Process simulation of ammonia synthesis over optimized Ru/C catalyst
and multibed Fe + Ru configurations
Antonio Tripodi, Matteo Compagnoni, Elnaz Bahadori, Ilenia Rossetti1
Chemical Plants and Industrial Chemistry Group, Dip. Chimica, Università degli Studi di Milano,
INSTM Unit Milano-Università and CNR-ISTM, via C. Golgi, 19, I-20133 Milano, Italy
Supplementary Information
Figure S1: Scheme of the micro-pilot plant adopted. 1) Inlet gas from cylinder; 2) Shut off globe
valve; 3) Filter (2 μm); 4) MSK mass flowmeter; 5) non-return valve; 6) Bursting disc; 7) Vent; 8)
Chemical trap for possible poisons, containing an iron commercial catalyst coupled with eletric
oven; 9) Testing reactor coupled with electric oven; 10) PTFE-membrane relief valve; 11) Threeway valve; 12) Flowmeter; 13) Chemical absorption trap for ammonia (H2SO4).
1
Corresponding author: ilenia.rossetti@unimi.it – fax: +39-02-50314300
Equilibrium for H2:N2=3:1
80%
NH3 fraction (mol/mol)
70%
60%
70 bar - PRKS
50%
100 bar - PRKS
40%
150 bar - PRKS
30%
20%
10%
0%
300
350
400
450
500
550
600
T (°C)
Figure S2: Equilibrium fractions for ammonia for a mixture containing 3 moles of hydrogen per
mole of nitrogen at different pressures (in bar) – calculation performed minimizing the total Gibbs
free energy with APV32 Pure-Component databanks and SRK equation of state data.
Figure S3: A) Example of data simulation for the test at T = 430°C, P = 70 bar and H2/N2 = 3 v/v.
Experimental points (orange circles), simulated values (green squares). B) Parity plot for the outlet
ammonia vol%.
A. Kinetic and Thermodynamic models
According to the reviewed literature, as summarized above, the gap between the intrinsic reaction
kinetic and the whole process modelling is still to be fulfilled. The very example of ammonia
process provided by Aspen Tech itself can be examined in this way: in fact, the reactor model
resorts to an external subroutine, where many parameters are derived by plant experience and could
be used only if they were derived for the same catalyst for whom the kinetic expression is given
(see [1]. Notice, for example, that the expression of the rate upon a volume basis makes it hardly
useful when void fractions, pellet sizes and bulk densities different from those of the referenced
catalyst are considered, leaving the only tunable parameter ‘catalyst activity’ to be varied almost
arbitrarily).
On the other hand, the overall mass balances rely on a separation block whose calculation was
recently reassessed according to undisclosed plant data, that may be different from those used to
adjust the kinetic subroutine. Moreover, it is altogether unclear whether the species’ activities
calculated by the recommended model (RKS-BM: Redlich-Kwong-Soave with Boston-Mathias
modification) through the recycle line are coherent with those calculated by the kinetic subroutine
formula: even if the reactor and separator blocks can be still considered reliable, (as long as they
should reproduce real plant equipment), this poses at least a theoretical issue concerning the
consistency of the overall calculation, especially because the recycle structure makes the outcome
of one thermodynamic model to be influenced by the other’s. Since in this work different intrinsic
kinetics models are compared without attempting a detailed reactor’ simulation (i.e. neglecting the
corrections for the mass-transport phenomena), the review of the background thermodynamic was
done on the separation section, and the same model used for the whole simulation. The
recommended RKS-BM model was compared to the other commonly employed NRTL-RK system
(Non-Random Two Liquid, also used in the same provided example in other blocks upstream)
reproducing literature data [2–5] as reported in Figures S4 and S5 below. In general, the two
systems behaves similarly reproducing the ternary NH3-N2-H2 system (especially at higher
pressures), while the NRTL-RK system returned better results evaluating the ammonia vapor
fraction in more complex plant mixtures. Nevertheless, the RKS-BM package assures a fairly good
calculation of the nitrogen and hydrogen vapor content, unlike the other. Considering that: i) the
overall loop simulation is heavily influenced by the recycled vapor flow, but is much less sensitive
to the ammonia residual fraction (see following section), and that ii) the 4-species mixture
employed is not as demanding as the 5-chemicals system reviewed, the RKS-BM system was
retained.
