Vaporization material balance problem

Solve material balance problems involving vaporization and condensation. 

The solution of material balance problems involving partial saturation, condensation, and vaporization will now be illustrated. Remember the drying problems in Chap. 2 They included water and some bone-dry material, as shown at the top of Fig. 3.19. To complete the diagram, we add the air that is used to remove the water from the material being dried. 

You can analyze material balance problems involving water vapor in air in exactly the same feshion as you analyzed the material balance problems for the drying of leather (or paper, etc.), depending on the information provided and sought. (Humidity and saturation problems that include the use of energy balances and humidity charts are discussed in Chap. 4.)... 

Example This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required. If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation. 

The performance of a given column or the equipment requirements for a given separation are established by solution of certain mathematical relations. These relations comprise, at every tray, heat and material balances, vapor-liquid equilibrium relations, and mol fraction constraints. In a later section, these equations will be stated in detail. For now, it can be said that for a separation of C components in a column of n trays, there still remain a number, C + 6, of variables besides those involved in the dted equations. These must be fixed in order to define the separation problem completely. Several different combinations of these C + 6 variables may be feasible, but the ones commonly fixed in column operation are the following ... 

Until the advent of computers, multicomponent distillation problems were solved manually by making tray-by-tray calculations of heat and material balances and vapor-liquid equilibria. Even a partially complete solution of such a problem required a week or more of steady work with a mechanical desk calculator. The alternatives were approximate methods such as those mentioned in Sections 13.7 and 13.8 and pseudobinary analysis. Approximate methods still are used to provide feed data to iterative computer procedures or to provide results for exploratory studies. 

The solution of a flash problem requires the satisfaction of material balances in addition to the equilibrium between the vapor and the liquid. Let us take 1 mole of total feed as a basis and denote the number of moles of liquid formed as and the number of moles of vapor formed as v Overall mass balance requires... 

In the table the second, third, and fourth problems each result from a permutation of the known and unknown quantities that occur in the bubble-T calculation. We refer to these as P-problems, because each problem is well-posed when values are specified for P independent intensive properties, where the value of T is given by the phase rule (9.1.14). However, the flash problem in Table 11.1 differs from the others in that it is an P -problem it is well-posed when values are specified for T independent intensive properties, with the value of T given by (9.1.12). Flash calculations pertain to separations by flash distillation in which a known amount N of one-phase fluid, having known composition z, is fed to a flash chamber. When T and P of the chamber are properly set, the feed partially flashes, producing a vapor phase of composition xP in equilibrium with a liquid of composition x ). The problem is to determine these compositions, as well as the fraction of feed that flashes NP/N. Unlike the other problems in Table 11.1, the flash problem involves the relative amounts in the phases and therefore a solution procedure must invoke not only the equilibrium conditions (11.1.1) but also material balances. 

The mole fraction of vapor A in the free-fiowing gas (z = L) is xal, while that at the vapor-liquid surface (z = 0) is xao- The vapor concentration at z = 0 can be computed from knowledge of the vapor pressure of liquid A. In order to solve this problem, we write a component material balance over a differential volume element SAz. A differential element in only one dimension (A2 ) is needed because the concentration is only a function of the one dimension, 2. 

Problems encountered in acquiring stable gas-phase conditions in the laboratory also contribute to the relative lack of atmospheric pesticide reaction rate and product data. Semi-volatile organics, which conoprise the majority of pesticides, can sorb onto the surfaces of the laboratory reaction vessel. The wall interference reaction rates and products may or may not be similar to those occurring under actual atmospheric vapor-phase conditions (P,/0). Experimental designs that can provide environmentally relevant reaction rates, clwacterization of gas-phase and oxidative transformation products, and maintain material balance at environmental tenq>eratures has yet to be established. 

The difficulty In controlling accumulator level through the manipula tion of reflux poses another problem, however. It is actually the material balance on the top tray which determines what the composition profile will be. Changing the rate of flow of distillate being withdrawn from the accumulator has no effect on composition if the flow of reflux or vapor... 

In order to solve these problems, we need to derive the thermodynamic relationships between the vapor and liquid phase compositions, and then combine this information with the appropriate material balance. 

For a dew point problem, it is the vapor phase composition that is known, while the liquid phase composition is unknown. Rearranging the combined equilibrium and material balance equations as before will not provide any benefit in this case. However, let s return to Raoult s law. 

Try the following problem to sharpen your skills in working with material and energy balances. Crude oil is heated to 525° K and then charged at a rate of 0.06 m /hr to the flash zone of a pilot-scale distillation tower. The flash zone is maintained at an absolute temperature of 115 kPa. Calculate the percent vaporized and the amounts of the overhead and bottoms streams. Assume that the vapor and liquid are in equilibrium. 

In contrast, most equipment can safely tolerate higher degrees of heat density than those defined for personnel. However, if anything vulnerable to overheating problems is involved, such as low melting point construction materials (e.g., aluminum or plastic), heat-sensitive streams, flammable vapor spaces, or electrical equipment, then the effect of radiant heat on them may need to be evaluated. When this evaluation is required, the necessary heat balance is performed to determine the resulting surface temperature, for comparison with acceptable temperatures for the equipment. 

The basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

In the usual distillation problem, the operating pressure, the feed composition and thermal condition, and the desired product compositions are specified. Then the relations between the reflux rates and the number of trays above and below the feed can be found by solution of the material and energy balance equations together with a vapor-liquid equilibrium relation, which may be written in the general form... 

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