Equilibrium flashes

Unlike the flash equilibrium of Chap. 2, the extract and raffinate phases (compared to vapor-liquid) are miscible to some degree, as seen in the triangle diagram. Point D, for example, shows how much of the solvent (benzene) can dissolve into the feed (water) at equilibrium of the two liquid phases. Similarly, point M shows how much feed water will dissolve into benzene at equilibrium. 

An organic chemistry professor performed a flash distillation experiment in a laboratory for his students. A 10-kgmol/h liquid feed mixture consisted of 20 mol % ethanol and 80 mol % water at 1 atm. While the professor was able to determine that 30 mol % of the feed vaporized at 70°F, he lacked the necessary equipment to measure the liquid and vapor compositions of the more volatile component, ethanol. Determine the liquid and vapor compositions, as well as the percent ethanol recovery from the flash. Equilibrium data for the ethanol-water system at 1 atm are provided in MTO.l. 

This phenomenon can be calculated using flash equilibrium techniques. It is important that we try to understand this phenomenon qualitatively. The tendency of any one component in the process stream to flash to the vapor phase depends on its partial pressure. The partial pressiure of a component in a vessel is defined as the number of molecules of that component in the vapor space divided by the total number of molecules of all components in the vapor space times the pressure in the vessel. Since the partial pressure of a component is a function of the system s pressure, an increase in the system s pressure will increase the component s partial pressure. The increase in partial pressure reduces the component s equihbrium constant, and the molecules of that component tend toward the liquid phase. As the separator pressure is increased, the liquid flow rate out of the separator increases. 

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

The most frequent application of phase-equilibrium calculations in chemical process design and analysis is probably in treatment of equilibrium separations. In these operations, often called flash processes, a feed stream (or several feed streams) enters a separation stage where it is split into two streams of different composition that are in equilibrium with each other. 

The equilibrium ratios are not fixed in a separation calculation and, even for an isothermal system, they are functions of the phase compositions. Further, the enthalpy balance. Equation (7-3), must be simultaneously satisfied and, unless specified, the flash temperature simultaneously determined. 

The same fundamental development as presented here for vapor-liquid flash calculations can be applied to liquid-liquid equilibrium separations. In this case, the feed splits into an extract at rate E and a raffinate at rate R, which are in equilibrium with each other. The compositions of these phases are... 

Equation (7-8). However, for liquid-liquid equilibria, the equilibrium ratios are strong functions of both phase compositions. The system is thus far more difficult to solve than the superficially similar system of equations for the isothermal vapor-liquid flash. In fact, some of the arguments leading to the selection of the Rachford-Rice form for Equation (7-17) do not apply strictly in the case of two liquid phases. Nevertheless, this form does avoid spurious roots at a = 0 or 1 and has been shown, by extensive experience, to be marltedly superior to alternatives. 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Liquid-liquid equilibrium separation calculations are superficially similar to isothermal vapor-liquid flash calculations. They also use the objective function. Equation (7-13), in a step-limited Newton-Raphson iteration for a, which is here E/F. However, because of the very strong dependence of equilibrium ratios on phase compositions, a computation as described for isothermal flash processes can converge very slowly, especially near the plait point. (Sometimes 50 or more iterations are required. )... 

We have repeatedly observed that the slowly converging variables in liquid-liquid calculations following the isothermal flash procedure are the mole fractions of the two solvent components in the conjugate liquid phases. In addition, we have found that the mole fractions of these components, as well as those of the other components, follow roughly linear relationships with certain measures of deviation from equilibrium, such as the differences in component activities (or fugacities) in the extract and the raffinate. 

FLASH determines the equilibrium vapor and liquid compositions resultinq from either an isothermal or adiabatic equilibrium flash vaporization for a mixture of N components (N 20). The subroutine allows for presence of separate vapor and liquid feed streams for adaption to countercurrent staged processes. 

The temperature and composition of each feed stream and the stream ratios are specified along with a common feed pressure (significant only for the vapor stream) and the flash pressure. For an isothermal flash the flash temperature is also specified. Resulting vapor and liquid compositions, phase ratios, vaporization equilibrium ratios, and, for an adiabatic flash, flash temperature are returned. 

FLASH CONDUCTS ISOTHERMAL (TVPE=1) OR ADIABATIC [Pg.322]

THE SUBROUTINE ACCEPTS BOTH A LIQUID FEED OF COMPOSITION XF AT TEMPERATURE TL(K) AND A VAPOR FEED OF COMPOSITION YF AT TVVAPOR FRACTION OF THE FEED BEING VF (MOL BASIS). FDR AN ISOTHERMAL FLASH THE TEMPERATURE T(K) MUST ALSO BE SUPPLIED. THE SUBROUTINE DETERMINES THE V/F RATIO A, THE LIQUID AND VAPOR PHASE COMPOSITIONS X ANO Y, AND FOR AN ADIABATIC FLASHf THE TEMPERATURE T(K). THE EQUILIBRIUM RATIOS K ARE ALSO PROVIDED. IT NORMALLY RETURNS ERF=0 BUT IF COMPONENT COMBINATIONS LACKING DATA ARE INVOLVED IT RETURNS ERF=lf ANO IF NO SOLUTION IS FOUND IT RETURNS ERF -2. FOR FLASH T.LT.TB OR T.GT.TD FLASH RETURNS ERF=3 OR 4 RESPECTIVELY, AND FOR BAD INPUT DATA IT RETURNS ERF=5. 

