Pressure-Specified Bubble Point

BUDEP calculates the bubble-point pressure or the dew-point pressure for a mixture of N components (N j< 20) at specified temperature and liquid or vapor composition. The subroutine also furnishes the composition of the incipient vapor or liquid and the vaporization equilibrium ratios. 

For a given drum pressure and feed composition, the bubble- and dew-point temperatures bracket the temperature range of the equilibrium flash. At the bubble-point temperature, the total vapor pressure exerted by the mixture becomes equal to the confining drum pressure, and it follows that X = 1.0 in the bubble formed. Since yj = KjXi and since the x/s stiU equal the feed concentrations (denoted bv Zi s), calculation of the bubble-point temperature involves a trial-and-error search for the temperature which, at the specified pressure, makes X KjZi = 1.0. If instead the temperature is specified, one can find the bubble-point pressure that satisfies this relationship. 

After the model is built, the program can be generated and compiled. At execution time, the user has considerable flexibility and we chose to predict the bubble point pressure for a fixed temperature and specified total svstem composition in order to compare some of our results with the data of Otsuku (14). Figure 3 presents the results for a system composed of 10.14 wt% CO2 and NH3 at a temperature of 80° where the %C02 in the CO2 and NH3 was varied. 

When the wetting fluid is expelled from the largest pore, a bulk gas flow will be detected on the downstream side of the filter system (Fig. 7). The bubble point measurement determines the pore size of the filter membrane, i.e., the larger the pore the lower the bubble point pressure. Therefore, filter manufacturers specify the bubble point limits as the minimum allowable bubble point. During an integrity test, the bubble point test has to exceed the set minimum bubble point. 

A completely wetted filter membrane provides a liquid layer across which, when a differential pressure is applied, the diffusive airflow occurs in accordance with Fick s law of diffusion (Fig. 8). This pressure is called test pressure and commonly specified at 80% of the bubble point pressure. In an experimental elucidation of the factors involved in the process, Reti simplified the integrated form of Fick s law to read as follows ... 

At the specified temperature, estimate the bubble point pressure and the equilibrium vapor composition using the K-values based on Raoult s law (Equations 2.18 through 2.20). The liquid composition is the same as the feed composition. 

Bubble point temperatures and vapor compositions on a stage are calculated iteratively by assuming a temperature and computing the bubble point pressure. A solution is reached when the calculated pressure matches the specified value (110 kPa). The calculations below demonstrate the final iteration for the solvent feed stage Ng. 

Equation (7-19) is useful for calculating bubble-point temperature at a specified pressure or bubble-point pressure at a specified temperature. 

Stage locations for all feeds stage temperatures (frequently all equal) total flow rates of any side streams and total number of stages. Stage pressures need not be specified but are understood to be greater than corresponding stage bubble-point pressures to prevent vaporization. 

To perform a bubble test, the membrane must be kept constantly wet. Gas, normally N2, is then connected to the inlet side of the filter and the outlet is connected to tubing that is placed into a vessel containing water. As gas is allowed to flow into the filter housing, the pressure is slowly increased using the gas tank regulator. The bubble point is that pressure where a stream of bubbles first appears on the outlet or filtrate side of the membrane. If the measured bubble point pressure is less than the manufacturer s specified value, the membrane has been compromised and should not be used. The bubble point should be recorded prior to start-up and at the end of botding as well as after any interruptions (i.e., upon return from worker break periods). 

Set the vapor fraction to 0 and the temperature to the desired temperature where you want to find out the vapor pressure. Then HYSYS will calculate the pressure the calculated pressure is the vapor pressure (or more precisely the bubble-point pressure = the vapor pressure) at the specified temperature—similarly, if you want to calculate the dew point, set the vapor fraction to 1. The result depends on many parameters, for example, selection of EOS, components in a mixture. Using Antoine equation, the vapor pressure of pure n-hexane at 130°C is 500.2 kPa (Figure 1.9), and the vapor pressure of pure n-heptane, n-octane, and n-nonane is 236 kPa, 113.4 kPa, and 56.33 kPa, respectively. The vapor pressure using Peng-Robinson EOS at 130 is 496 kPa, the same as that obtained by Antoine equation (Figure 1.10). For the gas mixture at 130°C, the vapor pressure is 280 kPa (Figure 1.11). 

If the calculated bubble-point pressme is higher than the specified sales vapor pressure, a higher separation temperature is assumed and the calculations repeated imtil the desired vapor pressure is reached. If the bubble-point pressure is lower than the specified sales product s vapor pressure, the temperature assumed is too high and a lower temperature must be assumed and calculations repeated as before. Separator sizes can be calculated for each separation stage using the principles in the tutorials on two-phase separators and three-phase separators. The cost of the separators can he estimated based on these sizes. 

