Bubble point pressure, calculation

In the case of the bubble point pressure calculation (see Fig. 2.2-1), the liquid composition, xh and the temperature, T, are known and the vapour phase composition, y and the pressure, P, must be calculated. For the iterative calculations an initial guess for the bubble point... 

First, the initial trial value of bubble-point pressure is 247 psia since this is the bubble-point pressure calculated in Example 12-2 under the assumption of ideal-solution behavior. Determine Kj values at 150°F and 247 psia from Appendix A. 

At a pressure midway between the dew-point pressure and the bubble-point pressure calculate the weights of the liquid phase and tire vapor phase in pounds. 

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 ... 

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

The critical properties for both carbon dioxide and toluene are given in Table 6.6-1. The binary interaction parameter for the COi-toluene mixture is. not given in Table 9,4-1. However, as the value for CO -benzene is 0.077 and that for COi-rt-heptane is 0.10, we estimate that the COi-toluene interaction parameter will be 0.09. Using this value and the bubble point pressure calculation in either the programs or the MATHCAD worksheet for the Peng-Robinson equation of state for mixtures (de.scribed in Appendix B and on the CD-ROM accompanying this book), the following values were obtained ... 

Bubble-Point Pressure Calculation. In this case tanperature T and liquid-phase composition are known. Total system pressure is easily calculated (with no iteration involved) from ... 

A bubble point pressure calculation on the distillate determined the minimum operating pressure in the condenser, which was below the atmospheric one. 

Bubble and dew point calculations are presented in the next two Examples with the simplest approach, the use of K values from Eqs 14.5.1 through 14.5.5. They can be also carried out with the computer subroutines, using the SRK EoS, given by Daubert (1985), that can be easily adapted to other EoS and for bubble point pressure calculations, using the EoS of Chapter 10, with the Program VLEEOS presented in Appendix E, which can be easily modified to perform B.P. temperature calculations. 

Prepare a flow diagram for a bubble point pressure calculation with the Chao-Seader method. 

VLEEOS Performs bubble point pressure calculations for binary mixtures using cubic equations of state. 

For bubble-point and dew-point pressure calculations, the appropriate forms are, respectively ... 

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. 

The saturation pressure, P, is different from the bubble point pressure (see. Vidal, 1973) and has no physical reality it merely serves as an intermediate calculation. 

For mixtures, the calculation is more complex because it is necessary to determine the bubble point pressure by calculating the partial fugacities of the components in the two phases at equilibrium. 

Below is a typical oil PVT table which is the result of PVT analysis, and which would be used by the reservoir engineer in calculation of reservoir fluid properties with pressure. The initial reservoir pressure is 6000 psia, and the bubble point pressure of the oil Is 980 psia. 

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. 

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. 

All these calculations with an equation of state are iterative, and in the following discussion the basic approach for the bubble point pressure and flash calculation will be described briefly. 

A liquid sample from a black oil reservoir had a volume of 227.0 cc in a laboratory cell at reservoir temperature and bubble-point pressure. The liquid was expelled through laboratory equipment which is the equivalent of the field separator-stock tank system. The oil volume collected in the stock tank was 167.4 cc. The separator produced 0.537 scf of gas, and the stock tank produced 0.059 scf of gas. Calculate the formation volume factor of the oil and the solution gas-oil ratio. 

Solution gas oil ratio at pressures above the bubble point is calculated by adding the estimate of stock-tank gasroil ratio from Figure 9-3 to the producing separator gas oil ratio. 

The following pressure-production history is available for an oil well. The producing gas-oil ratio is calculated with sales-gas volumes, i.e., stock-tank gas is vented and not measured. The separator operates at 67°F and 100 psig the specific gravity of the separator gas is 0.788, and the gravity of the stock-tank oil is 46.0° API. Estimate the bubble-point pressure and the solution gas-oil ratio at the bubble point for this black oil. Compare your answers with laboratory data which indicate a bubble-point pressure of 1928 psig and a solution gas-oil ratio at the bubble point of 623 scf/STB. 

At pressures above bubble-point pressure, oil formation volume factors are calculated from a combination of flash vaporization data and separator test data. 

First, calculate at pressures above bubble-point pressure. 

Calculate a value of coefficient of isothermal compressibility for use at pressures between 4500 psig and bubble-point pressure at 220°F for Good Oil Co. No. 4. 

This chapter begins with bubble-point pressure and solution gas-oil ratio, and then explains methods of estimating the density of reservoir liquids. The results of the density calculations are used to estimate oil formation volume factors. A technique for adjusting the results of the correlations to fit field derived bubble-point pressure is presented. 

The calculation of liquid density at pressures above the bubble point is a two-step procedure. First, the density at the bubble point must be computed using one of the methods previously described. Then this density must be adjusted to take into account the compression due to the increase in pressure from bubble-point pressure to the pressure of interest. 

First, calculate the density of the reservoir liquid at bubble-point pressure of 2635 psia at 220°F. 

Since these calculations are applicable only for a liquid at a pressure equal to or below its bubble-point pressure, this method is useful only for saturated liquids. 

Tables of oil formation volume factor and solution gas-oil ratio tabulated against pressure are adjusted by changing the values of pressure. A delta pressure is calculated as the difference between field derived bubble-point pressure and bubble-point pressure from correlation.

Calculate the density of the reservoir liquid of Exercise 11-13 at the initial reservoir pressure of 4800 psia given that the coefficient of isothermal compressibility between bubble-point pressure and 4800 psia is 14.5 x 106 psi-1. 

Calculation of the Bubble-Point Pressure of an Ideal Liquid Solution... 

EXAMPLE 12—2 Calculate the bubble-point pressure at a temperature of 150°F for the mixture given in Example 12—1. Assume ideal-solution behavior. 

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. 

Pressure does not appear implicitly in Equation 12-21. Pressure is represented in the equilibrium ratio. Thus bubble-point pressure cannot be calculated directly as in the case of ideal solutions. 

The bubble-point pressure at a given temperature may be determined by selection of a trial value of pressure, from which values of equilibrium ratios are obtained. Then the summation of Equation 12-21 is computed. If the sum is less than 1.0, the calculation is repeated at a lower pressure. If the sum is greater than 1.0, a higher trial value pressure is chosen. 

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