modeling, laboratory experimentation, and field observation will inevitably be necessary to satisfy current regulatory requirements for a geochemical no-migration deep-well injection. This section covers the computer methods and models available for predicting geochemical fate. 

The van der Waals and Platteeuw method has been extended to flash programs by a number of researchers (Bishnoi et al., 1989 Cole and Goodwin, 1990 Edmonds et al., 1994, 1995 Tohidi et al., 1995a Ballard and Sloan, 2002). These flash calculations predict the equilibrium amount of the hydrate phase relative to associated fluid phases. 

The contribution "Application of Meso-Scale Field-based Models to Predict Stability of Particle Dispersions in Polymer Melts" by Prasanna Jog, Valeriy Ginzburg, Rakesh Srivastava, Jeffrey Weinhold, Shekhar Jain, and Walter Chapman examines and compares Self Consistent Field Theory and interfacial Statistical Associating Fluid Theory for use in predicting the thermodynamic phase behavior of dispersions in polymer melts. Such dispersions are of quite some technological importance in the... 

Gordon, P.A. (2001b) Statistical associating fluid theory. 2. Estimation of parameters to predict Lube-ranged isoparaffin properties. Ind. Eng. Chem. Res., 40, 2956-2965. 

Empirical relationships between gas character and fluid properties allow the prediction of the phase and fluid properties of untested (and sometimes unlogged) hydrocarbon-bearing zones. The 5 C and dryness (e.g. C / XlCi... C3) of associated and free gases correlate with a number of fluid properties, including phase, API gravity and saturation pressure. These same trends can be recognized in the mud gas hydrocarbon and dryness data and, once calibrated with the MDT information, predictions can be made for untested zones. When integrated with ancillary information (when available) such as reservoir pressure, show information and wireline log data, these empirically based phase and fluid predictions are extremely accurate. 

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

For the application of supercritical carbon dioxide as a medium for the production of polyolefins, it is important to have rehable thermodynamic data for the systems involved. Knowledge of the phase behavior of the reaction mixture is crucial to properly choose process variables such as temperature and pressure in order to achieve maximum process efficiency. For this reason, the ethylene-poly (ethylene-co-propylene) (PEP)-C02 system has been taken as a representative model system [3]. The effect of molecular weight as well as the influence of CO2 on the phase behavior has been studied experimentally by cloud-point measurements. In addition, the Statistical Associating Fluid Theory (SAFT) has been applied to predict the experimental results. 

All of the cubic equations of state presented so far are generally termed two-parameter equations of state. In this respect, each one of them predicts a constant compressibility factor at the critical point Zc=PcVd T, irrespective of the nature of the compound for van der Waals Zc = 0.375, for Redlich-Kwong and Soave-Redlich-Kwong Zc = 0.333 and for Peng-Robinson Zc = 0.307. The actual values may vary significantly, especially for polar and associating fluids for methane Zc = 0.286, for propane Zc = 0.276, for pentane and benzene Zc = 0.268 and for water Zc = 0.229. To correct for this deficiency, a number of authors have proposed three or four adjustable parameters to the cubic equation of state. The most popular three-parameter cubic equation of state was proposed by Patel and Teja is given by ... 

The modern cubic equations of state provide reliable predictions for pure-component thermodynamic properties at conditions where the substance is a gas, liquid or supercritical. Walas and Valderrama provided a thorough evaluation and recommendations on the use of cubic equation of state for primary and derivative properties. Vapour pressures for non-polar and slightly polar fluids can be calculated precisely from any of the modem cubic equations of state presented above (Soave-Redlich-Kwong, Peng-Robinson or Patel-Teja). The use of a complex funetion for a (such as those proposed by Twu and co-workers ) results in a significant improvement in uncertainty of the predicted values. For associating fluids (such as water and alcohols), a higher-order equation of state with explicit account for association, such as either the Elliott-Suresh-Donohue or CPA equations of state, are preferred. For saturated liquid volumes, a three-parameter cubic equation of state (such as Patel-Teja) should be used, whereas for saturated vapour volumes any modern cubic equation of state can be used. 

