Dew-point equation

We now derive the dew-point equation from the same basic statement of vapor-liquid equilibrium, starting with equation (9.3), in the previous section ... 

This is the dew-point equation for a three-component system. 

Equilibrium equations including the bubble-point and dew-point equations. 

The bubble- and dew-point equations. The equilibrium equation (Eq. 4.3) and the composition constraint [Eq. (4.1)] are combined to get the bubble-point equation,... 

The bubble-point and dew-point equations are used in some of the solution methods to help determine the stage temperature. 

The theta method. This method has been primarily applied to the Thiele-Geddes equations but a form of the theta method equation has also been applied to the equations of the Lewis-Matheson method. The main independent variable of the method is a convergence promoter, theta (or 6). The convergence promoter 0 is used to force an overall component and total material balance and to adjust the compositions on each stage. These new compositions are then used to calculate new stage temperatures by an approximation of the dew- or bubble-point equation called the Kb method. The power of the Kb method is that it directly calculates a new temperature without the sort of failures that occur when iteratively solving the bubble- or dew-point equations. 

When the liquid phase is ideal, Ki depends only on the temperature, the pressure, and the vapor composition. The procedure for determining the dew point in such a case is to (1) guess a temperature (2) calculate the Kt, which equal f°/iP, where is the fugacity of pure liquid i at the system temperature and pressure, , is the fugacity coefficient of the i th species in the vapor phase, and P is the system pressure and (3) check if the preceding dew-point equation is satisfied. If it is not, repeat the procedure with a different guess. 

In this method, the equations describing the system are all solved simultaneously using, for instance, the Newton-Raphson technique. Applied to phase boundary conditions, the basic relationships in Equations 2.7, 2.8, and 2.12 take a special form. Since / is either zero at the bubble point or one at the dew point. Equation... 

Since this is the dew point, the gas-phase composition is essentially the overall composition, and therefore we have the following dew point equation ... 

In this method the equations desalbing the system are all solved simultaneously using, for instance, the Newton-Raphson technique. Applied to phase boundary conditions, the basic relationships in Equations 2.7, 2.8, and 2.12 take a spedal form. Since y/ is either zero at the bubble point or one at the dew point. Equation 2.7 reduces to the trivial relationship Z = Xj or Z = Yj. Equation 2.8 need not be involved in the simultaneous solution of the system equations. Once the phase boundary conditions are determined, this equation may be solved independently to calculate the heat duty required to bring the feed to its bubble point or dew point. Thus, the only equation to be solved for bubble or dew point calculations is Equations 2.12. 

Related Calculations. When the liquid phase is nonideal, the K values depend on the liquid composition, in this case the dew composition, which is not known. The procedure then is to guess both the liquid composition and the temperature and to check not only whether the dew-point equation is satisfied, but also whether the values of Xj calculated by the equations x,- = y,- /Ki are the... 

Is science really this easy Much of the science applied to process engineering is straightforward. In order to show you how to calculate the temperature of the vapor leaving the depropanizer in Fig. 14.4, we will use the dew-point equation. 

Dew-point equation Used to predict when a vapor will start to condense. 

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