Bubble-point pressure: defined

The channels all converge to a common location at the tank outlet in order to ensure that there is communication between propellant and tank outlet during the mission. As liquid is withdrawn from the tank and vapor approaches the screen, surface tension forces block vapor entrance into the channel, but allow the liquid to flow freely. Screen channel LADs succeed in preventing gas ingestion so long as the pressure differential across the screen does not exceed the bubble point pressure (defined in Chapter 3). 

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... 

The required pressure range is defined by the dew point pressure and the bubble point pressure at 50°C. These are calculated by Equations 2.21 and 2.20 ... 

Bubble Point Pressure Test Membrane filters have discrete pores or capillaries penetrating from one side of the membrane to the other. When a membrane has been completely wetted, Squid is held in these capillary pores by surface tension. The Bubble Point of a membrane is defined as the minimum gas pressure required to break this surface tension and force the liquid out of the capillaries. Bubble point is a measure of relative pore size. 

Analogous to the bubble point pressure, the reseal pressure can be defined from a simplification of the general 3D YT.E for the pressure drop across a curved L/V interface embedded within the 3D space of the mesh. Consider the L/V interface formed within the LAD mesh screen as shown in Eigures 3.16 and 3.17. Retaining assumptions 1-4 from the bubble point model in Section 3.2.2, the following additional assumptions are required to solve the reseal pressure ... 

The first parameter to be varied was the screen mesh, and it was anticipated that the effective pore diameter should order with the fineness of the mesh. To isolate the screen mesh dependence, only data from Figures 5.8a-c and 5.9a-c taken close to the NBP (at or near liquid saturation conditions) are included for comparison, and also to allow direct comparison with Equation (3.16), which only holds for saturated liquid states. Pure saturated liquid states are impossible to achieve using a gas to pressurize other than the vapor. Therefore, near saturated liquid states are defined as points which lie very close (less than 2% away of the difference in pressure between pressure and critical pressure) to the saturation line. This definition confines the comparison of data points from Figures 5.8a-c and 5.9a-c to those located near the black saturation curve and minimizes the effect of subcooling the liquid on bubble point pressure. 

For any LAD mesh type, a pore throat defines the point within the pore where cross-sectional area is a minimum for a gas or vapor bubble to pass through the wetted screen, while the pore mouth defines the point where area is a maximum. The effective pore diameter, and thus bubble point pressure, is related to the pore throat. Statistically, the screen breaks down when a gas bubble passes through the largest pore throat, and thus path of least resistance, of the LAD screen. Likewise, the largest pore mouth controls the screen reseal pressure. 

The fitting coefficients were determined in the following manner For each subcooled bubble point pressure data point, a corresponding model generated saturated bubble point was calculated at each state. The subcooled gain, defined as the ratio of bubble point pressures ... 

Figure 10.15 plots the comparison of experimental and model generated bubble point pressures for the consolidated database of 5224 data points. Table 10.6 compiles the model performance against all of the data sets, organized by author where d,

data points that lie with 5% and 10% of the model prediction respectively, and the mean absolute error (MAE) is defined as ... 

The experiment could be repeated at a number of different temperatures and initial pressures to determine the shape of the two-phase envelope defined by the bubble point line and the dew point line. These two lines meet at the critical point, where it is no longer possible to distinguish between a compressed gas and a liquid. 

This value of co can be called the saturation value or ( ). since it applies only with flashing liquids (i.e., in the flashing region for pressures less than the bubble point, as seen in Fig. 23-32). A generalization defines omega to apply also with noncondensable gases by using Oo= x%v%/v0... 

At pressures above the bubble point, the coefficient of isothermal compressibility of oil is defined exactly as the coefficient of isothermal compressibility of a gas. At pressures below the bubble point an additional term must be added to the definition to account for the volume of gas which evolves. 

The coefficient of isothermal compressibility of a liquid is defined in Chapter 8. Equations 8-7 apply to a liquid at pressures above its bubble point. Equation 8—24 applies to a reservoir liquid at pressures below its bubble point. Figure 8-7 shows the effect a decline in reservoir pressure has on oil compressibility. 

At pressures above the bubble point the compressibility of water is defined as... 

Example The dew point is defined an all-vapor system except for one very small increment of liquid. Now take the feed again, and consider the fact that this is a flash-off crude still sidestream vapor at 20 psig (34.7 psia). The dew point is to be determined to set the proper sidestream stripper overhead temperature for this desired product. This problem is worked similarly to the bubble point. Simply hold the pressure (34.7 psia) constant, and vary the temperature. Note that when you find the temperature at which just a small amount of liquid is formed, the sign SYSTEM IS ALL VAPOR goes off and the flash component summary appears. Note also that the previous flash summary will remain on the screen (if you had a previous run) until you input a flash zone temperature and click on Run Prog. 

