Bubble-point equation pressure calculation using

The first term on the right side of the Equation 16-4 is related to cw at pressures above the bubble point and is calculated using Figures 16-12 and 16-13. 

The bubble point equation can be used to back calculate/estimate interfacial temperature. Using the effective pore diameter for a 325 x 2300 screen from Chapter 4, the methane surface tension curve fitting parameters, and the experimental bubble point data using the three different pressurant gases from the current chapter, one can estimate the interfacial temperature ... 

Are we missing the pressure PT in the flash drum shown in Fig. 9.2 Let s calculate this pressure, using the bubble-point equation and the vapor pressure chart shown in Fig. 9.1 ... 

Figure 10.3-5 Flow diagram of an algorithm for the bubble point pressure calculation using an equation of state.

Prepare an Excel spreadsheet that calculates for a mixture the bubble point at pressures of 15,16,..., 25 atm and produces a plot of the bubble point versus pressure with suitable annotations and title. Use Goal Seek to solve the single nonlinear equation at each pressure. Data for the system are given in Figure 1.4. 

Bubble-point and dew-point pressures are calculated using a first-order iteration procedure described by the footnote to Equation (7-25). 

The calculation of y and P in Equation 14.16a is achieved by bubble point pressure-type calculations whereas that of x and y in Equation 14.16b is by isothermal-isobaric //cm-/(-type calculations. These calculations have to be performed during each iteration of the minimization procedure using the current estimates of the parameters. Given that both the bubble point and the flash calculations are iterative in nature the overall computational requirements are significant. Furthermore, convergence problems in the thermodynamic calculations could also be encountered when the parameter values are away from their optimal values. 

The system methanol-cyclohexane can be modeled using the NRTL equation. Vapor pressure coefficients for the Antoine equation for pressure in bar and temperature in Kelvin are given in Table 4.176. Data for the NRTL equation at 1 atm are given in Table 4.186. Assume the gas constant R = 8.3145 kIkmol 1-K 1. Set up a spreadsheet to calculate the bubble point of liquid mixtures and plot the x-y diagram. 

The membrane pore size can be calculated from the measured bubble point Pj, by using the dimensionally consistent Equation 10.9. This is based on a simphstic model (Figure 10.6) that equates the air pressure in the cyhndrical pore to the cosine vector of the surface tension force along the pore surface [6] ... 

Equation 8-11 may be used with the flash vaporization data to calculate oil compressibility at pressures above the bubble point. 

Relative oil volume and solution gas-oil ratio from the differential vaporization can be used also to calculate c0 at pressures below the bubble point. The above equations become... 

Again we will consider that the quantity of gas at the bubble point is negligible. Thus we can substitute ng = 0 and nL = n into Equation 12-16 to obtain an equation which can be used to calculate the bubble-point pressure at a given temperature or the bubble-point temperature at a given pressure. 

An approximate value of bubble-point pressure for use as the initial trial value can be calculated using Equation 12-11. When the correct bubble-point pressure has been established by this trial-and-error process, the composition of the infinitesimal amount of gas at the bubble point is given by the terms in the summation. 

Phase envelopes for typical natural gas tend to be fairly broad. That is, they cover a large range of temperature and pressure. On the other hand, the phase envelopes for acid gas mixtures tend to be quite narrow. Figure 3.2 shows the phase envelope for a mixture containing 50 mol% H2S and 50 mol% C02. This phase envelope was calculated using the Peng-Robinson equation of state, and the bubble, dew, and critical points are labeled. 

To obtain the composition of the top and bottom products, first calculate the relative volatility of each component using the conditions of the feed as a first guess. The relative volatility depends on temperature and pressure. The bubble point of the feed at 400 psia (27.6 bar) and at the feed composition, calculated using ASPEN [57], is 86.5 °F (130 °C). The K-values of the feed are listed in Table 6.7.1. Bubble and dew points could also be calculated using K-values from the DePriester charts [31] and by using the calculation procedures given in Chapter 3. Next, calculate the relative volatility of the feed stream, defined by Equation 6.27.18, for each component relative to the heavy key component. 

As simple as these equations are, they result in some unexpected problems. Consider first the case where is assigned. The practical problem becomes the determination of the bubble point at some given temperature. The pressure corresponding to the bubble point is —that part is easy. One can now renormalize to x = bIp, and use Eq. (33) to calculate the vapor phase composition X (x). Notice, however, that X (a ) will not have the same functional form as X (x) while the latter has a first moment equal to unity, = 1, the former has (- l)th moment equal to unity, = 1. If, for instance, one uses a gamma distribution,. J (x) = a,x), (x) will not be given by a gamma distribution. 

