Isothermal evaporation water

Type V isotherms of water on carbon display a considerable variety of detail, as may be gathered from the representative examples collected in Fig. 5.14. Hysteresis is invariably present, but in some cases there are well defined loops (Fig. 5.14(b). (t ), (capillary-condensed water. Extreme low-pressure hysteresis, as in Fig. 5.14(c) is very probably due to penetration effects of the kind discussed in Chapter 4. 

Water evaporation occurs when the vapor pressure of the water at the surface, which is temperature dependent, is greater than the water pressure in the subsurface, which is dependent on relative humidity and temperature. The isothermal evaporation process is described by Stumm and Morgan (1996) via a reaction progress model, in which the effects of the initial reaction path are based on the concept of partial equilibrium. Stumm and Morgan (1996) describe partial equilibrium as a state in which a system is in equilibrium with respect to one reaction but out of equilibrium with respect to others. As an example, Stumm and Morgan (1996) indicate (Fig. 7.1) that water with a negative residual alkalinity (i.e.. 

Fig. 7.1 Isothermal evaporation (25°C) of natural water leading to CaCO precipitation 2[Ca +] > [Aik] (with pCOj = 10 atm). The concentration factor is the degree by which the water has been reduced by volume compared to the initial solution. (Stumm and Morgan 1996)...

The spring waters of the Sierra Nevada result from the attack of high C02 soil waters on typical igneous rocks and hence can be regarded as nearly ideal samples of a major water type. Their compositions are consistent with a model in which the primary rock-forming silicates are altered in a closed system to soil minerals plus a solution in steady-state equilibrium with these minerals. Isolation of Sierra waters from the solid alteration products followed by isothermal evaporation in equilibrium with the eartKs atmosphere should produce a highly alkaline Na-HCO.rCOA water a soda lake with calcium carbonate, magnesium hydroxy-silicate, and amorphous silica as precipitates. 

Now consider the isothermal evaporation of water from a surface and the subsequent diffusion through a stagnant air layer, as shown in Fig. 11-4. The free surface of the water is exposed to air in the tank, as shown. We assume that the system is isothermal and that the total pressure remains constant. We further assume that the system is in steady state. This requires that there be a slight air movement over the top of the tank to remove the water vapor which... 

Structure of the material by a model based largely on evidence from total and non-evaporable water contents and water vapour sorption isotherms. Powers later modified the model in minor respects (P34). 

The content of non-evaporable water, relative to that in a fully hydrated paste of the same cement, was used as a measure of the degree of hydration. Portland cement paste takes up additional water during wet curing, so that its total water content in a saturated, surface dry condition exceeds the initial w/c ratio. Evidence from water vapour sorption isotherms indicated that the properties of the hydration product that were treated by the model were substantially independent of w/c and degree of hydration, and only slightly dependent on the characteristics of the individual cement. The hydration product was thus considered to have a fixed content of non-evaporable water and a fixed volume fraction, around 0.28, of gel pores. 

Water composition is also affected by concentration resulting from evaporation (and evapotranspiration). Example 15.1 will illustrate the principles, procedures, and calculations of the effect of concentrating natural waters by isothermal evaporation for a few simplified systems. These calculations illustrate how the reaction path of natural waters during evaporation depends on the Ca /UCO ratio. In a reaction progress model the effects of initial reactions on a reaction path, for example, on the appearance of a solid stable phase and on the redistribution of aqueous species, are described. Reaction progress models are usually based on the concept of partial equilibrium. Partial equilibrium describes a state in which a system is in equilibrium with respect to one reaction, but out of equilibrium with respect to others. 

Example 15.1. Isothermal Evaporation of a Natural Water Leading to CaCOj Precipitation Compute pH and solution composition during isothermal evaporation (25 C) for three types of calcium bicarbonate-containing waters... 

How much water must be evaporated off before sodium chloride begins to be deposited, and how much pure sodium chloride can be obtained by isothermal evaporation of the solution at 25° ... 

