Bubblepoint calculation

Basieally we need a relationship that permits us to caleulate the vapor eom-position if we know the liquid composition, or vice versa. The most common problem is a bubblepoint calculation calculate the temperature T and vapor composition y, given the pressure P and the liquid composition Xj. This usually involves a trial-and-error, iterative solution because the equations can be solved explicitly only in the simplest cases. Sometimes we have bubblepoint calculations that start from known values of Xj and T and want to find P and yj. This is frequently easier than when pressure is known because the bubblepoint calculation is usually noniterative. 

The problem is best understood by considering an example. One of the most common iterative calculations is a vapor-liquid equilibrium bubblepoint calculation. 

Example of iterative bubblepoint calculation using Newton Raplison algoridim... 

Now using temperature and liquid compositions, we can do a bubblepoint calculation to determine the pressure on the tray P and the vapor composition y . Note that this bubblepoint calculation is usually not iterative since we know the temperature. 

Initial estimates must be made of the top and bottom temperatures so that the A, and 5, can be estimated. These estimates will be adjusted by bubblepoint calculations after b and d have been found by the first iteration. 

The pressure in the reactor is determined by a bubblepoint calculation at the known temperature and liquid composition. Equation (2.73) is used to convert from... 

I Bubblepoint calculation in condenser using Newton-Raphson... 

The holdup in the condenser is assumed to be negligible, so the thermal and composition dynamics are neglected. This means that xcj is equal to y, at each point in time. The condenser process temperature Tc is determined from a bubblepoint calculation from the known pressure Pc and liquid composition xCj. Instantaneous thermal effects mean that the energy balance can be used to calculate the rate of condensation ... 

Although VLE problems with other combinations of variablesare possible, engineering interest centers on dewpoint and bubblepoint calculations there are four classes ... 

This equation finds application in bubblepoint calculations, where the vapor-phase composition is imknown. For a binary system with X2= 1 —xi,... 

Dewpoint and bubblepoint calculations are readily made witlr software packages such as Mathcad and Maple , in wliich iteration is an integral part of an equation-solving routine. Mathcad programs for solution of Ex. 10.3, parts ( aitlirough(d), are given in App. D,2. 

Thus for bubblepoint calculations, where the are known, the problem is to find the set of A -... 

Thus for bubblepoint calculations, where die liquid-phase composition is known, the problem is to find die set of K-values diat satisfies Eq. (14.53). A block diagram of a computer program forBUBL P calculations is shown by Fig. 14.8. 

The last equation relates the vapor composition to the liquid composition for a constant relative volatility multicomponent system. Of course, if relative volatilities are not constant, this equation cannot be used. What is required is a bubblepoint calculation, which is discussed in Section 1.5. 

Let us assume that the liquid and vapor phases are both ideal (y/ = 1 and oj = 1). In this situation, the bubblepoint calculation involves an iterative calculation to find the temperature T that satisfies the equation... 

Consider the distillation column shown in Figure S-7. where all the non-keys are HNKs. Note that the column is now numbered from the bottom up, since that is the direction in which we will step off stages. With no LNK, a good first guess of concentrations can be made at the bottom of the column, and we can start the stage-by-stage calculations by calculating the reboiler tenperature and the values of yj R from a bubble-point calculation. For the bubblepoint calculation, we want to find the tenperature that satisfies the stoichiometric equation. 

The vapor-liquid equilibrium is assumed ideal. Column pressure P is optimized for each case. With pressure P and tray hquid compositions x j known at each point in time on each tray, the temperature T and the vapor compositions y j can be calculated. This is a bubblepoint calculation and can be solved by a Newton-Raphson iterative convergence method. 

The vapor compositions and temperatures on each tray are computed using bubblepoint calculations with Eqs. (16.4) and (16.5). 

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