Distillation constant-temperature equilibrium

The calculational base consists of equilibrium relations and material and energy balances. Equilibrium data for many binary systems are available as tabulations of x vs. y at constant temperature or pressure or in graphical form as on Figure 13.4. Often they can be extended to other pressures or temperatures or expressed in mathematical form as explained in Section 13.1. Sources of equilibrium data are listed in the references. Graphical calculation of distillation problems often is the most convenient... 

When does a liquid boil Clearly, boiling at constant pressure—say, atmospheric pressure—begins when we increase the temperature of a liquid or solution and the vapor pressure reaches a pressure of one atmosphere. Alternatively, the pressure over a liquid or solution at constant temperature must be reduced until it reaches the vapor pressure at that temperature (e.g., vacuum distillation). Yet it is well known that liquids can be superheated (and vapors supersaturated) without the occurrence of phase transfer. In fact, liquids must always be superheated to some degree for nucleation to begin and for boiling to start. That is, the temperature must be raised above the value at which the equilibrium vapor pressure equals the surrounding pressure over the liquid, or the pressure must be reduced below the vapor pressure value. As defined earlier, these differences are called the degree of superheat. When the liquid is superheated, it is metastable and will reach equilibrium only when it breaks up into two phases. 

In this procedure the difference in the vapor pressure of a pure solvent and the solvent in equilibrium with a polymer is measured at constant temperature. The weight fraction of solvent is usually determined by determining the volume of solvent which is transferred (distilled over) to a known weight of polymer. 

Suppose some of this vapor is removed and condensed to a liquid. The vapor in equilibrium with this new solution would be still richer in the more volatile component, and the process could be continued further (see Fig. 11.16). This progression underlies the technique of separating a mixture into its pure components by fractional distillation, a process in which the components are successively evaporated and recondensed. What we have described so far corresponds to a constant-temperature process, but actual distillation is conducted at constant total pressure. The vapor pressure-mole fraction plot is transformed into a boiling temperature-mole fraction plot (Fig. 11.17). Note that the component with the lower vapor pressure (component 2) has the higher boiling point, T. If the temperature of a solution of a certain composition is raised until it touches the liquid line in the plot, the vapor in equilibrium with the solution is richer in the more volatile component 1. Its composition lies at the intersection of the horizontal constant-temperature line and the equilibrium vapor curve. 

Suppose the grey tin and white tin are m equilibrium Then m the transfer of 8 moles from grey to white the work at constant temperature and volume is zero Carrying the process out by the distillation... 

So far the discussion has been specific to systems at constant temperature equivalently, pressure could be fixed and temperature and liquid phase composition taken as the variables. Although much experimental vapor-liquid equilibrium data are obtained in constant-temperature experiments, distillation columns and other vapor-liquid separations equipment in the chemical process industry are operated more nearly at constant pressure. Therefore, it is important that chemical engineers be familiar with both types of calculations. 

While we have studied the properties of binary mixtures at constant temperature so far we shall now examine the behaviour of these mixtures at constant pressure. The conditions are those found in distillation, which is normally an isobaric process tending to establish equilibrium between the liquid and vapour phases. A boiling point diagram shows the boiling points and the equilibrium compositions of binary mix-... 

The isopiestic method is a highly accurate but time-consuming relative method. In a constant-temperature enclosure the solvent distills isothermally from a reference solution of known activity to a solution of unknown activity or vice versa, which entails a change in concentration. At equilibrium the solvent activities of both samples are equal and (R denotes reference solution)... 

Thermometer Placement. If a fhermometer is used, be sure that the bulh is placed in the stem of fhe Hickman head just below the well. If it is placed higher, it may not he surrounded by a constant stream of vapor from the material being distilled. If fhe fhermometer is not exposed to a continuous stream of vapor, it may not reach temperature equilibrium. As a result, the temperature reading would he incorrect (low). 