While the DGT-based SAFT approach is easy to implement and can provide a good representation of the surface tension of pure fluids and mixtures, it typically requires the use of empirical adjustable parameters, the so-called influence parameters, which limit the predictive ability of the method. In contrast, DFT treatments, although more complex and numerically more demanding, do not rely on adjustable parameters to provide information on the interfacial properties. Chapman was the first to suggest the possibility of incorporating a SAFT-like description of associating fluids within a DFT... 

NRHB model can be used to predict the monomer fractions (fractions of non-hydrogen-bonded molecules) of pure self-associating fluids and their mixtures with inert solvents. According to the formalism of von Solms et al. [70], the fraction of nonbonded molecules for a pure self-associating fluid is given by the following equation ... 

Experimental data including the acidic species in the vapor phase within the above concentration range are scarce. Only very few publications of VLE data in that range are available [168, 173]. In contrast, numerous vapor pressure curves are accessible in literature. Chemical equilibrium data for the polycondensation and dissociation reaction in that range (>100 wt%) are so far not published [148]. However, a starting point to describe the vapor-Uquid equilibrium at those high concentratirMis is given by an EOS which is based on the fundamentals of the perturbation theory of Barker [212, 213]. Built on this theory, Sadowski et al. [214] have developed the PC-SAFT (Perturbed Chain Statistical Associated Fluid Theory) equation of state. The PC-SAFT EOS and its derivatives offer the ability to be fuUy predictive in combination with quantum mechanically based estimated parameters [215] and can therefore be used for systems without or with very little experimental data. Nevertheless, a model validation should be undertaken. Cameretti et al. [216] adopted the PC-SAFT EOS for electrolyte systems (ePC-SAFT), but the quality for weak electrolytes as phosphoric... 

To conclude, predictive cubic EoS (PPR78, PR2SRK, PSRK, VTPR, UMR-PR) make a perfect job to simulate the phase behaviour of crude oils, gas condensate and natural gases. For processes in which water and/or glycol are present (e.g. transportation processes), it is advised to use more complex EoS like the CPA (Cubic-Plus-Association) by (Derawi et al., 2003) or equation deriving from the SAFE (Statistical Associating Fluid Theory) which are however non predictive (many parameters have to be fitted on experimental data). 

The polymer solutions warrant use of a special class of lattice models sueh as Flory-Huggins. For eorrelation purposes Sanchez-Lacombe method is usually sufficient, but one may also use Statistical Association Fluid Theory (SAFT) models to obtain a more accurate representation and predictive power in expense of computational burden. A more comprehensive treatise of structure of the models are given by Aslam and Sunol" as shown in Figure 20.1.13. 

Contemporary Approaches. Numerous advanced theories have been formulated in the last decades to reproduce or even predict experimental findings for polymer containing mixtures. Most of them are particularly suitable for the description of some phenomena and special kinds of systems, but all have in common that they have lost the straightforwardness characterizing the Flory-Huggins theory. The following, incomplete collocation states some of the wider used approaches These are the different forms of the lattice fluid and hole theories (38), the mean field lattice gas model (39), the Sanchez-Lacombe theory(40), the cell theory (41), various perturbation theories (42), the statistical-associating-fluid-theory (43) (SAFT), the perturbed-hard-sphere chain theory (44), the... 

Bias, F. J. Vega, L. F. (1998b). Prediction of Binary and Ternary Diagrams Using the Statistical Associating Fluid Theory (SAFT) Equation of State. Ind. Eng. Chem. Res. 1998,37,660-674. 

Llovell, F. Galindo, A. Bias, F.J. Jackson, G. (2010a). Classical density functional theory for the prediction of the surface tension and interfadal properties of fluids mixtures of chain molecules based on the statistical associating fluid theory for potentials of variable range. /. Chem. Phys. 133,024704 1-19. 

In Section 5.2.8 we shall look at pressure-depth relationships, and will see that the relationship is a linear function of the density of the fluid. Since water is the one fluid which is always associated with a petroleum reservoir, an understanding of what controls formation water density is required. Additionally, reservoir engineers need to know the fluid properties of the formation water to predict its expansion and movement, which can contribute significantly to the drive mechanism in a reservoir, especially if the volume of water surrounding the hydrocarbon accumulation is large. 

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