V. TRANSFERENCIAS DE DATOS DESDE EUROPA A ESTADOS UNIDOS
2. EL FUTURO DE LAS TRANSFERENCIAS DE DATOS TRANSATLÁNTICAS TRAS LA "CLOUD ACT"
In Section 1.3.3 we have derived Eq. (1.18) for calculating the minimum dry air requirement for combustion of one kmol of a gaseousfuel. A similar expression, Eq. (1.24), has been derived to calculate the minimum dry air requirement for complete combustion of one kilogram of a solid or a liquid fuel. We stress here again that Eqs. (1.18) and (1.24) are for calculating the dry air requirements.
However, combustion or atmospheric air is seldom completely dry and it con-tains moisture (water vapour). Accurate calculations of combustion stoichiometry should account for the presence of water vapour. In this paragraph we show how to do it. We recall that air that contains no water vapour is called dry air. Atmo-spheric or combustion air containing water vapour is named here as combustion air. The temperature of air in combustion applications ranges from about −20 to about 1300◦C. In most of the furnace applications combustion air is supplied at pressures that are slightly higher than ambient air pressure of 1 bar. However, in gas turbines and engines the combustion air is typically compressed to 20–30 bar pressure.
1.5.1 Absolute and relative humidity
It is convenient to treat combustion air as a mixture of water vapour and dry air since the composition of dry air remains constant but the amount of water vapour changes. It is certainly convenient to treat the water vapour in combustion air as an ideal gas and for ambient air pressures such an assumption is perfectly valid.
1.5 Humid Combustion Air
Even for pressures up to 30 bar and temperatures up to 1300◦C the ideal gas assumption is justifiable and the maximum departure from reality is typically in the range 0.2–6 %. Then the combustion air is treated as an ideal-gas mixture whose pressure is the sum of the partial pressure of the dry air (pdry air) and that of the water vapour (pv)
p = pdry air+ pv (1.31)
The partial pressure of water vapour (pv) is typically referred to as the vapour pressure. The temperature, however, is uniform throughout the dry-air/water-vapour mixture so that
T = Tdry air= Tv (1.32)
Usually the total pressure (p) is known whereas the partial pressure of water vapour (pv) depends on how much moisture is present in the mixture. For an ideal-gas mixture, the mole fraction of water vapour is then
xv= pv
p (1.33)
The amount of water vapour in the combustion air can be specified in various ways. However, the simplest way is to specify the mass of water vapour present in a unit of dry air. This is called absolute or specific humidity and in this lecture series is denoted as ϕ and is expressed in kg of water vapour per kg of dry air since where Mv and Mdry air are the molar masses of water and dry air, respectively whilst nv and ndry air stand for the number of moles of water vapour and dry air, respectively.
Dry air contains no water vapour and therefore its specific humidity is zero. Now let us add some water vapour to this dry air so the specific humidity (ϕ) increases.
If we add more water vapour the specific humidity keeps increasing until the air can hold no more moisture. At this point the air is said to be saturated with moisture vapour and it is called saturated air. The amount of water vapour in saturated air at a given temperature and total pressure can be determined using Eq. (1.34) by replacing pv by the saturation pressure psat of water at the given temperature. The saturation pressure of water vapour is plotted in Fig. 1.8 as a function of temperature using a relationship4
4In Chapter 3, Example 3.3, we will derive Eq. (1.35) using Clausius-Clapeyron equation.
1 Stoichiometry
psat= 611 · exp
−5304.3 · 1
T − 1
273.16
in Pa (1.35)
Water Vapour
pinkPasat
Temperature in K
10
5
0
280 290 300 310 320
Fig. 1.8: Saturation pressure of water vapour as a function of temperature. The plot is obtained using Eq. (1.35) which in the plotted range provides pressure values that are within 2 % accuracy with the values listed in steam tables [7].
The ratio of the amount of moisture the air holds to the maximum amount of moisture the air can hold (at the saturation state) at the same temperature is called the relative humidity γ
γ = pv
pv,sat
(1.36) where pv,sat stands for the saturation water vapour pressure at the specified tem-perature. The relative humidity (γ) ranges from 0 for dry air to 1 for saturated air. The amount of moisture that combustion air can hold depends on its tem-perature. Thus, the relative humidity of air (γ) changes with temperature even when its specific humidity (ϕ) remains constant. Using the relative humidity and the saturation pressure of water vapour, the specific humidity (ϕ) can then be calculated as follows:
ϕ = 0.662 · γ · psat
p − γ · psat (1.37)
1.5 Humid Combustion Air
1.5.1.1 Wet air requirement
In the previous paragraphs we have developed simple formulae for calculating the dry air requirements (ldry air); Eq. (1.17) for gaseous fuels while Eq. (1.23) for liquid and solid fuels. The above considerations on the combustion air humidity allows for inclusion of water vapour since
lwet air= ldry air+ ϕ · ldry air= (1 + ϕ) · ldry air (1.38) If there is a need to calculate the enthalpy of wet combustion air it can be easily done since
hwet air = hdry air+ ϕ · hvapour (1.39) where h stands for specific enthalpy in J/g (or kJ/kg). The enthalpy of water vapour at ambient air pressure in the temperature range −10 to 50◦C can be determined approximately using
hvapour(T ) ∼= 2501.3 + 1.82 · T in kJ/kg where T in◦C (1.40) For higher temperatures and higher pressures values from steam tables should be used.