From Table 13-5 it can be seen that the variables subject to the designer s control are C -i- 3 in number. The most common way to utilize these is to specify the feed rate, composition, and pressure (C -i- 1 variables) plus the drum temperature To and pressure To. This operation will give one point on the equilihrium-flash cuive shown in Fig. 13-26. This cui ve shows the relation at constant pressure between the fraction V/F of the feed flashed and the drum temperature. The temperature at V/F = 0.0 when the first bubble of vapor is about to form (saturated liquid) is the bubble-point temperature of the feed mixture, and the value at V/F = 1.0 when the first droplet of liquid is about to form (saturated hquid) is the dew-point temperature. 

At the dew-point temperature y still equals Zj, and the relationshm X Xi = X i/K-i = 1.0 must be satisfied. As in the case of the bubble point, a trial-and-error search for the dew-point temperature at a specified pressure is involved. Or, if the temperature is specified, the dew-point pressure can be calculated. 

Compute a new set of values of tear variables by computing, one at a time, the bubble-point temperature at each stage based on the specified stage pressure and corresponding normalized values. The equation used is obtained by combining Eqs. (13-69) and (13-70) to eliminate yj j to give... 

Many variations are possible around the basic flash calculation. Pressure and V/F can be specified and T calculated, and so on. Details can be found in King7. However, two special cases are of particular interest. If it is necessary to calculate the bubble point, then V/F = 0 in Equation 4.55, which simplifies to ... 

Thus, to calculate the bubble point for a given mixture and at a specified pressure, a search is made for a temperature to satisfy Equation 4.58. Alternatively, temperature can be... 

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) ... 

Fixed pressure and specified phase fraction (i.e., dew and bubble points)... 

The bubble point is defined as that hydrocarbon component condition at which the system is all liquid, with the exception of only one drop (infinitely small) of vapor present. The amount of vapor is specified as a matter of convenience so that the composition of the liquid is the composition of the total system. This means that if we want to find the bubble point of a liquid composition, we simply flash it for a very small amount of vapor specified. You can do this with the RefFlsh program quickly by trial and error. How Simply try varied temperatures with the pressure held constant. The program RefFlsh will tell you if your temperature is out of the phase envelope by stating SYSTEM IS ALL... 

There are three basic phase equilibrium calculations (1) a flash calculation - phase split at specified conditions, (2) bubble point calculation, and (3) dew point calculation. For bubble and dew points, there are two types of calculations. First, the temperature is specified and the pressure is calculated. The alternative occurs when the pressure is specified and the temperature is calculated. 

For a total condenser, the vapor composition used in the equilibrium relations is that determined during a bubble point calculation based on the actual pressure and liquid compositions found in the condenser. These vapor mole fractions are not used in the component mass balances since there is no vapor stream from a total condenser. It often happens that the temperature of the reflux stream is below the bubble point temperature of the condensed liquid (subcooled condenser). In such cases it is necessary to specify either the actual temperature of the reflux stream or the difference in temperature between the reflux stream and the bubble point of the condensate. 

Explain in your own words the terms bubble point, boiling point, and dew point of a mixture of condensable species, and the difference between vaporization and boiling. Use Raoult s law to determine (a) the bubble-point temperature (or pressure) of a liquid mixture of known composition at a specified pressure (or temperature) and the composition of the first bubble... 

The problems of interest are finding the conditions for onset of vaporization, the bubble-point for the onset of condensation, the dewpoint and the compositions and the relative amounts of vapor and liquid phases at equilibrium under specified conditions of temperature and pressure or enthalpy and pressure. The first cases examined will take the A, to be independent of composition. These problems usually must be solved by iteration, for which the Newton-Raphson method is suitable. The dependence of K on temperature may be represented adequately by... 

A conventional bubble point calculation involves the specification of the liquid mole fractions and pressure the subsequent computation of the vapor-phase mole fractions and the system temperature. For a binary system (and only for a binary system) we may specify the temperature and pressure and compute the mole fractions of both phases. Thus, our first step is to estimate the interface temperature T. The second step is to solve the equilibrium equations for the mole fractions on either side of the interface. This step is, in fact, equivalent to reading the composition of both phases from a T-x-y equilibrium diagram. 

The existence of a valid two-phase flash can be verified with the design equations for the bubble point, dew point, and equilibrium data calculated at the specified pressure and temperature. The design equations for the bubble and dew points are ... 

---