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Mal-distribution of temperature in an industrial dual-bed reactor for conversion of CO2 to methanol
Applied Thermal Engineering 91 (2015) 1059e1070
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Mal-distribution of temperature in an industrial dual-bed reactor for conversion of CO2 to methanol A. Mirvakili a, M.R. Rahimpour a, b, * a b
Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran Department of Chemical Engineering and Materials Science, University of California, Davis, One Shields Avenue, Davis, CA 95616, United States
h i g h l i g h t s Gas cooled reactor of dual type methanol faces with a significant problem. Temperature drop in the last of the reactor increased drastically. Temperature is less than dew point temperature in the porous media. Methanol and water are condensed at the last of the reactor. Self-heat recuperation technology is developed to energy saving.
g r a p h i c a l a b s t r a c t Steam Flare
Purge gas
513 K
Drum
536 K Methanol water 308 K Sea water
411 K 316 K
495 K 537 K
Fresh Feed
393 K
Air Cooler
513 K Boiling water
444 K
329 K
463 K
Methanol water 369 K
385 K
Boiling water
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 May 2015 Accepted 24 August 2015 Available online 21 September 2015
Design of dual type methanol reactor includes a gas cooled reactor for methanol synthesis. The gas cooled reactor faces with the problem of gas condensate formation and two phase flow in the practical operating conditions owing to a high temperature drop in the last 2 m of the reactor length. In this study, three strategies are proposed in order to prevent gas condensate formation in the gas cooled reactor which is designed based on dual type design. The first strategy is utilization of a partial condenser before the gas cooled reactor, the second strategy is injection of hot synthesis gas (HGS) to the last 2 m of the reactor and the third is warming the shell side of the reactor with steam in a jacket (JS) around the last 2 m of the reactor. Simulation results show that, the most effective strategy (ES) is application of a partial condenser to separate the methanol and water in the inlet of the gas cooled reactor by condensation. In ES, the dew point temperature in the porous media reduces via in-situ methanol and water removal at the inlet of the gas cooled reactor and gas temperature ascends along the length of the reactor. Moreover, methanol production enhances about 7.9% and CO2 decreases 2.6% in ES rather than in the conventional methanol synthesis reactor (CR). The elimination of the gas condensate formation on one hand and enhancing the methanol production and decreasing CO2 emission on the other hand can be considered as the superiority of the suggested ES to the CR and other strategies. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Gas condensate formation Dew point in porous media Gas cooled reactor CO2 conversion Industrial methanol synthesis
1. Introduction
* Corresponding author. Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran. E-mail address: [email protected] (M.R. Rahimpour). http://dx.doi.org/10.1016/j.applthermaleng.2015.08.067 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
Methanol is produced from synthesis gas (carbon monoxide and hydrogen) which is mainly derived from oil, coal or, biomass. One of the most important applications of methanol is providing a feedstock for the plastics industry. Moreover, methanol can be used
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directly in internal combustion engines of vehicles and aircrafts, with similar efficiency to diesel engines. Minor improvements in production efficiency of important chemicals may result in significant profit increase, energy conservation and environmental protection, especially for a chemical such as methanol which is produced in a worldwide scale [1]. Process of methanol synthesis has attracted great deal of attention till now. The kinetics of the methanol synthesis presented by Graaf et al. [2] which is considered in this study is based on the hydrogenation of CO2 and CO, as provided by reactions (1) and (2). Because the CuO/ZnO/Al2O3 catalysts are known to catalyze the wateregas-shift reaction (3) as well, this reaction is also included in the kinetic model.
CO þ 2H2 4CH3 OH
DH298 ¼ 90:55kJ=mol
CO2 þ 3H2 4CH3 OH þ H2 O CO2 þ H2 4CO þ H2 O
DH298 ¼ 49:43kJ=mol
DH298 ¼ þ41:12kJ=mol
(1) (2) (3)
Kralj et al. [3] have optimized methanol plant using the NLP model developed earlier by including an additional flow rate of hydrogen (H2), decreasing flow rate of high-pressure steam in crude methanol recycling, and increasing methanol production by 2.5%. Kansha et al. [4] have investigated the feasibility of applying self-heat recuperation technology to the methanol synthesis process and they have developed an innovative process for methanol synthesis from an energy saving point of view [5]. Recently, a twostage methanol synthesis reactor was introduced instead of a single-type for CO conversion to methanol [6]. This system is an advanced technology for converting synthesis gas to methanol at low cost and in large quantities. The configuration of this system is based on the two stage reactor system. The first stage is a high temperature water-cooled reactor that is combined in series with a low temperature gas cooled reactor. Partial conversion of CO to methanol is accomplished in the gas cooled reactor. In Iran, a domestic petrochemical company has applied methanol synthesis process based on dual type technology which has been faced a major problem in the gas cooled reactor after 2 years. Actually, in the gas cooled reactor the temperature drops until it becomes less than the dew point temperature which causes the volatile components in the gas stream be condensed. In the applied system, the dew point in the packed bed should be calculated considering the porous media. The effect of porous media on the dew point calculations has been previously studied. In most studies, oil and gas reservoirs have been considered as a porous media. Results of several reported experimental studies indicate that the presence of a porous medium has a significant influence on the equilibrium behavior of hydrocarbon mixtures [7e11]. Trebin and Zadora [9] concluded that the initial condensation pressures (dew points) of gas condensate mixtures in porous media can be 10 to 15 percent higher than those observed in conventional Pressure, volume, temperature (PVT) cells. An important parameter for obtaining the thermodynamic properties in the porous media is capillary pressure which cannot be measured easily. There have been few studies on modeling the onset of the capillary pressure in porous media. Masoodi et al. [12] have developed a simple and general formula for the capillary pressure in the porous media, which relates the capillary pressure to the microstructure of various porous media. In the present study, dew point temperature in the porous media is obtained and composition of the liquid phase (condensate) is determined. The condensate is a solution of 71% methanol and 29% water, which is significantly corrosive. Thus; the catalysts and other metallic equipments faces the high risk of corrosion. Due to corrosion, catalysts are crushed and porosity of the bed decreases and the pressure drop increases at the end of the reactor as a result.
Moreover, at the end of the reactor, temperature reduces more than the other parts of the reactor which results in more methanol and water condensation. The current work mainly focuses on the study of gas condensate formation in the packed bed gas cooled reactor as well as, proposing three configurations in order to prevent gas condensate formation. For this purpose, a partial condenser is embedded after the water cooled reactor which cools the inlet gas to the second reactor in ES configuration and warming of the gas in the last 2 m of the reactor in HGS and JS configurations is proposed. These strategies are investigated considering the energy consumption. Although ES configuration needs more energy because of containing two heating equipments, an innovative energy saving method has been applied in this study for the ES configuration. A novel self-heat recuperation technology developed by Yasuki Kansha for heating and cooling thermal processes has been applied in which not only latent heat but also sensible heat is circulated in a feed-effluent heat exchanger of the thermal process. The required energy for partial condenser and heat exchanger in ES is not provided from an outer source; therefore the energy consumption reduces drastically in ES configuration. 2. Process description 2.1. Conventional dual type methanol synthesis reactor Schematic diagram of a conventional dual type methanol synthesis reactor is shown in Fig. 1(a). The dual type Methanol Reactor is basically a vertical shell and tube heat exchanger with fixed tube sheets. Reactions of methanol synthesis are performed over commercial CuO/ZnO/Al2O3 catalyst. The catalyst is packed in shell side of the gas-cooled reactor and vertical tubes of water-cooled reactor. Partial conversion of the syngas to methanol accomplishes in the first reactor, which is an isothermal reactor. The methanol-containing gas, leaving the first reactor is routed to the second downstream reactor without prior cooling. In the gas cooled reactor, cold feed gas for the first reactor is routed through tubes in a countercurrent flow with the reacting gas. Thus, the reaction temperature is continuously reduced over the reaction path in the second reactor, and the equilibrium driving force for methanol synthesis maintained over the entire catalyst bed. Temperature of the first reactor is higher than the second reactor and the main catalyst deactivation occurs in the gas cooled reactor. Therefore, lower operating temperature in the gascooled reactor results in a practically unlimited catalyst service life. In addition, reaction control extends the life time of the catalyst in the water-cooled reactor. The input data and industrial design of the catalyst pellet for the conventional two-stage methanol synthesis reactor have been listed in Tables 1 and 2. 2.2. SE strategy Fig. 1(b) shows the schematic diagram of SE strategy for methanol synthesis reactor configuration. SE strategy is the application of a partial condenser after water cooled reactor in the conventional configuration. Half of the gas leaving the water cooled reactor is sent to a partial condenser and it is cooled to 96 C. As a result, 40% of methanol and 20% of water are condensed and separated from the gas stream. Then, the remaining non-condensed gas will be heated to 260 C and mixed to another half of the gas stream leaving the first reactor and sent to the gas cooled reactor. 2.3. HGS strategy Fig. 1(c) shows the schematic diagram of HGS strategy for methanol synthesis reactor configuration. As shown in Fig. 1(c),
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month from the startup, steam from drum of water cooled reactor is sent to the jacket and it warms the gas in the shell of the gas cooled reactor.