Illustrates use of subroutine FLASH for vapor-liquid equilibrium separation calculations for up to 10 components and of subroutine PARIN for parameter loading. 

The flash curve of a petroleum cut is defined as the curve that represents the temperature as a function of the volume fraction of vaporised liquid, the residual liquid being in equilibrium with the total vapor, at constant pressure. 

The vapor pressure of a crude oil at the wellhead can reach 20 bar. If it were necessary to store and transport it under these conditions, heavy walled equipment would be required. For that, the pressure is reduced (< 1 bar) by separating the high vapor pressure components using a series of pressure reductions (from one to four flash stages) in equipment called separators , which are in fact simple vessels that allow the separation of the two liquid and vapor phases formed downstream of the pressure reduction point. The different components distribute themselves in the two phases in accordance with equilibrium relationships. 

Edmister, W.C. and K.K. Okamoto (1959), Applied hydrocarbon thermodynamics. Part 12 equilibrium flash vaporization correlations for petroleum fractions . Petroleum Refiner, Vol. 38, No. 8, p. 117. 

How does one monitor a chemical reaction tliat occurs on a time scale faster tlian milliseconds The two approaches introduced above, relaxation spectroscopy and flash photolysis, are typically used for fast kinetic studies. Relaxation metliods may be applied to reactions in which finite amounts of botli reactants and products are present at final equilibrium. The time course of relaxation is monitored after application of a rapid perturbation to tire equilibrium mixture. An important feature of relaxation approaches to kinetic studies is that tire changes are always observed as first order kinetics (as long as tire perturbation is relatively small). This linearization of tire observed kinetics means... 

In a series of papers by Leung and coworkers (AlChE J., 32, 1743-1746 [1986] 33, 524-527 [1987] 34, 688-691 [1988] J. Loss Prevention Proc. Ind., 2[2], 78-86 [April 1989] 3(1), 27-32 [Januaiy 1990] Trans. ASME J. Heat Transfer, 112, 524-528, 528-530 [1990] 113, 269-272 [1991]) approximate techni ques have been developed for homogeneous equilibrium calculations based on pseudo-equation of state methods for flashing mixtures. 

In a submerged-tube FC evaporator, all heat is imparted as sensible heat, resulting in a temperature rise of the circulating hquor that reduces the overall temperature difference available for heat transfer. Temperature rise, tube proportions, tube velocity, and head requirements on the circulating pump all influence the selec tion of circulation rate. Head requirements are frequently difficult to estimate since they consist not only of the usual friction, entrance and contraction, and elevation losses when the return to the flash chamber is above the liquid level but also of increased friction losses due to flashing in the return line and vortex losses in the flash chamber. Circulation is sometimes limited by vapor in the pump suction hne. This may be drawn in as a result of inadequate vapor-liquid separation or may come from vortices near the pump suction connection to the body or may be formed in the line itself by short circuiting from heater outlet to pump inlet of liquor that has not flashed completely to equilibrium at the pressure in the vapor head. 

For a given drum pressure and feed composition, the bubble- and dew-point temperatures bracket the temperature range of the equilibrium flash. At the bubble-point temperature, the total vapor pressure exerted by the mixture becomes equal to the confining drum pressure, and it follows that X = 1.0 in the bubble formed. Since yj = KjXi and since the x/s stiU equal the feed concentrations (denoted bv Zi s), calculation of the bubble-point temperature involves a trial-and-error search for the temperature which, at the specified pressure, makes X KjZi = 1.0. If instead the temperature is specified, one can find the bubble-point pressure that satisfies this relationship. 

For 2ibinary feed, specification of the flash-drum temperature and pressure fixes the equilibrium-phase concentrations, which are related to the values by... 

A third fundamental type of laboratory distillation, which is the most tedious to perform of the three types of laboratory distillations, is equilibrium-flash distillation (EFV), for which no standard test exists. The sample is heated in such a manner that the total vapor produced remains in contact with the total remaining liquid until the desired temperature is reached at a set pressure. The volume percent vaporized at these conditions is recorded. To determine the complete flash curve, a series of runs at a fixed pressure is conducted over a range of temperature sufficient to cover the range of vaporization from 0 to 100 percent. As seen in Fig. 13-84, the component separation achieved by an EFV distillation is much less than by the ASTM or TBP distillation tests. The initial and final EFN- points are the bubble point and the dew point respectively of the sample. If desired, EFN- curves can be established at a series of pressures. 

The equilibrium vapor pressure of a flammable hquid at its closed-cup flash point about equ s its LFL in percent by volume. Thus, the vapor pressure of toluene at its closed-cup flash point (4.4°C or 40°F) of 1.2 percent (1.2 kPa) is close to its LFL of 1.1 percent. The composite LFL of a mixture may be estimated by Le Cnatelier s Rule ... 

FIG. 26-69 Ratio of mass flux for inclined pipe flow to that for orifice discharge for flashing liquids by the homogeneous equilibrium model. Leung, J. of Loss Prev. Process Ind. 3 pp. 27-32, with kind peimission of Elsevier Science, Ltd, The Boulevard, Langford Lane, Kidlington, 0X5 IGB U.K., 1990.)... 

FIG. 26-70 Accuracy in HEM predictions for slightly to moderately siibcooled flashing flow. Comparison with data for water by Sozzi and Sutherland (1975) also ASME Symposium on Non-Equilibrium Two-Phase Flows (1975) (Nozzle type 2). 

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