131245357 52610363 methanol production from syngas reactor design
DESCRIPTION
Methanol ProductionTRANSCRIPT
ABSTRACT
In this project we studied on manufacturing methanol. We made investigations for methanol manufacturing process. The flow chart for the process, reactor configurations are asked. Firstly, using thermodynamic properties of C0,H2 and CH3OH, equilibrium line is plotted and 100 bar is selected. Constant rate curves are obtained by using reaction rate expression which is given at term project part. The operating lines goes through the extremums of these curves. Adiabatic energy balance equation for each reactor gives adiabatic line equations. These adiabatic line equations plotted until the reaching desired conversion of 0.55.This conversion is attained with 6 plug flow reactors.
Reactor Design Project
Methanol is considered as a potential source of energy and as an intermediate to produce alternative motor vehicle fuels, fuel additives and number of petrochemicals. Conventionally, methanol is produced from synthesis gas (gas mixture of carbon monoxide and hydrogen produced by reforming of natural gas) in a series of fıxed bed catalytic reactors at a relatively high pressure. It is also possible to produce synthesis gas by gasification of biomass or coal.
CO 2H 2 CH 3 OH
In this project you are asked to design the reactor(s) to be used for a methanol production at a rate of 400 tons/day:
(A) Search the literature for methanol production. Discuss the operating conditions of the process and the critical points for pressure selection.
(B) Considering a feed composition of 30% CO and 70% H2, examine the thermodynamics of methanol synthesis reaction in order to decide on the operating pressure. Plot equilibrium conversion versus temperature graphs in a pressure range of 50-120 bars. In the Equilibrium calculations you should use the fugacities.
(C) Taking the pressure as 100 bars and considering a target conversion of CO as 55% decide about the reactor configurations, operation mode (adiabatic, non-adiabatic, isothermal), reactor inlet temperature(s).
(D) Design the reactor(s) to find the catalyst volume and total reactor volume.
In methanol synthesis, a catalyst containing Cu/ZnO system, with the addition of aluminum is generally used. You may use the rate expression given in the data page.
DATA
For systems where the synthesis gas is composed of only CO and H2, the following rate equation was proposed for the hydrogenation of CO over a Cu/Zno on alumina catalyst for a temperature range between 450-650K and pressures 50-100 bar.
at 250˚C
The catalytic packed bed bulk density was given as
INTRODUCTION
Methyl Alcohol as an Industrial Chemical
Methanol (methyl alcohol), CH3OH, is clear, water- white liquid with a mild odor at ambient temperatures. From its discovery in the late 1600s, methanol has grown to become the 21st largest
commodity chemical with over 12x106 metric tons annually produced in the world. Methanol has been called wood alcohol (or wood spirit) because it was obtained commercially from the destructive distillation of wood for over a century. However, true wood alcohol contained more contaminants (primarily acetone, acetic acid, and ally alcohol) than the chemical- grade methanol available today.
Table 1.1 Physical Properties of Methanol
Property ValueFreezing point oC -97,68Boiling point oC 64,70Critical temperature oC 239,43Critical pressure kPa 8096Critical volume mL/mol 118Critical compressibility factor z in PV=znRT 0,224Heat of formation(liquid) at 25oC kj/mol -239,03Free energy of formation(liquid) at 25oC kj/mol -166,81Heat of fusion J/g 103Heat of vaporization at boiling point J/g 1129Heat of combustion at 25oC J/g 22662Flammable limits in air
Lower, vol % 6Upper, vol % 36
Autoignition temperature, oC 420Flash point, closed cup, oC 12Surface tension, mN/m (dyn/cm) 22,6Specific heat
of vapor at 25 oC, J/(g.K) 1,370of liquid at 25 oC, J/(g.K) 2,533
Vapor pressure at 25 oC, kPa 16,96Solubility in water MiscibleDensity at 25 oC, g/m3 0,78663refractive index, nD
20 1,3284viscosity of liquid at 25 oC, mPa.s(cP) 0,541Dielectric constant at 25 oC 32,7Thermal conductivity at 25 oC, W/(m.K) 0,202
For many years the largest use for methanol has been as a feedstock in the production of formaldehyde, consuming almost half of the entire methanol produced. In the future,
3
Formaldehyde’s importance to methanol will decrease as newer uses increase such as the production
of acetic acid and methyl tert-butyl ether (MTBE, a gasoline octane booster). Methanol’s direct use
as a fuel may be significant in special circumstances.
1.2 Manufacturing and Processing
Modern industrial- scale methanol production is based on exclusively on synthesis from pressurized mixtures of hydrogen, carbon monoxide, and carbon dioxide gases in the presence of metallic heterogeneous catalysts. The required synthesis pressure is dependent on the activity of the particular catalyst. By convention, technology is generally distinguished by pressure as follows; lower pressure processes, 5-10 MPa (50-100atm); medium pressure processes, 10-25 MPa (100-250 atm); and high pressure processes, 25-35 MPa (250-350 atm). [1]
In the late 1960a medium and low pressure methanol technology came into use with the successful development of highly active, durable copper-zinc oxide catalysts. Copper catalysts’ sensitivity to poisons required careful purification of feed streams. Low and medium pressure technology has advantages of reduces compression power, good catalyst life, larger capacity single- train converter designs and milder operating pressures.
Some reactions rate expressions uses for methanol production is listed on appendix D.1
1.3Natural Gas
· Hydrocracking of heavy hydrocarbons:
CnH(2n+2) + (n-1)H2 nCH4
· Steam reforming of CH4:
CH4 + H2O CO +3H2
Water gas shift:
CO + H2O CO2+H2
For low pressure catalysts, the excess hydrogen improves the catalyst effectiveness.
Thus, converter costs are reduced and the necessity of shifting and removing excess hydrogen
from the synthesis feed gas, as commonly practiced with high pressure technology, is avoided.
Excess hydrogen is vented during synthesis and used as fuel in the reforming step. Thus, a high
overall energy efficiency is mainted which makes the process economical. [1]
4
Table 1.2 Equilibrium CO, CO2 Conversion, and Exit CH3OH Concentration vs
Pressure and Temperature
Temperature CO conversion, % CO2 conversion, % Exit CH3OH, vol %, 5MPa 10MPa 30MPa 5MPa 10MPa 30MPa 5MPa 10MPa 30MPaoC200 95.6 99.0 99.9 44.1 82.5 99.0 27.8 37.6 42.3250 72.1 90.9 98.9 18.0 46.2 91.0 16.2 26.5 39.7300 25.7 60.6 92.8 14.3 24.6 71.1 5.6 14.2 32.2350 -2.3 16.9 73.0 19.8 23.6 52.1 1.3 4.8 21.7400 -12.8 -7.2 38.1 27.9 30.1 44.2 0.3 1.4 11.4
1.4 Catalyst
Methanol, an important industrial chemical is produced on a large scale so
called “low pressure” (50-100 bar) process. The formation of methanol is catalyzed
by Cu-Zn-Al or Cu-Zn-Cr mixed oxides important design factors in modeling a
methanol reactor are the values of equilibrium constants of the following reaction. [2]
CO+2H2 CH3OH
CO2+H2 CO+H2O
Catalyst used in high pressure (25-35 MPa or 250-350atm) synthesis is zinc
oxide-chromium oxide. It is a more robust catalyst than the low pressure copper-
based catalyst and can tolerate higher temperature and sulfur levels. The copper-
zinc oxide catalyst, However, is more attractive and can be operated at lower
pressure (5-25 MPa or 50-250 atm) and temperature (200-300 C). [1]
1.5 Low Pressure Processes
A more active catalyst than the above can be made from a combination of copper and
zinc together with a textural promoter such as chromia or alumina. These permit the use of a
lower pressure in the range of about 5 to 10 MPa, and a temperature of about 240 to 260
centigrade degrees. Recent laboratory studies indicate that the active phase is a solution of Cu
in ZnO and that methanol yield are increased by the presence of CO2, H2O or O2 in the synthesis
gas. If none of these is present, the catalyst gradually loses activity, since the Cu-ZnO phase
apparently may be gradually reduced to inactive copper metal. This process is irreversible once
the crystallites of copper metal have grown. The fact that the copper produces a chemical effect
rather than a physical effect is also shown by the fact that this catalyst exhibits considerably
lower apparent activation energy than the Zno-Cr2O3 catalyst. Low pressure process utilizes a
single bed of catalyst and quench cooling, obtained by
5
lozenge distributors especially designed to obtain good gas distribution and gas
mixing and to permit rapid loading and unloading of catalyst. A low pressure
methanol synthesis process is advantageously combined with production of
synthesis pressure, thus avoiding the necessity of intermediate gas compression.
