Bubblepoint

Minimum reflux for binary or psuedobinary mixtures is given by the following when separation is essentially complete (Xd 1) and D / F is the ratio of overhead product and feed rates RmD/F = 1/( a-1), when feed is at the bubblepoint (Rm + 1)D/F = a/(a-1), when feed is at the dewpoint. 

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 reactors shown in Fig. 3.1 would operate at atmospheric pressure if they were open to the atmosphere as sketched. If the reactors are not vented and if no inert blanketing is assumed, they would run at the bubblepoint pressure for the specified temperature and varying composition Therefore the pressures could be different in each reactor, and they would vary with time, even though temperatures are assumed constant, as the C s change. 

Let us look now at vapor-liquid systems with more than one component. A liquid stream at high temperature and pressure is flashed into a drum, i.e., its pressure is reduced as it flows through a restriction (valve) at the inlet of the drum. This sudden expansion is irreversible and occurs at constant enthalpy. If it were a reversible expansion, entropy (not enthalpy) would be conserved. If the drum pressure is lower than the bubblepoint pressure of the feed at the feed temperature, some of the liquid feed will vaporize. 

A single feed stream is fed as saturated liquid (at its bubblepoint) onto the feed tray N,. See Fig. 3.12. Feed flow rate is F (mol/min) and composition is z (mole fraction more volatile component). The overhead vapor is totally condensed in a condenser and flows into the reflux drum, whose holdup of hquid is Mj) (moles). The contents of the drum is assumed to be perfectly mixed with composition Xo The liquid in the drum is at its bubblepoint Reflux is pumped back to the top tray (iVj-) of the column at a rate R. Overhead distillate product is removed at a rate D. 

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

Example 4.1. We are given the pressure P and the hquid composition x. We want to find the bubblepoint temperature and the vapor composition as discussed in Sec. 2.2.6. For simphcity let us assume a binary system of components 1 and 2. Component 1 is the more volatile, and the mole fraction of component 1 in the hquid is x and in the vapor is y. Let us assume also that the system is ideal Raoult s and Dalton s laws apply. 

Newton-Raphson amounts to using the slope of the function curve to extrapolate to the correct value. Using the bubblepoint problem as a specific example, let us define the function f Ty... 

The technique requires the evaluation offthe derivative of the function jjj., with respect to temperature. In our bubblepoint example this can be... 

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

An appropriate multicomponent bubblcpoint subroutine must be used. This may be a little more complex because of nonidealities, but as far as the main program is concerned, the bubblepoint subroutine is provided with known liquid compositions and a known pressure, and its job is to calculate the temperature and vapor compositions. 

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. 

Overhead from the first fractionator is condensed and charged to the second tower. There substantially pure propylene oxide is taken overhead. The bottoms is dumped. Tower pressure is 15 psig, and the overhead bubblepoint is 100°F. Reactions are... 

As many as six stages are represented on Figure 7.30, combined with interstage condensers in several ways. Barometric condensers are feasible only if the temperature of the water is below its bubblepoint at the prevailing pressure in a particular stage. Common practice requires the temperature to be about 5°F below the bubblepoint. Example 7.13 examines the feasibility of installing intercondensers in that process. 

The individual stage pressures and corresponding water bubblepoint temperatures from the steam tables are... 

When barometric condensers are used, the effluent water temperature should be at least 5°F below the bubblepoint at the prevailing pressure. A few bubblepoint temperatures at low pressures are ... 

A mixture with initial dewpoint 139.9°C and final bubblepoint 48.4°C is to be condensed with coolant at a constant temperature of 27°C. The gas film heat transfer coefficient is 40 W/m2 K and the overall coefficient is 450. Results of the calculation of the condensing curve are... 

Forced circulation reboilers may be either horizontal or vertical. Since the feed liquid is at its bubblepoint, adequate NPSH must be assured for the pump if it is a centrifugal type. Linear velocities in the tubes of 15-20 ft/sec usually are adequate. The main disadvantages are the costs of pump and power, and possibly severe maintenance. This mode of operation is a last resort with viscous or fouling materials, or when the fraction vaporized must be kept low. 

Representative x-y diagrams appear in Figure 13.4. Generally they are plots of direct experimental data, but they can be calculated from fundamental data of vapor pressure and activity coefficients. The basis is the bubblepoint condition ... 

In order to relate yx and xu the bubblepoint temperatures are found over a series of values of xv Since the activity coefficients depend on the composition of the liquid and both activity coefficients and vapor pressures depend on the temperature, the calculation requires a respectable effort. Moreover, some vapor-liquid measurements must have been made for evaluation of a correlation of activity coefficients. The method does permit calculation of equilibria at several pressures since activity coefficients are substantially independent of pressure. A useful application is to determine the effect of pressure on azeotropic composition (Walas, 1985, p. 227). 

The problems of interest are finding the conditions for onset of vaporization, the bubblepoint for the onset of condensation, the... 

Similarly, when Eq. (13.27) represents the effect of pressure, the bubblepoint pressure is found with the N-R algorithm ... 

At temperatures and pressures between those of the bubblepoint and dewpoint, a mixture of two phases exists whose amounts and compositions depend on the conditions that are imposed on the system. The most common sets of such conditions are fixed T and P, or fixed H and P, or fixed S and P. Fixed T and P will be considered first. 

The procedure will be described only for the case of bubblepoint temperature for which the calculation sequence is represented on Figure 13.5. Equations (13.8) and (13.32) are combined as... 

The liquid composition is known for a bubblepoint determination, but the temperature is not at the start, so that starting estimates must be made for both activity and fugacity coefficients. In the flow diagram, the starting values are proposed to be unity for all the variables. After a trial value of the temperature is chosen, subsequent calculations on the diagram can be made directly. The correct value of T has been chosen when E X = 1-... 

Figure 13.5. Calculation diagram for bubblepoint temperature Walas, Phase Equilibria in Chemical Engineering, Butterworths,...

Bubblepoint Temperature with the Virial and Wilson Equations... 

A mixture of acetone (1) + butanone (2) + ethylacetate (3) with the composition x1 = x2 = 0.3 and x3 = 0.4 is at 20 atm. Data for the system such as vapor pressures, critical properties, and Wilson coefficients are given with a computer program in Walas (1985, p. 325). The bubblepoint temperature was found to be 468.7 K. Here only the properties at this temperature will be quoted to show deviations from ideality of a common system. The ideal and real K, differ substantially. 

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. 

BP (bubblepcdnt) methods. Temperatures are corrected iteratively by determinations of bubblepoints. The method is satisfactory for mixtures with relatively narrow ranges of volatilities. The parent program of this type is that of Wang and Henke (1966) which is flowsketched on Figure 13.17 and described in the next section. The availability of a FORTRAN program was cited earlier in this section. 

Box 1. Initial estimates of the temperature are made by taking linear variation between estimated overhead dewpoint and bottoms bubblepoint. The vapor rates are estimated on the basis of constant molal overflow with due regard to input or output sidestreams. 

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