Modified Raoult S Law Activity Coefficient Equation

BRIWSA3Yc/hqdefault.jpg' alt='Modified Raoult S Law Activity Coefficient Equation' title='Modified Raoult S Law Activity Coefficient Equation' />Distillation is the most widely used method of separating fluid mixtures on a commercial scale, it is thus an important part of many processes in the oil and chemical industries. Many of the tall, thin towers which may be seen in an oil refinery or chemical plant are distillation columns. The most common column diameter is about 2. Column heights may be as much as 3. The advantages of distillation are a High purity products b Economies of scale c Well established technology and competitive supply of equipment d Use of low temperature, low cost energy e Well suited for energy integration into the surrounding process. It is generally accepted that if it is possible to achieve a separation by distillation, then distillation will be the most economical method to use. Unless azeotropes are formed see below, this means that nearly all mixtures where all components have a molecular weight between 1. Low molecular weight fluids with a critical temperature below 5. C may not be condensed by cheap cooling water, and the additional costs associated with refrigerated or cryogenic distillation may mean that another separation process will be cheaper, at least for small scale operation. Large molecular weight materials may thermally decompose or polymerize at their boiling temperature even when distilled under a high vacuum. Within the 4. 0 to 1. In 1. 99. 2, Darton estimated the world wide throughput of distillation columns as Oil Refining, 5 billion tonnes per year and petrochemicals, 1. This article describes how distillation columns work, what they contain and how they are designed. CE 201 Earth Materials and Processes 2034 Earth Materials Structure of Solid Earth, Rock cycle, Common rock forming minerals, Types of rocks and its. Bubble Point and Dew Point with Raoults Law Key concept. When calculating either a bubble point or a dew point, one quantity is key, and this is the overall. This study guide deals with the application of thermodynamics to the description of the properties of materials. Spreading coefficient, Gibbs adsorption equation and electrical properties of interfaces. SCHEME OF EXAMINATION. Raoults law. An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture. The separation of a mixture by distillation depends on the difference between the compositions of a boiling liquid mixture and the vapor mixture in equilibrium with the liquid. For example, the equilibrium line in Figure 1a correlates the mole fraction of benzene in the vapor, y, in equilibrium with x, the mole fraction of benzene in the liquid for a binary mixture of benzene and toluene. Benzene is more volatile than toluene i. A distillation column with a boiler at the bottom and a condenser at the top provides a means of countercurrent contact between the rising vapor and the descending liquid, such that at all levels the benzene moves from the liquid into the vapor and the toluene moves from the vapor into the liquid. Thus, benzene concentrates at the top of the column and toluene at the bottom. For some mixtures, a constant boiling mixture or azeotrope exists where the composition of the vapor is the same as that of the liquid. For example, the equilibrium line of benzene and ethanol shown in Figure 1b has an azeotrope at 0. This is a low boiling point azeotrope, i. Separation is limited by the composition of the azeotrope. The prediction of vapor liquid equilibria ab initio from the molecular structure of the mixture components is not yet possible because a there is no complete molecular theory of liquids and b the equations of state for mixtures of vapors are still essentially empirical. The determination, correlation and prediction of vapor liquid equilibrium have been studied for at least a century and is the subject of specialist texts Walas 1. Reid et al. 1. 97. Collections of experimental data are available Gmehling and Onken 1. The brief outline of the subject which follows includes the definition of parameters used in designing distillation columns. For an ideal liquid mixture in contact with a low pressure vapor, the equilibrium compositions may be predicted from Raoults and Daltons Law, so that for a component, i. For nonideal liquids and higher pressures approaching but less than the critical pressure, it is necessary to introduce additional terms so that Eq. The vapor phase fugacity coefficient i may be estimated from a suitable equation of state. The liquid phase activity coefficient is more difficult to predict but if some experimental data are available, methods derived from the Gibbs Duhem Equation are available for predicting or correlating changes in activity coefficients with composition. Activity Coefficients may be predicted from the molecular groups of the components by methods such as the UNIFAC method, now widely used Fredenslund et al. A review of methods of predicting vapor liquid equilibrium V. L. E. is presented by Prausnitz Prausnitz 1. The two most commonly used ways of exploiting