Bubble point calculation

Example 3 Detv and Bubble Point Calculations As indicated by Example 2a, a binary system in vapor/liquid equilibrium has 2 degrees of freedom. Thus of the four phase rule variables T, P, x, and t/i, two must be fixed to allow calculation of the other two, regardless of the formulation of the equilibrium equations. Modified Raoults law [Eq. (4-307)] may therefore be applied to the calculation of any pair of phase rule variables, given the other two. 

The necessary vapor pressures and activity coefficients are supplied by data correlations. For the system acetone(l)/n-hexane(2), vapor pressures are given by Eq. (4-142), the Antoine equation  

When T and Xi are given, the calculation is direct, with final values for vapor pressures and activity coefficients given immediately by Eqs. (A), (B), and (C). In all other cases either T or Xi or both are initially unknown, and calculations require trial or iteration. 

Because y = Xf for the azeotropic state, tti2 = 1. Substitution for the two ratios by Eq. (4-307) provides an equation for calculation of tti2 from the thermodynamic functions  

Given values are italic calculated results are boldface. 

The most common VLE problem is to calculate the temperature and vapor composition yj that is in equilibrium with a liquid at a known total pressure of the system P and with a 

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For the special case of a bubble-point calculation (incipient vaporization), a is 0 (also Q = 0) and Equation (7-13) becomes... 

Application of these equations gives the results in Table 13-12. A set of T is calculated from the normahzed by bubble-point calculations. Corresponding values of are obtained from y = K x. Once newA. andT are available, new values of Vn are calculated from energy balances by using data from Maxwell (Data Book on Hydiocaihons, Van Nostrand, Princeton, N.J., 1950). First, an estimate of condenser duty is computed from an energy balance around the condenser. 

Why not put new lyrics to an old tune This is an excellent idea, and many have done this very thing. Rice" started w ith the Smith-Brinkley raethod" used to calculate distillation, absorption, extraction, etc., overhead and bottoms compositions, and developed distillation equations for determining the liquid composition on any tray. This together with bubble point calculations yield a column temperature profile useful for column analysis. 

As discussed by Franks (1972), in order to solve this system of equations, a value of temperature T must be found to satisfy the condition that the difference term 6 = P - Zpj is very small, i.e., that the equilibrium condition is satisfied. This is known as a bubble point calculation. The above system of defining equations, however represent, an implicit algebraic loop and the trial and error solution procedure can be very time consuming, especially when incorporated into a dynamic simulation program. 

The highly interactive nature of the balance and equilibria equations for the distillation period are depicted in Fig. 3.66. An implicit, iterative algebraic loop is involved in the calculation of the boiling point temperature at each time interval. This involves guessing the temperature and calculating the sum of the partial pressures, or mole fractions. The condition required is that Zyi + yw = 1. The iterative loop for the bubble point calculation is represented by the five interconnected blocks in the lower right hand corner of Fig. 3.66. The model of Prenosil (1976) also included an efficiency term E for the steam heating, dependent on liquid depth L and bubble diameter D. 

BUBBLE - Bubble Point Calculation for a Batch Distillation Column... 

As in Example BSTILL, a column containing four theoretical plates and reboiler is assumed, together with constant volume conditions in the reflux drum. The liquid behaviour is, however, non-ideal for this water-methanol system. The objective of this example is to show the need for iterative calculations required for bubble point calculations in non-ideal distillation systems, and how this can be achieved with the use of simulation languages. 

For convenience, only four stages were used in this model. An iterative solution is required for the bubble point calculations and this is based on the half-interval method. A FORTRAN subroutine EQUIL, incorporated in the ISIM program, estimates the equilibrium conditions for each plate. The iteration routine was taken from Luyben and Wenzel (1988). The program runs very slowly. 

The heating period begins with FLAG set initially to zero. When Xy > 1 then FLAG becomes 1, and the distillation period begins at statement 10. At each time interval the subroutine TCALC is used to make the iterative bubble point calculation. The component mass balance determines the removal of volatiles in the vapour, where the total molar flow rate, V, is determined from the energy balance. 

The program continues with a subroutine for the bubble point calculation, which is given on the diskette. 

Bubble-point calculation, feed (liquid feed)... 

If the K-value requires the composition of both phases to be known, then this introduces additional complications into the calculations. For example, suppose a bubble-point calculation is to be performed on a liquid of known composition using an equation of state for the vapor-liquid equilibrium. To start the calculation, a temperature is assumed. Then, calculation of K-values requires knowledge of the vapor composition to calculate the vapor-phase fugacity coefficient, and that of the liquid composition to calculate the liquid-phase fugacity coefficient. While the liquid composition is known, the vapor composition is unknown and an initial estimate is required for the calculation to proceed. Once the K-value has been estimated from an initial estimate of the vapor composition, the composition of the vapor can be reestimated, and so on. 

Table 4.10 Bubble-point calculation for a methanol-water mixture using the Wilson equation. 

Table 4.9 Bubble-point calculation for an ideal methanol-water mixture.

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

Bubble point calculation, 24 680, 685 Bubble process, 23 408 Bubble shapes, 11 776-777 in foams, 12 7—11... 

BDPEBB = limit of accuracy on bubble point calculation, tKx must be... 

For a liquid liquid mixture of given composition and at a given temperature (or pressure) the pressure (or temperature) at which the first bubble of vapour phase appears and its composition is calculated (bubble point calculation). 

The pressure in the drum is still fixed at 122 psia. So, it seems as if we will have to run the drum hotter. But how much hotter Suppose we raise the drum temperature to 160°F, and repeat our bubble-point calculation ... 

The Library Studio Developer s Kit further extends Library Studio by embedding Microsoft s Visual Basic for Applications (VBA) into the Library Studio application. With VBA, the user can import data from statistical packages, such as DOE, or export data for further manipulation, such as a bubble point calculation. Additionally, modifications to the Library Studio user interface are possible via custom add-ins, such as commands to produce automated designs or validate a design intended for a particular instrument. 

Calculate the sum on the lefithand side of Eq. (1.15) for bubble-point calculation. If smaller than uuity, increase temperature. If greater than unity, decrease temperature. Rapeat steps 2 and 3 until converged. 

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