Example 1.4
In Example 1.3 we have calculated the air requirement and the composition of dry and wet combustion products as a function of the excess air ratio for coal Fettnuss.
In Example 1.3 we have ignored the moisture content of the combustion air. The objective of this example is to include the moisture and by doing so to examine its effect on the results of the calculations. We assume here that the combustion air is supplied at 1 bar pressure and at a 20◦C temperature. Its relative humidity is 75 %.
Assumptions: the fuel is combusted to carbon dioxide and water.
One begins with calculating the saturation pressure of water vapour at 20◦C using Eq. (1.35) The absolute humidity is then
ϕ = 0.662 · γ · psat
1 Stoichiometry
so the minimum amount of wet combustion air is
lwet air,min = (1+ϕ) · ldry air,min= 1.0116 · 10.9496 = 11.0766 kg wet air/kg of fuel (1.43) The moisture supplied with the combustion air stream occurs in the (wet) com-bustion products so (see Example 1.3)
Vwet= 0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · ϕ · ldry air,min
18 (1.44)
and
Vwet = 0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · 0.007 06kmol wet products kg of fuel “as fired”
(1.45) Composition of wet combustion products is therefore as follows:
xH2O=
0.043 136
2 +0.03518 + λ · 0.007 06 Vwet
= 0.0235 + λ · 0.007 06
0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · 0.007 06 xCO2,wet =
0.824 658 12
Vwet
= 0.0687
0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · 0.007 06 xSO2,wet =
0.006 882 6 2
Vwet
= 0.0002
0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · 0.007 06 xO2,wet = (λ − 1) · lO2,min
Vwet
= (λ − 1) · 0.0787
0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · 0.007 06 xN2,wet = 0.79 · λ · ldry air,min
Vwet
= 0.79 · λ · 0.3743
0.0929 + 0.2957 · λ + 0.0787 · (λ − 1) + λ · 0.007 06 All the above mole (volume) fractions are in kmol/kmol of wet products.
1.5 Humid Combustion Air
At 10 % excess air ratio (λ = 1.1) the above formulae provide:
xH2O = 0.0721 xCO2,wet = 0.1584 xSO2,wet = 0.000 46 xO2,wet = 0.018 14 xN2,wet = 0.7498
Comments:
(a) Taking into account the combustion air moisture has resulted in a 1.2 % cor-rection to the minimum air requirement.
(b) However, the mole fraction of water vapour in (wet) combustion products has increased by around 31 %.
(c) Obviously neither the amount of the dry combustion products nor its com-position is affected by combustion air moisture content.
End of Example 1.4
1.5.2 Dew Point Temperature of Combustion Products
Typically combustion products contain water vapour. When for example a nat-ural gas is combusted the water vapour content in the combustion products may be as high as 16 % for λ = 1.2 as shown in Example 1.2. When coal Fettnuss is combusted the water content of around 7 % (see Example 1.4) is expected. While designing combustion systems it is required that combustion products are cooled down to low temperatures before they are released to the atmosphere. Thus, by cooling down the combustion products we may expect that below a certain temperature the water vapour begins to condensate. The dew-point temperature (Tdp) is defined as the temperature at which condensation begins when the com-bustion products (or generally moist air) is cooled at a constant pressure. In other words, Tdp is the saturation temperature of water corresponding to the vapour pressure, as shown in Fig. 1.9.
As a matter of fact Eq. (1.35) can be used to determine the due-point temperature if the pressure is given. Let us assume that there is 7 vol% water vapour content in combustion products of coal Fettnuss combustion. If the combustion products are at 1 bar pressure, the partial pressure of vapour is 7000 N/m2 and using Eq. (1.35) we can estimate that the dew-point temperature is around 312.4 K (39.3◦C).
Thus, in order to avoid condensation it is desired to keep the combustion products at temperatures typically 40–60◦C higher than the due point temperature.
Dew points vary with the amounts of O2, CO2, SO2, NOx,HCl in combustion products. In particular sulphur oxides have a pronounced effect on the dew point temperature as shown in Fig. 1.9 for several excess air ratios.
1 Stoichiometry
T
T1 Tdp
s p=cons
t.
v
1 2
Fig. 1.9: Cooling of combustion products (or moist air) at a constant temperature.
The T -s diagram shows the dew-point temperature.
The excess air curves are not equally spaced since the extra oxygen tends to produce more SO3 which exerts a catalytic effect in raising the dew point. For example the above estimated dew-point temperature of 39.3◦C would be almost doubled if 2 ppm of SO2was present. This is the reason that operators of coal-fired power station boilers maintain the flue gases at temperatures above 180–200◦C.
1.0 2.0 3.0 4.0 5.0
Weight % sulfur in fuel oil
Aciddewpoint,°C
135 140
130
120
115 145
20%excessair 15%
10%
5%
Fig. 1.10: Effect of sulphur and excess air on acid due point for a crude oil (adapted from [8]).