Theory of deaeration
Principle of physical deaeration
The equilibrium between gas dissolved in water and gas in steam is given by Raoult´s law. This law states that the ratio between the partial gas pressure in the steam and the product of the coefficient of activity and the concentration of the gas in the water at a given temperature is constant, if the gas in the steam fulfillls the condition P.V/T = constant, then:
Pg = h · a · Cg (1)
Pg = the partial gas pressure in the steam
h = distribution coefficient
a = the coefficient of activity
Cg = the concentration of the gas in the water
At low, partial pressures, oxygen and carbon dioxide in steam behave according to the relationship P.V/T = constant.
The coefficient of activity is a measure for the deviation from the ideal behavior of the gas dissolved in water or, in other words, a measure for the interaction between the dissolved gas and the water. For oxygen the coefficient of activity is 1.0, if the concentration is smaller than 50 ppm. That of carbon dioxide greatly depends on the dissolved quantity of carbon dioxide and the chemical composition of the water.
The ratio constant h is determined by the kind of gas and the temperature. Table 1 shows the values of h for oxygen and carbon dioxide.
|14.3 x 10-3
|0.298 x 10-3
|18.4 x 10-3
|0.427 x 10-3
|22.6 x 10-3
|0.581 x 10-3
|26.8 x 10-3
|0.767 x 10-3
|30.2 x 10-3
|0.963 x 10-3
|33.4 x 10-3
|1.170 x 10-3
|35.8 x 10-3
|1.420 x 10-3
|38.2 x 10-3
|39.7 x 10-3
|40.6 x 10-3
|40.7 x 10-3
Table 1. Distribution coefficient h of oxygen and carbondioxide for water at different temperatures in bara/ppm.
The principle on which the physical deaeration process is based is the tendency towards restoring the equilibrium as defined by the above-mentioned law after that equilibrium has previously been disturbed. The disturbances of equilibrium that bring about deaeration of the water are the decrease in the partial gas pressure in the steam and the increase of the temperature of the water. At water temperatures below boiling point the decrease in the partial gas pressure is brought about by removing gas from the steam. By increasing the temperature the solubility of the gas in the steam decreases at a constant partial pressure. If the water temperature is raised to boiling point at the prevailing pressure in the deaerator, the total pressure is equal to the water-vapor pressure, which implies that the partial gas pressure is zero. The water temperature rises as a result of condensation of the steam.
Decrease of the partial gas pressure and/or increase of the temperature are not the only factors of importance in the deaeration process, since the transport velocity of the gas also plays a role. This velocity is determined by:
- the diffusion of the gas in the water
- the flow of the water and of the steam
- the ratio between the area of the contact surface water-steam and the volume of water.
Diffusion of the gas in the water
When water is deaerated, the concentration of the gas molecules in the water is lower at the contact surface than elsewhere in the water. In the steam, this is exactly the other way around. Owing to the differences in concentration and the thermal movement of the gas molecules, transportation of gas molecules takes place towards the contact surface in the water and away from the contact surface in the steam. At the contact surface, Raoult´s law invariably applies. It will be clear that the deaeration rate is determined by the phase in which the transportation of the gas molecules is slowest. As the ratio between the diffusion coefficient (a measure for the thermal movement) of the gas in water and that of the gas in steam is approximately 10-4, the deaeration rate is fully determined by the transportation of the gas molecules in the water.
Fig. 2 Schematic display of gas concentration in the steam/water contact area with convection and diffusion.
Flow of water and steam
The flow of water and steam raises the deaeration rate. In the interfacial layer on either side of the water-steam contact, surface flow in a direction perpendicular to the contact surface can not occur. The gas transport there is still exclusively only possible due to diffusion. In places further away from the contact surface, the flow equalizes the concentration of the gas, see figure 2. Hence, the gas transport in the two media is controlled by a narrow diffusion zone along the contact surface. Owing to the great difference between the diffusion coefficient of the gas in water and that of the gas in steam, the deaeration rate will be determined by the diffusion zone on the water side of the contact surface. The gas transport in this diffusion zone is maximum at the lowest possible partial pressure in the steam. This condition is fulfilled when the gas is rapidly discharged from the deaerator by flow in the steam.
Ratio between contact surface water-steam and water volume.
To ensure efficient deaeration it is necessary to make the transport route that the gas molecules have to travel by diffusion as short as possible. This can be achieved by formation of the water into very tiny droplets before the steam is passed through the water.
- A. Droplet deaeration
- B. Bubble-formation in droplets
- C. Effects in droplet deaeration
- D. Influence of droplet size
- E. Effect of surface tension
The residence time of the water in the steam compartment of the sprayer is too short in some cases to ensure optimum deaeration and for this reason provision is made for post deaeration, which takes place in the water reservoir. The gas that has remained behind is expelled by conducting steam through the water by means of a steam rake.