V. L. E. in column calcuations are those of the Equilibrium Constant or K value, and relative volatility, a. The K value provides a linear relationship for each component between its concentrations in the vapor and liquid, that is y Kx. Thus from Eq. 1 or 1a. A components K value thus varies with both temperature and pressure. In general, either temperature or pressure is specified. The procedure for calculating the composition of, say, the vapor in equilibrium with a known composition multicomponent liquid is based on adjusting by trial the other variable, such that yi 1. Kixi. In distillation column calculations, the variable is usually temperature so that the equilibria calculations yield a column temperature profile. The complex nature of this calculation means that nowadays all multicomponent column designs are done by means of computer based numerical methods see, for example, Prausnitz et al. Relative volatility is defined as the ratio of the K value of one component to that of another, that is. For ideal mixtures, ij PvtiPvtj. Both vapor pressures Pvti and Pvtj depend strongly on temperature, but their ratio, ij, is often relatively constant throughout the column. Relative volatility provides an estimate of the difficulty of a particular separation, i. The dependence of vapor pressures on temperature provides the link between the difficulty of a particular separation and the difference in normal boiling points of the components, i. C difference for easy separation 1C difference, difficult separation. A difficult separation requires a large column and a large energy input. Design of Distillation Columns. The procedure is introduced by first considering a binary mixture Figure 2 shows a distillation column. Some of the liquid from the condenser at the top of the column, Lc, is returned as reflux. The reflux ratio is defined as the ratio of the liquid returned to the column divided by the liquid removed as product, i. R LcD. Figure 2 also shows the column as a series of theoretical plates. A theoretical plate is defined as a vapor liquid contacting device such that the vapor leaves it in equilibrium with the liquid which leaves it. The first stage of column design is to calculate a the column reflux ratio and b the number of theoretical plates. The theoretical plates in Figure 2 are numbered from the top of the column, and streams leaving a plate in equilibrium have the number of that plate. Thus, stream V2 leaving plate 2 has vapor concentration y. L2 has liquid concentration x. If y. 2 and x. 2 refer to benzene in the benzene toluene binary mixture, then y. Figure 1a. A mass balance may be used to obtain a relationship between the concentrations of any component in the streams passing each other countercurrently between the plates and the product streams leaving the ends of the column. Thus for the column section above the feed in Figure 2, between plates 1 and 2. How to determine K Values Campbell Tip of the Month. Modeling and design of many types of equipment for separating gas and liquids such as flash separators at the well head, distillation columns and even a pipeline are based on the phases present being in vapor liquid equilibrium. The thermodynamic equilibrium between vapor and liquid phases is expressed in terms equality of fugacity of component i in the vapor phase, fi. V, and the fugacity of component i in the liquid phase, fi. L, is written as. Equation 1 is the foundation of vapor liquid equilibrium calculations however, we rarely use it in this form for practical applications. For calculation purposes, Eq. Ki is called the vaporliquid equilibrium ratio, or simply the K value, and represents the ratio of the mole fraction in the vapor, yi, to the mole fraction in the liquid, xi. Equation 2 is also called Henrys law and K is referred to as Henrys constant. For the more volatile components the Kvalues are greater than 1. Depending on the system under study, any one of several approaches may be used to determine K values. Obviously, experimental measurement is the most desirable however, it is expensive and time consuming. Alternatively, there are several graphical or numerical tools that are used for determination of K values. This Tip of the Month presents a history of many of those graphical methods and numerical techniques. In general K values are function of the pressure, temperature, and composition of the vapor and liquid phases. The components making up the system plus temperature, pressure, composition, and degree of polarity affect the accuracy and applicability, and hence the selection, of an approach. The widely used approaches are K value charts, Raoults law, the equation of state Eo. S approach f, activity coefficient approach or combination of Eo. S and the Eo. S and Eo. S approach requires use of a digital computer. K Value Charts. There are several forms of K value charts. One of the earliest K value charts for light hydrocarbons is presented in reference 1. In these charts, K values for individual components are plotted as a function of temperature on the x axis with pressure as a parameter. In each chart the pressure range is from 7. Pa 1. 