Thermodynamic Equilibrium
As indicated by the double arrows, equations 2-4 to 2-8 are all reversible reactions, that is to say, they may proceed both from right to left as well as from left to right. In general, the forward and the reverse reactions take place simultaneously and at different rates. For any given temperature these reaction rates are proportional to the quantity of reactants available to drive the reaction in the direction under consideration.
If we take the CO shift reaction (2-7) as an example, the forward reaction rate, Гр is proportional to the molar concentrations of CO and H20 per unit volume, or
rf=kf- [CO] • [H20]
where the constant of proportionality Ay is temperature dependant. Similarly, for the reverse reaction,
rr=K' [C02] • [H2
Over a period of time these two reaction rates will tend to reach a common value and the gas composition will have reached a state of equilibrium. Under these circumstances
К _ [C02 • [H2]
P kf [CO] • [H20]
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where Kp is the temperature dependant equilibrium constant for the CO shift reaction. Assuming ideal gases this can also be expressed as
where Pco is the partial pressure and vco is the volume fraction —— of CO in the gas, and so on.
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Similarly the equilibrium constants for the other reactions can be expressed as
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for the Boudouard reaction (2-4),
for the water gas reaction (2-5), and
K _ PcO ' P H2 _ VCO ' V H2 pi p Рсн4 ' Рщо VCH4 ' VH2о
for the reforming reaction (2-8), where P is the total absolute pressure of the gas.
The temperature dependency of these equilibrium constants can be derived from fundamental data but are usually expressed as a correlation of the type
In (Кр т) =ln (KpfT0)+f(T)
where T is the absolute temperature in Kelvin. The derivation of the equilibrium constants is described in the file gasify. hlp on the companion website. The above (albeit nonlinear) equations 2-10 to 2-13 provide us with a means of determining the relative concentrations of the gas components in the syngas on the assumption that the reactions have reached equilibrium.
Note that in all the above discussions it has been assumed that the gases are ideal gases and no fugacities have been taken into account. Although many processes operate at pressures of 30-70 bar, this assumption is justified because of the very high temperatures in the processes, which lie very far from the critical temperature of
each compound. Note that even where the calculations are used for the low temperature CO shift reaction, which operates at temperatures of 200-250°C, this approximation gives sufficiently accurate results for basic designs.