As the steam bubbles through the water, there is a tendency according to Raoult´s law for an equilibrium to be established between the gas in the steam bubbles and the dissolved gas in their immediate vicinity. Adequate contact time is required to attain this equilibrium. This is the case when process conditions are so arranged that the steam bubbles are small and the distance they have to travel is great. A steam rake is the best means to achieve this.
A second function of the steam bubbles is to start and maintain the circulation in the water reservoir, whereby the diffusion path of the gas is considerably shortened. Compared with any other method of supplying the steam, the steam rake construction has the advantage that the circulation in the reservoir is more intensive.
Removal of carbon dioxide water
With a pH lower than 4 the activity coefficient of the total carbon dioxide dissolved in water is set at 1.0; with higher pH values the coefficient is smaller. Owing to the interaction with the water the dissolved carbon dioxide manifests itself not only as CO2, but also in the form of H2CO3 and the ions HCO3 and CO3 2-. The equilibria formulae are:
CO2 + H2O ↔ H2CO3 (6)
H2CO3 ↔ H+ + HCOˉ3 (7)
HCOˉ3 ↔ H+ + CO32- (8)
As the quantity of H2CO3, in comparison with that of the ions, is negligibly small, the equilibria (6) and (7) can be combined as follows:
CO2 + H2O ↔ H+ + HCOˉ3 (9)
With the aid of the equilibrium constants it is possible to calculate the ratios, at a given temperature, of the quantities of CO2, HCOˉ3 and CO32- with respect to the total dissolved quantity of carbon dioxide. In figure 9 these ratios at 25oC are graphically represented as a function of the acid value.
This graph was drawn up on the assumption that no other substances than CO2 were dissolved in the water. At temperatures above 25oC the curves in figure 4 shift a little to the left.
Fig. 4. Relation between molar ratio and pH.
Fig. 5. Relation between the partial pressure of carbon dioxide and oxygen in the steam and the amount of dissolved carbon dioxide and oxygen in the water.
During the deaeration process the dissolved carbon dioxide is removed from the water in the form of CO2. The ion HCOˉ3 indirectly takes part in the formation of the CO2process, because when the CO2 content drops it is converted into CO2 according to equation (9). If CO32 is present (pH > 8.3 at 25oC), it is technically absolutely impossible – owing to the absence of CO2 to drive off the carbon dioxide dissolved in the water by partially lowering the carbon-dioxide pressure in the steam. The pH of pure water containing dissolved carbon dioxide lies between 4 and 7, depending on the quantity of carbon dioxide. For a total carbon dioxide content in excess of 1 ppm at 25oC the following approximation formula applies:
pH = 5.5 – ½ log Ctot. CO2
Ctot. CO2 = the total carbon dioxide concentration in ppm. Between 0.01 and 1 ppm total carbon dioxide the pH calculated according to the approximation formula is 0.2 higher than the actual pH.
In pure water the carbon dioxide is only dissolved in the form of CO2 and HCOˉ3 ions. According to figure 4 the carbon dioxide is chiefly present as CO2 at pH = 4 and as HCOˉ3 at pH = 7. This implies that the less carbon dioxide is dissolved in the water, the greater the HCOˉ3 content is with respect to that of CO2. Figure 5, which represents the relationship between the partial carbon dioxide pressure in the steam and the total dissolved quantity of carbon dioxide at 20oC, illustrates how great the deviation from the equation Pco2-gas = h.C tot. CO2 is with small quantities of carbon dioxide. The deviation can be calculated with the aid of the activity coefficient of the total dissolved carbon dioxide, which has been made equal here to CO2/tot. CO2.
For the sake of comparison figure 5 also shows the relationship between solubility and partial gas pressure for oxygen. This illustrates how much more difficult it is to remove carbon dioxide from the water than oxygen. To be able to lower the oxygen content in water at 20 °C to 0.005 ppm a partial oxygen pressure of 1.13 x 10-4 bara is essential. At the same carbon dioxide pressure it is only possible to lower the carbon dioxide content in the water to 0.280 ppm. If by adding acid care is taken to keep the pH lower than 4, a content of 0.195 ppm can be attained. The carbon dioxide is then chiefly dissolved as CO2.
The lowering of the total carbon dioxide content to very low values cannot be achieved with a deaerator. To attain pressures in the steam are essential and these are hard or impossible to realize. Owing to the lack of data it is impossible to give a diagram as shown in figure 10 also at 100 °C. On the strength of the data mentioned in the present article, however, it can be predicted that the removal of carbon dioxide will be easier at temperatures above 20 °C.