Fresh feed (synthesis gas)
(a)
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Tubes
Catalyst Purge gas
Shell (reaction side) Product
Methanol purification
crud methanol
3. Mathematical model
Fresh feed (synthesis gas)
3.1. Thermodynamics model
The second reactor (Gas cooled reactor)
The first reactor (Water cooled reactor)
Methanol and Water condensate
The second reactor (Gas cooled reactor)
(b)
The first reactor (Water cooled reactor)
xi ¼
X ðyi =Ki Þ ¼ 1
(4)
In modern practice, VLE calculations for light-hydrocarbon systems are accomplished by using computer calculations based on equations of state, such as the Soave-Redlich-Kwong (SRK) equation. In this approach, fugacity coefficients are used to express the fugacity of both the liquid and vapor phases relative to the ideal gas. In the following the phase equilibrium relations are presented [13]:
Catalyst Shell (reaction side) Product
Methanol purification
crud ethanol
Fresh feed (synthesis gas)
V
Tubes
(c)
The first reactor (Water cooled reactor)
Hot Synthesis Gas
Catalyst Purge gas
Shell (reaction side)
Fresh feed (synthesis gas)
Steam
The first reactor (Water cooled reactor)
Tubes
Catalyst Shell (reaction side)
crud methanol
Fresh feed (synthesis gas)
Product
jþ1
Steam Jacket
Fig. 1. The schematic diagrams of (a) conventional (CR) (b) ES methanol synthesis reactor (c) HGS (d) JS configurations.
the feed temperature of water gas cooled reactor is about 533 K which is named hot syn gas stream. In HGS strategy a proportion of hot syn gas stream is injected to the last 2 m of the reactor when temperature in this zone decreases to less than 513 K. indeed, there is a valve that adjust the flow rates of hot syn gas stream to the gas cooled reactor. The flow rate of stream is zero before 18 months and after that flow rate of hot gas injection increases gradually. 2.4. JS strategy Fig. 1(d) shows the schematic diagram of JS strategy for methanol synthesis reactor configuration. In this strategy a jacket is fabricated around the last 2 m of the gas cooled reactor. After 18
b Li f
(6)
bV f i
T Pc;i exp 5:37ð1 þ ui Þ 1 Tc;i (7)
p
where, Tc,i is the critical temperature of component i, Pc,i is the critical pressure of component i, ui is the acentric factor of component i. The liquid phase composition is estimated from:
xi
Methanol purification
(5)
The solution method is trial and error. At first an estimate of the dew point temperature is provided and then K-values for all components are calculated by Wilson correlation:
Ki ¼ The second reactor (Gas cooled reactor)
(d)
Purge gas
Ki ¼
Product
Methanol purification
L
b ¼ PL xi f b PG yi f i i
The second reactor (Gas cooled reactor)
crud methanol
X
Tubes
Purge gas
m
3.1.1. Dew point calculation in the porous media Dew point is defined as the pressure and temperature conditions at which the first liquid droplet forms.
¼
zi j
Ki
;
i ¼ 1; 2; …; nc
j ¼ iteration number
(8)
The liquid phase fugacity coefficient 4li is obtained.
P 4li ¼ 40i exp ZL0 L 1 Psi
(9)
where 4oi is the pure component fugacity coefficient evaluated at the pure component vapor pressure and Psi is estimated from the ClausiuseClapeyron equation as:
DHvi T 1 ci Psi ¼ Pci exp Tci T
(10)
Dew point calculation in the porous media is like the ordinary dew point calculation with the exception that the fluid pressure is equal to the summation of the gas pressure and capillary pressure. Capillary pressure depends on surface tension force and their calculations are complicated. Thermodynamic behavior of multicomponent mixtures in porous media differs from that in the free space. Equilibrium of the liquid (l) and gas (g) phases under the conditions of capillarity is described by the following system of equations [14]:
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Table 1 Specifications of catalyst and reactors of conventional two-stage methanol synthesis. Parameter
D t dp lp rs Cps Kc av ε Tube length Number of tubes Shell side pressure Tube side pressure Shell side temperature Shell side mass flow rate
mil ðPl ; zi Þ ¼ mig Pg ; zi
Water cooled reactor
Gas cooled reactor
Value
Value
4.5 13 5.4 3.6 1.46 2.81 0.004 625.7 0.34 8.4 5922
5.5 13 5.4 3.6 1.46 2.75 0.004 625.7 0.34 10.5 3026 71.2 76.98 e e
e 75 513 151,437
i ¼ 1; 2; …; M 1
(11)
M is the number of components.
Pl ¼ Pv þ Pc Pc ¼
(12)
1 ε s cos q ε G
(13)
Eq. (13) is identical to the expression for Pc derivation which is experimentally validated by Masoodi et al. [15], for modeling the wicking flow in wipes. Dew points may also be calculated for a specified pressure. In this case, the temperature is the unknown parameter. The gas phase fugacity coefficient is a correction factor to be multiplied by the partial pressure to give the fugacity of a component in a real gas mixture. It can be calculated from an equation of state by the following:
bi ¼ ln f
ZP 0
vnðZ 1Þ vni
P;T;nj
dP P
Unit
(14)
[m] [mm] [mm] [mm] [kg/m3] [kJ/kg C] [W/mK] [m2/m3] e [m] e [bar] [bar] [K] [Kg/hr]
not generally known in advance if the saturation points of the mixture actually exist at a specified temperature and pressure. 3.1.2. Flash calculation Flash calculations are used for processes with vapor/liquidequilibrium (VLE). A typical process that requires flash calculations is when a feed stream (F) is separated into a vapor (V) and liquid (L) product. In principle, flash calculations are straightforward and involve combining the VLE equations with the component mass balances, and in some case the energy balance. In this study, the fraction of gas condensate is calculated and the components of liquid phase are determined. The simplest flash is usually to specify p and T (pT -flash), because Ki depends mainly on p and T. the basic equation for flash calculation is:
xi ¼
zi 1 þ VF ðKi 1Þ
(17)
xi cannot be calculated directly because the vapor split V/F is not known. To find V/F we may use the relationships:
X
xi ¼ 1
(18)
i
and then new K-values are calculated from:
ln Ki ¼ ln
4Li
ln
X
4vi
(15)
Ki xi ¼
X
i
yi ¼ 1
(19)
i
Then new compositions of liquid phase and temperature are calculated. These calculations are iterative and complicated as it is
Results in an equation with good numerical properties; this is the so-called Rachford-Rice flash equation:
Table 2 Input design and an operation data of the conventional two-stage methanol synthesis reactor.
Table 3 The reaction rate constants, the adsorption equilibrium constants, and the reaction equilibrium constants for methanol synthesis.
Feed conditions Feed composition (mol%) CO CO2 H2 CH4 N2 H2O CH3OH Argon Inlet temperature (K) Total molar flow rate per tube (mol/s) Pressure (bar)
Design Value 8.68 8.49 64.61 9.47 8.2 0.1 0.37 0.24 401 1.80 76
Operation value 8.61 9.87 64.02 8.35 8.45 0.09 0.43 0.18 407.4 1.87 78
K ¼ Aexp (B/RT) k1 k2 k3 K ¼ Aexp (B/RT) KCO KCO2 1=2
ðKH2 O =KH2 Þ
KP ¼ 10(A/T¡B) KP1 KP2 KP3
A
B
(4.89 ± 0.029) 107 (1.09 ± 0.07) 105 (9.64 ± 7.30) 106
63,000 ± 300 87,500 ± 300 152,900 ± 6800
(2.16 ± 0.44) 105 (7.05 ± 1.39) 107 (6.37 ± 2.88) 109
46,800 ± 800 61,700 ± 800 84,000 ± 1400
5139 3066 2073
12.621 10.592 2.029
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Table 4 Mass and energy balance for solid and fluid phases in the exothermic and endothermic sides mass and energy balances for permeation side, pressure drop equation and boundary conditions. Definition
Equation
Mass and energy balances for solid phase
av cj kgi;g ðygi ysi Þ þ hri rb ¼ 0 P g av hf ðTi Tis Þ þ rb N i1 hri ðDHf ;i Þ ¼ 0
Mass and energy balances for fluid phase
X i
g F vyj vz þ g F g vT Ajc Cpj vzj
Ajc
Pressure drop (Ergun momentum balance)
dP dz
Boundary conditions
z ¼ 0;
zi ðKi 1Þ ¼0 1 þ VF ðKi 1Þ
(20)
which is a monotonic function in V/F and is thus easy to solve numerically. A physical solution must satisfy 0 V/F 1. Ki depends also on xi and yi, so one approach is add an outer iteration loop on Ki [13]. 3.2. Kinetics model 3.2.1. Reaction rate Reactions (1)e(3) are not independent as one is a linear combination of the other ones. In the current work, the rate expressions have been selected from Graaf et al. [16]. The rate equations combining with the equilibrium rate constants provide enough information about kinetics of methanol synthesis [17]. The corresponding rate expressions due to the hydrogenation of CO, CO2 and reversed wateregas shift reactions over commercial CuO/ZnO/ Al2O3 catalysts are:
h . i 3=2 1=2 k1 KCO fCO fH2 fCH3 OH fH2 KP1 . i r1 ¼ h 1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O KH2 fH2 O
(21)
h . i 3=2 3=2 k2 KCO2 fCO2 fH2 fCH3 OH fH2 O fH2 KP2 . i r2 ¼ h 1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O KH2 fH2 O
(22)
Table 5 Comparison between model results with design data and an operation data for fresh catalyst. Product condition
Plant
Model validation with design data Composition (mol %) CH3OH 0.104 CO 0.0251 CO2 0.0709 H2O 0.0234 H2 0.5519 N2/Ar 0.1107 CH4 0.114 Temperature (K) 495 Model validation with an operation data Composition (mol %) CH3OH 0.0987 CO 0.0266 CO2 0.0718 H2O 0.0183 H2 0.5558 N2/Ar 0.1008 CH4 0.128 Temperature (K) 493.5
Predicted
av cj kgi; ðysi ygi Þ ¼ 0 shell T tube Þ ¼ 0 i þ av hf ðTjs Tj Þ±pD 1 Ac U12 ðT g
2
ð1εÞ mug þ ε3 d2p g g yi;j ¼ yi0;j ;
¼ 150
ð1εÞu2g r ε3 dp g g Tj ¼ Tj0 ;
1:75
g
g
Pj ¼ Pj0
k3 KCO2 fCO2 fH2 fH2 O fCO KP3 . i r3 ¼ h 1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O KH2 fH2 O
The reaction rate constants, adsorption equilibrium constants and reaction equilibrium constants which occur in the formulation of kinetic expressions are tabulated in Table 3, respectively.
3.2.2. Mathematical model A one dimensional heterogeneous model, which is a conventional model for a catalytic reactor with heat and mass transfer resistances, has been developed for gas cooled reactor in order to determine the concentration and temperature distributions inside the reactor. In this model the following assumptions are used: The gas mixture is an ideal gas in both catalytic reactors. Both of the reactors are operated at steady-state conditions. Radial variations in both beds are negligible (one-dimensional model). Axial diffusion of mass and heat are negligible. Bed porosity in axial and radial directions is constant. Laminar plug flow is employed in both reactors. The chemical reactions are assumed to take place only in the catalyst particles. Heat loss to the surrounding is neglected.
T1A
T1C
Error %
T2A 0.1028 0.0238 0.0764 0.0265 0.5353 0.119 0.1161 489.5
1.15 5.46 7.75 13.24 3.007 7.5 1.84 1.11
0.0964 0.0245 0.0771 0.0179 0.5423 0.1068 0.135 487.6
2.33 7.89 7.38 2.18 2.42 5.95 5.46 1.19
(23)
T2C
T3A
T3C
T4A
T4C
T5A
T5C
T6A
T6C
T1B
T2B T3B T4B
T5B T6B
Fig. 2. The location of thermocouples in the gas cooled reactor.
