Bubble-point liquid, cooling

Answer—yes But why Well, the liquid is cooled by 5°F after it leaves the drum. The cooled liquid is not in equilibrium with the vapor in the drum. It has been subcooled by 5°F. This means that the bubble-point liquid has been cooled, without altering its composition. The vapor pressure of the liquid has been reduced. As can be seen in Fig. 25.3, subcooling this particular liquid by 5°F reduces its vapor pressure by about 2 psi. As the specific gravity of the liquid is 0.58, this is equivalent to an increase in the NPSH by 8 ft. Once again, our objective is to increase the flow from 250 to 300 GPM. Figure 25.2 tells us that the required NPSH increases from 20 to 26 ft. However, when we subcool the liquid by 5°F, the available NPSH increases from 20 to 28 ft. As the available NPSH now exceeds the required NPSH by 2 ft, the flow can be increased without risk of pump cavitation. 

As an exercise, the reader is invited to demonstrate that both for condenser and reboiler, the degrees of freedom are (A +4), identical with a flash. Typically, the specifications are input stream N. + 2) variables plus two others. Outlet pressure is usually imposed. The remaining variable may be liquid or vapour fraction, including bubble-point liquid (1=1), dew-point vapour (1=0), or sub-cooled liquid or superheated vapour (unusual). The above specifications enable to compute the duty Q, but this may be given also as specification. Note also that in steady state flowsheeting the reflux drum is included in the simulation of condenser. The type of condenser (partial, total, or sub-cooled liquid), as well as the type of reboiler (kettle or thermosyphon) does not change the analysis. 

Answer— yes But why Well, the liquid is cooled by 5°F after it leaves the drum. The cooled liquid is not in equilibrium with the vapor in the drum. It has been subcooled by 5°F. This means that the bubble-point liquid has been cooled without altering its composition. 

Calculate the reflux induced on Tray (D2 —1) by the use of subcooled reflux. This induced reflux is the amount of vapor from Tray (D2 - 2) which enters and is condensed on Tray (D2 - 1) for the purpose of converting the cooled pumpback reflux to bubble point liquid. 

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. 

Equations, determine sequences of simple and complex columns that minimize the overall vapor load. The recoveries will be assumed to be 100%. Assume the actual to minimum reflux ratio to be 1.1 and all the columns, with the exception of thermal coupling and prefractionator links, are fed with saturated liquid. Neglect pressure drop through columns. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters set to zero. Pressures are allowed to vary through the sequence with relative volatilities recalculated on the basis of the feed composition for each column. Pressures of each column are allowed to vary to a minimum such that the bubble point of the overhead product is 10°C above the cooling water return temperature of 35°C (i.e. 45°C) or a minimum of atmospheric pressure. 

From the three distinct 2D cross-sectional views (7.41a), (7.42), (7.43) of the P-T-x surface, we can now visualize the full 3D form of the surface as shown in Fig. 7.8. The surface is seen to resemble a curved envelope, clipped at each end to reveal the inside of the envelope through the hatched holes. Viewed toward the P—T plane, only the curved edge of the envelope is seen, as in (7.41a). However, viewed toward the P-xB plane or the T-xB plane, the inside of the envelope is seen as the hatch marks in (7.42) or (7.43), respectively. The upper P-T-x surface of the envelope is called the bubble-point surface, in reference to the first vapor bubbles that are seen as the liquid is heated to its boiling point. The P-T-xBap underside of the envelope is correspondingly called the dew-point surface, in reference to the first dewy droplets of liquid as the vapor is cooled to its condensation temperature. Although we normally see only the flat P-T, P-xB, or T-xb projections on the blackboard or book page, it is useful to keep in mind the full 3D form of the P-T-xB surface that underlies these 2D projections of the / = 3 system. 

