Syngas is produced from an oxygen-blown biomass gasifier. It is first passed through a water-gas shift reactor to convert CO to CO₂ and generate additional hydrogen from water and second through a pressure-swing adsorption unit to remove the CO₂, resulting in pure hydrogen, which is to be burned in a modified diesel engine that is capable of exploiting hydrogen's unique combustion properties to achieve high thermal efficiency.

One potential source of efficiency loss is the dissociation of water, which can occur at high temperatures, in the reaction:

H₂O <-> H₂ + 1/2 O₂      ...(Reaction 1)

You are unsure whether this would be a concern at the temperatures of interest, and so you seek to calculate the equilibrium composition and the adiabatic flame temperature of the combustion.

The equilibrium constant of reaction (1), evaluated at the system pressure of 75 atm*, is defined below in Eq. 1, where Xi are the mole fractions of the species, N is the total number of species involved, and the νi,pand νi,rare the stoichiometric coefficients of species in the products and reactants respectively that appear in Reaction 1:

Kp=∏iNXνi,p−νi,r.i...... (Eq. 1)

In the above, the operator ∏∏ is defined as:

∏iNai=a1×a2×...×aN

You can assume or take as givens:

• Combustion occurs at a constant pressure of 75 atm.
• The reactant temperature prior to combustion is 900 K.
• The relative air to fuel ratio λ (=1/Φ) is equal to 2.0, i.e. the combustion is overall lean with excess oxygen.
• Air consists of O₂ and N₂ in the ratio 1:3.76.
• The average species specific heat at constant pressure in both the reactant and product mixtures can be taken as c_p = 35 kJ/kmol/K.
• The formation enthalpies are:

h⁰_f,H2O = -240 MJ/kmol;

h⁰_f,O2 =h⁰_f,H2 = 0 MJ/kmol

• You can assume that Kp= 0.0001, approximately independent of temperature, (near to the estimated temperature of 2200 K). You are also reminded that Kp is evaluated at a reference pressure equal to the system pressure*, which removes the pressure dependence which would otherwise appear in Eq. 1.

Please respond to the questions below.

 

 * For anybody interested, and this is not required knowledge for the course but here, where Kp is defined not at standard state atmospheric pressure but at a different pressure, it is determined from:

Kp=exp(−ΔGT,P/(RuT)), where

ΔGT,P=∑1N(νi,p−νi,r)(g0i(T)+RuTln(P/P0))

This question could have been set with with Kp defined at atmospheric pressure, but then you would have needed to deal with the P/P0 factors in your calculation, and we didn't cover cases like that before, so I calculated this for the system pressure instead.

 

Calculate the amount of H₂ that is dissociated as a mole fraction of the original H₂ in the fuel, i.e. for one mole of H2 fuel, how much ends up as H₂ in the products?

Hint: when you write your Kp equation, you should get something like the below, which for the correct values of x, y and z would result (after squaring result the whole equation) in a cubic equation for b, the amount of hydrogen. Don't panic, I won't give you a cubic equation in the exam. Here, because the equilibrium constant is so small, the reactants are favoured over the products, and it is obvious that b will come out to be small, in which case you can approximate the Kp equation as:

Kp=b(A+b)x(B−b)y(C+b)z≈b(A)x(B)y(C)z

 

 part 1 ??

 

 

Determine the adiabatic flame temperature in K??