Mass balance vapor-liquid equilibrium

These equations can be solved simultaneously with the material balance equations to obtain x[, x, xf and x1,1. For a multicomponent system, the liquid-liquid equilibrium is illustrated in Figure 4.7. The mass balance is basically the same as that for vapor-liquid equilibrium, but is written for two-liquid phases. Liquid I in the liquid-liquid equilibrium corresponds with the vapor in vapor-liquid equilibrium and Liquid II corresponds with the liquid in vapor-liquid equilibrium. The corresponding mass balance is given by the equivalent to Equation 4.55 ... 

Even though a feasible mass balance has been set up, there is no guarantee that vapor-liquid equilibrium will... 

If pressure shift cannot be exploited, then the next option is to add an entrainer to the mixture that interacts differently with the components in the mixture to alter the vapor-liquid equilibrium behavior in a favorable way. When dealing with ternary systems, the mass balance and vapor-liquid equilibrium behavior can be represented on a... 

In general, the formulation of the problem of vapor-liquid equilibria in these systems is not difficult. One has the mass balances, dissociation equilibria in the solution, the equation of electroneutrality and the expressions for the vapor-liquid equilibrium of each molecular species (equality of activities). The result is a system of non-linear equations which must be solved. The main thermodynamic problem is the relation of the activities of the species to be measurable properties, such as pressure and composition. In order to do this a model is needed and the parameters in the model are usually obtained from experimental data on the mixtures involved. Calculations of this type are well-known in geological systems O) where the vapor-liquid equilibria are usually neglected. 

Vapor-Liquid Equilibrium Dissociation Balances Mass Balances Electroneutrality Deviations to Ideality... 

Physical Properties The on equilibrium-stage simulation are i and enthalpies these same properties are needed for nonequilibrium models as well. Enthalpies are required for the energy balance equations vapor-liquid equilibrium ratios are needed for the calculation of driving forces for mass and heat transfer. The need for mass- (and heat-) transfer coefficients means that nonequilibrium models are rather more demanding of physical property data than are equilibrium-stage models. These coefficients may depend on a number of other physical properties, as summarized in Table 13-12. 

Take a mixture of two or more chemicals in a temperature regime where both have a significant vapor pressure. The composition of the mixture in the vapor is different from that in the liquid. By harnessing this difference, you can separate two chemicals, which is the basis of distillation. To calculate this phenomenon, though, you need to predict thermodynamic quantities such as fugacity, and then perform mass and energy balances over the system. This chapter explains how to predict the thermodynamic properties and then how to solve equations for a phase separation. While phase separation is only one part of the distillation process, it is the basis for the entire process. In this chapter you will learn to solve vapor-liquid equilibrium problems, and these principles are employed in calculations for distillation towers in Chapters 6 and 7. Vapor-liquid equilibria problems are expressed as algebraic equations, and the methods used are the same ones as introduced in Chapter 2. 

What happened to the mass balances when you introduced a purge stream (You can run it without carbon dioxide, too.) What happened to the mass balances when vapor-liquid equilibrium was required Did the ratio of nitrogen to hydrogen in the recycle stream change Why or why not What if you had to solve the Rachford-Rice equation in the separator, the chemical equilibrium equation in the reactor, and set the purge fraction to maintain a maximum mole fraction of carbon dioxide in the inlet to the reactor. Could you do that all in Excel Would it converge Speculate. 

The column section can be solved by simultaneous solution of the component mass balance and energy balance equations and the vapor-liquid equilibrium relations. Additional equations include the temperature, pressure, and composition dependence of the equilibrium coefficients and enthalpies. The equations for stage j are as follows ... 

Unlike the binary case, the choice of two keys does not give determinate mass balances, because not all other mole fractions are calculable by mass balances alone and equilibrium calculations are required to calculate the concentrations of the dew-point vapor from the top plate and the bubble-point liquid leaving the reboiler. 

While the design of distillation columns can be quite complicated, we will consider only the simplest case here. The simplificadons we will use are that vapor-liquid equilibrium will be assumed to exist on each tray (or equilibrium stage) and in the reboiler, that the column operates at constant pressure, that the feed is liquid and will enter the distillation column on a tray that has liquid of approximately the same composition as the feed, that the molar flow rate of vapor V is the same throughout the column, and that the liquid flow rate L is constant on all trays above the feed tray, and is constant and equal to L -b F below the feed tray, where F is the molar flow rate of the feed to the column, here assumed to be a liquid. The analysis of this simplified distillation column involves only the equilibrium relations and mass balances. This is demonstrated in the illustration below. 

Note the difference between this method of calculation and the one used in the previous illustration. There we did vapor-liquid equilibrium calculations only for the conditions needed, and then solved the mass balance equations analytically. In this illustration we first had to do vapor-liquid equilibrium calculations for all compositions (to construct the. t- v diagram), and then for this binary mixture we were able to do all further calculations graphically. As shown in the following discussion, this makes it easier to consider other reflux ratios than the one u.sed in this illustration. 

A mass balance determines the equilibrium composition of vapor and liquid which are used to calculate a new set of equilibrium K-ratios. These steps are repeated until the K-ratios and the vaporized fraction do not vary. The tolerance of the function f(V/F), set to less than 10"4, was sufficient for most cases. 