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Table 6 Temperature operation data for different times along length of the gas cooled reactor. Temperature ( C)
Sensor location
1 2 3 4 5 6
Month 1
Month 3
Month 6
Month 9
Month 12
Month 15
Month 18
Month 21
Month 24
257 258.1 266.47 268.77 258.73 243.17
260 261.57 263.63 268.07 264.67 252.43
261.86 259.43 259.63 259.86 259.86 242.36
262.96 262.67 266.86 269.93 254.56 237.37
263.4 258.3 251.7 242.2 222 197.1
263.7 258.3 252.2 241.4 228.4 206.3
265 259.1 251.4 238.1 218.6 185.3
267.5 260.2 249.6 231.9 202.3 152
269.4 261.4 244.3 225.6 187.3 138
4. Model validation
To obtain the mole balance equation and the energy balance equation, a differential element along the axial direction inside the reactor was considered. The balances typically account for convection, transport to the solid phase. The mass and energy balances for solid and fluid phases in all sides, pressure drop equation and boundary conditions are summarized in Table 4. h is the effectiveness factor (the ratio of the reaction rate observed to the real rate of reaction), which is obtained from a dusty gas model calculations [17]. A set of above mentioned the differential-algebraic equations (DAE) are developed for the modeling of methanol reactors. The energy and mass balances obtained for the reactor are coupled with non-linear algebraic equations of the kinetic model, transport properties and other auxiliary correlations. A backward finite difference approximation is applied to solve these set of equations.
5. Results and discussion The temperature profiles of methanol synthesis reactors changes with time; therefore they are different from the predicted profile in the design (CR). Temperature of the gas cooled reactor
550
600
The First Reactor
Design condition
Temperature (K)
Time
450 Dew point
400
5
10 Lenght (m)
15
Design condition
Time 450
400
Two Phase
0
The First Reactor
500
500
350
The Second Reactor
The Second Reactor
550 Temperature (K)
The steady state model validation is performed between the industrial data reported by a domestic petrochemical company and the mathematical modeling of CR. The CR model results and the corresponding observed data of the pilot plant are presented in Table 5. A good agreement is observed between the modeling results and the pilot plant data. Therefore, this mathematical model performs well under the industrial conditions.
Dew point
20
350
(a)
0
5
10 Lenght (m)
15
20
(b)
550 JS
Temperature (K)
500 HGS 450 400
Dew Point
350
CR
300 250
0
5
10 Length (m)
15
20
(c)
Fig. 3. Temperature profiles (a) in the design (conventional) configuration (CR) (b) in ES (c) comparisons of HGS, JS and CR configuration.
A. Mirvakili, M.R. Rahimpour / Applied Thermal Engineering 91 (2015) 1059e1070
bed is measured by 18 thermocouples which are embedded in the six locations of the bed. The locations of these thermocouples are shown in Fig. 2 three thermocouples in a row are in a level of the gas cooled reactor but they are distributed in three different positions. Table 6, presents the temperature data related to the gas cooled reactor in different times according to the reported temperature of one day in three months. The presented data are average of three reported temperature in one level. As seen, temperature decreases gradually at the end of the reactor. Dew point in the porous media is calculated and compared with the bed temperature. The percentage of gas that condensed at the end of the reactor and its compositions are determined by a flash calculation at the last day of the operation. Results show that about 5% of gas converts to liquid which includes 71% methanol and 29% water. In Fig. 3(a), temperature profiles in the designed condition and temperature changes along two years are shown in CR. Temperature of the first reactor increases with time and also the temperature in the entrance of the second reactor enhances. However, Temperature in the second reactor decreases drastically. As far as the temperature of the gas cooled reactor becomes lower than dew point in the last 1 m of the reactor, methanol and water are condensed and causes a two phase flow at the end part of the second reactor of CR. Separation of 20% methanol and 10% water in the entrance of the second reactor results in an increased dew point temperature. Moreover, the methanol removal shifts the reaction to the product side and consequently the exothermic reaction rate and temperature increase. Fig. 3(b) demonstrates the temperature profile of ES. As shown in Fig 3(b), temperature of the gas in total length of the second reactor is higher than the dew point
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temperature of the gas in ES. Therefore, there would be no condensation problem in ES. Fig. 3(c) illustrates comparison of temperature profiles between HGS, JS and CR. Temperature of the gas cooled reactor in both strategies is higher than the dew point. Therefore, both strategies solve problem of gas condensate formation in the last of the gas cooled reactor. All configurations have been modeled and the performance of them has been compared with the CR in the following figures. The reactor length is divided into two segments where the reaction kinetic is controlling in an upper section and the equilibrium is predominant in the other section. The difference between modeling results of conventional reactor and proposed configurations is due to the unequal thermodynamics equilibrium conditions in the configurations. The comparison of methanol molar flow rate between HGS, JS and CR are shown in Fig. 4(a). Methanol production decreases in HGS and JS rather than CR. Although these strategies solve the problem of gas condensation formation, decreases the methanol molar flow rate. Therefore, HGS and JS strategies are not proper. The methanol molar flow rate along CR and ES are depicted in Fig. 4(b). Methanol is the main product of these configurations and it is produced along two reactors gradually in CR. However, methanol molar flow rate increases abruptly at the beginning of the second reactor in ES owing to the in-situ methanol removal. Some fractions of methanol and water are separated from the feed of the second reactor in ES by a partial condenser. This shifts the methanol production reaction (i.e., Eqs. (1) and (2)) to the production side. Furthermore, molar flow rate of methanol increases gradually at the rest of the second reactor in ES. Fig. 4(b), illustrates that the produced methanol in ES is less than CR. But the fact is that some
Fig. 4. Comparison of methanol molar flow (a) between CR, JS and HGS (b) between CR and ES (c) between CR, JS, HGS and ES.
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products that should become cold. Fig. 5(b) shows the procedure of thermal process of gas in conventional configuration. Gas in the tubes of gas cooled reactor is warmed by the gas in the shell. In the water cooled reactor, the tube side is cooled by boiling water in the shell. So, the boiling water phase changes to steam that is separated from the boiling water in drum and it is sent to utility unit. The gas product of gas cooled reactor is cooled by three heat exchangers and one air cooler. Steam, a portion of feed and sea water are used to cool the gas in three heat exchangers, respectively. An energy saving design for ES is proposed in this study which is illustrated in Fig. 5(c). In the first step of the thermal process after the water cooled reactor, the stream is cooled to 171 C and a portion of methanol synthesis feed which is warmed by the product of gas cooled reactor in CR, is warmed to 120 C in ES. After that, there is another heat exchanger for cooling the stream to 96 C and simultaneously, the boiling water which cools the product of gas cooled reactor, is warmed to 189 C and sent to utility unit. Thus, the stream is cooled to 96 C and 20% of methanol and 10% water are removed by condensation. The gas stream should be warmed to 260 C and mixed to the other half of the gas in order to enter to the gas cooled reactor. In this heat exchanger, the gas is heated to 259 C in tubes and the product of gas cooled reactor is cooled to 138 C in the shell side of the heat exchanger. Although, the ES configuration requires more energy rather than other
methanol was separated from the feed of the second reactor which is not shown in these figures. Thus, the total methanol molar flow rate in CR and ES are shown in Fig. 4(c). The superiority of ES configuration is evidently distinguished from this figure because the higher Methanol molar flow rate is achieved in this configuration. The methanol molar flow rate in ES is 7.9% more than the one in CR. Methanol molar flow rate in ES is higher than HGS and JS about 7.5% and 8.7% respectively. The methanol molar flow rate increases in ES owing to the methanol removal and changes in thermodynamic equilibrium. The factors affecting the production rate in the industrial methanol synthesis are parameters such as thermodynamic equilibrium limitations and catalyst deactivation and variation in the composition of the reacting gas. The energy requirements of the alternative design are shown in Fig. 5(a). ES configuration needs two heating equipments, one of them is the partial condenser and the other is a heat exchanger for warming the gas. Qc and Qh are regard to the released heat in partial condenser and the heat requirement in heat exchanger, respectively. The energy requirements for other configurations are shown by QJ and QHG for JS and HGS, respectively. As seen in Fig. 5(a), the highest energy requirement is regard to ES, because it contains two thermal equipments. However, an energy saving method called self-heat recuperation has been applied for ES configuration. In this method, the required heat is provided by the released energy of hot
Energy requirements (Kj/s)
(a) 6 x 10
(b)
4
Steam 316 K 338 K
308 K
5
393 K
513 K Drum
411 K
Sea water
4
Fresh Feed
537 K Air Cooler
3 Purge gas
2
449 K
401 K
Flare
1 0
329 K
Methanol water
Q1H
2 Q
3 Q JS
C
495 K
Q4HGS
385 K 463 K
Boiling water
513 K Boiling water
Steam
(c)
Flare
Purge gas
513 K
Drum
536 K Methanol water 308 K Sea water
411 K 316 K
495 K 537 K
Fresh Feed
393 K
Air Cooler
513 K Boiling water
444 K
329 K
463 K
Methanol water 369 K
385 K
Boiling water
Fig. 5. (a) comparison of energy requirement between JS, HGS and ES (b) schematic diagram of heating process in CR (c) schematic diagram of heating process in ES.
A. Mirvakili, M.R. Rahimpour / Applied Thermal Engineering 91 (2015) 1059e1070
80
35 ES
ES
30 CR
60 50
H2 Conversion (%)
CO Conversion (%)
The Second Reactor
The First Reactor
70
76
40
75
30
73
74
72
20
18.2 18.4 18.6 18.8 19 19.2
CR
25 20 15 10 5
10 0
1067
0
5
10 Lenght (m)
15
0
20
The First Reactor
0
5
(a)
The Second Reactor
10 Length (m)
15
20
(b)
20
CO2 Conversion (%)
The First Reactor
The Second Reactor
ES
15 CR
10
5
0
0
5
10 Length (m)
15
20
(c)
Fig. 6. A comparison between (a) CO (b) H2O (c) CO2 conversions in CR and ES.
configurations, the total energy requirement for the ES in this unit is provided with using the self-heat recuperation approach. A comparison between CO, H2O and CO2 conversions in CR and ES is shown in Fig. 6(a)e(c) respectively. Higher CO, H2 and CO2 conversion is achieved in ES compared with CR. The main reason for an increase in CO, H2 and CO2 conversion in ES are a decrease in methanol mole fraction in the feed of the second reactor of ES. CO,
H2 and CO2 are reactants, when the reactions shift to the product side in ES, reactants are consumed more. H2 is consumed more than CO and CO2 because hydrogen is consumed in the hydrogenation of CO and CO2 as shown in Eqs. (1) and (2). In addition, the water gas shift (WGS) reaction (i.e., Eq. (3)) shifts to the production side via water removal and more hydrogen is consumed in ES as a result.