Ksenzenko, V.I., Khojamamedov, A.M., Kuliev, Ch.A., and Ovezova, O., The behaviour of rare and isolated elements during the isothermic evaporation of underground mineralized waters at the Gaurdak deposit , Izvestia AS TSSR, Series of Physical-technical chemical and geological sciences, 1978, (3), 104-107. 

The scale of operation often has an overriding importance on the selection of the equipment because of the means used for heat transfer. For very small-scale crystallization work it is common to use radiation. The capacity of such equipment varies from a few liters up to several hundreds of liters per day (of solution cooled). For operation on scales up to several thousand liters per day, it is possible to use tanks with water-cooled coils and an agitator. For large-scale applications where the quantity of solution is thousands of liters per day, it is almost universal practice to use vacuum evaporation to remove the solvent this is true whether the solution is cooled by adiabatic evaporation or in equipment where crystallization occurs because of isothermal evaporation. 

The effect of isothermal evaporation on such a system can be shown as follows. If water is evaporated from an unsaturated solution represented by... 

Figure 4.33. Representation of water content a) isothermal evaporation , b) crystallization by cooling...

For this gas-film-controlled system, the rate of mass transfer is proportional to gas rate to approximately the 0.8 power. This is similar to data on the isothermal evaporation of pure liquids from a pipe wall into a turbulent air stream. There, Gilliland and Sherwood showed that the mass transfer rate is proportional to the gas mass velocity to the 0.83 power [4]. For systems evaporating water into an air stream, the effect of the liquid rate is similar to that for absorption. Because a large percentage of the heat is transferred by the vaporization of water, it is reasonable to find that the effect of gas and liquid rates is similar to that for other gas-film-controlled mass transfer operations. 

The thermos phon circulation rate can be as high as 10 to 15 times the coolant evaporation rate. This, in turn, eliminates any significant temperature difference, and the jacket is maintained under isothermal conditions. In this case, the constant wall temperature assumption is satisfied. During starting of the thermosiphon, the bottom can be 20-30°C hotter, and the start of circulation can be established by observing that the difference between the top and bottom jacket temperature is diminishing. Figure 2.2.5 (Berty 1983) shows the vapor pressure-temperature relationship for three coolants water, tetralin, and Dowtherm A. 

The discussion of the last section is then useful in considering the evaporative cycles. We shall see that the effect of water injection downstream of the compressor (and possibly in the cold side of the heat exchanger) may lead towards the [CBTJiXr type of plant, with increased cold side effective specific heat and hence increased heat exchanger effectiveness. Water injection in the compressor may lead to a plant with isothermal compression. 

It can be seen from Figure 13.5 that for the air-water system a straight line, of slope equal to the enthalpy of dry saturated steam (2675 kJ/kg), is almost parallel to the isothermals. so that the addition of live steam has only a small effect on the temperature of the gas. The addition of water spray, even if the water is considerably above the temperature of the gas, results in a lowering of the temperature after the water has evaporated. This arises because the. latent heat of vaporisation of the liquid constitutes the major part of the enthalpy of the vapour. Thus, when steam is added, it gives up a small amount of sensible heat to the gas, whereas when hot liquid is added a small amount of sensible heat is given up and a very much larger amount of latent heat is absorbed from the gas. 

The N2 adsorption-desorption isotherms of dried chitosan gel and chitosan-zeolite composites are reported in Figure 4 (a). Dried chitosan gels present a surface area lower than 5 m2 g"1 and virtually no porosity, the evaporation of water having brought about the coalescence of the polymer fibrils. The composites with a small amount of zeolites (less than 8 % for the zeolite X composite) present a type 4 isotherm leaning towards... 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

In order to achieve the isothermal heat addition and isothermal heat rejection processes, the Carnot simple vapor cycle must operate inside the vapor dome. The T-S diagram of a Carnot cycle operating inside the vapor dome is shown in Fig. 2.2. Saturated water at state 2 is evaporated isothermally to state 3, where it is saturated vapor. The steam enters a turbine at state 3 and expands isentropically, producing work, until state 4 is reached. The vapor-liquid mixture would then be partially condensed isothermally until state 1 is reached. At state 1, a pump would isentropically compress the vapor-liquid mixture to state 2. 

---