Ahernate Method for Catculaling the Bubble-Point Pressure of an Ideal Two-Component System. Although Raoult s Law can be used directly to calculate the bubble-point pressure of an ideal solution, an alteiTiate method which is applicable to two-component systems will now be presented. Since equations 5 to 8 ai e applicable an3rwhere in the two-phase region they apply at the bubble point and the dew point. At the bubble point the system is essentially all liquid except for an infinitesimal amount of vapor. Consequently, the composition of the liquid will be equal to the overall composition of the system. If the overall composition is substituted for x and Xz in equations 5 and 6 then either may be solved for Pt at a given temperature. The value of Pt calculated in this manner is equal to the bubble-point pressure. The com position of tlie infinitesimal amount of vapor at the bubble point may be computed by substitution in equations 7 and 8. 

Calculation of Bubble-Point Pressure and Dew-Point Pressure Using Equilibrium Constants. Since the total pressure P

bubble-point and dew-point pressure as was done in the case of ideal solutions. A method will now be presented for calculating the bubble-point pressure and the dew-point pressure, which is applicable to both binary and multicomponent systems which are non-ideal. At the bubble point the system is entirely in the liquid state except for an infinitesimal amount of vapor. Consequently, since ti, = 0 and n — n% equation 19 becomes... 

The calculations were done using vapor pressure data available in Reid et al. (1987) for each of the species Table VI gives the results. The temperature selected for evaluating the vapor pressure is the bubble point at 1 atm for the feed mixture, i.e., at 434.21 K. Using the relative volatilities and feed flows shown in Table VI, we can estimate the marginal vapor rates shown in Table VII using the equation... 

This equation is often adequate when applied to systems at low to moderate pressures and is therefore widely used. Bubble point and dew point calculations are only a bit more complex than the same calculations with Raoult s law. 

In the case of a total condenser, the vapor-phase compositions used in the calculation of the equilibrium relations and the summation equations are those that would be in equilibrium with the liquid stream that actually exists. That is, for a total condenser, the vapor composition used in the equilibrium relations is the vapor composition determined during a bubble point calculation based on the actual pressure and liquid compositions found in the condenser. These compositions are not used in the component mass balances since there is no vapor stream from a total condenser. 

The program VDWMIX is used to calculate multicomponent VLE using the PRSV EOS and the van der Waals one-fluid mixing rules (either IPVDW or 2PVDW see Sections 3.3 to 3.5 and Appendix D.3). The program can be used to create a new input file for a multicomponent liquid mixture and then to calculate the isothermal bubble point pressure and the composition of the coexisting vapor phase for this mixture. In this mode the information needed is the number of components (up to a maximum of ten), the liquid mole fractions, the temperatures at which the calculations are to be done (for as many sets of calculations as the user wishes, up to a maximum of fifty), critical temperatures, pressures (bar), acentric factors, the /f constants of the PRSV equation for each compound in the mixture, and, if available, the experimental bubble point pressure and the vapor phase compositions (these last entries are optional and are used for a comparison between the experimental and calculated results). In addition, the user is requested to supply binary interaction parameteifs) for each pair of components in the multicomponent mixture. These interaction parameters can be... 

Equation 7-29 is used to determine the bubble point temperature and pressure. In using Equation 7-29, the temperature or pressure is fixed, while the other parameter is varied until the criterion for a stable system is satisfied. A combination of temperature and pressure is altered, if the summation of the calculated vapor composition is different from unity. There is no known direct method that will allow a reasonable estimation of the amount of change required. However, Dodge [4], Hines and Maddox [5] have provided techniques for reducing the number of trials that is required. 

Calculate the activity coefficients, bubble point pressure, and the vapor composition as a function of liquid composition for the hydrofluoric acid— water binary at 120°C. Use the van Laar equation with the constants calculated in Problem 1.10. Vapor pressure data may also be obtained from Problem 1.10. Assume ideal gas behavior in the vapor phase. 

When the distribution coefficients are composition-dependent, the above method must be modified to account for the effect of composition. A search for the unknown bubble point or dew point temperature or pressure is started on the basis of some composition-independent relationship between the X-values and the temperature and pressure, such as Equations 2.20 and 2.21. Component fugacities are then calculated for the vapor phase and the liquid phase, and the /f-values are updated using Equation 2.15. The calculations are repeated until Equation 2.16 or 2.17, as well as Equation 2.12, are satisfied. The iterative scheme for the bubble point pressure calculation may proceed along the following steps ... 

The vapor pressures at 40°C are p = 20 kPa, = 313 kPa. Using the van Laar liquid activity equation, calculate the A -valucs of ethanol and benzene at 40°C when the ethanol mole fraction in the liquid is 0.25, and determine the bubble point pressure. Assume ideal gas behavior in the vapor phase. 

---