These low pressure processes are usually the process of choice in new installations.
To produce relatively pure methanol product directly requires care in
catalyst manufacture , and requires procedures to avoid catalyst contamination. [3].
1.5.1 Catalyst Characteristic
Zinc oxide serves several important functions that enhance the stability
and life of the catalysts.
· Its credited with an important role in the proprietary manufacturing
produce that creates a high- surface area of copper
· Along with alumina, it prevents copper agglomeration
· ZnO reacts readily with copper, poisons such as sulfur and chlorine compounds. [4]
1.5.2Side Reactions
Prior to commercialization of the low-to-medium pressure process using copper
catalysts, the most troublesome side reaction was the reverse of thee steam reforming
reaction. Occurs in high pressure plants above 450 C and causes exit bed temperatures to
exceed 600 C. Such runaway temperatures usually require reactor shutdown to prevent
catalyst and equipment damage. The low pressure copper-based catalysts operate in a
lower temperature range, ie, 200-300 C , where the methanation reaction is unimportant.
Alcohols other than methanol are produced in small quantities with ethanol the
chief impurity. Formation of the higher alcohols can be suppressed by keeping the reaction
temperature as low as possible for the methanol production rate desired. High hydrogen
concentration also suppresses the formation of higher alcohols and the other by products.
Other by products produced is small amounts are aldehydes, ketones, ethers and esters. [1]
6
2.THERMODYNAMIC DATA
Table 2.1 Thermodynamics properties of methanol,carbon monoxide and hydrogen gaseous
Components H 298 (kj/mol) G298 (kj/mol)
CH3OH (Methanol) -201,2 -162
H2 0 0
CO -110,52 -137,2( Referrence : Sandler , S.I, Chemical and Engineerig Thermodynamics, Third edition, John
Wiley & Sons Inc. , 1999 , page 759)
CP,CO (T,K) 27,113 + 0,655 X102 T – 0,1 X105
T2 [j /mol.K]
CP,H2 (T,K) = 26,113 + 0,435 X102 T – 0,033 X105
T2 [j /mol.K]
CP,CH3OH (T,K) = 19,038 + 9,146 X102 T – 1,218 X105 T2 - 8,034 X 109 T3 [j /mol.K]
( Referrence : Sandler , S.I, Chemical and Engineerig Thermodynamics, Third edition, John
Wiley & Sons Inc. , 1999 , page 745-747)
Table 2.2 Critical tempertaure and pressure of substances
513.2 K 79.54 barCO 133 K 34.96 barH 2 33.3 K 12.97 bar
7
3.CALCULATIONS
3.1. Obtaining equilibrium constant as a function of temperature, Kf
(T) : + H 298 and G298 values are given at thermodynamics data part.
H p r
od u c t s
t a n
H 298 = (-201,2)-(-110,52)
= -90,68 kj/mol = -90680 j/mol
G p r
o d u c t s
Gt an
G298 = (-162,0)-(-137,2)
= -24,8 kj/mol = -24800j/mol
G RT ln K298 8,314J
298K ln K298 =-24800 j/molmol K
ln K298 = 10,0097 K298 = 22243,38
dInKf H .... Van't Hoff Equation (InKf )T InK T H
dT
dT RT 2 T
0 RT 2
CP C
P,CHOH
2C
P,H2 C
P,CO
T T
dH cpdTTR TR
+ Cp values of substances are given at thermodynami properties part.
CP = -60,301 + 7,621X102 T – 1,052 X105 T2 - 8,034 X 109 T3 (J/mol.K)
T
H = H298 + Cp dT298
H = - 75985,54 + (60,301 T) (0,0381 T2 ) (3,5067 106 T3 ) (2,0085 109 T4 )
8
T 1 T H(T)dT d ln Kf 298 2
R T298
R=8,3145 J/mol.K;
ln K298 = 10,0097
(InKf)= InK298 +
(9,32935 9139,46
7,2529ln(T) 4,5826 103 T 4,2178 107 T2 2,4151010 T3 )
T
Kf exp(19,33905 9139,46
7,2529ln(T) 4,5826 103 T 4,2178 107 T2 2,415 1010 T3 ) T
Table 3.1 Equilibrium constant versus temperature data
T Kf
400 1,619805420 0,415906440 0,119779460 0,03814480 0,013267500 0,00499520 0,002012540 0,000863560 0,000392580 0,000187600 9,33E-05
9
3.2 Plotting equilibrium conversion versus temperature graphs in a pressure
range of 50-120 bars
K T K K y Pn f / P ( fugacity coefficient) Basis:
100 moles/s Feed composition enter the reactor
CO 2H 2 CH 3OH
CO A , H2 B , CH3OH C
A 2B C
30 70-a -2a a---- ---- ----30-a 70-2a a
nT = 30 – a + 70 – 2a + a = 100 – 2a CA0 = 30 (due to basis 100 moles reactant)
a=CA0 . XAe a = 30 XAe
Ky
yc
yA .yB 2
K
ic
n (1 1 2) 2 ia .ib 2
+ With changing the operating pressure, reduced pressure (Pr) and temperature (Tr) values
be changed . So, fugacities of substances might be changed. According to this change,
obtained different equilibrium conversion( XAe ) versus temperature functions by pressures.
