Peng liquid density

Of the cubic EoS given in Table 2-354, the Soave and Peng-Robinson are the most accurate, but there is no general mle for which EoS produces the best estimated volumes for specific fluids or conditions. The Peng-Robinson equation has been better tuned to liquid densities, while the Soave equation has been better tuned to vapor-liquid equilibrium and vapor densities. In solving the cubic equation for volume, a convenient initial guess to find the vapor root is the ideal gas value, while an initial value of 1.05h is convenient to locate the liquid root. 

The liquid density calculated from the Soave EoS is 24.2 percent below the DIPPR 801 recommended value of 29.69 kmol/m, while that calculated from the Peng-Robinson EoS is 13.9 percent below the recommended value. 

This equation (Peng and Robinson, 1976) was developed with the goal of overcoming some of the deficiencies of the Soave equation, namely its inaccuracy in the critical region and in predicting liquid densities. The equation is similar to the Soave equation in that it is cubic in the volume, expresses its parameters in terms of the critical temperature, critical pressure, and acentric factor, and is based on correlating pure-component vapor pressure data. The equation is written as... 

The Peng-Robinson equation is widely used for the same applications as the Soave equation. Although it may be more accurate than the Soave equation in the critical region and for calculating liquid densities, it is not generally recommended for the latter since better methods for predicting liquid densities are available. 

Peng and Robinson report the results of comparisons of their equation with Soaves. They find that the two equations give similar values for gas densities and gas-phase enthalpy deviations, but that the Peng-Robinson equation yields improved correlation of pure-component vapor pressures and better estimates of liquid densities. 

The Soave-Redlich-Kwong equation is rapidly gaining acceptance by the hydrocarbon processing industry. Further developments, such as that of Peng and Robinson,are likely to improve predictions of liquid density and phase equilibria in the critical region. In general however, use of such equations appears to be limited to relatively small, nonpolar molecules. Calculations of phase equilibria with the S-R-K equations require initial estimates of the phase compositions. 

All cubic EOS discussed perform poorly concerning the liquid density, where the parameter a or, respectively, the a-function have a negligible influence. Figure 2.17 illustrates the deviations of the liquid molar volume at Tr = 0.7 for the Soave-Redlich-Kwong and the Peng-Robinson equation of state. The 40 substances regarded are characterized by their critical compressibility... 

This work presents a temperature-dependent volume translated model for Peng-Robinson equation of state (PR EOS) for calculating liquid densities of pure compounds and mixtures in the saturated region. For pure compounds, the average absolute percent deviation (AAPD) were calculated in the reduced temperature range of (0.3-0.99). Similarly for mixtures, the (AAPD) of different binary, ternary and multicomponent mixtures were determined. The AAPD for 29 pure compounds and different mixtures(binary, ternary and multicomponents) were 1.29 and 1.35 respectively. The accuracy of this model was compared well with three well-known liquid density correlations and other earlier volume translated models. 

This equation improves the liquid density prediction, but still cannol describe volumetric behavior around the critical point because of fundamental reason that will be discussed later. There are thousands of cubic equations of states, and many noncubic equations. The non cubic equations such as the Benedict-Webb-Rubin equation (1942) ant its modification by Starling (1973) have a large number of constants they describe accurately the volumetric behavior of pure substances But for hydrocarbon mixtures and crude oils, because of mixing rub complexities, they may not be suitable (Katz and Firoozabadi, 1978) Cubic equations with more than two constants also may not improv the volumetric behavior prediction of complex reservoir fluids. In fact most of the cubic equations have the same accuracy for phase-behavio prediction of complex hydrocarbon systems the simpler equation often do better. Therefore, the discussion will be limited to the Peng... 

Predictions of saturated liquid densities of pure fluids from the Soave-Redlich-Kwong equation of state and, to a lesser extent, the Peng-Robsinson equation of state deviate from experimental data. This should be expected given the... 

Ahlers, J. Gmehling, J. (2001). Development of an universal group contribution equation of state. I. Prediction of liquid densities for pure compounds with a volume translated Peng-Robinson equation of state. Fluid Phase EcjuiUb., Vol.191, pp. 177 -188... 

Use the Peng-Robinson equation of state to calculate the vapor pressure of ethane at 32°F. Also, calculate the densities of the liquid and gas at 32°F. Compare your answers with values from Figures 2-7, 2-12, and 3-3. 

Use the Peng-Robinson equation of state to calculate the compositions and densities of the equilibrium liquid and gas of the mixture given below at 160°F and 2000 psia. Use binary interaction coefficients of 0.02 for methane-n-butane, 0.035 for methane-n-decane, and 0.0 for n-butane-n-decane. 

Example Estimate the molar density of liquid and vapor saturated ammonia at 353.15 K, using the Soave and Peng-Robinson EoS. 

Figure 5.T4 Calculated densities of the gas and liquid phases at P-T conditions along the SLV line for the naphthalene-xenon system using the Peng-Robinson equation with two mixture parameters fitted to the SLV line (McHugh et al., 1988).

Using one of the Peng-Robinson equation-of-state programs in Appendix B with the liquid (high-density) root, we obtain for/i-pentane... 

For the given values of p and T, calculate the liquid-vapor equilibrium for the mixture with the composition (20.13), and also the density and the molecular weights of liquid and gaseous phases, using the Peng-Robinson equation of state (see Section 5.7) ... 

Teletzke et al. (1982) used Equation 2.50 and the Peng-Rohinson equation of state (Peng and Robinson, 1976) to calculate density profiles for various values of the temperature T and bulk density n. They found that below the saturation density n ° relatively thick films can form near the solid when the temperature is below but not too far from the critical temperature of the fluid. Under these conditions the gradient energy contribution is relatively small, as would be expected in the neighborhood of the critical point. For densities above b°. where the bulk phase is a liquid-vapor mixture, the liquid completely wets the solid (i.e., there is no equilibrium contact angle). 

---