Mass vapor fraction

A puncture in the liquid space of the vessel or a break in the bottom-attachment or dip-leg pipe, initially, at least, discharges liquid plus any solids present without any noncondensable components. The liquid can begin to flash when the pressure drops to the bubble point pressure Pbub. If the liquid is extremely volatile, it could totally evaporate when the pressure drops below the dew point, producing vapor plus solids. The initial mass vapor fraction Xo is zero as is the initial volume fraction (Xq. 

Figure 2.29 Select mass vapor fraction of heater outlet as a target variable.

Figure 2.30 Specifying the target mass vapor fraction of the outlet stream.

Figure 2.28 shows how to select the adjust variable (in this case, the heat duty to the crude heater) and we select the target variable (in this case, the mass vapor fraction of the crude heater outlet) and the set the target variable value in Figure 2.29 and Figure 2.30. 

The corresponding acoustic velocity /(dp/dp, ), is normally much less than the acoustic velocity for gas flow. The mixture density is given in terms of the individual phase densities and the quality (mass flow fraction vapor) x by... 

When the VOC-laden gas stream contains a mixture of VOCs, then the calculations must be performed using the methods described for single-stage equilibrium calculations in Chapter 4. The temperature at the exit of the condenser must be assumed, together with a condenser pressure. The vapor fraction is then solved by trial and error using the methods described in Chapter 4, and the complete mass balance can be determined on the basis of the assumption of equilibrium. 

Unlike O, mass dependent fractionation is widespread for Ca in inclusions it ranges from -3.8 to 6.7 %o (Niederer and Papanastassiou 1984) which is about four times the terrestrial range (Schmitt et al. 2003). However, 80% of samples fall within an interval of 2%o. The mass fractionation is the result of complex sequences of condensation and vaporization. The connection to Mg isotopic fractionation is not obvious for these samples as the resolution of Mg measurements is much smaller. 

Figure 4. Graph of temperature, vapor fraction, and isotopic composition of water vapor and condensate as a function of elevation for an air mass with a starting T and RH of 295 K and 80 % (modified after Rowley and Garzione 2007). Note that the vapor and condensate are the isotopic composition reflected in the scale along the top of the graph with A(8lsO) normalized relative to the initial isotopic composition of the condensate. The isotopic composition of modeled condensate is not the same as precipitation as is discussed below.

The distribution of the mass in the boiling liquid m and saturated vapor m" is described by the vapor fraction x ... 

Thermophysical property tables give the specific volumes for liquid i/ and saturated vapor v" for each pressure so that the vapor fraction and the mass distribution can be determined ... 

With the vapor fractions of two states defined by a pressure increase Ap, the evaporated hydrogen mass Am" is also determined. 

One of the earliest flow diagrams for horizontal flow was devised by Baker.An example is given in Fig. 12 based on the work of Schicht from Butterworth and Hewitt.The vertical axis is Gx/X and the horizontal axis is (1 — x)hj/jx, where G is the total mass flow rate and x is the quality, i.e., the gas or vapor phase mass flow fraction ... 

Most common is the process of mass-dependent fractionation, in which the stable isotope ratio is altered as the consequence of physical processes differentially affecting atoms or molecules of different mass. Isotopes are fractionated relative to one another according to thermodynamic, kinetic, and diffusion processes. A simple example is the way in which oxygen isotopes in water molecules are fractionated during the process of evaporation. Water molecules containing the lower mass isotope leO are more likely to become water vapor than those containing the higher mass isotope lsO. Hence the water vapor is enriched in isotope leO and the liquid water is enriched in isotope lsO. 

A mass balance determines the equilibrium composition of vapor and liquid which are used to calculate a new set of equilibrium K-ratios. These steps are repeated until the K-ratios and the vaporized fraction do not vary. The tolerance of the function f(V/F), set to less than 10"4, was sufficient for most cases. 

V = mass fraction vapor Xz = distance-averaged vapor fraction a = proportionality constant r = frequency... 

With this, all mass flow rates are now known. Since all vapor in stream 6 exits as stream 8 and all liquid exits as stream 7, the liquid and vapor fractions in stream 6 are... 

Note that w and f(= 1 — w) are the fraction mass vaporization rates of water and fuel, respectively. f is found from the following expression ... 

The droplet surface temperature (TJ and surface mass fraction of water and fuel (F vs and Fps) are obtained from the liquid phase and interface equations, to be discussed later. The fractional mass vaporization rate of fuel (ef) is obtained from (40.4). The mass vaporization rate is then calculated using (40.5) and (40.7). Using (40.1) and (40.2a and b), H may be calculated. The transient heating rate of droplet, 2l is obtained from (40.3). 

Stream Information. Directed arcs that represent the streams, with flow direction from left to right wherever possible, are numbered for reference. By convention, when streamlines cross, the horizontal line is shown as a continuous arc, with the vertical line broken. Each stream is labeled on the PFD by a numbered diamond. Furthermore, the feed and product streams are identified by name. Thus, streams 1 and 2 in Rgure 3.19 are labeled as the ethylene and chlorine feed streams, while streams 11 and 14 are labeled as the hydrogen chloride and vinyl-chloride product streams. Mass flow rates, pressures, and tempera-mres may appear on the PFD directly, but more often are placed in the stream table instead, for clarity. The latter has a column for each stream and can appear at the bottom of the PFD or as a separate table. Here, because of formatting limitations in this text, the stream table for the vinyl-chloride process is presented separately in Table 3.6. At least the following entries are presented for each stream label, temperature, pressure, vapor fraction, total and component molar flow rates, and total mass flow rate. In addition, stream properties such as the enthalpy, density, heat capacity, viscosity, and entropy, may be displayed. Stream tables are often completed using a process simulator. In Table 3.6, the conversion in the direct chlorination reactor is assumed to be 100%, while that in the pyrolysis reactor is only 60%. Furthermore, both towers are assumed to carry out perfect separations, with the overhead and bottoms temperatures computed based on dew- and bubble-point temperatures, respectively. 

A schematic diagram of a tray is shown in Figure 16-10. The column is operating at steady state. A mass balance will be done for the mass balance envelope indicated by Ae dashed outline. The vapor above the trays is assumed to be well mixed thus, the inlet vapor mole frac V does not depend on the position along the tray, The vapor leaving the balance envelope has not yet had a chance to be mixed and its corrposition is a function of position G. The rising vapor bubbles are assumed to perfectly mix the liquid vertically. Thus, x does not depend upon the vertical position z, but the vapor fraction y does depend on z. The liquid mole frac can be a function of the distance G along the tray measured from the start of the active... 

Description for the case of CSTR a component mass balance has been expressed in terms of Damkohler munber and the vapor fraction. 

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