Tr T / TC
Pr P / PC
Reduced temperature and pressure values of substances are shown on Appendix A.1
+ At P = 50 bar, temperature range of 400-600
K ; Table 3.2 Reduced Pressures at P=50 bar
Pr(metanol) Pr(CO) Pr(H2)0,628614534 1,43020595 3,855050116
10
Fugacity coefficient of substances are read on a graph by parameters Tr,Pr,
shown on Appendix A.1
Table 3.3 Equilibrium constant and Xae values for temperature range of 400-600K, P=50bar
T Kf K(fugacity coefficient) Ky Xae400 1,619805 0,15049 26909,64 0,99940420 0,415906 0,23764 4375,284 0,99650440 0,119779 0,35310 848,0635 0,98380460 0,03814 0,49655 192,0247 0,95751480 0,013267 0,70088 47,32129 0,86850500 0,00499 0,74634 16,71539 0,76720520 0,002012 0,78482 6,409849 0,63150540 0,000863 0,81485 2,649156 0,47240560 0,000392 0,84074 1,164987 0,31600580 0,000187 0,86378 0,541032 0,19120600 9,33E-05 0,88197 0,264582 0,10870
Sample calculation : At T=400K (P=50bar)
30XAe ic
Kf
100-60XAe
50
2
30-30XAe 70 60XAe 2 ia .ib 2
100 60XAe 100 60XAe 30XAe
1,619805 100-60XAe 0,1538 502
2 (1,017)2 1,01230-30XAe
70 60XAe
100 60XAe 100 60XAe 30XAe
26909,64 =100-60XAe
30-30XAe
70 60XAe
2
100 60XAe 100 60XAe
An equation Ky = f( XAe ) such as:
30XAe
Ky 100-60XAe
30-30X 70 60X 2
Ae Ae
100 60XAe 100 60XAe We calculate Xae value using a matlab function (See Appendix A.2)
11
By using other Ky values on this matlab function, we get the Xae values on Table 3.3
+ At P = 75 bar, temperature range of 400-600
K ; Table 3.4 Reduced Pressures at P=75 bar
Pr(metanol) Pr(CO) Pr(H2)0,9429218 2,145308924 5,782575173
Fugacity coefficient of substances are read on a graph by parameters Tr,Pr,
shown on Appendix A.1
Table 3.5 Equilibrium constant and Xae values for temperature range of 400-600K, P=75bar
K(fugacityT Kf coefficient) Ky Xae400 1,619805 0,092810483 98172,15 0,9998420 0,415906 0,156250745 14972,54 0,9989440 0,119779 0,231447055 2911,074 0,9948460 0,03814 0,325141594 659,8286 0,9845480 0,013267 0,434626865 171,6992 0,9427500 0,00499 0,557073141 50,38741 0,8733520 0,002012 0,642367583 17,62038 0,7735540 0,000863 0,685524544 7,085048 0,6476560 0,000392 0,722445487 3,050439 0,4993580 0,000187 0,752806781 1,396763 0,3496600 9,33E-05 0,778071256 0,6748 0,2237
Sample calculation : At T=400K (P=75bar)
30XAe ic
Kf
100-60XAe
75
2
30-30XAe 70 60XAe 2 ia .ib 2
100 60XAe 100 60X
Ae 30XAe
100-60XAe 2
1,619805 0,09281 7530-30X 70 60X 2Ae Ae
100 60XAe 100 60XAe 30XAe
98172,15 =100-60XAe
30-30XAe
70 60XAe
2
100 60XAe 100 60XAe An equation Ky = f( XAe ) such as:
12
30XAe
Ky 100-60XAe
30-30X 70 60X 2
Ae Ae
100 60XAe 100 60XAe We calculate Xae value using a matlab function (See Appendix A.2)
By using other Ky values on this matlab function, we get the Xae values on Table 3.5
+ At P = 120 bar, temperature range of 400-600
K ; Table 3.6 Reduced Pressures at P=120 bar
Pr(metanol) Pr(CO) Pr(H2)1,508674881 3,432494279 9,252120278
Table 3.7 Equilibrium constant and Xae values for temperature range of 400-600K, P=120bar
K(fugacityT Kf coefficient) Ky Xae400 1,619805 0,063209575 369013,7 0,99999420 0,415906 0,099519313 60179,7 0,9997440 0,119779 0,14732625 11707,52 0,9987460 0,03814 0,207338687 2648,886 0,9943480 0,013267 0,278338222 686,3599 0,9806500 0,00499 0,359381778 199,9485 0,9486520 0,002012 0,44432146 65,21412 0,8915540 0,000863 0,523088292 23,77009 0,8065560 0,000392 0,581157042 9,707646 0,6956580 0,000187 0,627223183 4,291649 0,5624600 9,33E-05 0,665798469 2,018792 0,42
Sample calculation : At T=400K (P=120bar)
30XAe ic
Kf
100-60XAe
120
2
30-30XAe 70 60XAe 2 ia .ib2
100 60XAe 100 60X
Ae 30XAe
1,619805 100-60XAe 0,063209575 752
230-30X 70 60X Ae Ae
100 60XAe 100 60XAe
13
30XAe
369013,7 =100-60XAe
30-30XAe
70 60XAe
2
100 60XAe 100 60XAe An equation Ky = f( XAe ) such as:
30XAe
Ky 100-60XAe
30-30X 70 60X 2
Ae Ae
100 60XAe 100 60XAe We calculate Xae value using a matlab function (See Appendix A.2)
By using other Ky values on this matlab function, we get the Xae values on Table 3.7
Finaly, Xae – T graph plotted on graph 3.1 at selected pressure of 50,75 and 120 bar.
Figure 3.1 Xae versus Temperature(K) graph for methanol production at given conditions
14
3.3 Drawing constant rate curves to get operating line
The rate expression which will be used for obtaining kinetic data is
given in the reactor desing project part as :
r k(PCO P2H2
PCH3OH ) ; Ke
Dalton’s law presents an expression about relation between ya (molar fraction)
and pressure as PA PT ya . Total amount of A in the total mixture (ya FA / FT ) can
also be defined.
yA F A PA PA
FA PT …(3.1);
FT PT FT
A 2B CFa0 Fb0
-Fa0Xa -2Fa0Xa Fa0Xa
------------------------------------
FA
F
A0
F
A0 X
A
FB FB0 2FA0 XA
FC
F
A0 X
A
FT FA0 (1 2XA ) FB0
Using formula 3.1 and expressions above, these are derived :
r ra ; r=-ra ; FA CA V0 ;1
FA C A0
(1 X A
) V0 ;
1 XAF
B (C B0
2C A0
X A
) V0 ;
1 XA
FC C
A0 X
A V0 ;
1 XA
FT FA FB FC
FT C A0
C B0
2C A0
X A V0 ;
1 XA
15
C A0
(1
X
A )
V0
(1 XA )PA
1 X A 100 100 (Carbon Monoxide)C
A0
C B0
2C A0
X A V (1 2X
A) 7
0
31 XA(C B0
2C A0
X A
) V 7 2XA0
3PB
1 XA 100 100 (Hydrogen gas)C
A0
C B0
2C A0
X A V (1 2X
A) 7
0
31 XAC
A0X
A V0 X
A
PC 1 XA
100 100 (Methanol)C A0
C B0
2C A0
X A V (1 2X
A) 7
0
31 XA
All of the partial pressure expressions’ numerators and denominators are divided
by CA0 , (CB0 / CA0 70 / 30) The rate expression is obtained as a function of
temperatures(T) and molar fractions (Xa).
