Dimethyl Ether from Syngas, Kinetic Equations with Rate, Equilibrium Constants and Adsorption Coefficients

Methanol formation

CO + 2H₂ ↔ CH₃OH                                                 −43.4 kcal/mol-DME ------(1)

CO₂ + 3H₂ ↔ CH₃OH + H₂O                                     −13.5 kcal/mol-DME ------(2)

Methanol dehydration to DME

2CH₃OH ↔ CH₃OCH₃ + H₂O                                   −5.6 kcal/mol-DME ---------(3)

Water gas shift reaction (WGS)

CO + H₂O ↔ CO₂ + H₂                                              −9.8 kcal/mol-DME ---------(4)

Rate constants	Parameters, Aexp(B/RT )	A	B
	k1	7380	-54307
	k2	5059	-67515
	k3	1062	-43473
	k4	73976	-20436
Adsorption coefficients	KCO	3.934×10-6	37373
	KCO2	1.858×10-6	53795
	KH2	0.6716	-6476
	KCH3OH	3.480×10-6	54689

Equilibrium constants:

ln K_f1,K_f2 : 4213/T – 5.752 lnT – 1.707×10^-3T +2.682×10^-6T² – 7.232×10^-10T³ + 17.6

ln K_f3 : 4019/T + 3.707 lnT – 2.783×10^-3T +3.8×10^-7T² – 6.561×10^-4/T³ – 26.64

ln K_f4 : 2167/T – 0.2258 lnT – 1.037×10^-3T – 2.331×10^-7T² – 1.277

Rate equations:

R_CO = k₁f_COf²_H2(1-β₁) / (1+ K_CO f_CO+ K_CO2 f_CO2 + K_H2 f_H2)³

R_CO2 = k₂f_CO2f³_H2(1-β₂) / (1+ K_CO f_CO+ K_CO2 f_CO2 + K_H2 f_H2)⁴

R_DME = k₃f_CH3OH(1-β₃) / (1+ √(K_CH3OH f_CH3OH))²

R_WGS = k₄f_H2O(1-β₄) / (1+ K_CO f_CO+ K_CO2 f_CO2 +√ (K_H2 f_H2))

β₁ = f_CH3OH / K_f1f_COf²_H2

β₂ = f_CH3OH f_H2O / K_f2f_CO2f³_H2

β₃ = f_DME f_H2O / K_f3f³_CH3OH

β₄ = f _CO2f_H2 / K_f4f_CO f_H2O

Where, f = fugacity;
fugacity of methanol = f_CH3OH
The above parameters are for Langmuir-Hinshelwood Hougen Watson which is as an adsorption-desorption model on the surface of the respective catalyst.