Saturation temperature calculation

Example 4.1 Saturated steam at a pressure 9.8 10 3 MPa, condenses on a vertical wall. The wall temperature is 5 K below the saturation temperature. Calculate the following quantities at a distance of H = 0.08 m from the upper edge of the wall the film thickness 5(H), the mean velocity wm of the downward flowing condensate, its mass flow rate M/b per m plate width, the local and the mean heat transfer coefficients. 

Alternatively, the saturation temperature calculated from the Antoine equation at pressure 2 bar is 395.6 K = 122.4 °C. Since the system temperature is lower, it is compressed liquid, (i.e., at constant pressure, temperature would have to be raised to 122.4 °C for the liquid to boU). Both calculations give the same answer. 

If the vapor is superheated at the inlet, the vapor may first be desuperheated by sensible heat transfer from the vapor. This occurs if the surface temperature is above the saturation temperature, and a single-phase heat-transfer correlation is used. If the surface is below the saturation temperature, condensation will occur directly from the superheated vapor, and the effective coefficient is determined from the appropriate condensation correlation, using the saturation temperature in the LMTD. To determine whether or not condensation will occur directly from the superheated vapor, calculate the surface temperature by assuming single-phase heat transfer. 

Experimentally it has been shown that for air-water systems the value of Tj /Zc c, the psychrometric ratio, is approximately equal to 1. Under these conditions the wet-bulb temperatures and adiabatic-saturation temperatures are substantially equal and can be used interchangeably. The difference between adiabatic-saturation temperature and wet-bulb temperature increases with increasing humidity, but this effect is unimportant for most engineering calculations. An empirical formula for wet-bulb temperature determination of moist air at atmospheric pressure is presented by Liley [Jnt. J. of Mechanical Engineering Education, vol. 21, No. 2 (1993)]. 

Often in plant operations condensate at high pressures are let down to lower pressures. In such situations some low-pressure flash steam is produced, and the low-pressure condensate is either sent to a power plant or is cascaded to a lower pressure level. The following analysis solves the mass and heat balances that describe such a system, and can be used as an approximate calculation procedure. Refer to Figure 2 for a simplified view of the system and the basis for developing the mass and energy balances. We consider the condensate to be at pressure Pj and temperature tj, from whence it is let down to pressure 2. The saturation temperature at pressure Pj is tj. The vapor flow is defined as V Ibs/hr, and the condensate quality is defined as L Ibs/hr. The mass balance derived from Figure 2 is ... 

Calculations involving to systems where the Lewis relation is not applicable are very much more complicated because the adiabatic saturation temperature and the wet-bulb temperature do not coincide. Thus the significance of the adiabatic cooling lines on the psychrometric chart is very much restricted. They no longer represent the changes which take place in a gas as it is humidified by contact with liquid initially at the adiabatic saturation temperature of the gas, but simply give the compositions of all gases with the same adiabatic saturation temperature. 

The bulk temperature Tb onb is close to saturation temperature Ts, when the values calculated using Eqs. (6.32), (6.33) and (6.34) do not differ significantly from unity. In Fig. 6.11 the experimental results reported by Kennedy et al. (2000) are presented as the dependence of the value /c,onb (Eq. 6.32) on the Peclet number. The data may be described by the single line of /c,onb = 0.96. In this case the bulk temperature 2b,onb, at ONE point should not differ significantly from 7s. Experimental results given in Table 6.4 support this statement. 

The results of numerical calculations of the velocity distribution within the vapor and liquid domains for two values of the difference between wall and saturation temperatures are shown in Fig. 10.17. It is seen that the vapor velocity reaches 100-150 m/s in the region of micro-film. The liquid velocity is much smaller than those in vapor. 

If the degree of superheat is large, it will be necessary to divide the temperature profile into sections and determine the mean temperature difference and heat-transfer coefficient separately for each section. If the tube wall temperature is below the dew point of the vapour, liquid will condense directly from the vapour on to the tubes. In these circumstances it has been found that the heat-transfer coefficient in the superheating section is close to the value for condensation and can be taken as the same. So, where the amount of superheating is not too excessive, say less than 25 per cent of the latent heat load, and the outlet coolant temperature is well below the vapour dew point, the sensible heat load for desuperheating can be lumped with the latent heat load. The total heat-transfer area required can then be calculated using a mean temperature difference based on the saturation temperature (not the superheat temperature) and the estimated condensate film heat-transfer coefficient. 

The coefficients a and b in Equation 23.10 can be correlated as functions of the saturation temperature difference across the turbine9. In fact, the coefficients in Equation 23.10 are related to the pressure drop across the turbine. However, in the model, the pressure drop is replaced by its equivalent saturation temperature difference. Use of temperature difference allows easier interface to utility calculations with process heating and cooling demands. Thus ... 