7 (XA
100)(1 XA ) 2XA (1 2XA )
7
ra (k) (( 100) (3
100)2
3
)(1 2XA )
7(1 2XA )
7 3,567E 12 exp(90130 / 8,314 T)3 3
k 743,198 exp(-80000 / (8,3145 T))
The constant rate curves are drawen by cooperation with an C#.NET program
and Excel . (See Appendix B.1 for C# program)
Constant rate curves are drawen for the vaules of r; 0; 0,05, 0,1, 0,35, 0,5, 1, 2, 5 and
8 Kinetics and thermodynamics equilibrium lines (r=0) are shown on figure 3.2
16
Figure 3.2 Equilibrium lines from kinetics and thermodynamics
Table 3.1 Constant rates T,Xa data
r=0,1 r=0,35 r=0,5 r=0T Xa T Xa T Xa T Xa462 0 492 0,01 502 0,04 400 0,98463 0,03 494 0,08 506 0,16 401 0,98465 0,12 498 0,2 507 0,19 408 0,97466 0,15 505 0,35 515 0,35 409 0,97467 0,18 507 0,38 517 0,38 410 0,97475 0,38 509 0,41 523 0,45 411 0,97476 0,4 512 0,45 524 0,46 434 0,95478 0,43 513 0,46 525 0,47 435 0,95479 0,45 514 0,47 536 0,54 436 0,95481 0,48 522 0,54 539 0,55 437 0,95482 0,49 530 0,58 543 0,56 504 0,83502 0,66 539 0,6 558 0,56 505 0,83504 0,67 548 0,6 567 0,54 506 0,83553 0,64 559 0,58 581 0,49 508 0,82554 0,64 583 0,49 586 0,47 533 0,74555 0,63 598 0,42 588 0,46 538 0,72559 0,62 600 0,41 597 0,42 548 0,68561 0,61 602 0,4 599 0,41 598 0,43567 0,58 604 0,39 618 0,32 600 0,42569 0,57 606 0,38 627 0,28 660 0,16613 0,35 663 0,15 696 0,08667 0,14
Other constant rate datas given at appendix B.2.
17
Figure 3.3 Constant rate curves at 100 bar
3.4 Energy Balance
Inlet stream : FCO, F H2
Outlet stream : F CH 3 OH , FCO,
F H2 General Energy Balance equation :
TR Tf
FC dT FC dT Q ( H )F Xi(inlet)
i Pi i(outlet) i Pi Removedbythewalls R A0 AT0 TR
Flow reactors are used for methanol production.At PFR reactors adiabatic operations
are easier to control than isothermal operations. So, heat lost by the system is neglected.
Cp(T) functions listed on thermodynamics data chapter and HR |298 is
calculated in calculations 3.1.
18
3.4.1 Adiabatic lines to calculate number of reactors to achieve 0.55 conversion of A
Taken basis 100 mol/s feed composition
FT0 100mol / s 70molH2 2g 30molCO 28g 980g / s ;molCOmolH2
FA0 30mol / s ;
Mmethanol 32g / molF F F X 0 30 0,55 16,5mol / s
methanol = 528 g/s methanol(CH3OH) (CH3OH)0 (CO)0 CO
Daily production = 528g (60 60 24)s 1ton6 45,61 ton/day methanols 1day 10 g
Figure 3.4.1 Adiabatic lines and number of reactors
According to figure 3.4 six plug flow reactor must be used to achive 0,55 conversion at the exit.
Figure 3.4.2 6 PFR Reactors
19
3.5 Reactor Volumes
Calculation 3.5.1 Reactor 1
Energy balance for reactor 1:
TR TfQ
R byflows (FA0C PA FB0C PB)dT (F AC PA F BC PB F BC PB)dT
T0 TRTR Tf
QR byflows
(F CPA F C
PB)dT (F C
PA F X C F C
PB 2F X C F X C
PC)dT
A0 B0 A0 A0 A1 PA B0 A0 A1 PB A0 A1
T0 TR
Tf
XA1
(FA0
C PA
F
B0 C
PB )dT
T0Tf
(FA0C PA 2FA0 CPB FA0 CPC )dT ( HR )FA0
TR
Tf FB0
Tf FB0 (C PA CPB )dT
(CPA CPB )dTF
A0XA1 T0
FA0 T0
Tf
( H R |T ) (C PA 2C PB C PC )dT ( HR )TR
XA1 88,0433(T T ) 0,0167(T 2 T 2 ) 1,77 10 6 (T 3 T 3)
f 0 f 0 f 0
90680 (60,301(298 T ) 0,038105(298 2 T 2) 3,507 10 6 3 T 3 ) 2,0085 10 9 4 4 ))( 298 (298 T0 0 0 0
….. 3.5.1
V 0,1593 dX1 A
………… 3.5.2F RAo o A
3.5.1 and 3.5.2 solved simultaneously.
7 2XA (
XA
100)(1 XA )
(1 2XA ) 72 33
ra (k) (( 100) ( 100) )(1 2XA )
7(1 2XA )
7 3,567E 12 exp(90130 / 8,314 T)3 3
k 743,198 exp(-80000 / (8,3145 T))
20
From adiabatic line equation and –ra equation, data on table 3.5.1
obtained Table 3.5.1 Reactor-1 data
To Tf Xa k Pco Ph2 Pch3oh Ke (-ra) 1/-ra
490 490 0 2,20397E-06 30 70 0 0,014456 0,323983 3,086582
490 500 0,009866 3,2641E-06 29,8809 69,82135 0,297754 0,009287 0,475376 2,103597
490 510 0,019696 4,76028E-06 29,76082 69,64123 0,597958 0,006071 0,686615 1,456419
490 520 0,029492 6,84225E-06 29,63972 69,45958 0,900698 0,004034 0,97692 1,023625
490 530 0,039255 9,70108E-06 29,51757 69,27636 1,206064 0,002722 1,369968 0,729944
490 540 0,048988 1,35777E-05 29,39434 69,09151 1,514147 0,001864 1,894161 0,527938
490 550 0,058692 1,87725E-05 29,26998 68,90498 1,825039 0,001294 2,582348 0,387244
490 560 0,06837 2,56562E-05 29,14447 68,7167 2,138834 0,00091 3,470503 0,288143
490 570 0,078022 3,46819E-05 29,01775 68,52662 2,45563 0,000648 4,594486 0,217652
490 580 0,087652 4,6398E-05 28,88979 68,33469 2,775525 0,000467 5,983472 0,167127
490 590 0,09726 6,14627E-05 28,76055 68,14083 3,098619 0,00034 7,647774 0,130757
490 600 0,106848 8,06591E-05 28,62999 67,94499 3,425015 0,00025 9,557504 0,10463
490 610 0,116418 0,000104912 28,49807 67,74711 3,754818 0,000186 11,60663 0,086158
490 620 0,125971 0,000135305 28,36475 67,54712 4,088137 0,00014 13,55422 0,073778
490 630 0,13551 0,000173099 28,22997 67,34495 4,42508 0,000106 14,93089 0,066975
490 640 0,145035 0,000219751 28,0937 67,14054 4,765762 8,1E-05 14,89287 0,067146
490 650 0,154548 0,000276936 27,95588 66,93382 5,110296 6,24E-05 11,99905 0,08334
490 655 0,1593 0,000310066 27,88638 66,82957 5,284045 5,49E-05 8,788086 0,11379
By -1/ra vs Xa data on table 3.5.1 excel regression gives this equation
-1/ra=y(Xa)= (-157200*x^5) + (85543*x^4) - (18291*x^3) + (1979.3*x^2) - (114.38*x) + (3.0754);
Using simpson’s integration rule the equation above is integrated by
simpson matlab function (See Appendix C.1 for simpson fuction and reactor