The surface tension of surfactant solutions was measured as a function of bulk surfactant molal concentration (mol/kg H2O) with a Wilhelmy-plate-type tension meter (Kyowa CBVP). The accuracy of the surface tension measurements is +0.1 mN/m. The equilibrium surface tension was determined as the value obtained when the surface tension became constant within 0.1 mN/m for 10 min. Near CMC, about 3-5 h were usually required to reach the equilibrium. All measurements were carried out in a thermostated device maintained at a constant temperature of 25, 35, 40, and 45 °C. All glassware and Wilhelmy glass plate were washed in an aqueous solution of chromic acid and sulfuric acid, rinsed in triple distilled water and dried before each measurement. 

The reaction is exothermic and requires a reactor design (adiabatic fixed bed with recycle or tubular) that keeps the temperature essentially constant. The equilibrium constant for this reaction is about 100 (Voloch et al, 1986). The reaction takes place below 100 C and at a high enough pressure to assure its occurrence in the liquid phase (about 200psig). In most commercial units, the catalyst is a cation exchange resin which limits the MTBE reaction temperatures due to catalyst stability constraints. The methanol/isobutene ratio is kept close to 1 to avoid the formation of oligomers at too low a methanol concentration or excess methanol in the C4 overhead stream. The upper limit in the methanol/isobutene ratio is due to the formation of an azeotrope with the C4 s in the distillation process which is about 4% methanol in the overhead stream. Typical yields from an MTBE unit at 1/1 methanol to isobutene ratio over a resin catalyst are shown in Table 22 (Miller and Piel, 1989). 

A fundamental difference between the two flowsheets is the ability in the conventional process to adjust reactor temperature and distillation column temperamres completely independently, which is not possible in the reactive distillation process. In the conventional system, the reactor temperature can be set at an optimum value and distillation temperatures can be independently set at their optimum values by adjusting column pressures. In reactive distillation, these temperatures are not independent because only one pressure can be set in the vessel. Therefore, the design of a reactive distillation requires a tradeoff between temperatures conducive for reaction (kinetics and equilibrium constants) and temperatures favorable for vapor-liquid separation. The temperature dependency of the relative volatilities will illustrate this important difference between the two processes. 

SC (simultaneous correction) method. The MESH equations are reduced to a set of N(2C +1) nonlinear equations in the mass flow rates of liquid components ltJ and vapor components and the temperatures 2J. The enthalpies and equilibrium constants Kg are determined by the primary variables lijt vtj, and Tf. The nonlinear equations are solved by the Newton-Raphson method. A convergence criterion is made up of deviations from material, equilibrium, and enthalpy balances simultaneously, and corrections for the next iterations are made automatically. The method is applicable to distillation, absorption and stripping in single and multiple columns. The calculation flowsketch is in Figure 13.19. A brief description of the method also will be given. The availability of computer programs in the open literature was cited earlier in this section. 

Azeotropic Systems. An azeotropic system is one wherein two or more components have a constanl boiling point at a particular composition. Such mixtures cannot be separated by conventional distillation methods. If rhe constant boiling point is a minimum, the system is said lo exhibit negomv azeotropy if it is a maximum, positive azeotropy. Consider a mixture of water and alcohol in the presence of the vapor. This system of two phases and two components is divarianl. Now choose some fixed pressure and study the composition of the system at equilibrium us a function of temperature. The experimental results arc shown schematically in Fig. 5. 

EQUILIBRIUM DIAGRAM. A diagram showing the phase fields of an alloy system under the conditions of complete equilibrium using as coordinates the temperature, the compositions in terms of the components, and the pressure. The most frequently used equilibrium diagrams in metallurgy are drawn with the pressure considered constant. See iron-carbon diagram under iron Metals, Alloys, and Steels. See also Distillation. 

The law of mass action, the laws of kinetics, and the laws ol distillation all operate simultaneously in a process of this type. Esterification can occur only when the concentrations of the acid and alcohol are in excess of equilibrium values otherwise, hydrolysis must occur The equations governing the rate of the reaction and the variation of the rale constant (as a function of such variables as temperature, catalyst strength, and proponion of reactants) describe Ihe kinetics of the liquid-phase reaction. The usual distillation laws must he modified, since must esterifications arc somewhat exothermic and reaction is occurring on each plate. Since these kinetic considerations are superimposed on distillation operations, each plate must be treated separately by successive calculations after Ihe extent of conversion has been determined. See also Distillation. 

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