Rate Measures Transfer Units Approach To Equilibrium And Bypassing

What Controls Mass/Heat Transfer: Liquid or Gas Transfer or Bypassing Either gas side or liquid side of the interface can be controlling.

Liquid-Controlled In fractionation systems with high viscosity or component relative volatility that greatly exceeds 1, the liquid side will be controlling. This is clearly illustrated by Fig. 14-47 which shows a sharp decline in efficiency with either a rise in liquid viscosity or a rise in component relative volatility.

Note that high component relative volatility means the same thing as sparingly soluble. Oxygen dissolving in a fermentation reactor is an example of a system being liquid-controlled due to a sparingly soluble gas. Another application that is liquid-controlled is the removal of high relative volatility components out of residual oil.

Still another case where liquid controls is in condensing a pure vapor, as in Example 23, or absorbing a pure gas, as in Example 24.

Gas-Controlled The gas side dominates in gas cooling applications. An example is the quenching of a furnace effluent with a vaporizing liquid. In this application the liquid is nearly uniform in temperature. Restated, the reduction in driving force across the liquid side of the interface is unimportant.

Other applications that are gas-side-controlled include removal of a component such as NH3 from a gas by using an acidic liquid, or removing a component such as SO2 from a gas with a basic liquid. See Examples 19 through 22.

Bypassing-Controlled Trayed or packed columns operate with countercurrent flow and can achieve many equilibrium stages in series by good distribution of gas and liquid, and careful control of details. Other devices such as sprays are vulnerable to bypassing and are limited to one equilibrium stage.

Rate Measures for Interfacial Processes Terminology used for reporting rate data can be confusing. Normally rate data are reported on a volumetric basis with transfer rate and effective area combined. For example, kLa denotes mass-transfer data per unit volume. The L subscript means it is referenced to the molar concentration difference between the interface and the bulk liquid. This is commonly used on data involving a sparingly soluble (high relative volatility) component. Note that the lowercase k means the data deal only with the resistance in the liquid phase.

Less commonly, data are given as kGa. The G subscript means it is referenced to the molar concentration difference between the interface and the gas. This might be used for data on absorbing a gas such as NH3 by a highly acidic liquid. Note that kGa only deals with the resistance in the gas phase.

When one is dealing with direct contact heat transfer, the corresponding terms are hLa and hGa. Here the driving force is the temperature difference. The L subscript means that we are dealing with a liquid-limited process such as condensing a pure liquid. How to convert kLa data to an hLa value is illustrated by Example 23.

There are ways to combine the liquid and gas resistance to get an overall transfer rate such as KGa (as denoted by the uppercase K). However, data are rarely reported in this form.

Approach to Equilibrium Although rate measures such as kGa and hGa are often cited in the literature, they are often not as useful to designers as the simpler concept of approach to equilibrium. Approach to equilibrium compares the transfer between liquid and gas phases to the best possible that could be achieved in a single backmixed equilibrium stage.

Approach to equilibrium is easy to understand and easy to apply. Examples 17 through 23 illustrate its use.

Example 17: Approach to Equilibrium—Perfectly Mixed, Com-plete Exchange This would be approximated by a very long pipeline contactor where an acidic aqueous stream is injected to cool the gas and remove NH3.

If the adiabatic saturation temperature of the gas is 70°C, at the exit of the contactor, the gas would be cooled to 70°C.

Similarly, at the exit of the contactor, the NH3 in the gas would be zero, regardless of the initial concentration.

Example 18: Approach to Equilibrium—Complete Exchange but with 10 Percent Gas Bypassing A spray column is used, and an acidic liquid rains down on the gas of Example 17. If the initial NH3 is 1000 ppm and 10 percent of the gas bypasses, the NH3 in the exit gas would be

0.1(1000) = 100 ppm Similarly, if the gas enters at 120°C, at the exit we would find 10 percent of the differential above the adiabatic saturation temperature. For an adiabatic saturation temperature of 70°C, the exit gas temperature would be

Approach to Equilibrium—Finite Contactor with No Bypassing When there is no bypassing, the measure that sets the approach is the ratio of change to driving force. This ratio is called the number of transfer units NG. It is dimensionless. For heat-transfer applications, it can be envisioned as a conventional heat exchanger where a vaporizing liquid cools a gas:

Where TG = gas temperature and TL = liquid temperature. The number of transfer units NG can also be calculated as the capability for change divided by the thermal capacitance of the flowing

(system volume)(hGa) (volumetric flow rate)pGcG

(gas contact time)(hGa) PqCg

where a = interfacial area per unit volume hG = heat-transfer coefficient from interface to gas pG = gas density cG = gas specific heat

Note that in the above, performance and properties all refer to the gas, which is appropriate when dealing with a gas-limited transfer process.

This leads to a way to estimate the approach to equilibrium.

where E = "approach to equilibrium" fractional removal of NH3 or fractional approach to adiabatic liquid temperature Ng = number of transfer units calculated relative to gas flow

Example 19: Finite Exchange, No Bypassing, Short Contactor

A short cocurrent horizontal pipeline contactor gives 86 percent removal of NH3. There is no bypassing because of the highly turbulent gas flow and injection of liquid into the center of the pipe. What would we expect the exit gas temperature to be?

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