Adiabatic Reactor Analysis for Methanol Synthesis Plant Note Book Series: PNBS-0604

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Adiabatic Reactor Analysis for
Methanol Synthesis
Plant Note Book Series: PNBS-0604
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Adiabatic Reactor Analysis for Methanol Synthesis
An important industrial reaction is the combination of carbon monoxide with
hydrogen to produce methanol. Methanol is quite useful for a variety of chemical
synthesis reactions, including the transesterification of triglycerides in vegetable
oils for biodiesel production. The gaseous mixture of carbon monoxide and
hydrogen can be used to synthesize a wide array of hydrocarbons, including
synthetic fuels, and is therefore often referred to as “syn-gas”. Syngas can be
obtained from coal, as discussed in this paper by Octave Levenspiel (Professor,
Oregon State University).
The overall reaction for methanol synthesis from syngas is written as:
CO + 2 H2 CH3OH
And can be approximated as an elementary reaction, such that the rate
expression (assuming irreversible reaction, as written above) is:
Where, ko = 5.7x1010
L2
.mol-2
.min-1
, EA = 100.5 kJ/mol

I. Energy Balance and the Conversion-Temperature Relationship
The Thermodynamics of reaction species are (From Felder & Rousseau)
Species Cp(J/mol.K) Hf (kJ/mol) at 298K
CO 29 -110.5
H2 28.8 0
CH3OH 43 -201.2
We can then calculate the change in thermodynamic properties (Enthalpy and
heat capacity) upon reaction, using stoichiometry.
∆Cprxn = 1*43 – 2*28.8 – 1*29 = -43.6 J/mol.K
∆Hrxn = -201.2 – 2*0 – 1*(-110.5) = -90.7 kJ/mol.K
For an adiabatic reactor (either a CSTR or PFR w/o significant heat dispersion),
the energy balance yields the following temperature vs. conversion dependency
(Fogler, eqn 8-30),

II. Mass Balance and Rate Expression
We can write a general stoichiometric table for this reaction system, accounting
for the presence of inert diluent, I.
Species Initial Change Final
CO
H2
CH3OH
Inert 0
Total
If we assume that everything is ideal gas, then concentration = moles/volume,
and accounting for changing volume with temperature and conversion, (Pressure
is constant, or pressure drop defined by momentum balance, e.g. Ergun
equation)
Our concentrations for each species can then be calculated from stoichiometric
table, in terms of conversion, pressure and temperature.

We can substitute these terms into the rate expression, as follows:
III. Inlet Conditions
• Feed Temperature To = 25o
C or 298.15 Kelvin
• Feed Pressure Po = 1 atm
• Molar Feed Rate FTO = 1 mol/min
• Stoichiometric Feed, No diluent , ,
We further assume that there is no pressure drop associated with gas flow
through the continuous reactor, i.e. P = Po.
IV.A. Calculation 1: Solve for 5% conversion (X = 0.05)
Using Equation (8-30) from Fogler,
= 350.97 Kelvin
For our rate expression, substituting T = 350.97 and X = 0.05,
= 2.8x10-=
11 mol.min-1.L-1

For obtaining a Levenspiel plot (for sizing either a CSTR or PFR), we want to
calculate ,
Liters.
IV.B. Calculation 2: Solve for 10% conversion (X = 0.10)
= 404.7 Kelvin
=
= 3.4x10-9
mol.min-1
.L-1
.
calculate ,
Liters.

IV.C. Calculation 3: Solve for 50% Conversion (X = 0.50)
Using Equation (8-30) from Fogler,
= 870.8 Kelvin
= 9.1x10-3
mol.min-1
.L-1
calculate ,
Liters.

IV.D. Generate Data for Levenspiel Plot
X T k -rCO Fao/-rCO
0.05 351.0 6.28 x 10-5
2.82x10-11
1.18x1010
0.10 404.7 6.08 x 10-3
3.43x10-9
9.73x107
0.15 459.4 2.13 x 10-1
1.18x10-7
2.83x106
0.20 515.0 3.65 x 100
1.83x10-6
1.82x105
0.25 571.7 3.74 x 101
1.63x10-5
2.05x104
0.30 629.3 2.59 x 102
9.60x10-5
3.47x103
0.35 688.0 1.34 x 103
4.14x10-4
8.04x102
0.40 747.8 5.44 x 103
1.30x10-3
2.38x102
0.45 808.7 1.84 x 104
3.88x10-3
8.60x101
0.5 870.5 5.33 x 104
9.12x10-3
3.65x101
0.55 934.0 1.36 x 105
1.87x10-2
1.79x101
0.60 998.4 3.14 x 105
3.38x10-2
9.85x100
0.65 1064.0 6.64 x 105
5.49x10-2
6.08x100
0.70 1130.9 1.30 x 106
7.99x10-2
4.17x100
0.75 1199.1 2.39 x 106
1.04x10-1
3.20x100
0.80 1268.7 4.15 x 106
1.20x10-1
2.78x100
0.85 1339.7 6.87 x 106
1.17x10-1
2.85x100
0.90 1412.1 1.09 x 107
8.76x10-2
3.81x100
0.95 1486.0 1.67 x 107
3.61x10-2
9.23x100
0.96 1501.0 1.81 x 107
2.55x10-2
1.31x101
0.97 1516.0 1.96 x 107
1.58x10-2
2.11x101
0.98 1531.0 2.12 x 107
7.75x10-3
4.30x101
0.99 1546.2 2.29 x 107
2.13x10-3
1.56x102
We can then plot this data to see how to best perform this reaction.

We can see from the plot that a CSTR will get us to a conversion of ~ 85% - after
that we would prefer a PFR to keep reactor volume to a minimum.
Caveat
Sometimes people write for a gas-phase reaction the rate expression in terms of
partial pressures

Our true form of the rate expression, which is in terms of concentrations, is
Comparing the two, we see that
Which when linearized does not fit an Arrhenius relationship.

Adiabatic Reactor Analysis for Methanol Synthesis Plant Note Book Series: PNBS-0604

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