Bubble point example

FIGURE 3.5 Logic diagram for determining bubble point (Example 3.11). 

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

The relative volatiHties Ot) are defined by Eq. (13-33), is the mini-mum-reflux ratio (L v + i/D)min,. nd q describes the thermal condition of the feed (e.g., 1.0 for a bubble-point feed and 0.0 for a saturated-vapor feed). The Xi p values are available from the given feed composition. The 0 is the common root for the top-section equations and the bottom-section equations developed by Underwood for a column at minimum reflux with separate zones of constant composition in each section. The common root value must fall between 06/, and Ot/, where hk and Ik stand for heavy key and light key respectively. The key components are the ones that the designer wants to separate. In the butane-pentane splitter problem used in Example 1, the light key is /1-C4 and the heavy key is i-C. ... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

If the mixture shown in Example 8-2 is flashed at a temperature midway between the bubble point and dew point,... 

As in Example BSTILL, a column containing four theoretical plates and reboiler is assumed, together with constant volume conditions in the reflux drum. The liquid behaviour is, however, non-ideal for this water-methanol system. The objective of this example is to show the need for iterative calculations required for bubble point calculations in non-ideal distillation systems, and how this can be achieved with the use of simulation languages. 

The top and bottom temperatures (dew points and bubble points) were calculated by the methods illustrated in Example 11.9. Relative volatilities are given by equation 8.30 ... 

The average volatilities will be taken as those estimated in Example 11.5. Normally, the volatilities are estimated at the feed bubble point, which gives a rough indication of the average column temperatures. The dew point of the tops and bubble point of the bottoms can be calculated once the component distributions have been estimated, and the calculations repeated with a new estimate of the average relative volatilities, as necessary. 

As these values are close to those assumed for the calculation of the dew points and bubble points in Example 11.5, there is no need to repeat with new estimates of the relative volatilities. 

If the K-value requires the composition of both phases to be known, then this introduces additional complications into the calculations. For example, suppose a bubble-point calculation is to be performed on a liquid of known composition using an equation of state for the vapor-liquid equilibrium. To start the calculation, a temperature is assumed. Then, calculation of K-values requires knowledge of the vapor composition to calculate the vapor-phase fugacity coefficient, and that of the liquid composition to calculate the liquid-phase fugacity coefficient. While the liquid composition is known, the vapor composition is unknown and an initial estimate is required for the calculation to proceed. Once the K-value has been estimated from an initial estimate of the vapor composition, the composition of the vapor can be reestimated, and so on. 

The degree of removal of microbes of a certain size by a membrane is normally expressed by the reduction ratio, R. For example, if a membrane of a certain pore size is fed 10 microbes per cm- and it stops them all except one, the value of log reduction ratio log R is 7. It has been shown [7] that a log-log plot of R (ordinate) against the bubble points (abscissa) of a series of membranes will produce a straight line with a slope of 2. 

The iterative calculations start by assuming a guess for AT, (it is necessary to assume a value for Xj and -for example the values previously obtained in the dew- and bubble-points evaluation). With these values of AT, the eq. (2.3-12) is solved iteratively for Z. With this value ofZ, using equations (2.3-8) and (2.3-9) new values of vapour- and liquid-phase compositions are calculated and new values of Kt calculated for the next iteration. The iterations stop when satisfactory convergence is reached. 

EXAMPLE 2-3 Determine the critical temperature and critical pressure of a mixture of50.02 mole percent methane and 49.98 mole percent ethane. Also determine the bubble-point pressure and dew-point pressure of this mixture at 20°F. 

EXAMPLE 2-6 Consider a mixture of 47.6 weight percent n-pentane and 52.4 weight percent n-heptane. Estimate the specific volume of the liquid at its bubble point at 400°F. Also estimate the specific volume of the gas at its dew point at 400°F. 

EXAMPLE 9—1 Estimate bubble-point pressure from the pressure-production history of Figure 9—2. 

EXAMPLE 9-2 Estimate the solution gas-oil ratio at pressures above the bubble point for the reseiyoir oil of Figure 9-2. It is known that the gas includes both separator and stock-tank gas. 

EXAMPLE 9-3 A reservoir is producing 40.7°API stock-tank oil and 0.786 specific gravity separator gas. Separator gas-oil ratio appears to be constant at 676 scf/STB. Separator conditions are 100 psig and 75°F. Estimate solution gas-oil ratio at the bubble point for this black oil. 

EXAMPLE 10-1 The data from a flash vaporization on a black oil at 220°F are given below, Determine the bubble-point pressure and prepare a table of pressure and relative volume for the reservoir fluid study. 

EXAMPLE 10-8 Calculate coefficients of isothermal compressibility at pressures above bubble point for Good Oil Co. No. 4,... 

EXAMPLE 11- 2 Estimate values of solution gas-oil ratio at various pressures below bubble-point pressure for the reservoir oil of Example 11—1. 

EXAMPLE 11-4 Use the data given in Figure 11—2 to calculate the density of a reservoir liquid at its bubble point of 2635 psia at a reservoir temperature of 220°F. The composition of the well stream is as follows. 

EXAMPLE 11-7 The producing gas-oil ratio of a well is 768 scflSTB, and the specific gravities of the gas and stock-tank oil are 0.786 and 40.7°API, respectively. The liquid in the reservoir is at its bubble point at reservoir conditions of 2635 psia and 220°F. Calculate the density of this liquid at reservoir conditions. 

EXAMPLE 11—9 Calculate the formation volume factor of the oil described in Example 11-7 at its bubble-point pressure of 2635 psia at 220°F. 

EXAMPLE 11-12 Estimate the formation volume factor of the oil in Example 11-10 at a reservoir pressure of 5,000 psig and reservoir temperature of 22(FF. Use a value of 15.4 X 10 6 psi J for the coefficient of isothermal compressibility of the oil between 5015 psia and the bubble point. 

EXAMPLE 11—13 Examination of reservoir pressure measurements shows that the bubble-point pressure of the reservoir oil of Example 11-1 is 2635 psia and 220°F. The table below gives results of Examples 11-1, 11-2, and 11-11. Adjust the table to agree with the field derived bubble-point pressure. 

EXAMPLE 11-18 Estimate a value of oil viscosity for the reservoir oil of Example 11 1 at the bubble-point. 

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. 

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. 

Fig. 12-3. 2zjKj vs. trial value of bubble-point pressure (part of solution to Example 12-6). 

EXAMPLE 12-8 The following hydrocarbon mixture has a bubble point of600 psia at 80°F. Determine the fraction of the gas that will be vaporized when this liquid is differentially vaporized to 400 psia at 80°F. Use K-values from Appendix A. 

EXAMPLE 13-1 Calculate the producing gas-oil ratio, stock-tank oil gravity, and oil formation volume factor which will result from a two-stage separation of the hydrocarbon mixture below. Use separator conditions of75°F and 100 psig and a stock-tank temperature qf75°F. The mixture is a liquid at its bubble point at reservoir conditions of 2620 psig and 220°F. Use K-factors from Appendix A. Use decane K-factors for heptanes plus. 

These equations can be used also to calculate the bubble points and dew points of mixtures. The solution techniques in these applications differ from those used in Example 15-2. 

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