0.7 H2
0.6
0.7
CR
0.5 Mole fraction
Mole fraction
0.5 0.4 0.3
0.4 0.3 0.2
0.2 CO
0.1 0
ES
H2
0.6
H2O 0
0 5
10 Length (m)
(a)
15
20
CO2
CO
0.1
CO2
H 2O 0
5
10 Length (m)
(b)
Fig. 7. The mole fraction of CO, CO2, H2 and H2O along the length of (a) CR and (b) ES.
15
20
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Molar Flowrate of Methanol (mol/s)
3000 2500 2000 1500 1000 500 0
2 0.2 3 0.3 4 5 9 10 0.4 60.5 70.6 80.7 0.8 0.9 111 01 0.1 Fraction of Seperated Methanol
Fig. 8. Methanol molar flow rate production changes with the changing of methanol removal percent.
The mole fraction of CO, CO2, H2 and H2O is depicted along the CR and ES in Fig. 7(a) and (b), respectively. The mole fractions have not changed significantly in CR and ES. However, mole fraction of CO at ES is lower than that in CR because, methanol and water removal shifts the hydrogenation of CO to the product side. Therefore, CO is consumed in ES more than CR. However, there is no significant reduction in CO mole fraction in the ES compared with the CR. The carbon dioxide mole fraction in ES is less than the one in CR. Indeed, CO2 is consumed in ES about 2.6% more than in CR. Comparison between CO and CO2 in Fig. 7(a) and (b) shows that the methanol and water removal from the inlet of the second reactor affects CO2 hydrogenation (Eqs. (2) and (3)) more than CO hydrogenation (Eq. (1)). Therefore, CO2 is consumed more than CO in ES. A reduction in CO2 mole fraction in the purge gas of the unit is another superiority of the ES configuration compared to the CR. As expected, hydrogen is consumed in ES more than CR. All three reactions shift to the product side via methanol and water removal from the inlet of the second reactor. Hydrogen mole fraction in ES is about 0.02 lower than one in CR. Water is another product in the methanol synthesis which is removed by a partial condenser from the inlet reactant gas to the second reactor of ES. Although water mole fraction decreases in the inlet of the second reactor, the mole fraction of water at the end of the second reactor of ES and CR are almost similar. The reason is that the reactions shift to the product
Fig. 9. (a) changes produced methanol molar flow rates (b) changes carbon monoxide flow rate (c) changes carbon dioxide flow rate (d) changes temperature with changing the methanol removal percent in the inlet of the gas cooled reactor.
A. Mirvakili, M.R. Rahimpour / Applied Thermal Engineering 91 (2015) 1059e1070
side and water is produced which compensate the reduction of water in the feed of the second reactor in ES. The effect of percentage of methanol removal from the inlet of the second reactor on the methanol production is shown in Fig. 8. As seen, the methanol molar flow rate enhances with increasing the methanol removal percentage. The reason of this enhancement in methanol molar flow rate is obviously that the reactions become far from the thermodynamic equilibrium when the methanol is separated in the inlet of the second reactor. Therefore, methanol will be produced more than the previous condition. As increasing the methanol separation leads to increase in cost, the minimum methanol removal is considered in order to resolve the gas condensate problem in the second reactor of the CR. The effect of percentage of the methanol separation on the produced methanol, CO and CO2 molar flow rates and temperature are depicted along the second reactor of ES in Fig. 9(a)e(d). As seen in Fig. 9(a), the reaction rate in the entrance of the second reactor increases with increasing methanol removal percentage. Although, it seems that methanol molar flow rate decreases, it increases with increasing methanol in-situ removal. Because, methanol molar flow rate is the sum of produced methanol and separated methanol from the inlet of the second reactor. Fig. 9(b) and (c) show that CO and CO2 molar flow rates decrease with increasing the fraction of methanol separation due to increase in reaction rates and more CO and CO2 consumptions. Fig. 9(d) illustrates that the temperature peak rises by increasing the methanol separation in ES. Increasing the methanol separation follows the enhancement in reaction rates at the entrance of the second reactor of ES. So, the increase in the production rate causes ascending temperature at the entrance of the second reactor. 6. Conclusion The gas cooled reactor in the dual type methanol synthesis process has a significant problem of gas condensate formation. The pressure drop increased gradually in the bed, while it increases sharply at the last 2 m of the reactor length. Consequently, the temperature reduces strongly at the end of the bed until it reaches to the lower temperature than the dew point temperature. The formation of gas condensate including methanol and water which are drastically corrosive in combination, causes severe corrosion damage for the applied catalysts and the pipelines. Therefore, the pressure and temperature drop increase due to catalyst crushing at the last part of the gas cooled reactor and more gas condensates will be formed. In order to resolve this problem, three strategies which are named HGS, JS and ES are developed. In HGS, a portion of hot synthesis gas injected to the last 2 m of the reactor and warms the last of the reactor. JS strategy proposes that the last 2 m of the reactor heated by steam in the jacket around this zone. And also the most influential strategy is ES which placing the partial condenser after the water cooled reactor leads to a better reactor performance by removing condensed methanol and water from the inlet of the second reactor (the gas-cooled reactor). The partial condenser cools half of the feed stream to 96 C. Consequently, 40% methanol and 20% water is condensed and separated, after that the noncondensed residual cooled gas is heated to about 260 C and mixed with the remained half of the reactant gas which are then sent to the second reactor as a feed. Methanol and water removal accelerates the reactions of CO and CO2 with H2 towards methanol. This increase in the production rate causes the temperature rise in the entrance of the second reactor. Moreover, it reduces the dew point temperature of the reacting gas in the bed. The performances of all configurations are investigated by considering a one dimensional heterogeneous model for the fixed-bed reactors. The mathematical model is validated with the data gathered from a domestic
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petrochemical industry. A good agreement is observed between the industrial data and the mathematical modeling. Results show that, methanol molar flow rate increases about 7.9% in ES rather than CR and it decreases about 0.19% and 1.57% in HGS and JS respectively rather than CR. 2.6% decrease of carbon dioxide consumption rate in the ES compared with CR, which is appealing from the environmental viewpoint, can be considered as one of the superiorities of the ES configuration as well as resolving the gas condensate problem and also enhancing the methanol production. An innovative self-heat recuperation technology is utilized in ES in order to energy saving. Nomenclature av Ac Cp dp Ei fi F hf Hi DHf,i kg K ki Ki Ki Kpi L Mi P Pc Pl Pv R Rp ri T U Xi yi yis z Z
specific surface area of catalyst pellet (m2 m3) cross section area of each tube (m2) specific heat of the gas at constant pressure (J mol1 K1) particle diameter (m) activation energy for elementary reaction step i, kJ/kmol fugacity total molar flow rate (mol s1) gas-solid heat transfer coefficient (W m2 K1) Henry's coefficient of component i enthalpy of formation of component i (J mol1) mass transfer coefficient for component i (m s1) conductivity of gas phase (W m1 K1) reaction rate coefficient, (mol kg1 s1 bar1/2) adsorption equilibrium constant, bar1 K value equilibrium constant based on partial pressure for component i reactor length (m) molecular weight of component i (g mol1) total pressure (for exothermic side: bar; for endothermic side: Pa) capillary pressure (Kpa) liquid pressure (KPa) vapor pressure (KPa) universal gas constant (J mol1 K1) particle radius (m) reaction rate of component i (mol kg1 s1) temperature (K) overall heat transfer coefficient between exothermic and endothermic sides (W m2 K1) conversion of component i mole fraction of component i (mol mol1) mole fraction of component i in the solid phase(mol mol1) axial reactor coordinate (m) compressibility factor
Greek letters DHi enthalpy of reaction εs void fraction of catalyst ε porosity of bed G ratio of volume to surface area of particle g volume fraction of catalyst occupied by solid particles in bubble gi activity coefficient of component i s surface tension (N/m) f fugacity coefficient q contact angle (degrees) m chemical potential mi viscosity of fluid phase (kg m1 s1) nci critical volume of component i (cm3 mol1)
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r rB rs h
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density of fluid phase (kg m3) density of catalytic bed (kg m3) density of catalyst (kg m3) catalyst effectiveness factor
Superscripts g in bulk gas phase s at the surface of the catalyst Subscripts 0 inlet conditions k reaction number index l liquid phase v vapor phase References [1] C.J. Schack, M.A. Mcneil, R.G. Rinker, Methanol synthesis from hydrogen, carbon monoxide and carbon dioxide over a Cuo/ZnO/Al2O3 catalyst: I. steadystate kinetics experiments, Appl. Catal. 50 (1989) 247. [2] G.H. Graaf, H. Scholtens, E.J. Stamhuis, A.A.C.M. Beenackers, Intra-particle diffusion limitation in low-pressure methanol synthesis, Chem. Eng. Sci. 45 (1990) 773e783. [3] A. Kova c Kralj, P. Glavic, Multi-criteria optimization in a methanol process, Appl. Therm. Eng. 29 (2009) 1043e1049. [4] Y. Kansha, M. Ishizuka, C. Song, Atsushi Tsutsumi, An Innovative Methanol Synthesis Process Based on Self-Heat Recuperation. Appl. Therm. Eng. 70 (2014) 1189e1194. http://dx.doi.org/10.1016/j.applthermaleng.2014.05.002.