0 to 1. 00. C 4. 0 to 5. 00 F. Early high pressure experimental work revealed that, if a hydrocarbon system of fixed overall composition were held at constant temperature and the pressure varied, the K values of all components converged toward a common value of unity 1. This pressure was termed the Convergence Pressure of the system and has been used to correlate the effect of composition on K values, thus permitting generalized K values to be presented in a moderate number of charts. In more recent publications 2, the K values are plotted as a function of pressure on the x axis with temperature and Convergence Pressure as parameters. In order to use these charts, one should determine the Convergence Pressure first. The determination of convergence Pressure is a trial and error procedure and can be found elsewhere 6. For computer use, later in 1. K Value charts were curve fitted to the following equations by academic and industrial experts collaborating through the Natural Gas Association of America 7. In Eq 3 T is temperature in R, P is pressure in psia and the fitted values of the bij coefficients are reported in an NGAA publication 7. A relatively simple nomograph is normally presented in undergraduate thermodynamics and unit operations text books. In the nomograph, the K values of light hydrocarbons, normally methane through n decane, are plotted on one or two pages. Charts of this type do allow for an average effect of composition, but the essential basis is Raoults law and equilibrium constants derived from them are useful only for teaching and academic purposes. Raoults Law. Raoults Law is based on the assumptions that the vapor phase behaves as an ideal gas and the liquid phase is an ideal solution. Under these conditions the fugacities are expressed as. The saturation pressure of a component is represented by Pi. Sat and the pressure of the system is represented by P. Substituting from Eqs 4 and 5 in Eq 1 gives. The vapor pressure may be read from a Cox chart or calculated from a suitable equation in terms of temperature. A typical Cox chart may be found in reference 8. The Antoine 5 equation is recommended for calculating vapor pressure Values of A, B, and C for several compounds are reported in the literature 5. Complex vapor pressure equations such as presented by Wagner 5, even though more accurate, should be avoided because they can not be used to extrapolate to temperatures beyond the critical temperature of each component. Raoults law is applicable to low pressure systems up to about 5. MPa or to systems whose components are very similar such as benzene and toluene. This method is simple but it suffers when the temperature of the system is above the critical temperature of one or more of the components in the mixture. At temperatures above the critical point of a component, one must extrapolate the vapor pressure which frequently results in erroneous K values. In addition, this method ignores the fact that the K values are composition dependent. Correlation Method. As mentioned earlier, determination of K values from charts is inconvenient for computer calculations. Therefore, scientists and engineers have developed numerous curve fitted expressions for calculation of K values. However, these correlations have limited application because they are specific to a certain system or applicable over a limited range of conditions. Some of these are polynomial or exponential equations in which K values are expressed in terms of pressure and temperature. One of these correlations presented by Wilson 9, is where Tci, critical temperature, in R or K, Pci, critical pressure, in psi, k. Pa or bar, i is the acentric factor, P is the system pressure, in psi, k. Pa or bar, T is the system temperature, in R or K. P and Pc, T and Tc must be in the same units. This correlation is applicable to low and moderate pressure, up to about 3. Epac Controller Manual. MPa 5. 00 psia, and the K values are assumed to be independent of composition. Eo. S Approach. The fugacity of each component is determined by an Eo. S. In other words, both phases are described by only one Eo. S. It is a powerful tool and relatively accurate if used appropriately. This approach is widely used in industry for light hydrocarbon and non polar systems. Under these conditions the fugacities are expressed by. The fugacity coefficients for each component in the vapor and liquid phases are represented by V and i. L, respectively. Substitution of fugacities from Eqs 9 and 1. Eq 1 gives. The Eo. S method has been programmed in the GCAP for Volumes 1 2 of Gas Conditioning and Processing Software to generate K values using the SRK Eo. S 1. 0. Eo. S Activity Coefficient Approach. The approach is based on an Eo. S which describes the vapor phase non ideality through the fugacity coefficient and an activity coefficient model which accounts for the non ideality of the liquid phase. This approach is widely used in industry for polar systems exhibiting highly non ideal behavior. Under these conditions the fugacities are expressed by. The fugacity coefficients for each component in the vapor phase are represented by fi.