Bubblepoint Temperature and Pressure

The temperature at which a liquid of known composition first begins to boil is found from the equation 

The problem will be formulated for a specified final pressure and enthalpy, and under the assumption that the enthalpies are additive (that is, with zero enthalpy of mixing) and are known functions of temperature at the given pressure. The enthalpy balance is 

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

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Single-Stage Flash Calculations 375 Bubblepoint Temperature and Pressure 376 Dewpoint Temperature and Pressure 377 Flash at Fixed Temperature and Pressure 377 Flash at Fixed Enthalpy and Pressure 377 Equilibria with Ks Dependent on Composition 377... 

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. 

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. 

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 subcooled-liquid region lies above the upper surface of Fig. 10.1 the superheated-vapor region hes below the under surface. The interior space between the two surfaces is the region of coexistence of both liquid and vapor phases. If one starts with a liquid at F and reduces the pressure at constant temperature and composition along vertical hue F G, the first bubble of vapor appears at point L, which hes on the upper surface. Thus, L is a bubblepoint, and the upper surface is the bubblepoint surface. The state of the vapor brrbble in equilibrium with the hquid at L mrrst be represented by a point on the under surface at the temperature and pressure of L. This point is indicated by V. Line VL is an example of a tie line, which cormects points representing phases in equilibrium. 

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. 

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. 

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

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). 

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. 

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... 

The ethane is much lighter than the methyl chloride, so it accumulates in the condenser and acts essentially like an inert substance that blankets the condenser. The effect of the inert substance can be considered to reduce either (1) the bubblepoint temperature, thus reducing the differential temperature driving force and reducing heat transfer, or (2) the effective heat transfer area. Either effect is a reduction in heat transfer. So if the ethane is not vented off during the batch, the pressure cannot be controlled even with the chilled water valve wide open. 

For a binary (that is, two-component) mixture, if constant-pressure vapor-liquid equilibrium diagrams, such as Fig. 10.1-4 or that of Illustration 10.1-1. have been previously prepared, dewpoint and bubblepoint temperatures can easily be read from these diagrams. For the cases in which such information is not available, or if a multicomponent mixture is of interest, the trial-and-error procedure of Illustration 10.1 -2 is used to estimate these temperatures. 

It is important to note that the reactor operates at the bubblepoint temperature Tr of the liquid in the reactor and the condenser operates at the bubblepoint temperature 7c of the condensed liquid. Reactant components A and B are assiuned to be more volatile than product C, so the liquid in the condenser has more light components than the liquid in the reactor. This difference in compositions and the difference in pressure results in a condenser temperature that is lower than the reactor temperature. 

The third equation is used to provide a pressure-compensated temperature measurement in the methanol column. This is needed because, in the heat-integrated system, the pressure in the methanol column is not controlled. It floats with operating conditions. If more heat transfer is required in the reboiler/condenser, a larger temperature difference is required, and this is achieved by the pressure in the methanol column increasing, which raises the bubblepoint temperature in the reflux drum. 

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-liquid equilibrium is assumed to be ideal and the bubblepoint temperature calculation is used to find the tray temperature (see Table 18.1 for the vapor pressure data of pure components). The column pressure is fixed at 5.1 bar unless otherwise noted. 

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 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 ... 

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