[5] R.P.W. Struis, S. Stucki, M. Wiedorm, A membrane reactor for methanol synthesis, J. Memb. Sci. 113 (1996) 93e100. [6] P.J.A. Tijm, F.J. Waller, D.M. Brown, Methanol technology developments for the New Millennium, Appl. Catal. A Gen. 221 (2001) 275. [7] Sady E.S. Kh-Zade, Determination of the beginning of condensation in the presence of a porous medium, Neftl I Gaz. 12 (1963) 268e270. [8] A.G. Durmishiarr, Experimental investigation of hydrodvnarnic and thermodynamic properties of gas condensate systems during flow through porous media, Isvestia Acad. Nauk SSSR 1 (1964) 133e136. [9] F.A. Trcbin, Experimental study of the effect of a porous media on phase change in gas condensate system, Netl'I Gsz 8 (1968) 37. [10] E.S. Sadykh-zade, A study of the process of equilibrium rate attainment during condensation in gas-condensate system, NetYi Gaz. 8 (1968) 37. [11] G. Ping, S. Liangtian, L. Shilun, S. Lei, A theoretical study of the effect of porous media on the dew point pressure of a gas condensate, in: SPE 35644, SPE Gas Technology Symposium & Exhibition Held in Calgary, Alberta , Canada, 2E, April-1 May, 1996. [12] R. Masoodi, K.M. Pillai, A general formula for capillary suction pressure in porous media, J. Porous Media 15 (2012) 775e783. [13] J.M. Smith, H.C. Van Ness, M.M. Abbott, Introduction to Chemical Engineering Thermodynamics, seventh ed., The Mcgraw-Hill Chemical Engineering Series, 2005. [14] R. Defay, I. Prigogine, Surface Tension and Adsorption, Longmans & Green, London, 1966. [15] R. Masoodi, K.M. Pillai, P.P. Varanasi, The effect of hydraulic pressure on the wicking rate into the wipes, J. Engd. Fibers Fabr. 5 (2010) 49e66. [16] G.H. Graaf, P.J.J.M. Sijtsema, E.J. Stamhuis, G.E.H. Joosten, Chemical equilibrium in methanol synthesis, Chem. Eng. Sci. 41 (1986) 2883e2890. [17] M. Bertau, H. Offermanns, L. Plass, F. Schmidt, H.J. Wernicke, Methanol: the Basic Chemical and Energy Feedstock of the Future, Springer Heidelberg, New York Dordrecht London, 2014.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Mal-distribution of temperature in an industrial dual-bed reactor for conversion of CO2 to methanol A. Mirvakili a, M.R. Rahimpour a, b, * a b
Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran Department of Chemical Engineering and Materials Science, University of California, Davis, One Shields Avenue, Davis, CA 95616, United States
h i g h l i g h t s Gas cooled reactor of dual type methanol faces with a significant problem. Temperature drop in the last of the reactor increased drastically. Temperature is less than dew point temperature in the porous media. Methanol and water are condensed at the last of the reactor. Self-heat recuperation technology is developed to energy saving.
g r a p h i c a l a b s t r a c t Steam Flare
Purge gas
513 K
Drum
536 K Methanol water 308 K Sea water
411 K 316 K
495 K 537 K
Fresh Feed
393 K
Air Cooler
513 K Boiling water
444 K
329 K
463 K
Methanol water 369 K
385 K
Boiling water
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 May 2015 Accepted 24 August 2015 Available online 21 September 2015
Design of dual type methanol reactor includes a gas cooled reactor for methanol synthesis. The gas cooled reactor faces with the problem of gas condensate formation and two phase flow in the practical operating conditions owing to a high temperature drop in the last 2 m of the reactor length. In this study, three strategies are proposed in order to prevent gas condensate formation in the gas cooled reactor which is designed based on dual type design. The first strategy is utilization of a partial condenser before the gas cooled reactor, the second strategy is injection of hot synthesis gas (HGS) to the last 2 m of the reactor and the third is warming the shell side of the reactor with steam in a jacket (JS) around the last 2 m of the reactor. Simulation results show that, the most effective strategy (ES) is application of a partial condenser to separate the methanol and water in the inlet of the gas cooled reactor by condensation. In ES, the dew point temperature in the porous media reduces via in-situ methanol and water removal at the inlet of the gas cooled reactor and gas temperature ascends along the length of the reactor. Moreover, methanol production enhances about 7.9% and CO2 decreases 2.6% in ES rather than in the conventional methanol synthesis reactor (CR). The elimination of the gas condensate formation on one hand and enhancing the methanol production and decreasing CO2 emission on the other hand can be considered as the superiority of the suggested ES to the CR and other strategies. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Gas condensate formation Dew point in porous media Gas cooled reactor CO2 conversion Industrial methanol synthesis
1. Introduction
* Corresponding author. Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran. E-mail address: [email protected] (M.R. Rahimpour). http://dx.doi.org/10.1016/j.applthermaleng.2015.08.067 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
Methanol is produced from synthesis gas (carbon monoxide and hydrogen) which is mainly derived from oil, coal or, biomass. One of the most important applications of methanol is providing a feedstock for the plastics industry. Moreover, methanol can be used
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directly in internal combustion engines of vehicles and aircrafts, with similar efficiency to diesel engines. Minor improvements in production efficiency of important chemicals may result in significant profit increase, energy conservation and environmental protection, especially for a chemical such as methanol which is produced in a worldwide scale [1]. Process of methanol synthesis has attracted great deal of attention till now. The kinetics of the methanol synthesis presented by Graaf et al. [2] which is considered in this study is based on the hydrogenation of CO2 and CO, as provided by reactions (1) and (2). Because the CuO/ZnO/Al2O3 catalysts are known to catalyze the wateregas-shift reaction (3) as well, this reaction is also included in the kinetic model.
CO þ 2H2 4CH3 OH
DH298 ¼ 90:55kJ=mol
CO2 þ 3H2 4CH3 OH þ H2 O CO2 þ H2 4CO þ H2 O
DH298 ¼ 49:43kJ=mol
DH298 ¼ þ41:12kJ=mol
(1) (2) (3)
Kralj et al. [3] have optimized methanol plant using the NLP model developed earlier by including an additional flow rate of hydrogen (H2), decreasing flow rate of high-pressure steam in crude methanol recycling, and increasing methanol production by 2.5%. Kansha et al. [4] have investigated the feasibility of applying self-heat recuperation technology to the methanol synthesis process and they have developed an innovative process for methanol synthesis from an energy saving point of view [5]. Recently, a twostage methanol synthesis reactor was introduced instead of a single-type for CO conversion to methanol [6]. This system is an advanced technology for converting synthesis gas to methanol at low cost and in large quantities. The configuration of this system is based on the two stage reactor system. The first stage is a high temperature water-cooled reactor that is combined in series with a low temperature gas cooled reactor. Partial conversion of CO to methanol is accomplished in the gas cooled reactor. In Iran, a domestic petrochemical company has applied methanol synthesis process based on dual type technology which has been faced a major problem in the gas cooled reactor after 2 years. Actually, in the gas cooled reactor the temperature drops until it becomes less than the dew point temperature which causes the volatile components in the gas stream be condensed. In the applied system, the dew point in the packed bed should be calculated considering the porous media. The effect of porous media on the dew point calculations has been previously studied. In most studies, oil and gas reservoirs have been considered as a porous media. Results of several reported experimental studies indicate that the presence of a porous medium has a significant influence on the equilibrium behavior of hydrocarbon mixtures [7e11]. Trebin and Zadora [9] concluded that the initial condensation pressures (dew points) of gas condensate mixtures in porous media can be 10 to 15 percent higher than those observed in conventional Pressure, volume, temperature (PVT) cells. An important parameter for obtaining the thermodynamic properties in the porous media is capillary pressure which cannot be measured easily. There have been few studies on modeling the onset of the capillary pressure in porous media. Masoodi et al. [12] have developed a simple and general formula for the capillary pressure in the porous media, which relates the capillary pressure to the microstructure of various porous media. In the present study, dew point temperature in the porous media is obtained and composition of the liquid phase (condensate) is determined. The condensate is a solution of 71% methanol and 29% water, which is significantly corrosive. Thus; the catalysts and other metallic equipments faces the high risk of corrosion. Due to corrosion, catalysts are crushed and porosity of the bed decreases and the pressure drop increases at the end of the reactor as a result.
Moreover, at the end of the reactor, temperature reduces more than the other parts of the reactor which results in more methanol and water condensation. The current work mainly focuses on the study of gas condensate formation in the packed bed gas cooled reactor as well as, proposing three configurations in order to prevent gas condensate formation. For this purpose, a partial condenser is embedded after the water cooled reactor which cools the inlet gas to the second reactor in ES configuration and warming of the gas in the last 2 m of the reactor in HGS and JS configurations is proposed. These strategies are investigated considering the energy consumption. Although ES configuration needs more energy because of containing two heating equipments, an innovative energy saving method has been applied in this study for the ES configuration. A novel self-heat recuperation technology developed by Yasuki Kansha for heating and cooling thermal processes has been applied in which not only latent heat but also sensible heat is circulated in a feed-effluent heat exchanger of the thermal process. The required energy for partial condenser and heat exchanger in ES is not provided from an outer source; therefore the energy consumption reduces drastically in ES configuration. 2. Process description 2.1. Conventional dual type methanol synthesis reactor Schematic diagram of a conventional dual type methanol synthesis reactor is shown in Fig. 1(a). The dual type Methanol Reactor is basically a vertical shell and tube heat exchanger with fixed tube sheets. Reactions of methanol synthesis are performed over commercial CuO/ZnO/Al2O3 catalyst. The catalyst is packed in shell side of the gas-cooled reactor and vertical tubes of water-cooled reactor. Partial conversion of the syngas to methanol accomplishes in the first reactor, which is an isothermal reactor. The methanol-containing gas, leaving the first reactor is routed to the second downstream reactor without prior cooling. In the gas cooled reactor, cold feed gas for the first reactor is routed through tubes in a countercurrent flow with the reacting gas. Thus, the reaction temperature is continuously reduced over the reaction path in the second reactor, and the equilibrium driving force for methanol synthesis maintained over the entire catalyst bed. Temperature of the first reactor is higher than the second reactor and the main catalyst deactivation occurs in the gas cooled reactor. Therefore, lower operating temperature in the gascooled reactor results in a practically unlimited catalyst service life. In addition, reaction control extends the life time of the catalyst in the water-cooled reactor. The input data and industrial design of the catalyst pellet for the conventional two-stage methanol synthesis reactor have been listed in Tables 1 and 2. 2.2. SE strategy Fig. 1(b) shows the schematic diagram of SE strategy for methanol synthesis reactor configuration. SE strategy is the application of a partial condenser after water cooled reactor in the conventional configuration. Half of the gas leaving the water cooled reactor is sent to a partial condenser and it is cooled to 96 C. As a result, 40% of methanol and 20% of water are condensed and separated from the gas stream. Then, the remaining non-condensed gas will be heated to 260 C and mixed to another half of the gas stream leaving the first reactor and sent to the gas cooled reactor. 2.3. HGS strategy Fig. 1(c) shows the schematic diagram of HGS strategy for methanol synthesis reactor configuration. As shown in Fig. 1(c),
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month from the startup, steam from drum of water cooled reactor is sent to the jacket and it warms the gas in the shell of the gas cooled reactor.