If liquid drawn from a column cools below its bubble point, as a result of ambient-heat loss, we say it is subcooled. Mixing a small amount of steam with subcooled liquid, will reduce the partial pressure of any vapor in contact with the liquid, but not enough to promote boiling. Eventually, as more and more steam is mixed with a subcooled liquid, it will begin to boil. But, for a given amount of steam, the amount of vapor that can be boiled out of a liquid will always be less if the liquid is subcooled. In this way, ambient-heat loss reduces the stripping efficiency of steam. 

The vapor leaving each tray is in equilibrium with the liquid. This means that the vapor leaving each tray is at its dew point and the liquid leaving each tray is at its bubble point. As the top reflux rate is increased, all the trays are cooled. The vapors leaving trays 3, 4, and 5 are cooled. As a vapor at its dew point cools, the heavier components in the vapor condense into a liquid. The remaining vapors have a lower molecular weight because they are lighter. But this is only half the story. Let us continue ... 

The reason is condensate backup. The condensate backup causes subcooling that is, the liquid is cooled below its bubble point, or saturated liquid temperature. Perhaps a rat has lodged in the condensate outlet pipe. The rat restricts condensate drainage from the shell side. To force its way past the dead rat, the propane backs up in the condenser. The cold tubes in the bottom of the shell are submerged in liquid propane. The liquid propane is cooled below its bubble-point temperature. 

Toluene 1) and water(2) are essentially immiscible as liquids. Determine the dew-point temperatures and the compositions of the first drops of liquid formed when vapor mixtures of these species with mole fraction i, = 0.23 and r, = 0.77 are cooled at the constant pressure of 101.33 kPa. What is the bubble-point temperature and the composition of the last drop of vapor in each case The vapor pressure of toluene is given by the Antoine equation ... 

When a liquid is heated slowly at constant pressure, the temperature at which the first vapor bubble forms is the bubble-point temperature of the liquid at the given pressure. When a gas (vapor) is cooled slowly at constant pressure, the temperature at which the first liquid droplet forms is the dew-point temperature at the given pressure. Calculating bubble-point and dew-point temperatures can be a complex task for an arbitrary mixture of components. However, if the liquid behaves as an ideal solution (one for which Raoult s or Henry s law is obeyed for all components) and the gas phase can also be considered ideal, the calculations are relatively straightforward. 

The dew-point temperature of a gas (vapor) may be found using a method similar to that for bubble-point temperature estimation. Again, suppose a gas phase contains the condensable components A, B. C. .. and a noncondensable component G at a fixed pressure P. Let y/ be the mole fraction of component i in the gas. If the gas mixture is cooled slowly to its dew point, Tdp, it will be in equilibrium with the first liquid that forms. Assuming that Raoult s law applies, the liquid-phase mole fractions may be calculated as... 

The bubble-point temperature of a liquid mixture is the temperature at which the first vapor bubble forms if the mixture is heated at constant pressure. Contrary to what many students mistakenly assume, the bubble point is not the boiling temperature of the most volatile species in the liquid it is always higher than this temperature for an ideal liquid solution. The dew-point temperature of a vapor mixture is the temperature at which the first liquid droplet forms if the mixture is cooled at constant pressure. If Raoult s law applies to all species, either of these temperatures can be determined by trial and error using Equation 6.4-4 (for the bubble point) or Equation 6.4-7 (for the dew point). 

If a liquid mixture is heated above its bubble point, the vapor generated is rich in the more volatile mixture components. As vaporization continues, the system temperature steadily increases (unlike the case for a single-component system, in which T remains constant). Similarly, if a vapor mixture is cooled below its dew point, the liquid that condenses is rich in the less volatile components and the temperature progressively decreases. 

In areas surrounding the phase envelope, the system exists as a single phase. Below the dew point curve and at higher temperatures, it is a superheated vapor, while areas above the bubble point curve and to the left of it represent a sub-cooled liquid. In areas above the phase envelope between the sub-cooled liquid and the superheated vapor, the mixture is a dense or supercritical fluid, with properties changing gradually from those typical of a liquid to those typical of a vapor. 