volume functions) Simpson('reactorvolume1',0,0.1593,1000) gives
V1/Fa0 = 0.0879V1 = 30*0,0879 = 2,637
3.5.1 Reactor 2
V 0,2863 dXA2
F RAA20 0,1593
Inlet
A : FA1=FA0-FA0*XA1
B: FB1=FB0-2*FA0*XA1
C: FC1=FA0*XA1
outlet
A : FA2 = FA0 – FA0XA2
B : FB2 = FB0 – 2*FA0*XA2 C : FC2 =
FA0*XA2
21
TR Tf
FC dT FC dT Q ( H )F Xi(inlet) i Pi i(outlet) i Pi Removedbythewalls R A0 A
T0 TR
TR TR TR TR TR Tf
F
A0C
PAdT
FA0
X A1
CPA
dT
F
B0 C
PB dT
2
F
A0 X
A1C
PB dT
F
A0 X
A1 C
PC dT
FA0
CPA
dT
T0 T0 T0 T0 T0 TR
TF TF TF TF
F XA2
CPA
dT F C dT 2 F X C dT F X C dT ( H )F X A0 B0 PB A0 A2 PB A0 A2 PC R A0 A2
TR TR TR TR
Tf FB0
TR TR TR
(C PA CPB )dT X A1 ( 2CPB dT C
PC dT
C
PA )
FA0X
A2 T0 T0 T0 T0
( H R |T )TR TR TR
A = ( 2C
PBdT
CPC dT CPA )T0 T0 T0
A (60,301(298 T ) 0,038105(2982 T 2 ) 3,507 10 6 (2983 T 3) 2,0085 10 9(298 4 T 4))0 0 0 0
XA2
88,0433(T T ) 0,0167(Tf
2 T 2) 1,77 10 6(T 3 T 3) X Af 0 0 f 0 A1
2 2 6 3 3 2,0085 9 4 490680 (60,301(298 T ) 0,038105(298 T
0) 3,507 10 ( 298 T ) 10 (298 T ))
0 0 0
Table 3.5.2 Reactor-2 data
To Tf Xa k Pco Ph2 Pch3oh Ke (-ra) 1/-ra
497 4970,1833 2,90614E- 27,528 66,292 6,1792 0,0105 0,3498
2,85812 06 28 43 89 86 83
497 5070,1946 4,25746E- 27,355 66,032 6,6120 0,0068 0,5037 1,985159 06 19 78 37 85 3 89
497 5170,2060 6,14567E- 27,179 65,768 7,0521 0,0045 0,7129 1,402516 06 12 68 93 53 89 46
497 5270,2173 8,74859E- 27,000 65,500 7,4999 0,0030 0,9919 1,00819 06 02 03 43 58 56 09
497 5370,2287 1,22912E- 26,817 65,226 7,9554 0,0020 1,3554 0,737781 05 81 71 83 85 96 37
497 5470,2401
1,7055E-0526,632 64,948 8,4190 0,0014 1,8164 0,5505
9 39 59 14 42 35 29
497 5570,2516 2,33885E- 26,443 64,665 8,8907 0,0010 2,3803
0,420117 05 7 55 46 1 87
497 5670,2630 3,17187E- 26,251 64,377 9,3708 0,0007 3,0361 0,329361 05 64 46 94 17 86 61
497 5770,2745 4,25638E- 26,056 64,084 9,8596 0,0005 3,7389 0,267422 05 13 19 83 15 6 54
497 5870,2860 5,65477E- 25,857 63,785 10,357 0,0003 4,3812 0,228201 05 06 59 34 74 23 47
497 5970,2974 7,44142E- 25,654 63,481 10,864 0,0002 4,7448 0,210796 05 35 53 12 74 36 55
497 6070,3090 9,70439E- 25,447 63,171 11,380 0,0002 4,4230 0,22601 05 9 85 25 03 31 89
497 617 0,3205 0,0001254 25,237 62,856 11,906 0,0001 2,6964 0,3708
22
4 71 6 4 52 41 59
By -1/ra vs Xa data on table 3.5.2 excel regression gives this equation -
1/ra=y(Xa)= (38246*x^4) - (36734*x^3) + (13296*x^2) - (2154.8*x) + (132.5);
Simpson('reactorvolume2',0.1593,0.2863,1000)
V2/Fa20 = 0,0889FA20 FA0 (1 XA1 ) =30*(1-0,1593) = 25,221 mol/s
V2 = 25,221 * 0,0889 = 2,242
Other Reactors’ volume calculation shown on Appendix C.3
v1,v2,v3,v4,v5 and v6 values are not in unit of volume.
r k(PCOP2H2
PCH3OH ) (mol / kgcat min)Ke
k 7.6106 mol(kgcat) 1 min1 atm3 at 250 C
V1 dX AF [mol / s] ra[mol / kgcat min]
A0
After making unit correction (seconds convert to minute), kgcat unit is obtained.
Table 3.5.3 Catalyst uses
Reactors Calculated Catalyst mass(kg)
Reactor 1 2,637 158,22
Reactor 2 2,242 134,52
Reactor 3 1,394 83,64
Reactor 4 1,6075 96,45
Reactor 5 1,267 76,02
Reactor 6 0,501 30,06
Total catalyst mass 662.43
23
662,43kgcat 1m 3 catalyst 1m3 reactor =1,4786 m
1 1120kgcat (1 0.6)m3 catalyst
Table 3.5.4 Reactor volumes
Reactors Volume(lt)
Reactor 1 353,16
Reactor 2 300,26
Reactor 3 186,69
Reactor 4 215.29
Reactor 5 169,68
Reactor 6 67
Total volume 1478,6 lt
24
4.RESULTS & DISCUSSIONS
Firstly, thermodynamics equilibrium line is drawn by using van’t hoff equation
for different pressures (figure 3.1). Plot shows that methanol production is rising by
pressure increasing. But, at very high pressures catalyst lifetime is decreasing and
also reactor material may not resist the high pressures. So, Achieving 0.55
converion of methanol, pressure of 100 bar is selected.
Constant rate curves drawn as figure 4.1 by using –ra=f(Xa,T) formula. The line goes
through the maximum points of these curves is operating line.To close to operating line, first
reactor inlet temperature is selected 490. If more less T0 value is selected, the number of
reactors should be decreased. But, according to the rate equation(the function of temperature
and conversion); reaction rate is decreasing with temperature decreasing. If,T0 value is very
high, the reactor number will increase. So, optimum tempretature should be selected.
Figure 4.1 Adiabatic lines and number of reactors (Xa(y-axis) vs T(x-axis))
Xa=f(T) function is obtained by using adiabatic energy balance. Using
these lineer functions, adiabatic lines for each reactor are drawn(figure 4.1).
–ra=f(T,xa) is also function of temperature.adiabatic line and rate equations are solved
simultaneously and Xa vs -1/ra data are obtained.These data plotted on figure 4.2.Each reactor
25
functions is monitorized with excel.And using these functions in a simpson’s integration rule
matlab function, areas under the curves are calculated.These results equals to Vi/Fa0(i)
Fa0 unit is selected as [mol/s]. It is converted to mol/min. –ra unit is
[mol/kgcat*min]. After doing these unit conversions, areas under the curves(at figure
4.2) gives the result [kgcat]. The reactor volume results are obtained by dividing the
kgcat results by catalyst density and a volume conversion factor (volume of catalyst
to volume of reactor).(catalyst void volume is selected 0,6).
