Bubble-point systems

The results just discussed indicate that for bubble-point systems, the light-component K values are relatively insensitive to the number of subfractions (between 7 and 34) used for the heptanes plus, especially when the heptanes plus is characterized properly. This behavior has been noted for several oils and is important for two reasons (1) in a compositional reservoir model study, the number of components must be limited to 14-18 to keep computer time and costs from being prohibitively high and (2) when vaporization of an oil is being calculated, extremely high... 

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. 

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

Once the bubble point is reached (at point B), the first bubble of ethane vapour is released. From point B to C liquid and gas co-exist in the cell, and the pressure is maintained constant as more of the liquid changes to the gaseous state. The system exhibits infinite compressibility until the last drop of liquid is left In the cell (point C), which is the dew point. Below the dew point pressure only gas remains in the cell, and as pressure is reduced below the dew point, the volume increase is determined by the compressibility of the gas. The gas compressibility is much greater than the liquid compressibility, and hence the change of volume for a given reduction in pressure (the... 

When the pressure of a volatile oil or black oil reservoir is above the bubble point, we refer to the oil as undersaturated. When the pressure is at the bubble point we refer to it as saturated oil, since if any more gas were added to the system it could not be dissolved in the oil. The bubble point is therefore the saturation pressure for the reservoir fluid. 

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. 

In the solution gas drive case, once production starts the reservoir pressure drops very quickly, especially above the bubble point, since the compressibility of the system is low. Consequently, the producing wells rapidly lose the potential to flow to surface, and not only is the plateau period short, but the decline is rapid. 

As the temperature of the liquid phase is increased, the system ultimately reaches a phase boundary, the bubble point at which the gas phase (vapour) begins to appear, with the composition shown at the left end of the horizontal two-phase tie-line . As the temperature rises more gas appears and the relative amounts of the two phases are detemiined by applying a lever-ami principle to the tie-line the ratio of the fractionof molecules in the gas phase to that hn the liquid phase is given by the inverse of the ratio of the distances from the phase boundary to the position of the overall mole fraction Xq of the system. 

With a further increase in the temperature the gas composition moves to the right until it reaches v = 1/2 at the phase boundary, at which point all the liquid is gone. (This is called the dew point because, when the gas is cooled, this is the first point at which drops of liquid appear.) An unportant feature of this behaviour is that the transition from liquid to gas occurs gradually over a nonzero range of temperature, unlike the situation shown for a one-component system in figure A2.5.1. Thus the two-phase region is bounded by a dew-point curve and a bubble-point curve. 

In controlled venting operation, the quench tank pressure is maintained at a desired level by a pressure controller/control valve system or pressure rehef valve. This mode of operation is used when the discharge mixture bubble point is close to or below the maximum ambient temperature, and it is desired to hmit the maximum quench tank pressure. 

To aid in solving the tedious Underwood equation to ultimately arrive at (L/D)niin, Frank [100] has developed Figure 8-47, which applies for liquid feed at its bubble point and whether the system is binary or multicomponent, but does require that the key components are adjacent. Otherwise, the system must be solved for two values of 0 [74]. To obtain the necessary parameters for Figure 8-47, Frank recommends using the same overhead con-... 

As discussed by Franks (1972), in order to solve this system of equations, a value of temperature T must be found to satisfy the condition that the difference term 6 = P - Zpj is very small, i.e., that the equilibrium condition is satisfied. This is known as a bubble point calculation. The above system of defining equations, however represent, an implicit algebraic loop and the trial and error solution procedure can be very time consuming, especially when incorporated into a dynamic simulation program. 

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. 

Dew points and bubble points can be calculated from a knowledge of the vapour-liquid equilibrium for the system. In terms of equilibrium constants, the bubble point is defined by the equation ... 

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) ... 

The first bracket in this equation ensures that the bubble-point criterion is satisfied. The second bracket ensures that the vapor and liquid compositions are equal. The solution of this is given when x = y = 0.69 and x2 = y2 = 0.31 for the system of 2-propanol-water at 1 atm. 

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. 

If a partial condenser is to be used and a vapor top product taken, then the above criteria should be applied to the dew point of the vapor top product, rather than the bubble point of the liquid top product. Also, if a vapor top product is to be taken, then the operating pressure of the destination for the product might determine the column pressure (e.g. overhead top product being sent to the fuel gas system). There are two major exceptions to these guidelines ... 

While the main driving force in [43, 44] was to avoid direct particle transfers, Escobedo and de Pablo [38] designed a pseudo-NPT method to avoid direct volume fluctuations which may be inefficient for polymeric systems, especially on lattices. Escobedo [45] extended the concept for bubble-point and dew-point calculations in a pseudo-Gibbs method and proposed extensions of the Gibbs-Duhem integration techniques for tracing coexistence lines in multicomponent systems [46]. 

BUBBLE - Bubble Point Calculation for a Batch Distillation Column System... 

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. 

Figure 4. Comparison of predicted and experimental bubble point pressures for methanol-carbon dioxide system ((C)) (14) (A, V) (24) (---) predicted)...

COMPARISON OF PREDICTED AND EXPERIMENTAL BUBBLE POINT PRESSURE FOR THE NITROGEN-CARBON DIOXIDE, HYDROGEN SULFIDE, METHANOL SYSTEM AT -15°C (From Reference 9)... 

Bubble Point Constancy. Although the exact relationship between the bubble point and the "pore size" of a microfiltration membrane is a matter of dispute (11, 12, 13, 14), nevertheless, it remains the quickest and most convenient means for demonstrating the continuing integrity of a membrane filtration system. It is consequently important that the bubble point be both reproducible (within a given range) and constant. It was, therefore, of considerable interest to discover that the bubble points of both conventional and poly(vinylidene fluoride) membranes increased with immersion time in deionized water whereas those of Tyrann-M/E and polyamide remained essentially constant (Figure 6). 

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