Fresh feed (synthesis gas)
(a)
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Tubes
Catalyst Purge gas
Shell (reaction side) Product
Methanol purification
crud methanol
3. Mathematical model
Fresh feed (synthesis gas)
3.1. Thermodynamics model
The second reactor (Gas cooled reactor)
The first reactor (Water cooled reactor)
Methanol and Water condensate
The second reactor (Gas cooled reactor)
(b)
The first reactor (Water cooled reactor)
xi ¼
X ðyi =Ki Þ ¼ 1
(4)
In modern practice, VLE calculations for light-hydrocarbon systems are accomplished by using computer calculations based on equations of state, such as the Soave-Redlich-Kwong (SRK) equation. In this approach, fugacity coefficients are used to express the fugacity of both the liquid and vapor phases relative to the ideal gas. In the following the phase equilibrium relations are presented [13]:
Catalyst Shell (reaction side) Product
Methanol purification
crud ethanol
Fresh feed (synthesis gas)
V
Tubes
(c)
The first reactor (Water cooled reactor)
Hot Synthesis Gas
Catalyst Purge gas
Shell (reaction side)
Fresh feed (synthesis gas)
Steam
The first reactor (Water cooled reactor)
Tubes
Catalyst Shell (reaction side)
crud methanol
Fresh feed (synthesis gas)
Product
jþ1
Steam Jacket
Fig. 1. The schematic diagrams of (a) conventional (CR) (b) ES methanol synthesis reactor (c) HGS (d) JS configurations.
the feed temperature of water gas cooled reactor is about 533 K which is named hot syn gas stream. In HGS strategy a proportion of hot syn gas stream is injected to the last 2 m of the reactor when temperature in this zone decreases to less than 513 K. indeed, there is a valve that adjust the flow rates of hot syn gas stream to the gas cooled reactor. The flow rate of stream is zero before 18 months and after that flow rate of hot gas injection increases gradually. 2.4. JS strategy Fig. 1(d) shows the schematic diagram of JS strategy for methanol synthesis reactor configuration. In this strategy a jacket is fabricated around the last 2 m of the gas cooled reactor. After 18
b Li f
(6)
bV f i
T Pc;i exp 5:37ð1 þ ui Þ 1 Tc;i (7)
p
where, Tc,i is the critical temperature of component i, Pc,i is the critical pressure of component i, ui is the acentric factor of component i. The liquid phase composition is estimated from:
xi
Methanol purification
(5)
The solution method is trial and error. At first an estimate of the dew point temperature is provided and then K-values for all components are calculated by Wilson correlation:
Ki ¼ The second reactor (Gas cooled reactor)
(d)
Purge gas
Ki ¼
Product
Methanol purification
L
b ¼ PL xi f b PG yi f i i
The second reactor (Gas cooled reactor)
crud methanol
X
Tubes
Purge gas
m
3.1.1. Dew point calculation in the porous media Dew point is defined as the pressure and temperature conditions at which the first liquid droplet forms.
¼
zi j
Ki
;
i ¼ 1; 2; …; nc
j ¼ iteration number
(8)
The liquid phase fugacity coefficient 4li is obtained.
P 4li ¼ 40i exp ZL0 L 1 Psi
(9)
where 4oi is the pure component fugacity coefficient evaluated at the pure component vapor pressure and Psi is estimated from the ClausiuseClapeyron equation as:
DHvi T 1 ci Psi ¼ Pci exp Tci T
(10)
Dew point calculation in the porous media is like the ordinary dew point calculation with the exception that the fluid pressure is equal to the summation of the gas pressure and capillary pressure. Capillary pressure depends on surface tension force and their calculations are complicated. Thermodynamic behavior of multicomponent mixtures in porous media differs from that in the free space. Equilibrium of the liquid (l) and gas (g) phases under the conditions of capillarity is described by the following system of equations [14]:
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Table 1 Specifications of catalyst and reactors of conventional two-stage methanol synthesis. Parameter
D t dp lp rs Cps Kc av ε Tube length Number of tubes Shell side pressure Tube side pressure Shell side temperature Shell side mass flow rate
mil ðPl ; zi Þ ¼ mig Pg ; zi
Water cooled reactor
Gas cooled reactor
Value
Value
4.5 13 5.4 3.6 1.46 2.81 0.004 625.7 0.34 8.4 5922
5.5 13 5.4 3.6 1.46 2.75 0.004 625.7 0.34 10.5 3026 71.2 76.98 e e
e 75 513 151,437
i ¼ 1; 2; …; M 1
(11)
M is the number of components.
Pl ¼ Pv þ Pc Pc ¼
(12)
1 ε s cos q ε G
(13)
Eq. (13) is identical to the expression for Pc derivation which is experimentally validated by Masoodi et al. [15], for modeling the wicking flow in wipes. Dew points may also be calculated for a specified pressure. In this case, the temperature is the unknown parameter. The gas phase fugacity coefficient is a correction factor to be multiplied by the partial pressure to give the fugacity of a component in a real gas mixture. It can be calculated from an equation of state by the following:
bi ¼ ln f
ZP 0
vnðZ 1Þ vni
P;T;nj
dP P
Unit
(14)
[m] [mm] [mm] [mm] [kg/m3] [kJ/kg C] [W/mK] [m2/m3] e [m] e [bar] [bar] [K] [Kg/hr]
not generally known in advance if the saturation points of the mixture actually exist at a specified temperature and pressure. 3.1.2. Flash calculation Flash calculations are used for processes with vapor/liquidequilibrium (VLE). A typical process that requires flash calculations is when a feed stream (F) is separated into a vapor (V) and liquid (L) product. In principle, flash calculations are straightforward and involve combining the VLE equations with the component mass balances, and in some case the energy balance. In this study, the fraction of gas condensate is calculated and the components of liquid phase are determined. The simplest flash is usually to specify p and T (pT -flash), because Ki depends mainly on p and T. the basic equation for flash calculation is:
xi ¼
zi 1 þ VF ðKi 1Þ
(17)
xi cannot be calculated directly because the vapor split V/F is not known. To find V/F we may use the relationships:
X
xi ¼ 1
(18)
i
and then new K-values are calculated from:
ln Ki ¼ ln
4Li
ln
X
4vi
(15)
Ki xi ¼
X
i
yi ¼ 1
(19)
i
Then new compositions of liquid phase and temperature are calculated. These calculations are iterative and complicated as it is
Results in an equation with good numerical properties; this is the so-called Rachford-Rice flash equation:
Table 2 Input design and an operation data of the conventional two-stage methanol synthesis reactor.
Table 3 The reaction rate constants, the adsorption equilibrium constants, and the reaction equilibrium constants for methanol synthesis.
Feed conditions Feed composition (mol%) CO CO2 H2 CH4 N2 H2O CH3OH Argon Inlet temperature (K) Total molar flow rate per tube (mol/s) Pressure (bar)
Design Value 8.68 8.49 64.61 9.47 8.2 0.1 0.37 0.24 401 1.80 76
Operation value 8.61 9.87 64.02 8.35 8.45 0.09 0.43 0.18 407.4 1.87 78
K ¼ Aexp (B/RT) k1 k2 k3 K ¼ Aexp (B/RT) KCO KCO2 1=2
ðKH2 O =KH2 Þ
KP ¼ 10(A/T¡B) KP1 KP2 KP3
A
B
(4.89 ± 0.029) 107 (1.09 ± 0.07) 105 (9.64 ± 7.30) 106
63,000 ± 300 87,500 ± 300 152,900 ± 6800
(2.16 ± 0.44) 105 (7.05 ± 1.39) 107 (6.37 ± 2.88) 109
46,800 ± 800 61,700 ± 800 84,000 ± 1400
5139 3066 2073
12.621 10.592 2.029
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Table 4 Mass and energy balance for solid and fluid phases in the exothermic and endothermic sides mass and energy balances for permeation side, pressure drop equation and boundary conditions. Definition
Equation
Mass and energy balances for solid phase
av cj kgi;g ðygi ysi Þ þ hri rb ¼ 0 P g av hf ðTi Tis Þ þ rb N i1 hri ðDHf ;i Þ ¼ 0
Mass and energy balances for fluid phase
X i
g F vyj vz þ g F g vT Ajc Cpj vzj
Ajc
Pressure drop (Ergun momentum balance)
dP dz
Boundary conditions
z ¼ 0;
zi ðKi 1Þ ¼0 1 þ VF ðKi 1Þ
(20)
which is a monotonic function in V/F and is thus easy to solve numerically. A physical solution must satisfy 0 V/F 1. Ki depends also on xi and yi, so one approach is add an outer iteration loop on Ki [13]. 3.2. Kinetics model 3.2.1. Reaction rate Reactions (1)e(3) are not independent as one is a linear combination of the other ones. In the current work, the rate expressions have been selected from Graaf et al. [16]. The rate equations combining with the equilibrium rate constants provide enough information about kinetics of methanol synthesis [17]. The corresponding rate expressions due to the hydrogenation of CO, CO2 and reversed wateregas shift reactions over commercial CuO/ZnO/ Al2O3 catalysts are:
h . i 3=2 1=2 k1 KCO fCO fH2 fCH3 OH fH2 KP1 . i r1 ¼ h 1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O KH2 fH2 O
(21)
h . i 3=2 3=2 k2 KCO2 fCO2 fH2 fCH3 OH fH2 O fH2 KP2 . i r2 ¼ h 1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O KH2 fH2 O
(22)
Table 5 Comparison between model results with design data and an operation data for fresh catalyst. Product condition
Plant
Model validation with design data Composition (mol %) CH3OH 0.104 CO 0.0251 CO2 0.0709 H2O 0.0234 H2 0.5519 N2/Ar 0.1107 CH4 0.114 Temperature (K) 495 Model validation with an operation data Composition (mol %) CH3OH 0.0987 CO 0.0266 CO2 0.0718 H2O 0.0183 H2 0.5558 N2/Ar 0.1008 CH4 0.128 Temperature (K) 493.5
Predicted
av cj kgi; ðysi ygi Þ ¼ 0 shell T tube Þ ¼ 0 i þ av hf ðTjs Tj Þ±pD 1 Ac U12 ðT g
2
ð1εÞ mug þ ε3 d2p g g yi;j ¼ yi0;j ;
¼ 150
ð1εÞu2g r ε3 dp g g Tj ¼ Tj0 ;
1:75
g
g
Pj ¼ Pj0
k3 KCO2 fCO2 fH2 fH2 O fCO KP3 . i r3 ¼ h 1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O KH2 fH2 O
The reaction rate constants, adsorption equilibrium constants and reaction equilibrium constants which occur in the formulation of kinetic expressions are tabulated in Table 3, respectively.