Figure 4.2 -1/ra(y axis) vs Xa(x axis)
26
Appendix - A.1
Table App.A.1.1 Reduced temperatures of substances
T,K Tr(metanol) Tr(CO) Tr(H2)400 0,77942323 3,007518797 12,01201201420 0,81839439 3,157894737 12,61261261440 0,85736555 3,308270677 13,21321321460 0,89633671 3,458646617 13,81381381480 0,93530787 3,609022556 14,41441441500 0,97427903 3,759398496 15,01501502520 1,01325019 3,909774436 15,61561562540 1,05222136 4,060150376 16,21621622560 1,09119252 4,210526316 16,81681682580 1,13016368 4,360902256 17,41741742600 1,16913484 4,511278195 18,01801802
Table App.A.1.2 Fugacity coefficients of substances at P = 50 bar
T,K (CO) (methanol) (H2)
400 1,012 0,1538 1,017420 1,014 0,2424 1,017440 1,015 0,3591 1,016460 1,017 0,504 1,016480 1,018 0,7093 1,015500 1,018 0,7553 1,015520 1,019 0,7919 1,014540 1,019 0,8222 1,014560 1,02 0,8475 1,014580 1,02 0,869 1,013600 1,02 0,8873 1,013
Table App.A.1.3 Fugacity coefficients of substances at P = 75 bar
T (CO) (methanol) (H2)400 1,0900 0,1067 1,0270420 1,0220 0,1681 1,0260440 1,0240 0,2490 1,0250460 1,0260 0,3498 1,0240480 1,0280 0,4685 1,0240500 1,0290 0,5999 1,0230
27
520 1,0290 0,6904 1,0220540 1,0300 0,7375 1,0220560 1,0300 0,7757 1,0210580 1,0310 0,8075 1,0200600 1,0310 0,8346 1,0200
Table App.A.1.4 Fugacity coefficients of substances at P = 120 bar
T (CO) (methanol) (H2)400 1,03400 0,07151 1,04600420 1,03900 0,11270 1,04400440 1,04200 0,16700 1,04300460 1,04500 0,23480 1,04100480 1,04700 0,31520 1,04000500 1,04800 0,40580 1,03800520 1,05000 0,50170 1,03700540 1,05000 0,58950 1,03600560 1,05100 0,65430 1,03500580 1,05100 0,70480 1,03400600 1,05100 0,74670 1,03300
Appendix – A.2
30XAe
Ky 100-60XAe
30-30X 70 60X 2
Ae Ae
100 60XAe 100 60XAe By expanding this equation ;
XAe
3 ( 36 36 K ) X 2 (120 84 K 36 K ) X ( 100 49 K 84 K ) 49 K 0y Ae y yAe y y y
For Solving this equation on MATLAB R2007a, we defined these parameters:
a = ( 36 36 Ky )
b = (120 84 Ky 36 Ky )
c = ( 100 49 Ky 84 Ky )
d = 49 Ky
a,b,c,d are polynomial coefficients and there is a function on matlab to find roots of
high order functions by using these polynomial coefficients.
M.File of Matlab is ;
function a=c(A) a
= -36 - (36 * A);
28
b = 120 + (84 * A) + (36 * A); c = -100 - (49 * A) - (84 * A); d = 49*A;p=[a b c d];
a = roots(p);
and we call the function on command window like ‘ c(Ky) ‘
Example :
c (31217.42) gives the result
below ans =
1.1669 + 0.0075i
1.1669 - 0.0075i
0.9995
Our Xae value is 0,995. Other roots are imaginer and not validating Xae.(Xae
must be 0<Xae<1 and real )
By using other Ky values on this matlab function, we get the Xae values on Table
3.3, 3.5, 3.7.
29
Appendix B.1
The rate expression is derived as a function of T and Xa.
7(
XA
100)(1 XA ) 2XA (1 2XA )
7
r (k) (( 100) (3
100)2
3
3,567E 12 exp(90130 /8,314 T))
(1 2XA ) 7
(1 2XA ) 7
3 3
The execution of program is based on scanning T and Xa values at the range of
(400<T<650 T+=0.1) and (0<Xa<1 Xa+=0.01). In the program constant r value is given from
textbox and the program calculate and r value from T and Xa values. If r(given from textbox)
– r(calculated from equation) = 0 (almost 0, its sensivity differs by T and r to
obtain more data).
The variables are defined as;
k = 743.198 * (Math.Exp(-80000 / (8.3145 * T))); Pco = ((1 - Xa)/((10/3)-(2*Xa)))*100;Ph2 = (((7/3)-(2*Xa))/((10/3)-(2*Xa)))*100; Pch3oh = ((Xa)/((10/3)-(2*Xa)))*100;Ke = (0.000000000003567) * ((Math.Exp((90130) / (8.3145 * T)))); ra = (k * ro * ((Pco * (Ph2 * Ph2)) - (Pch3oh / Ke)));
Main code block of this program is :
for (T = 400; T < 700; T += 1){
for (Xa = 0; Xa < 1; Xa += 0.01){
k = 743.198 * (Math.Exp(-80000 / (8.3145 * T))); Pco = ((1 - Xa)/((10/3)-(2*Xa)))*100;Ph2 = (((7/3)-(2*Xa))/((10/3)-(2*Xa)))*100; Pch3oh = ((Xa)/((10/3)-(2*Xa)))*100;Ke = (0.000000000003567) * ((Math.Exp((90130) / (8.3145 * T)))); ra = (k * ((Pco * (Ph2 * Ph2)) - (Pch3oh / Ke)));
if (r <= 0.03 && (ra - r) < 0.000015&& (ra - r) > -0.000015){
listBox1.Items.Add(T.ToString() + " " + Xa.ToString() + " " + ra.ToString()); listBox2.Items.Add(T.ToString());listBox3.Items.Add(Xa.ToString());
}if (T < 470 && r > 0.03 && r <= 0.15 && (ra - r) < 0.00015 && (ra - r) > -0.00015){
listBox1.Items.Add(T.ToString() + " " + Xa.ToString() + " " + ra.ToString()); listBox2.Items.Add(T.ToString());
30
listBox3.Items.Add(Xa.ToString());}if (T<550 && T > 470 && r > 0.03 && r <= 0.15 && (ra - r) < 0.001 && (ra - r) > -0.001){
listBox1.Items.Add(T.ToString() + " " + Xa.ToString() + " " + ra.ToString()); listBox2.Items.Add(T.ToString());listBox3.Items.Add(Xa.ToString());
}
if (T > 550 && r > 0.03 && r <= 0.15 && (ra - r) < 0.03 && (ra - r) > -0.03){
listBox1.Items.Add(T.ToString() + " " + Xa.ToString() + " " + ra.ToString()); listBox2.Items.Add(T.ToString());listBox3.Items.Add(Xa.ToString());
}...
//(other if else loops exist here for other range of T for varying (r-ra) sensibilities.These
code block written to get uniform distributed data at temperature range 400 – 700 K)
else{
continue;}
All code block and .exe file of this program is given at CD-ROM (attached to report).
Figure A.3 A screenshot from constant rate program
31
Appendix B.2
Table B.2 constant rate data
r=1 r=2 r=5 r=8T Xa T Xa T Xa T Xa520 0,01 541 0,03 569 0 590 0,07523 0,1 542 0,06 570 0,02 597 0,14524 0,13 542 0,06 571 0,04 600 0,16532 0,29 543 0,08 572 0,06 604 0,18534 0,32 543 0,09 579 0,16 607 0,19538 0,37 544 0,11 580 0,17 627 0,2539 0,38 545 0,13 581 0,18540 0,39 545 0,13 582 0,19541 0,4 546 0,15 586 0,22541 0,4 546 0,15 596 0,26542 0,41 547 0,17 614 0,26546 0,44 547 0,17 624 0,24553 0,47 548 0,19 632 0,22553 0,47 549 0,2 643 0,19556 0,48 550 0,22573 0,48 550 0,22577 0,47 552 0,25581 0,46 553 0,26590 0,43 560 0,33605 0,37 561 0,34621 0,3 561 0,34659 0,16 564 0,36679 0,11 566 0,37
569 0,38569 0,38572 0,39573 0,39588 0,39588 0,39593 0,38597 0,37597 0,37615 0,31
For more little scattered constant rate data by different values of r are
available in the Excel file (constant rate curces at 100 bar.xls) on CD-ROM.