NH3-N2-H2 VLE (1)
0,18
NH3-N2-H2 VLE (2)
100 bar (exp1)
0,12
N2 vapor flow (kg/h)
NH3 vapor fraction (vol/vol)
50 bar (exp1)
300 bar (exp1)
100 bar (exp2)
300 bar (exp2)
0,06
0
50 bar (RKSBM)
50 bar (NRTLRK)
50 bar (exp3)
100 bar (RKSBM)
100 bar (NRTLRK)
100 bar (exp3)
48
47
-30
-20
-10
T (°C)
0
10
-20
-10
0
10
T (°C)
NH3-N2-H2 VLE (3)
50 bar (RKSBM)
50 bar (NRTLRK)
50 bar (exp3)
100 bar (RKSBM)
100 bar (NRTLRK)
100 bar (exp3)
10,60
NH3-N2-H2 VLE (4)
1,0E+04
(1-yNH3) / (1-xNH3) (mol/mol)
10,61
H2 vapor flow (kg/h)
49
-30 °C
-30 °C (exp4)
50 °C (NRTLRK)
50 °C
50 ° (exp4)
-30 °C (NRTLRK)
1,0E+03
1,0E+02
1,0E+01
1,0E+00
10,59
-20
-10
T (°C)
0
10
0
100
200
P (bar)
300
400
Figure S4: comparison between the RKS-BM calculation (solid lines) for a ternary mixture
ammonia-nitrogen-hydrogen (30.0:49.1:10.6 kg/h) with liquid and vapor phases in equilibrium, the
NRTL-RK one (dashed lines) and 4 different datasets: ‘exp1’ from [3], ‘exp2’-‘exp3’ from [2] and
references therein, ‘exp4’ as reported in [5].
NH3-N2-H2-Ar-CH4 Vapor-Liquid Equilibrium
NH3 vapor fraction (mol/mol)
0,4
49 bar (exp5)
98 bar (exp5)
294 bar (exp5)
0,3
0,2
0,1
0
0
10
20
30
40
50
60
T (°C)
Figure S5: comparison between the RKS-BM calculation (solid lines) of the 5-species mixture
ammonia-nitrogen-hydrogen-methane-argon (50.0:49.1:10.6:12.8:13.3 kg/h), the NRTL-RK one
(dashed lines, same input) and dataset ‘exp5’ that reports plant data as found in [4].
B. Computational Details: Equilibrium Constant
The quadratic term reported in Eq. (7) was at first neglected according to Aspen Plus © format for
the temperature dependence of equilibrium constants. An alternative strategy was to adjust the other
terms so to reproduce the same Keq(T) function in the considered temperature range, leading to a
slightly different expression with respect to the one reported in Table 1:
ln 𝐾′𝑒𝑞 = + 1.9 +
4609
− 2.71 ∗ ln 𝑇 + 0.00039 𝑇
𝑇
The adjustment was made minimizing the sum of the square differences: ∑𝑖(𝐾(𝑇𝑖 ) − 𝐾′(𝑇𝑖 ))2 via a
Newton method implemented within the MS-Excel™ solver plug-in. Notice that Table 1 reports the
coefficients with opposite sign, since the input form of Aspen Plus expects the inverse of the
equilibrium constant.
C. Computational Details: Recycle Convergence
Despite its apparent simplicity, the coupled reactor–separator behavior hides tricky features that
may not be handled correctly by the acceleration features of the default ‘Wittig’ convergence
algorithm and prove difficult to solve even for the ‘Broyden’ method (a quasi-Newton one).
Referring to the block scheme of Figure, denoting with s the fraction of any species recycled after
the separator-purge and with x the amount of ammonia produced within the reactor, then the
balances are expressed by 3 linear equations in the unknown flowrates F: 𝐴 × 𝐹 = 𝐵 where:
1
𝐴𝑁𝐻3 = [1
0
0
−1
𝑠𝑁𝐻3
1
0 ],
−1
0
𝐵𝑁𝐻3 = [−𝑥]
0
(S1)
1 0
𝐴𝑁2 = [1 −1
0 𝑠𝑁2
1
0 ],
−1
𝑛0
14
𝐵𝑁2 = [ 𝑥 ]
17
0
(S2)
1 0
𝐴𝐻2 = [1 −1
0 𝑠𝐻2
1
0 ],
−1
ℎ0
3
𝐵𝐻2 = [ 𝑥 ]
17
0
(S3)
with the column of every matrix representing the streams 1,2 and 3 of Figure S6, and n0, h0 are the
fresh nitrogen and hydrogen makeup flowrates.
Figure S6: simple block-scheme of an ammonia synthesis cycle, used to write the 9-equations
linear system [2,6].