Forty years ago these computed variables were calculated using pneumatic devices. Today they are much more easily done in the digital control computer. Much more complex types of computed variables can now be calculated. Several variables of a process can be measured, and all the other variables can be calculated from a rigorous model of the process. For example, the nearness to flooding in distillation columns can be calculated from heat input, feed flow rate, and temperature and pressure data. Another application is the calculation of product purities in a distillation column from measurements of several tray temperatures and flow rates by the use of mass and energy balances, physical property data, and vapor-liquid equilibrium information. Successful applications have been reported in the control of polymerization reactors. 

The set of Equations 25.42-25.48 can be solved provided the following information is available vapor-liquid equilibrium data, for example, the ternary equilibrium data for a typical esterification reaction mass and enthalpy balances around the feed point, reflux inlet, and reboiler to account for the flow rates, compositions, and thermal conditions of the external streams mass transfer coefficients in the absence of reaction (either by experimental determination or estimation from available correlations) liquid holdup (usually from available correlations) and an expression for the reaction rate. Then the equations can be solved by any convenient method, preferably the Runge-Kutta routine, to get the mole fraction of each component as a function of height. 

The McCabe-Thiele approach for a binary mixture can be described as follows. First, we take the vapor-liquid equilibrium diagram y/x plot). Then we draw the operating lines based on the mass balance for the liquid and the vapor phase. There is one operating line for the stripping section and one for the top (rectification or enriching) section. The assumption of (in each case) constant molar flows of liquid and vapor ensures strictly straight operating lines. 

These calculations combine vapor-liquid equilibrium relationships with total mass and component balances. Material of known composition Zj is fed into a flash drum at a known rate of F mols/min. Both the temperature and the pressure in the drum are given. Variables that are unknown are liquid and vapor compositions and liquid and vapor flow rates. See Figure 2.12. 

Figure 7.6 shows the variables involved in a differential distillation process. For a binary system, there are four the moles liquid in the still or boiler at any instant W and its mole fraction the rate of vapor withdrawal D (moles/s) and the instantaneous vapor composition The mass balances and the equilibrium relation yg = /(x ) provide only three of the required equations. For the fourth we must draw on an energy balance. This stands to reason, because the rate of vapor production D will evidently depend on... 

The properties of dissolution as gas solubility and enthalpy of solution can be derived from vapor liquid equilibrium models representative of (C02-H20-amine) systems. The developments of such models are based on a system of equations related to phase equilibria and chemical reactions electro-neutrality and mass balance. The non ideality of the system can be taken into account in liquid phase by the expressions of activity coefficients and by fugacity coefficients in vapor phase. Non ideality is represented in activity and fugacity coefficient models through empirical interaction parameters that have to be fitted to experimental data. Development of efficient models will then depend on the quality and diversity of the experimental data. 

According to equation (2.3), the Henry s law constant can be estimated by measuring the concentration of X in the gaseous phase and in the liquid phase at equilibrium. In practice, however, the concentration is more often measured in one phase while concentration in the second phase is determined by mass balance. For dilute neutral compounds, the Henry s law constant can be estimated from the ratio of vapor pressure, Pvp, and solubility, S, taking the molecular weight into consideration by expressing the molar concentration ... 

There are several characteristics common to the describing equations of all types of multicomponent, vapor-liquid separation processes, both single- and multi-stage, that make it possible to exploit the inside-out concept in similar ways to solve them efficiently and reliably. The equations have as common members component and total mass balance, enthalpy balance, constitutive and phase equilibrium equations. In addition, all such processes require K-value or fugacity coefficient and vapor and liquid enthalpy models. In all cases the describing equations have similar forms, and depend on the primitive variables (temperature, pressure, phase rate and composition) in essentially the same ways. Before presenting the inside-out concept, it will be useful to identify two classes of conventional methods and discuss their main characteristics. 

For a total condenser, the vapor composition used in the equilibrium relations is that determined during a bubble point calculation based on the actual pressure and liquid compositions found in the condenser. These vapor mole fractions are not used in the component mass balances since there is no vapor stream from a total condenser. It often happens that the temperature of the reflux stream is below the bubble point temperature of the condensed liquid (subcooled condenser). In such cases it is necessary to specify either the actual temperature of the reflux stream or the difference in temperature between the reflux stream and the bubble point of the condensate. 

If we count the equations listed, we will find that there are 2n + 4 equations per stage. However, only 2 n + 3 of these equations are independent. These independent equations are generally taken to be the n component mass balance equations, the n equilibrium relations, the enthalpy balance, and two more equations. These two equations can be the two summation equations or the total mass balance and one of the summation equations (or an equivalent form). The 2n + 3 unknown variables determined by the equations are the n vapor mole fractions the n liquid mole fractions, the stage temperature 7 and the vapor and liquid flow rates LJ and Ly. Thus, for a column of 5 stages, we must solve s 2n + 3) equations. 

The solution of a flash problem requires the satisfaction of material balances in addition to the equilibrium between the vapor and the liquid. Let us take 1 mole of total feed as a basis and denote the number of moles of liquid formed as and the number of moles of vapor formed as v Overall mass balance requires... 

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