32
Appendix C.1
Simpson’s integration M.File on matlab:
function I=Simpson(f,a,b,n) %f nin integrali simpson kuralı % n çift sayı olacak h=(b-a)/n;
S= feval(f,a);
for i=1:2:n-1
x(i)=a+h*i;S=S+4*feval(f,x
(i)); end
for i=2:2:n-2 x(i)=a+h*i; S=S+2*feval(f,x(i));
end S=S+feval(f,b); I=h*S/3;The function is called from command window like:
V1/Fa01=Simpson(‘reactorvolume1’,0,0.1563,1000)
‘reactorvolume1’ = is another m.file which includes function of -1/ra
by Xa; 0 = Xa0;
0.1563 = Xa1;
1000 = Diveding factor (if it is larger, result of the numerical result approaches
analytical result )
Appendix C.2
M.Files of reactor volume equations (-1/ra function by Xa) :
Reactor 1:function y1=reactorvolume1(x)y1=(-157200*x^5) + (85543*x^4) - (18291*x^3) + (1979.3*x^2) - (114.38*x) + (3.0754);
Reactor 2:function y2=reactorvolume2(x)y2=(38246*x^4) - (36734*x^3) + (13296*x^2) - (2154.8*x) + (132.5);
Reactor 3:function y3=reactorvolume3(x)y3=(65582*x^4) - (91531*x^3) + (48084*x^2) - (11278*x) + (997.57);
Reactor 4:function y4=reactorvolume4(x)y4=(119805*x^4) - (207253*x^3) + (134786*x^2) - (39071*x) + (4261.7);
Reactor 5:
33
function y5=reactorvolume5(x)y5=(177966*x^4) - (355243*x^3) + (266463*x^2) - (89032*x) + (11184);
Reactor6:
function y6=reactorvolume6(x)y6=(366299*x^4) - (785097*x^3) + (631702*x^2) - (226167*x) + (30405);
Appendix C.3
C.3.1 Reactor 3
V3 0,3863 dXA
FA30 0,2863
RA
Inlet
A : FA2=FA0-FA0*XA2
B: FB2=FB0-2*FA0*XA2
C: FC2=FA0*XA2
outlet
A : FA3 = FA0 – FA0XA3
B : FB3 = FB0 –
2*FA0*XA3 C : FC3 =
FA0*XA3
TR Tf
FC dT FC dT Q ( H )F Xi(inlet) i Pi i(outlet) i Pi Removedbythewalls R A0 A
T0 TR
TR TR TR TR TR Tf
F
A0C
PAdT
FA0
X A2
C PA
dT
F
B0C
PBdT
2
F
A0X
A2C
PBdT
F A0X
A2C
PCdT
F
A0C
PAdT
T0 T0 T0 T0 T0 TR
TF TF TF TF
F XA3
CPA
dT F C dT 2 F X C dT F X C dT (H )F X A0 B0 PB A0 A3 PB A0 A3 PC R A0 A3
TR TR TR TR
Tf FB0
TR TR TR
(CPA CPB )dT XA2 ( 2CPB dT CPC dT
CPA
)F
A0XA3 T0 T0 T0 T0
( HR |T )TR TR TR
A = ( 2CPBdT CPC dT CPA )T0 T0 T0
A (60,301(298 T ) 0,038105(298 2 T 2 ) 3,507 10 6 (2983 T 3 ) 2,0085 109 (2984 T4 ))0 0 0 0
XA3
88,0433(T T ) 0,0167(T 2 T 2 ) 1,77 106 (T 3 T 3) XA2 A
f 0 f 0 f 0
90680 (60,301(298 T ) 0,038105(298 2 T 2 ) 3,507 10 6 3 3 ) 2,0085 10 9 4 T 4 ))( 298 T (298
0 0 0 0
34
Table C.3.1 Reactor-3 data
To Tf Xa k Pco Ph2 Pch3oh Ke (-ra) 1/-ra
502 502 0,2863 3,52419E-06 25,85183 63,77774 10,37043 0,008519 0,366295 2,730037
502 512 0,2963 5,12434E-06 25,67561 63,51341 10,81098 0,005587 0,520835 1,919994
502 522 0,3063 7,34494E-06 25,4968 63,2452 11,25799 0,003724 0,72688 1,375743
502 532 0,3163 1,03863E-05 25,31535 62,97302 11,71163 0,002521 0,994431 1,005601
502 542 0,3263 1,45004E-05 25,13118 62,69677 12,17204 0,001731 1,330492 0,751602
502 552 0,3363 2,00009E-05 24,94425 62,41638 12,63937 0,001205 1,733817 0,576762
502 562 0,3463 2,72739E-05 24,75449 62,13173 13,11378 0,000849 2,185292 0,457605
502 572 0,3563 3,67905E-05 24,56183 61,84274 13,59543 0,000606 2,631077 0,380073
502 582 0,3663 4,91199E-05 24,3662 61,54931 14,08449 0,000438 2,95395 0,33853
502 592 0,3763 6,4944E-05 24,16755 61,25132 14,58113 0,00032 2,925888 0,341777
502 602 0,3863 8,50728E-05 23,96579 60,94869 15,08552 0,000236 2,131355 0,469185
By -1/ra vs Xa data on table C.3.1 excel regression gives this equation -
1/ra=y(Xa)= (65582*x^4) - (91531*x^3) + (48084*x^2) - (11278*x) + (997.57);
Simpson('reactorvolume3',0.2863,0.3863,1000)gives
V3/Fa30 = 0.0757FA30 FA0 (1 XA3 ) =30*(1-0,3863) = 18,411 mol/s
V3 = 18,411 * 0.0757= 1,394
Reactor 4
V 0,4663 dX4
R AFA40 0,3863 A
Tf FB0
TR TR TR
(C
PA CPB )dT XA3 ( 2CPB dT CPC dT CPA )
XA4 F
A0T0 T0 T0 T0
( HR |T )TR TR TR
A = ( 2CPBdT CPC dT CPA )T0 T0 T0
A (60,301(298 T0 ) 0,038105(2982 T02 ) 3,507 10 6 (2983 T0
3) 2,0085 10 9(298 4 T 04))
XA4
(88,0433(T T ) 0,0167(T 2 T 2 ) 1,77 10 6 (T 3 T 3 )) XA3 A
f0 f 0 f 0
90680 (60,301(298 T ) 0,038105(298 2 T2 ) 3,507 10 6 3 T 3 ) 2,0085 10 9 (298 4 T 4 ))(298
0 0 0 0
35
Table C.3.2 Reactor-4 data
To Tf Xa k Pco Ph2 Pch3oh Ke (-ra) 1/-ra
507 507 0,3863 4,25746E-06 23,96579 60,94869 15,08552 0,006885 0,369699 2,704904
507 517 0,3963 6,14567E-06 23,76086 60,64128 15,59786 0,004553 0,515938 1,938218
507 527 0,4063 8,74859E-06 23,55267 60,329 16,11833 0,003058 0,703841 1,420776
507 537 0,4163 1,22912E-05 23,34115 60,01173 16,64712 0,002085 0,935085 1,069422
507 547 0,4263 1,7055E-05 23,12623 59,68934 17,18443 0,001442 1,201953 0,831979
507 557 0,4363 2,33885E-05 22,90781 59,36171 17,73049 0,00101 1,477438 0,676848
507 567 0,4463 3,17187E-05 22,6858 59,02871 18,28549 0,000717 1,697902 0,588962
507 577 0,4563 4,25638E-05 22,46014 58,6902 18,84966 0,000515 1,733567 0,576845