3.2.2. Mathematical model A one dimensional heterogeneous model, which is a conventional model for a catalytic reactor with heat and mass transfer resistances, has been developed for gas cooled reactor in order to determine the concentration and temperature distributions inside the reactor. In this model the following assumptions are used: The gas mixture is an ideal gas in both catalytic reactors. Both of the reactors are operated at steady-state conditions. Radial variations in both beds are negligible (one-dimensional model). Axial diffusion of mass and heat are negligible. Bed porosity in axial and radial directions is constant. Laminar plug flow is employed in both reactors. The chemical reactions are assumed to take place only in the catalyst particles. Heat loss to the surrounding is neglected.
T1A
T1C
Error %
T2A 0.1028 0.0238 0.0764 0.0265 0.5353 0.119 0.1161 489.5
1.15 5.46 7.75 13.24 3.007 7.5 1.84 1.11
0.0964 0.0245 0.0771 0.0179 0.5423 0.1068 0.135 487.6
2.33 7.89 7.38 2.18 2.42 5.95 5.46 1.19
(23)
T2C
T3A
T3C
T4A
T4C
T5A
T5C
T6A
T6C
T1B
T2B T3B T4B
T5B T6B
Fig. 2. The location of thermocouples in the gas cooled reactor.
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Table 6 Temperature operation data for different times along length of the gas cooled reactor. Temperature ( C)
Sensor location
1 2 3 4 5 6
Month 1
Month 3
Month 6
Month 9
Month 12
Month 15
Month 18
Month 21
Month 24
257 258.1 266.47 268.77 258.73 243.17
260 261.57 263.63 268.07 264.67 252.43
261.86 259.43 259.63 259.86 259.86 242.36
262.96 262.67 266.86 269.93 254.56 237.37
263.4 258.3 251.7 242.2 222 197.1
263.7 258.3 252.2 241.4 228.4 206.3
265 259.1 251.4 238.1 218.6 185.3
267.5 260.2 249.6 231.9 202.3 152
269.4 261.4 244.3 225.6 187.3 138
4. Model validation
To obtain the mole balance equation and the energy balance equation, a differential element along the axial direction inside the reactor was considered. The balances typically account for convection, transport to the solid phase. The mass and energy balances for solid and fluid phases in all sides, pressure drop equation and boundary conditions are summarized in Table 4. h is the effectiveness factor (the ratio of the reaction rate observed to the real rate of reaction), which is obtained from a dusty gas model calculations [17]. A set of above mentioned the differential-algebraic equations (DAE) are developed for the modeling of methanol reactors. The energy and mass balances obtained for the reactor are coupled with non-linear algebraic equations of the kinetic model, transport properties and other auxiliary correlations. A backward finite difference approximation is applied to solve these set of equations.
5. Results and discussion The temperature profiles of methanol synthesis reactors changes with time; therefore they are different from the predicted profile in the design (CR). Temperature of the gas cooled reactor
550
600
The First Reactor
Design condition
Temperature (K)
Time
450 Dew point
400
5
10 Lenght (m)
15
Design condition
Time 450
400
Two Phase
0
The First Reactor
500
500
350
The Second Reactor
The Second Reactor
550 Temperature (K)
The steady state model validation is performed between the industrial data reported by a domestic petrochemical company and the mathematical modeling of CR. The CR model results and the corresponding observed data of the pilot plant are presented in Table 5. A good agreement is observed between the modeling results and the pilot plant data. Therefore, this mathematical model performs well under the industrial conditions.
Dew point
20
350
(a)
0
5
10 Lenght (m)
15
20
(b)
550 JS
Temperature (K)
500 HGS 450 400
Dew Point
350
CR
300 250
0
5
10 Length (m)
15
20
(c)
Fig. 3. Temperature profiles (a) in the design (conventional) configuration (CR) (b) in ES (c) comparisons of HGS, JS and CR configuration.
A. Mirvakili, M.R. Rahimpour / Applied Thermal Engineering 91 (2015) 1059e1070
bed is measured by 18 thermocouples which are embedded in the six locations of the bed. The locations of these thermocouples are shown in Fig. 2 three thermocouples in a row are in a level of the gas cooled reactor but they are distributed in three different positions. Table 6, presents the temperature data related to the gas cooled reactor in different times according to the reported temperature of one day in three months. The presented data are average of three reported temperature in one level. As seen, temperature decreases gradually at the end of the reactor. Dew point in the porous media is calculated and compared with the bed temperature. The percentage of gas that condensed at the end of the reactor and its compositions are determined by a flash calculation at the last day of the operation. Results show that about 5% of gas converts to liquid which includes 71% methanol and 29% water. In Fig. 3(a), temperature profiles in the designed condition and temperature changes along two years are shown in CR. Temperature of the first reactor increases with time and also the temperature in the entrance of the second reactor enhances. However, Temperature in the second reactor decreases drastically. As far as the temperature of the gas cooled reactor becomes lower than dew point in the last 1 m of the reactor, methanol and water are condensed and causes a two phase flow at the end part of the second reactor of CR. Separation of 20% methanol and 10% water in the entrance of the second reactor results in an increased dew point temperature. Moreover, the methanol removal shifts the reaction to the product side and consequently the exothermic reaction rate and temperature increase. Fig. 3(b) demonstrates the temperature profile of ES. As shown in Fig 3(b), temperature of the gas in total length of the second reactor is higher than the dew point
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temperature of the gas in ES. Therefore, there would be no condensation problem in ES. Fig. 3(c) illustrates comparison of temperature profiles between HGS, JS and CR. Temperature of the gas cooled reactor in both strategies is higher than the dew point. Therefore, both strategies solve problem of gas condensate formation in the last of the gas cooled reactor. All configurations have been modeled and the performance of them has been compared with the CR in the following figures. The reactor length is divided into two segments where the reaction kinetic is controlling in an upper section and the equilibrium is predominant in the other section. The difference between modeling results of conventional reactor and proposed configurations is due to the unequal thermodynamics equilibrium conditions in the configurations. The comparison of methanol molar flow rate between HGS, JS and CR are shown in Fig. 4(a). Methanol production decreases in HGS and JS rather than CR. Although these strategies solve the problem of gas condensation formation, decreases the methanol molar flow rate. Therefore, HGS and JS strategies are not proper. The methanol molar flow rate along CR and ES are depicted in Fig. 4(b). Methanol is the main product of these configurations and it is produced along two reactors gradually in CR. However, methanol molar flow rate increases abruptly at the beginning of the second reactor in ES owing to the in-situ methanol removal. Some fractions of methanol and water are separated from the feed of the second reactor in ES by a partial condenser. This shifts the methanol production reaction (i.e., Eqs. (1) and (2)) to the production side. Furthermore, molar flow rate of methanol increases gradually at the rest of the second reactor in ES. Fig. 4(b), illustrates that the produced methanol in ES is less than CR. But the fact is that some
Fig. 4. Comparison of methanol molar flow (a) between CR, JS and HGS (b) between CR and ES (c) between CR, JS, HGS and ES.
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products that should become cold. Fig. 5(b) shows the procedure of thermal process of gas in conventional configuration. Gas in the tubes of gas cooled reactor is warmed by the gas in the shell. In the water cooled reactor, the tube side is cooled by boiling water in the shell. So, the boiling water phase changes to steam that is separated from the boiling water in drum and it is sent to utility unit. The gas product of gas cooled reactor is cooled by three heat exchangers and one air cooler. Steam, a portion of feed and sea water are used to cool the gas in three heat exchangers, respectively. An energy saving design for ES is proposed in this study which is illustrated in Fig. 5(c). In the first step of the thermal process after the water cooled reactor, the stream is cooled to 171 C and a portion of methanol synthesis feed which is warmed by the product of gas cooled reactor in CR, is warmed to 120 C in ES. After that, there is another heat exchanger for cooling the stream to 96 C and simultaneously, the boiling water which cools the product of gas cooled reactor, is warmed to 189 C and sent to utility unit. Thus, the stream is cooled to 96 C and 20% of methanol and 10% water are removed by condensation. The gas stream should be warmed to 260 C and mixed to the other half of the gas in order to enter to the gas cooled reactor. In this heat exchanger, the gas is heated to 259 C in tubes and the product of gas cooled reactor is cooled to 138 C in the shell side of the heat exchanger. Although, the ES configuration requires more energy rather than other
methanol was separated from the feed of the second reactor which is not shown in these figures. Thus, the total methanol molar flow rate in CR and ES are shown in Fig. 4(c). The superiority of ES configuration is evidently distinguished from this figure because the higher Methanol molar flow rate is achieved in this configuration. The methanol molar flow rate in ES is 7.9% more than the one in CR. Methanol molar flow rate in ES is higher than HGS and JS about 7.5% and 8.7% respectively. The methanol molar flow rate increases in ES owing to the methanol removal and changes in thermodynamic equilibrium. The factors affecting the production rate in the industrial methanol synthesis are parameters such as thermodynamic equilibrium limitations and catalyst deactivation and variation in the composition of the reacting gas. The energy requirements of the alternative design are shown in Fig. 5(a). ES configuration needs two heating equipments, one of them is the partial condenser and the other is a heat exchanger for warming the gas. Qc and Qh are regard to the released heat in partial condenser and the heat requirement in heat exchanger, respectively. The energy requirements for other configurations are shown by QJ and QHG for JS and HGS, respectively. As seen in Fig. 5(a), the highest energy requirement is regard to ES, because it contains two thermal equipments. However, an energy saving method called self-heat recuperation has been applied for ES configuration. In this method, the required heat is provided by the released energy of hot
Energy requirements (Kj/s)
(a) 6 x 10
(b)
4
Steam 316 K 338 K
308 K
5
393 K
513 K Drum
411 K
Sea water
4
Fresh Feed
537 K Air Cooler
3 Purge gas
2
449 K
401 K
Flare
1 0
329 K
Methanol water
Q1H
2 Q
3 Q JS
C
495 K
Q4HGS
385 K 463 K
Boiling water
513 K Boiling water
Steam
(c)
Flare
Purge gas
513 K
Drum
536 K Methanol water 308 K Sea water
411 K 316 K
495 K 537 K
Fresh Feed
393 K
Air Cooler
513 K Boiling water
444 K
329 K
463 K
Methanol water 369 K
385 K
Boiling water
Fig. 5. (a) comparison of energy requirement between JS, HGS and ES (b) schematic diagram of heating process in CR (c) schematic diagram of heating process in ES.