The first issue of such a system is recognized as in any case: ∆𝐴 = 𝑠(1 − 𝑠), where s is actually
much less than 1 only for ammonia. In other words, the recycled flows of nitrogen and hydrogen
tends to diverge non-linearly as the purge fraction is decreased. This causes the ‘Flash2’ block to
separate less liquid, since the thermodynamic model calculates a higher dew point as the mixture
becomes richer in the non-condensable species, so the parameter s can decrease, between two
simulation steps, even if the purge fraction is constant. Besides the inherent difficulty for the
numerical methods to calculate the A-1 matrix as Δ ≈ 0, the convergence iterations may bring the
succession ∆𝑘 → ∆𝑘+1 to approach 0 and the successions 𝐹𝑘 → 𝐹𝑘+1 , (𝐹𝑘+1 − 𝐹𝑘 )𝑘′ to diverge.
These combined features may result in: i) an earlier calculation error (if Δ is too little), ii) a
tolerance error (typical for the Secant or Wittig algorithms as ∆𝐹⁄𝐹 becomes too large), iii) a nested
‘division-by-0’ error (typical for the Newton method, sensitive to the derivative 𝜕 ∆𝐹⁄𝜕𝐹 ) or iv) a
‘flash-failure’ error as the separator block cannot handle any liquid phase formation. Another
numerical perturbation for the convergence steps lies in the nitrogen split fraction at the flash block,
that varies according to the liquid phase formation.
A help to the system stability comes from the removal of hydrogen operated in the reactor, but this
feature may not be sufficient if i) the ammonia fraction in the separator is still too low (and hence
the liquid phase outflow cannot match the fresh feed inflow) or ii) the catalyst load is too low.
Also checking carefully the above system parametrization beforehand, the numerical stability of
these closed-cycle simulation relies critically on the supposed purge fraction and a sound initial
guess of the tear-stream exiting the reactor (shifting upwards the ammonia flow and downward the
hydrogen one is often of help). Notice that purging a non-negligible gas flow of 1%, the value of
∆𝐴 for hydrogen can be so low as to make tolerance warning or errors be issued, even if the reports
are practically correct.
As an example, consider the simulations sequence reported in: the reactor calculation of the kinetic
model Ошибка! Источник ссылки не найден. (for 3 adiabatic beds initially loaded with 3 kg of
catalyst each, fed at 400 °C and 100 bar) yields ca. 9 kg/h of ammonia at open recycle. This result is
used as the first guess for the reactor outlet stream in a semi-closed loop, whose result is in turn the
first guess for a further calculation until the cycle is closed.
After every run the simulation results were reinitialized, to evaluate the convergence capability of
the algorithm when it relies only on the controlled input represented by the tear-stream
specification. Moreover, this option becomes mandatory when automated case-by-case simulations
are planned, since the calculus is not much sensitive to the recirculating flow values of hydrogen
and nitrogen and may fail to update them. The first convergence issue (between cases 6 and 7)
reflects the sudden decrease of the calculated Δ as the purge fraction becomes low. Then, it can be
noticed that the algorithm works better while coping with specie’s build-up (case 9) than with
specie’s depletion (cases 10-11 and 12-13), which is due to the fact that the hydrogen removal
within the liquid ammonia is always negligible respect to its removal at the purge. Nevertheless,
cases 14-16 seem to show that the proper initialization of the tear stream is the most important
procedure to adopt, since the same cycle conditions handled (yet not easily) in case 13 become
troublesome to reach from different starting points (even if already closer to the results): a more
careful inspection of the simulation reports for case 14 (here not shown) indicates that the tearstream last pass deviation (𝐹𝑘+1 − 𝐹𝑘 ) is acceptable from a practical point of view, as confirmed by
the results of the manual calculation (bracketed numbers, performed with Matlab®) using the
values of x and s retrieved from the Aspen Plus blocks. In this case, the key to reorder the
convergence is to surmise a wrong tear stream flow of Nitrogen (very sensitive to build-up like
hydrogen, but on higher absolute values), which is most likely due to the oscillating behavior of the
error that may spring from starting points too near to the results with this kinds of algorithms. The
marked dependence of the tear convergence on a suitable (rather than precise) tear-stream initial
guess, actually prevents the use of the automated ‘sensitivity analysis’ tool over a widespread range
of system conditions.
As for the manual calculation correctness, it depends on the alignment of s and x to their realistic
values, and has to be checked a-posteriori because these parameters are strongly non-linear
functions of the species’ flows (even at fixed temperature and pressure) and their explicit
representation would turn the system into a non-linear one. It can be readily verified that the
nitrogen vapor separation is the main issue of the iterative calculation: the bracketed results for case
14 were retrieved supposing a vapor/total N2 fraction of 0.999 (kg/kg), while increasing this
quantity by 0.1% (to 0.9999) the recycled flow increases by 20% (from 1099 to 1292), amounting
to a sensitiveness of the order of 102.