507 587 0,4663 5,65477E-05 22,23071 58,34606 19,42323 0,000374 1,339535 0,746528
507 587 0,4663 5,65477E-05 22,23071 58,34606 19,42323 0,000374 1,339535 0,746528
By -1/ra vs Xa data on table C.3.2 excel regression gives this equation
-1/ra=y(Xa)= (119805*x^4) - (207253*x^3) + (134786*x^2) - (39071*x) + (4261.7); Simpson('reactorvolume4',0.3863,0.4663,1000)gives
V4/Fa40 = 0.1004FA40 FA0 (1 XA4 ) =30*(1-0,4663) =16,011
mol/s V4 = 16,011 * 0,1004= 1,6075
Reactor 5
V 0,5243 dXA5
… C.5.1F RA50 0,4663 A
(88, 0433(T T ) 2 2 T ) 6 3 3 T )) X AXA 5
0, 0167(T 1,77 10 (T0f 0 f 0 f A 4
90680 (60, 301(2980 T ) 0, 038105(298 0 T 6 3
)(3
) 3, 298507 10T 2, 00085 10 (298…C.5.2 Solving simultaneously equation C.5.1 and C.5.2
Table C.3.3 Reactor-5 data
To Tf Xa k Pco Ph2 Pch3oh Ke (-ra) 1/-ra
514 514 0,4663 5,51309E-06 22,23071 58,34606 19,42323 0,005146 0,396415 2,522606
514 519 0,4713 6,60261E-06 22,11455 58,17183 19,71362 0,0042 0,463111 2,159311
514 524 0,4763 7,88028E-06 21,99742 57,99614 20,00644 0,003441 0,537237 1,861376
514 529 0,4813 9,3738E-06 21,87931 57,81896 20,30174 0,00283 0,618375 1,61714
514 534 0,4863 1,11142E-05 21,76019 57,64028 20,59953 0,002336 0,705488 1,417458
514 539 0,4913 1,31362E-05 21,64006 57,46008 20,89986 0,001935 0,79665 1,255256
514 544 0,4963 1,54783E-05 21,5189 57,27835 21,20276 0,001608 0,888692 1,12525
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514 549 0,5013 1,81837E-05 21,3967 57,09505 21,50825 0,001341 0,976726 1,023828
514 554 0,5063 2,12999E-05 21,27345 56,91017 21,81638 0,001122 1,053527 0,949192
514 559 0,5113 2,48796E-05 21,14913 56,7237 22,12717 0,000942 1,108712 0,901947
514 564 0,5163 2,8981E-05 21,02373 56,5356 22,44067 0,000793 1,127685 0,886772
514 572 0,5243 3,67905E-05 20,82081 56,23122 22,94797 0,000606 1,029673 0,971182By -1/ra vs Xa data on table C.3.3 excel regression gives this equation -1/ra=y(Xa)=
(177966*x^4) - (355243*x^3) + (266463*x^2) - (89032*x) + (11184);
Simpson('reactorvolume5',0.4663,0.5243,1000) gives
V5/Fa50 = 0.0888FA50 FA0 (1 XA5 ) =30*(1-0,5243) = 14,271 mol/s
V5 = 14,271 * 0,0888 = 1,267
Reactor 6
V 0,5533 dX6 R A ….C.6.1F
A60 0,5243 A
XA5
(88,0433(T T ) 0,0167(T 2 T 2 ) 1,77 106 (T3 T3 )) X Af 0 f 0 f 0 A4
90680 (60,301(298 T ) 2 T 2 ) 6 (2983 T 3 ) 9 (298 4 T 4 ))0,038105(298 3,507 10
0
2,0085 10
0 0 0
…C.6.2
Solving simultaneously equation C.6.1 and C.6.2
Table C.3.4 Reactor-6 data
To Tf Xa k Pco Ph2 Pch3oh Ke (-ra) 1/-ra
533 533 0,5243 1,07448E-05 20,82081 56,23122 22,94797 0,002426 0,605749 1,650848
533 537 0,5283 1,22912E-05 20,71828 56,07742 23,2043 0,002085 0,664023 1,505973
533 542 0,5333 1,45004E-05 20,5891 55,88365 23,52725 0,001731 0,73527 1,360045
533 547 0,5383 1,7055E-05 20,45878 55,68816 23,85306 0,001442 0,7999 1,250157
533 552 0,5433 2,00009E-05 20,32729 55,49093 24,18178 0,001205 0,850469 1,175822
533 557 0,5483 2,33885E-05 20,19463 55,29194 24,51343 0,00101 0,876376 1,141063
533 562 0,5533 2,72739E-05 20,06078 55,09116 24,84806 0,000849 0,862807 1,159007
By -1/ra vs Xa data on table C.3.4 excel regretion gives this equation
-1/ra=y(Xa)= (366299*x^4) - (785097*x^3) + (631702*x^2) - (226167*x) + (30405)
Simpson('reactorvolume6',0.5243,0.5533,1000) gives
V6/Fa60 = 0.0374FA60 FA0 (1 XA6 ) =30 *(1-0,5533) = 13,401 mol/s
37
V6 = 13,401 * 0,0374 = 0,501
Appendix D.1
Rate equation uses for methanol productions[7]
38
References
1- Wade L.E. Gengelbach, R.B. Taumbley, J.L. Hallhover W.L. Kırk-Other Encyclopedia of Chemical Technology, 3rd. Edition, Wiley New York 1981 Vol 15 page 398-4152- G.H. Graaf, Sıytsema P.J.J., Stamhuıs E.J., Joosten G.E.H. Chem. Eng.Sci. Vol 41, 11, page 2883 (1986)
3- Satterfield N.D., Heterogeneous Catalysis in Practice, McGraw Hill, 1980
4- Howard F. Rase, Handbook of Commercial Catalysts, Crc Pres,2000, page 429-430 5- Sandler , S.I, Chemical and Engineerig Thermodynamics, Third edition, John Wiley & Sons Inc. , 1999 , page 759
6- Smith, J.M., VanNess, H.C., “Introduction to Chemical Engineering Thermodynamics”, 3rd Ed., McGrow Hill, Newyork, 1996.7- http://www.rajwantbedi.com/dg1_final.pdf
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SYMBOLS
Cpi : Heat capasity , J/mol.K
q : Fugacity coefficient
G298 : Standart Gibbs energies of formation , J/mol
H 298 : Standart Enthalpies , J/mol
Kf : Equilibrium constant
Ky : Equilibrium constant (molar fractions)
K : Equilibrium constant(fugacity coefficients)
Tr : Reduced Temperature
Pr : Reduced Pressure
P : Pressure , bar
R : Ideal gas law constant , 8,314 J/mol.K
T : Temperature , K
XA : Fractional conversion of Carbon monoxide
XAe : Equilibrium conversion of Carbon monoxide
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