A. Mirvakili, M.R. Rahimpour / Applied Thermal Engineering 91 (2015) 1059e1070
80
35 ES
ES
30 CR
60 50
H2 Conversion (%)
CO Conversion (%)
The Second Reactor
The First Reactor
70
76
40
75
30
73
74
72
20
18.2 18.4 18.6 18.8 19 19.2
CR
25 20 15 10 5
10 0
1067
0
5
10 Lenght (m)
15
0
20
The First Reactor
0
5
(a)
The Second Reactor
10 Length (m)
15
20
(b)
20
CO2 Conversion (%)
The First Reactor
The Second Reactor
ES
15 CR
10
5
0
0
5
10 Length (m)
15
20
(c)
Fig. 6. A comparison between (a) CO (b) H2O (c) CO2 conversions in CR and ES.
configurations, the total energy requirement for the ES in this unit is provided with using the self-heat recuperation approach. A comparison between CO, H2O and CO2 conversions in CR and ES is shown in Fig. 6(a)e(c) respectively. Higher CO, H2 and CO2 conversion is achieved in ES compared with CR. The main reason for an increase in CO, H2 and CO2 conversion in ES are a decrease in methanol mole fraction in the feed of the second reactor of ES. CO,
H2 and CO2 are reactants, when the reactions shift to the product side in ES, reactants are consumed more. H2 is consumed more than CO and CO2 because hydrogen is consumed in the hydrogenation of CO and CO2 as shown in Eqs. (1) and (2). In addition, the water gas shift (WGS) reaction (i.e., Eq. (3)) shifts to the production side via water removal and more hydrogen is consumed in ES as a result.
0.7 H2
0.6
0.7
CR
0.5 Mole fraction
Mole fraction
0.5 0.4 0.3
0.4 0.3 0.2
0.2 CO
0.1 0
ES
H2
0.6
H2O 0
0 5
10 Length (m)
(a)
15
20
CO2
CO
0.1
CO2
H 2O 0
5
10 Length (m)
(b)
Fig. 7. The mole fraction of CO, CO2, H2 and H2O along the length of (a) CR and (b) ES.
15
20
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Molar Flowrate of Methanol (mol/s)
3000 2500 2000 1500 1000 500 0
2 0.2 3 0.3 4 5 9 10 0.4 60.5 70.6 80.7 0.8 0.9 111 01 0.1 Fraction of Seperated Methanol
Fig. 8. Methanol molar flow rate production changes with the changing of methanol removal percent.
The mole fraction of CO, CO2, H2 and H2O is depicted along the CR and ES in Fig. 7(a) and (b), respectively. The mole fractions have not changed significantly in CR and ES. However, mole fraction of CO at ES is lower than that in CR because, methanol and water removal shifts the hydrogenation of CO to the product side. Therefore, CO is consumed in ES more than CR. However, there is no significant reduction in CO mole fraction in the ES compared with the CR. The carbon dioxide mole fraction in ES is less than the one in CR. Indeed, CO2 is consumed in ES about 2.6% more than in CR. Comparison between CO and CO2 in Fig. 7(a) and (b) shows that the methanol and water removal from the inlet of the second reactor affects CO2 hydrogenation (Eqs. (2) and (3)) more than CO hydrogenation (Eq. (1)). Therefore, CO2 is consumed more than CO in ES. A reduction in CO2 mole fraction in the purge gas of the unit is another superiority of the ES configuration compared to the CR. As expected, hydrogen is consumed in ES more than CR. All three reactions shift to the product side via methanol and water removal from the inlet of the second reactor. Hydrogen mole fraction in ES is about 0.02 lower than one in CR. Water is another product in the methanol synthesis which is removed by a partial condenser from the inlet reactant gas to the second reactor of ES. Although water mole fraction decreases in the inlet of the second reactor, the mole fraction of water at the end of the second reactor of ES and CR are almost similar. The reason is that the reactions shift to the product
Fig. 9. (a) changes produced methanol molar flow rates (b) changes carbon monoxide flow rate (c) changes carbon dioxide flow rate (d) changes temperature with changing the methanol removal percent in the inlet of the gas cooled reactor.
A. Mirvakili, M.R. Rahimpour / Applied Thermal Engineering 91 (2015) 1059e1070
side and water is produced which compensate the reduction of water in the feed of the second reactor in ES. The effect of percentage of methanol removal from the inlet of the second reactor on the methanol production is shown in Fig. 8. As seen, the methanol molar flow rate enhances with increasing the methanol removal percentage. The reason of this enhancement in methanol molar flow rate is obviously that the reactions become far from the thermodynamic equilibrium when the methanol is separated in the inlet of the second reactor. Therefore, methanol will be produced more than the previous condition. As increasing the methanol separation leads to increase in cost, the minimum methanol removal is considered in order to resolve the gas condensate problem in the second reactor of the CR. The effect of percentage of the methanol separation on the produced methanol, CO and CO2 molar flow rates and temperature are depicted along the second reactor of ES in Fig. 9(a)e(d). As seen in Fig. 9(a), the reaction rate in the entrance of the second reactor increases with increasing methanol removal percentage. Although, it seems that methanol molar flow rate decreases, it increases with increasing methanol in-situ removal. Because, methanol molar flow rate is the sum of produced methanol and separated methanol from the inlet of the second reactor. Fig. 9(b) and (c) show that CO and CO2 molar flow rates decrease with increasing the fraction of methanol separation due to increase in reaction rates and more CO and CO2 consumptions. Fig. 9(d) illustrates that the temperature peak rises by increasing the methanol separation in ES. Increasing the methanol separation follows the enhancement in reaction rates at the entrance of the second reactor of ES. So, the increase in the production rate causes ascending temperature at the entrance of the second reactor. 6. Conclusion The gas cooled reactor in the dual type methanol synthesis process has a significant problem of gas condensate formation. The pressure drop increased gradually in the bed, while it increases sharply at the last 2 m of the reactor length. Consequently, the temperature reduces strongly at the end of the bed until it reaches to the lower temperature than the dew point temperature. The formation of gas condensate including methanol and water which are drastically corrosive in combination, causes severe corrosion damage for the applied catalysts and the pipelines. Therefore, the pressure and temperature drop increase due to catalyst crushing at the last part of the gas cooled reactor and more gas condensates will be formed. In order to resolve this problem, three strategies which are named HGS, JS and ES are developed. In HGS, a portion of hot synthesis gas injected to the last 2 m of the reactor and warms the last of the reactor. JS strategy proposes that the last 2 m of the reactor heated by steam in the jacket around this zone. And also the most influential strategy is ES which placing the partial condenser after the water cooled reactor leads to a better reactor performance by removing condensed methanol and water from the inlet of the second reactor (the gas-cooled reactor). The partial condenser cools half of the feed stream to 96 C. Consequently, 40% methanol and 20% water is condensed and separated, after that the noncondensed residual cooled gas is heated to about 260 C and mixed with the remained half of the reactant gas which are then sent to the second reactor as a feed. Methanol and water removal accelerates the reactions of CO and CO2 with H2 towards methanol. This increase in the production rate causes the temperature rise in the entrance of the second reactor. Moreover, it reduces the dew point temperature of the reacting gas in the bed. The performances of all configurations are investigated by considering a one dimensional heterogeneous model for the fixed-bed reactors. The mathematical model is validated with the data gathered from a domestic
1069
petrochemical industry. A good agreement is observed between the industrial data and the mathematical modeling. Results show that, methanol molar flow rate increases about 7.9% in ES rather than CR and it decreases about 0.19% and 1.57% in HGS and JS respectively rather than CR. 2.6% decrease of carbon dioxide consumption rate in the ES compared with CR, which is appealing from the environmental viewpoint, can be considered as one of the superiorities of the ES configuration as well as resolving the gas condensate problem and also enhancing the methanol production. An innovative self-heat recuperation technology is utilized in ES in order to energy saving. Nomenclature av Ac Cp dp Ei fi F hf Hi DHf,i kg K ki Ki Ki Kpi L Mi P Pc Pl Pv R Rp ri T U Xi yi yis z Z
specific surface area of catalyst pellet (m2 m3) cross section area of each tube (m2) specific heat of the gas at constant pressure (J mol1 K1) particle diameter (m) activation energy for elementary reaction step i, kJ/kmol fugacity total molar flow rate (mol s1) gas-solid heat transfer coefficient (W m2 K1) Henry's coefficient of component i enthalpy of formation of component i (J mol1) mass transfer coefficient for component i (m s1) conductivity of gas phase (W m1 K1) reaction rate coefficient, (mol kg1 s1 bar1/2) adsorption equilibrium constant, bar1 K value equilibrium constant based on partial pressure for component i reactor length (m) molecular weight of component i (g mol1) total pressure (for exothermic side: bar; for endothermic side: Pa) capillary pressure (Kpa) liquid pressure (KPa) vapor pressure (KPa) universal gas constant (J mol1 K1) particle radius (m) reaction rate of component i (mol kg1 s1) temperature (K) overall heat transfer coefficient between exothermic and endothermic sides (W m2 K1) conversion of component i mole fraction of component i (mol mol1) mole fraction of component i in the solid phase(mol mol1) axial reactor coordinate (m) compressibility factor
Greek letters DHi enthalpy of reaction εs void fraction of catalyst ε porosity of bed G ratio of volume to surface area of particle g volume fraction of catalyst occupied by solid particles in bubble gi activity coefficient of component i s surface tension (N/m) f fugacity coefficient q contact angle (degrees) m chemical potential mi viscosity of fluid phase (kg m1 s1) nci critical volume of component i (cm3 mol1)
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r rB rs h
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density of fluid phase (kg m3) density of catalytic bed (kg m3) density of catalyst (kg m3) catalyst effectiveness factor
Superscripts g in bulk gas phase s at the surface of the catalyst Subscripts 0 inlet conditions k reaction number index l liquid phase v vapor phase References [1] C.J. Schack, M.A. Mcneil, R.G. Rinker, Methanol synthesis from hydrogen, carbon monoxide and carbon dioxide over a Cuo/ZnO/Al2O3 catalyst: I. steadystate kinetics experiments, Appl. Catal. 50 (1989) 247. [2] G.H. Graaf, H. Scholtens, E.J. Stamhuis, A.A.C.M. Beenackers, Intra-particle diffusion limitation in low-pressure methanol synthesis, Chem. Eng. Sci. 45 (1990) 773e783. [3] A. Kova c Kralj, P. Glavic, Multi-criteria optimization in a methanol process, Appl. Therm. Eng. 29 (2009) 1043e1049. [4] Y. Kansha, M. Ishizuka, C. Song, Atsushi Tsutsumi, An Innovative Methanol Synthesis Process Based on Self-Heat Recuperation. Appl. Therm. Eng. 70 (2014) 1189e1194. http://dx.doi.org/10.1016/j.applthermaleng.2014.05.002.
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