Bankoff calculated Tx by using Gunter s experimental data and obtained the interesting result that, in each series of runs, Tx rises steeply toward the saturation temperature as burnout is approached. This gives a fairly thick bubble layer, which increases the degree of superheat near the wall. Bankoff concluded that burnout occurs when the core is unable to remove the heat as fast as it can be transmitted by the wall layer. ... 

In a vaporization process, the pressure at each axial position must be known so that the saturation temperature can be calculated and the rate of phase change predicted. In Section I, the present state of the art for calculating pressure drop and holdups in isothermal incompressible two-phase... 

We can calculate Qln + Evap if we determine the steam saturation temperature from the steam... 

Assume a condenser built with a single tube if 12.5 mm I.D., which is fed with 150 kg/h of R-22 refrigerant (Du Pont). Calculate the tube length needed, assuming a wall at a constant temperature of 24.4 °C and a saturation temperature of 30°C. The fluid properties are shown in the Table 3.4-5. 

Calculate the heat exchanger duty. Note that the exchanger outlet temperature, T2, is equal to the compressor inlet temperature. The benzene enters the exchanger as a subcooled liquid. In the exchanger the liquid is first heated to the saturation temperature at P1 vaporized and... 

On its way downwards, the liquid phase is of course depleted with respect to its more volatile component(s) and enriched in its heavier component(s). At the decisive locus, however, where both phases have their final contact (i.e., the top of the column), the composition of the liquid is obviously stationary. For a desired composition of the gas mixture, the appropriate values for the liquid phase composition and the saturator temperature must be found. This is best done in two successive steps, viz. by phase equilibrium calculations followed by experimental refinement of the calculated values. The multicomponent saturator showed an excellent performance, both in a unit for atmospheric pressure [18] and in a high-pressure apparatus [19, 20] So far, the discussion of methods for generating well defined feed mixtures in flow-type units has been restricted to gaseous streams. As a rule, liquid feed streams are much easier to prepare, simply by premixing the reactants in a reservoir and conveying this mixture to the reactor by means of a pump with a pulsation-free characteristic. 

This publication arranges the published papers on adsorption of polymers with special regard to experiment and theory. A summary of all investigated systems is given. The experimental methods are outlined and the amounts adsorbed are discussed as a function of the system and experimental parameters (polymer, adsorbent, solvent, molecular, concentration, time, weight and temperature). Calculated and experimental amounts of saturation, the number of contact points per molecule adsorbed, the thickness of the adsorbed layer, the adsorption isotherms, the heats of adsorption, the effects of desorption are compared. Assumptions on the structur of the adsorbed layer and the mechanism of polymer adsorption are made and discussed. 

The saturation temperature of steam at the boiler pressure of 8,600 kPa is 300.06°C, and the temperature to which the feedwater can be raised in the heaters is certainly less. This temperature is a design variable, which is ultimately fixed by economic considerations. However, a value must be chosen before any thermodynamic calculations can be made. We have therefore arbitrarily specified a temperature of 226°C for the feedwater stream entering the boiler. We have also... 

If the vapor to be condensed is superheated, the preceding equations may be used to calculate the heat-transfer coefficient, provided the heat flow is calculated on the basis of the temperature difference between the surface and the saturation temperature corresponding to the system pressure. When a noncondensable gas is present along with the vapor, there may be an impediment of the heat transfer since the vapor must diffuse through the gas before it can condense on the surface. The reader should consult Refs. 3 and 4 for more information on this subject. 

The methods presented above are applicable only for conditions in which the heat transferred is a straight-line function of temperature. For systems that do not meet this condition, the total heat-release curve can be treated in sections, each section of which closely approximates the straight-line requirement. A log mean temperature difference can then be calculated for each section. Common examples in which this approach is encountered include (1) total condensers in which the condensate is subcooled after condensation, and (2) vaporizers in which the fluid enters as a subcooled liquid, the liquid is heated to the saturation temperature, the fluid is vaporized, and the vapor is heated and leaves in a superheated state. 

Sup eat of a pore vapor is removed at the same coeffidrat as fOT condensation of the sahirated vapOT if the exit coolant temperature is less than the saturation temperature (at the pressure existing in the v x phase) and if the (constant) saturation temperature Is used in calculating the mean temperature differmce. But see note k tor vapor mixtures with or without noncooidensable gas. 

SubcooUng heat load is transferred at the same coefficient as latent heat load in kettle reboilers, using the saturation temperature in the mean temperature difference. For horizontal and vertical thermosiphons, a separate calculation is required for the sensible heat transfer area, using appropriate sensible heat transfer coefficients and the liquid temperature- profile for the mean temperature difference. 

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