These considerations help to clarify the choice of the RKS-BM method, as also shown by the test
calculation sequence listed from case 17 onward. While cases 18-20 were tired just to check the
already known tear-stream sensitiveness also with the NRTL-RK, the step between cases 17-18 and
cases from 22 on confirm that the total recycle flow and the computational load are strongly
influenced by the correct description of all the species present in the vapor phase: on this basis, the
NRTL-RK model was put aside despite its better reproduction of the ammonia split.
Case
Purged
vapor
(kg/kg)
Tear stream Flow guess
(kg/h)
N2
H2
NH3
CH4
Tear stream Flow results
(kg/h)
N2
H2
NH3
CH4
Iterations
Converged
open
99%
-
-
-
-
41.2
8.89
10.1
0.283
4
yes
1
80%
41.2
8.89
10.1
0.283
50.0
10.8
11.5
0.350
6
yes
2
60%
50.0
10.8
11.5
0.350
65.6
14.2
13.0
0.465
8
yes
3
40%
65.6
14.2
13.0
0.46
96.5
20.8
15.4
0.697
10
yes
4
20%
96.5
20.8
15.4
0.697
184
39.8
21.4
1.39
13
yes
5
10%
184
39.8
21.4
1.39
348
75.1
31.3
2.77
15
yes
6
5%
348
75.1
31.3
2.77
656
141
47.6
5.52
21
yes
yes
7
1%
656
141
47.6
5.52
2929
632
153
27.4
332
8
0.5%
2929
632
153
27.4
5695
1229
278
54.8
23
yes
8529
1840
386
55.7
13
yes
Inlet reactor Temperature lowered from 400 to 350 °C
9
0.5%
5695
1229
278
54.8
Catalyst load increased to 10 kg x bed – 20 kg x bed
10
0.5%
8529
1840
386
55.7
5712
1232
279
54.8
22
yes
11
0.5%
5712
1232
279
54.8
2728
588
165
51.6
24
yes
Pressure decreased to 75 bar – increased to 125 bar
12
0.5%
2728
588
165
51.6
5949
1283
343
55.1
26
yes
13
0.5%
5949
1283
343
55.1
1161
250
98.9
43.8
412
yes
Pressure and Temperature restored to 100 bar – 400 °C
13
0.5%
1161
250
98.9
43.8
417
89.5
76.6
32.7
30
yes
Catalyst load decreased to 10 kg x bed
14
0.5%
417
89.5
76.6
32.7
(1099)
(282)
(106)
-
552
no
15
0.5%
1181
254
106
45.2
1181
254
106
45.4
542
yes
16
0.5%
1200
250
100
40
1181
254
106
45.4
362
yes
17
1%
420
90
73
20
879
189
88.4
24.4
26
yes
238
85.3
7.78
432
yes
Separation block model: NRTL-RK
18
1%
879
189
88.4
24.4
558
19
1%
600
200
80
5
-
27
no
20
1%
550
200
80
5
-
552
no
21
1%
500
200
80
5
558
432
yes
238
85.3
7.77
Separation block model: RKS-BM
22
1%
500
200
80
5
-
552
no
23
1%
780
200
80
5
-
552
no
24
1%
500
150
80
5
-
552
no
25
1%
900
180
80
5
879
189
88.4
24.4
392
yes
26
0.5%
880
180
85
24
1180
255
106
45.5
452
yes
Table S1: test calculation sequence to check the recycle convergence performances (algorithm: Broyden,
tolerance: 10-5).
2
Convergence steps exceed the default value of 30.
[1]
(2008).
[2]
C.A. Vancini, La sintesi dell’Ammoniaca, Hoepli, Milan, 1961.
[3]
A.T. Larson,, C.A. Black, J. Am. Chem. Soc. 47(4) (1925) 1015–20. 10.1021/ja01681a014.
[4]
K. V. Reddy,, A. Husain, Ind. Eng. Chem. Process Des. Dev. 19(4) (1980) 580–6.
10.1021/i260076a013.
[5]
M.R. Sawant,, A.W. Patwardhan,, V.G. Gaikar,, M. Bhaskaran, Fluid Phase Equilib. 239(1) (2006) 52–
62. 10.1016/j.fluid.2005.10.014.
[6]
B. Evans,, S. Hawkins,, G. Schulz ed., Ullmann’s Encyclopedy of Industrial Chemistry, VCH, Weinheim,
1991.