1 can be used to get the values of fiL and fiV in Equation 5. In estimating vapor-liquid equilibria K values, Fig. Values of f/P for the less-than-unity reduced isotherms were extended to higher than saturation pressure using some experimental vapor-liquid equilibrium data. The plot is a composite of the work of Lewis, Kay, and Newton. 1 shows a generalized chart for f/P as a function of Tr and Pr1. Fugacitiesį/P values for pure components have been found from generalized correlations of pressure-volume-temperature data. Integrating the right hand side of Equation 10 and rearranging gives Equation 11.Īssuming VL to be independent of pressure over the range involved results in Equation 12.
Equation 9, therefore, shows fugacity for a pure liquid at a total pressure equal to its vapor pressure.2 The subscript p* on a fugacity denotes the fugacity at a pressure equal to the vapor pressure.Įquation 10 shows the basic definition of fugacity. A pure component is in equilibrium with its vapor only at a pressure equal to the vapor pressure of the liquid. The fugacity of a component in the liquid state is identical with its fugacity in the vapor with which the liquid is in equilibrium. Setting f = p at p = 0 enables canceling the two indeterminate terms in the integration.
Subtracting Equation 6 from Equation 7 and integrating from p = 0 to p = p, and rearranging gives Equation 8. For a nonideal gas, Equation 7 applies, in which fugacity is substituted for pressure.2 Pure vaporįor an ideal gas, Equation 6 holds true. Kideal is a function of system temperature and pressure and independent of composition. fiL and fiV are the fugacities of component i in the pure liquid or vapor states at the system temperature and pressure. Click here to enlarge imageįor ideal solutions for which Amagat’s Law of additive volumes holds, the fugacities iL and iV can be found with Equations 3 and 4, which are known as the Lewis and Randall Fugacity Rule.1Ĭombining Equations 2-4 gives the relationship in Equation 5 for ideal K values. An expression for Ki formulated in terms of the fugacity equality is Equation 2. The bar above f signifies value of fugacity in a mixture. The superscripts, V and L, indicate vapor and liquid phases, respectively, and the subscript i denotes a given component.
Depriester chart for equilibrium tv#
The equilibrium phase distribution ratio (K value) is defined in Equation 1 (see attached equation box).įor a system in equilibrium, TV = TL, PV = PL, and iV = iL Other methods require looking up charts or figures, where accuracy can be compromised. For preliminary design work and checking performance of existing columns, however, K values for multicomponent systems based on system pressure and temperature suffice.ĭepriester nomographs do not explain the basis how the K values are obtained.
Depriester chart for equilibrium software#
The K values thus obtained depend on pressure and temperature of the multicomponent system and not on concentration.Ĭoncentration-dependent K values can be calculated from empirical correlations involving lengthy calculations or from equations of state using commercial software because hand calculations are unwieldy. Depriester nomographs can be used to obtain estimates of K values. This article also explains the first principles for calculating K values from fugacity of real gases and liquids.Ī K value is required whenever one designs a distillation column or assesses the performance of an operating column. The proposed method, therefore, requires looking up only one chart-the generalized fugacity chart (which is a well-spaced-out chart and can be read accurately) and the rest of the calculations use equations, thus enabling rapid calculation. The method is based on the generalized fugacity charts of Lewis, Kay, and Newton, and uses reduced temperatures and pressures as parameters.Ī third-degree polynomial is prepared from Lu’s chart for calculating liquid molarity, which is used for calculating liquid phase fugacity from fugacity of saturated liquid. A new method to estimate equilibrium phase distribution ratios (K values) improves on the shortcomings of older methods.