Phase temperatures

Phase Temperature range, °C Linear expansion coefficient X 10 /K Transformation expansion, 100 AL/L... 

Determination of the Gas-Phase Temperature. The development given above is in terms of interface conditions, bulk Hquid temperature, and bulk gas enthalpy. Often the temperature of the vapor phase is important to the designer, either as one of the variables specified or as an important indicator of fogging conditions in the column. Such a condition would occur if the gas temperature equaled the saturation temperature, that is, the interface temperature. When fogging does occur, the column can no longer be expected to operate according to the relations presented herein but is basically out of control. 

Gas-phase temperatures have been obtained by an extension of the graphical method illustrated (22). When equation 30 is divided by equation 34, the result is... 

Classical Adiabatic Design Method The classical adiabatic method assumes that the heat of solution serves only to heat up the liquid stream and that there is no vaporization of solvent. This assumption makes it feasible to relate increases in the hquid-phase temperature to the solute concentration x by a simple eutnalpy balance. The equihbrium curve can then be adjusted to account For the corresponding temperature rise on an xy diagram. The adjusted equilibrium curve will become more concave upward as the concentration increases, tending to decrease the driving forces near the bottom of the tower, as illustrated in Fig. 14-8 in Example 6. 

Product recoveiy from reversed micellar solutions can often be attained by simple back extrac tion, by contacting with an aqueous solution having salt concentration and pH that disfavors protein solu-bihzation, but this is not always a reliable method. Addition of cosolvents such as ethyl acetate or alcohols can lead to a disruption of the micelles and expulsion of the protein species, but this may also lead to protein denaturation. These additives must be removed by distillation, for example, to enable reconstitution of the micellar phase. Temperature increases can similarly lead to product release as a concentrated aqueous solution. Removal of the water from the reversed micelles by molecular sieves or sihca gel has also been found to cause a precipitation of the protein from the organic phase. 

Corrosion of metals by fuel ashes only occurs where the fuel ash contains a liquid phase. Temperatures at which the first liquid will form are inversely proportional to the oxygen partial pressure. Thus, when firing fuels at high excess air ratios, fuel ash corrosion occurs at lower temperatures than when firing fuels with low excess air ratios. 

Today, the use of CHIRBASE as a tool in aiding the chemist in the identification of appropriate CSPs has produced impressive and valuable results. Although recent developments diminish the need for domain expertise, today the user must possess a certain level of knowledge of analytical chemistry and chiral chromatography. Nevertheless, further refinements will notably reduce this required level of expertise. Part of this effort will include the design of an expert system which will provide rule sets for each CSP in a given sample search context. The expert system will also be able to query the user about the specific requisites for each sample (scale, solubility, etc.) and generate rules which will indicate a ranked list of CSPs as well their most suitable experimental conditions (mobile phase, temperature, pH, etc.). 

Heat to raise air from the blower discharge temperature to the regenerator dense phase temperature... 

The regenerator dense phase temperature (see Figure 8-7) can be adversely affected by the feed quality, the condition of the catalyst, the operating variables, and the mechanical conditions of the unit ... 

NOj, levels in the FCC flue gas typically range from 50-500 ppm. Nitrogen content of the feed, excess oxygen, regenerator residence time, dense phase temperature, and CO promoter all influence the concentration of NO. ... 

The oscillations of the phase temperatures can be presented in the following form... 

The basic scheme for the numerical solution is the same as that used for the 1 -D model, except that in this case the solid temperature field used to solve the DAE system for each monolith channel must be calculated from the three-dimensional solid-phase energy balance equation. The three-dimensional energy balance equation can be solved by a nonlinear finite element solver (such as ABAQUS) for the solid-phase temperature field while a nonlinear finite difference solver for the DAE system calculates the gas-phase temperature and... 

Transcriptionnal activity of pel genes responds differentially to catabolic repression, growth phase, temperature and nitrogen starvation. Iron limitation proved to be involved in the induction of severd of the pectinase encoding genes [7]. 