The condenser is the stage where overhead vapors are condensed and liquid is returned to the top of the column as reflux. The condenser is partial if only part of the vapor is condensed and refluxed and the remainder leaves the condenser as vapor distillate. This type of condenser adds one equilibrium stage to the column trays because it holds a vapor phase and a liquid phase at equilibrium with each other. A total condenser is one where the entire overhead vapor is condensed (cooled to the bubble point temperature or subcooled to a lower temperature), part of the condensate is returned as reflux, and the remaining part is taken as liquid distillate. This type of condenser does not count as an equilibrium stage because no vapor-liquid separation takes place in it. The liquid distillate composition is identical to the composition of the vapor leaving the column top tray. 

Figure 9.4 shows another phase diagram at constant pressure. The x-axis shows the vapor-liquid mole fraction of the binary mixture. The y-axis shows temperature. The dew point line shows the temperature at which a superheated vapor mixture will begin to condense when cooled for all compositions of the mixture. The bubble point line shows the temperature at which a subcooled mixture will first begin to... 

In the preceding treatment it is assumed that the condenser removes latent heat only and that the condensate is liquid at its bubble point. Then the reflux L is equal to L, the reflux from the condenser, and F = F,. If the reflux is cooled below the bubble point, a portion of the vapor coming to plate 1 must condense to heat the reflux so Fj < F and L > L. The additional amount AL that is condensed inside the column is found from the equation... 

In Fig. 18.136 the feed is assumed to be at its bubble point. No condensation is required to heat the feed, so F = F and L = F+ L. If the feed is partly vapor, as shown in Fig. 18.13c, the liquid portion of the feed becomes part of L and the vapor portion becomes part of V. If the feed is saturated vapor, as shovm in Fig. IS-nii, the entire feed becomes part of F so L = L and V = F+V. Finally, if the feed is superheated vapor, as shown in Fig. 18.13c, part of the liquid from the rectifying column is vaporized to cool the feed to a state of saturated vapor. 

HEATING AND COOLING REQUIREMENTS. Heat loss from a large insulated column is relatively small, and the column itself is essentially adiabatic. The heat effects of the entire unit are confined to the condenser and the reboiler. If the average molal latent heat is X and the total sensible heat change in the liquid streams is small, the heat added in the reboiler is VX, either in watts or Btu per hour. When the feed is liquid at the bubble point (q 1), the heat supplied in the reboiler is approximately equal to that removed in the condenser, but for other values of q this is not true. (See page 554.)... 

Consider a binary mixture of components A and B, to be separated into two product streams using conventional distillation. The mixture is fed in the column as a saturated liquid (i.e., at its bubble point), onto the feed tray / (Figure 4.10), with a molar flow rate (mol/min) F/ and a molar fraction of component A, overhead vapor stream is cooled and completely condensed, and then it flows into the reflux drum. The cooling of the overhead vapor is accomplished with cooling water. The liquid from the reflux drum is partly pumped back in the column (top tray, N) with a molar flow rate FR (reflux stream) and is partly removed as the distillate product with a molar flow rate FD. Let us call Mrd the liquid holdup in the reflux drum and xD the molar fraction of component A in the liquid of the reflux drum. It is clear that xD is the composition for both the reflux and distillate streams. 

This procedure is repeated until the liquid phase appears in the cell, indicating that the liquid-vapor region has been reached. At this point, sufficient gas is added to the cell to form a measurable liquid level, represented by point 5. The cell is then slowly cooled until solid crystals are formed and the three phases coexist in equilibrium at point 6. Additional points on the three-phase line can be determined by alternately raising the cell pressure by addition of more gas and lowering the temperature as illustrated by points 7, 8, and 9. Following this path, a pressure is then reached at which the equilibrium cell is full of liquid at 10, the bubble point at the measured pressure. The temperature can then be lowered along line 10-11, keeping the cell just full of liquid, until a minute amount of solid is formed at 11, usually referred to as the crystal or solidus point. 

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