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. 

Define vapor pressure, triple point, equilibrium, dew point, bubble point, saturated, superheated, subcooled, and quality, and be able to locate the region or point in a p-T chart in which each term applies. 

At the critical point the mole fraction of CO2 Xi is 0.888 (Figure 9). In Figure 9 the part of the curve with Xi < 0.888 is the bubble point curve, and a homogenous mixture above the bubble point can be regarded as a subcritical fluid. The part of the curve with X] > 0.888 is the dew point curve, and a homogeneous mixture above the dew point is a vapor or a supercritical mixture. The mixed solvent near critical region at fixed temperature is defined as the solvent of which the composition and pressure are close to the critical composition and critical pressure ofthe mixture. 

Bubble points and dew points may be generated as described above for a given mixture over ranges of temperature and pressure. The locus of bubble points is the bubble point curve and the locus of dew points is the dew point curve. The two curves together define the phase envelope. In addition to the bubble point curve (total liquid saturated) and the dew point curve (total vapor saturated), other curves may be drawn representing constant vapor mole fraction. All these curves meet at one point, the critical point, where the vapor and liquid phases lose their distinctive characteristics and merge into a single, dense phase. 

Fig. 6 depicts the type of relationship that might be found between downstream gas flow rate and upstream gas pressure in a typical in-process automated bubble point test. The transition pressure is not clearly defined. Actual bubble points (transition pressures) obtained with this type of equipment differ from theoretical bubble points calculated for the same membrane from direct measurement of pore size, and from laboratory-type bubble point testing. 

Magnolia Field fluids properties, summarized in Table 1, are strikingly heterogeneous. Figure 5 illustrates this by way of a cross plot of fluid saturation pressure (bubble point and dew point pressures for oil and gas-condensate tests respectively) against measured reservoir pressure for available MDT samples. In very general terms, four fluid types may be defined. Undersaturated oils (solid circles in Fig. 5) are by far the most common. Noteworthy within this family are the two samples that have saturation... 

It is important to note that, since 3 = 2 and the pressure is fixed, the specification of only one additional thermodynamic variable completely defines a binary vapor-liquid mixture. If the composition of the liquid is Xa, both the vapor-phase composition yA and the bubble-point temperature Ti are uniquely fixed. 

A simple pressure-temperature projection of the pressure-temperature-composition diagram for a mixture is given in Figure 2. It is necessary to define the terms bubble point, dew point, maxcondentherm, and maxcondenbar. A bubble point is a state of liquid mixture at which, if the pressure is decreased slightly, a second phase, a vapour, appears. Similarly, a dew point is a state of a vapour at which, if the pressure is increased slightly, a liquid phase appears. The dew point locus and the bubble point locus are continuous curves meeting at the critical point. The maxcondentherm and maxcondenbar are the maximum temperature and maximum pressure respectively on the bubble point-dew point... 

For the condenser. Aspen IPE uses the cooling water utility. However, its default inlet and outlet temperatures were changed from 75 and 95 F to 90 and 120°F. Also, Aspen IPE has three built-in utilities for steam at 100, 165, and 400 psia. Because 100 psia steam condenses at 377.8°F and the bubble point temperature of the bottoms product at 252 psia is 260.8 F, when 100 psia steam is used in the reboiler, AT = 117°F, which often results in undesirable film boiling as discussed in Section 13.1 of the book. To reduce the approach temperature difference, and assure nucleate boiling, a low pressure steam utility, at 50 psia, is defined. 

What is the minimum number of variables to specify fully a stream A stream can be defined as the flow of material between two units in a flowsheet. The variables normally associated with a stream are its temperature, pressure, total flow, overall mole fractions, phase fractions and phase mole fractions, total enthalpy, phase enthalpies, entropy, etc. Assuming phase and chemical equilibrium, how many of those variables must be specified to completely fix the stream Without further considerations, for this case, intuition gives us the correct answer. We know without writing equations that if we specify temperature, pressure, and individual component flows, the stream is fully specified. Of course, a priori we cannot know the final state of the stream (i.e., multiphase or single phase liquid, vapor, solid, or a mixture of them). If we are interested in a stream with some specific conditions like saturated liquid, we cannot specify simultaneously pressure and temperature but pressure (or temperature) and phase fraction. A convention in process simulators is that when vapor (liquid) phase fraction is specified to zero or one, saturated conditions are assumed (bubble point or dew point). However, when vapor or liquid phase fractions are calculated, a value of one (zero) does not mean saturated conditions but that the stream is in vapor (liquid) phase. 

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