Reaction conditions 0.1 g of the zeolite Y modified catalyst, tested in a conventional glass microreactor with racemic butan-2-ol (7.35 x 10" mol h-1), prevaporized in a nitrogen diluent (6.2 -6.7 x 10" mol h-1). Products were analyzed using on-line GC with a 40m capillary y- cyclodextrin colimm with trifluoroacetyl stationary phase, temperature programmed from 25-70 "C with a split ratio of 120 1. 

Because homogeneous catalysis is usually carried out in the liquid phase, temperature control is relatively easy. However, the temperature must not be too high to prevent degradation of the catalyst complexes. 

It is assumed that there are no heat losses from the column and that there is zero heat exchange between the gas and liquid phases. Consequently the gas phase temperature will remain constant throughout the column. A liquid phase heat balance, for element of volume dV is given by... 

Pervaporation. Pervaporation differs from the other membrane processes described so far in that the phase-state on one side of the membrane is different from that on the other side. The term pervaporation is a combination of the words permselective and evaporation. The feed to the membrane module is a mixture (e.g. ethanol-water mixture) at a pressure high enough to maintain it in the liquid phase. The liquid mixture is contacted with a dense membrane. The other side of the membrane is maintained at a pressure at or below the dew point of the permeate, thus maintaining it in the vapor phase. The permeate side is often held under vacuum conditions. Pervaporation is potentially useful when separating mixtures that form azeotropes (e.g. ethanol-water mixture). One of the ways to change the vapor-liquid equilibrium to overcome azeotropic behavior is to place a membrane between the vapor and liquid phases. Temperatures are restricted to below 100°C, and as with other liquid membrane processes, feed pretreatment and membrane cleaning are necessary. 

An expression for the net rate of phase change can also be derived by assuming that the phase-change process is controlled solely by the rate at which heat can be transferred between the bulk liquid and the liquid surface. In this penetration theory approach, the liquid surface temperature is assumed to equal the gas-phase temperature. The heat transfer within a liquid element is assumed to occur by pure conduction, and therefore... 

The evaluation of rnel a in this case requires an a priori description of the phase temperature profiles. In general, investigators have assumed that gas and liquid are in thermal equilibrium. Therefore, Eq. (77) can be simplified to yield... 

If the vapor-phase temperature is to be evaluated from the Clausius-Clapeyron equation, the pressure in the two-phase tubular contactor must be known at each axial position. This need once again illustrates the necessity of obtaining an understanding of the hydrodynamics of two-phase systems in order to carry out the design of heat-transfer contactors. 

The assumptions inherent in the derivation of the Hertz-Knudsen equation are (1) the vapor phase does not have a net motion (2) the bulk liquid temperature and corresponding vapor pressure determine the absolute rate of vaporization (3) the bulk vapor phase temperature and pressure determine the absolute rate of condensation (4) the gas-liquid interface is stationary and (5) the vapor phase acts as an ideal gas. The first assumption is rigorously valid only at equilibrium. For nonequilibrium conditions there will be a net motion of the vapor phase due to mass transfer across the vapor-liquid interface. The derivation of the expression for the absolute rate of condensation has been modified by Schrage (S2) to account for net motion in the vapor phase. The modified expression is... 

The method is also applicable to liquids and solids (Sowada and Warman, 1982 Sowada et at, 1982) for the condensed rare gases, a correction is needed for recombination. Sowada et at (1982) obtained the following values of thermalization times, within 20% accuracy, given here in parenthesis as (phase, temperature... 

Heterogeneous phases (solid and gas) may give rise to inter-phase temperature gradients. 

Summary of literature data on methane decomposition catalysts and preferred temperature range. Catalysts 1 = nickel, 2 = iron, 3 = carbon, and 4 = other transition metals (Co, Pd, Pt, Cr, Ru, Mo, W). The dotted line arbitrarily separates heterogeneous (catalytic) and homogeneous (noncatalytic, gas phase) temperature regimes of the methane decomposition reaction. 

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