Integration of the Design Equation
Integration indicated by equation (15) is usually performed by values of V1 and kya averaged over the column height. This introduces small error in light of the low concentration of water vapor in the gas stream. Beyond this, knowledge of the relation between the enthalpy in the main gas phase and that at the gas-liquid interface is necessary. Such a relation can be obtained by now considering the transfer process on the liquid side of the interface. Combining the enthalpy balance (Equation (5)) with the liquid transfer rate (Equation (9)) gives
Equation (18) applies at any point in an air-water contacting device. From it, the temperature and the enthalpy of the interface can be determined at any point for which the liquid temperature (TL), the gas enthalpy (HV), and the ratio of the liquid-phase heat transfer coefficient to the gas-
phase heat transfer coefficient to the gas-phase mass transfer coefficient based upon mole-ratio driving forces are known.
The interface conditions can be obtained through equation (18) using a graphical method.
A plot is drawn with coordinates of liquid-phase temperature versus enthalpy of the gas phase. On it, the locus of interface Hi and Ti values can be plotted by realizing that at the interface the vapor phase will be saturated at the interface temperature if the assumption that equilibrium exists at a phase boundary is tenable. From the saturation curve on the air-water humidity chart, the saturation molal humidity can be obtained for any desired temperature. The saturation, or interface, enthalpy can then be calculated or read from the humidity chart.
On the same plot, an “operating line” of HV versus TL can be plotted by combining equations (5) and (6) and integrating. This curve represents the path of bulk-phase conditions as the fluids pass through the unit. Thus,
Integration of the Design Equation
Integration indicated by equation (15) is usually performed by values of V1 and kya averaged over the column height. This introduces small error in light of the low concentration of water vapor in the gas stream. Beyond this, knowledge of the relation between the enthalpy in the main gas phase and that at the gas-liquid interface is necessary. Such a relation can be obtained by now considering the transfer process on the liquid side of the interface. Combining the enthalpy balance (Equation (5)) with the liquid transfer rate (Equation (9)) gives
Equation (18) applies at any point in an air-water contacting device. From it, the temperature and the enthalpy of the interface can be determined at any point for which the liquid temperature (TL), the gas enthalpy (HV), and the ratio of the liquid-phase heat transfer coefficient to the gas-
phase heat transfer coefficient to the gas-phase mass transfer coefficient based upon mole-ratio driving forces are known.
The interface conditions can be obtained through equation (18) using a graphical method.
A plot is drawn with coordinates of liquid-phase temperature versus enthalpy of the gas phase. On it, the locus of interface Hi and Ti values can be plotted by realizing that at the interface the vapor phase will be saturated at the interface temperature if the assumption that equilibrium exists at a phase boundary is tenable. From the saturation curve on the air-water humidity chart, the saturation molal humidity can be obtained for any desired temperature. The saturation, or interface, enthalpy can then be calculated or read from the humidity chart.
On the same plot, an “operating line” of HV versus TL can be plotted by combining equations (5) and (6) and integrating. This curve represents the path of bulk-phase conditions as the fluids pass through the unit. Thus,
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