OF AN ADIABATIC
iD-BED METHANATOR
OF AN ADIABATIC
FIXED-BED METHANATOR
o
>c o
h- o III I I' III I Hill! O 03PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECH-NISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS Ir. H. B BOEREMA, HOOG-LERAAR IN DE AFDELING DER ELEKTROTECHNIEK, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET
COLLEGE VAN DEKANEN TE VERDEDIGEN OP WOENSDAG 18 DECEMBER 1974 TE 14.00 UUR
DOOR
/ 6 ' - 2. i> o (i o
HANS VAN DOESBURG
SCHEIKUNDIG INGENIEUR GEBOREN TE ROTTERDAM
1974
DRUKKERIJ J. H. PASMANS, 'S-GRAVENHAGE
BIBLIOTHEEK TU Delft P 1832 3060
Let my last results Fit the bl dy theory
Anonymous engineer
(Himmelblau, Process Analysis and Simulation)
CHAPTER 1 INTRODUCTION
1.1 Dynamic behaviour of fixed-bed reactors
1.2 Methanation of carbon oxides
1.3 Outline of thesis
9
9
11
13
CHAPTER 2 THEORY OF FIXED-BED REACTOR MODELLING 15
2.1 Introduction 15
2.2 Approach to modelling of fixed-bed catalytic
reactors 15
CHAPTER 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
KINETICS OF CARBON OXIDE HYDROGENATION 24
Introduction 24
Kinetic measurements 25
Modelling of kinetic data 26
Catalyst 29
Experimental 31
Hydrogenation of COg 32
3.6.1 Hydrogen partial pressure equal to 1 atm. 32
3.6.2 Influence of the hydrogen partial pressure 38
Hydrogenation of CO 42
3.7.1 Hydrogen partial pressure equal to 1 atm. 42
3.7.2 Influence of the hydrogen partial pressure 46
Hydrogenation of mixtures of CO and CO2 50
Influence of reaction products 52
Discussion 53
CHAPTER 4 DEVELOPMENT OF METHANATOR MODEL 59
4.1 Introduction 59
4.2 Level II, transfer processes inside catalyst
pellet 59
4.2.1 Heat transport 59
4.3.1 Mass transport 63
4.3.2 Heat transport 64
4.3.3 Model reduction 65
4.4 Level IV, transfer processes in a layer of
catalyst 66
4.4.1 Mass transport 66
4.4.2 Heat transport 68
4.5 Level V, interaction with the environment 74
4.6 Model equations 75
CHAPTER 5 TRANSIENT BEHAVIOUR OF A PILOT METHANATOR 79
5.1 Introduction 79
5.2 Experimental 79
5.2.1 Reactor 79
5.2.2 Apparatus 81
5.2.3 Procedures 82
5.3 Hydrogenation of CO^ 83
5.3.1 Type 1 disturbances 83
5.3.2 Type 2 disturbances 93
5.3.3 Type 3 disturbances 95
5.4 Hydrogenation of CO 100
5.4.1 Type 1 disturbances 101
5.4.2 Type 2 disturbances 103
5.4.3 Type 3 disturbances 104
5.5 Hydrogenation of mixtures of CO and COp 106
5.5.1 Reactor model for mixed feeds 107
5.5.2 Type 1 disturbances 109
5.5.3 Type 2A disturbances 110
5.5.4 Type 2B disturbances 112
5.5.5 Type 2C disturbances 114
5.5.6 Type 2D disturbances 115
5.5.7 Type 2E disturbances 116
5.5.8 Type 3 disturbances 116
6.1 Reactor model 118
6.2 Reactor dynamics 120
6.3 Industrial methanation 121
SUMMARY 126
SAMENVATTING 129
APPENDIX I Mass transfer resistance within the catalyst
particle 132
II Numerical solutions of the model equations 137
LIST OF SYMBOLS 143
C H A P T E R 1
I N T R O D U C T I O N
\-.\ Dynamic behaviour of fixed-bed r e a c t o r s
Tubular reactors are often used for large-scale processes in the chemical and process industries. Many of these are heterogeneously catalyzed processes carried out in reactors packed with particles of a solid catalyst. The performance of such fixed-bed catalytic reactors under steady-state operating conditions can be predicted quite well by calculations using mathematical reactor models, provided that the relevant data on the rates of the chemical and physical phenomena occurring in the reactor are known with adequate accuracy. A review of this subject was given recently by Froment
(i.2.3).
By comparison, it is much more difficult to predict the transient behaviour of reactors, in particular of fixed-bed reactors. The development of satisfactory djmamic models for this purpose is important for a number of reasons:
- automation and optimizing control is being introduced in industry on an ever increasing scale;
- since the optimum of reactor performance is often located near constraint boundaries imposed by e.g. the strength of construction materials, catalyst deactivation, safety considerations, etc. such optimization is only feasible when good dynamic models of reactors are available;
- the transient behaviour of a reactor should be known in sufficient detail for planning start-ups, shut-downs and changes in operating conditions caused by changes of feed or dictated by the necessity to vary product quality;
- in some processes catalyst activity declines relatively rapidly; this requires cyclic operation with the attendant dynamic changes in concentration and temperature profiles during production and regeneration periods.
A good example of the necessity of predicting the dynamic behaviour is given by Wei ( 4 ) in his analysis of the transient behaviour of the automobile exhaust catalytic convertor. With this type of reacting system steady states are rarely attained because temperature, flow rate and feed composition vary rapidly and over a considerable range. This is particularly so in urban driving when cleaning the exhaust gas is very important to reduce air pollution.
The above illustrates the importance of studies on the non-stationary behaviour of reactors in general and of fixed-bed catalytic reactors in particular. However, this subject is by no means simple: the fixed-bed catalytic reactor presents one of the most difficult control problems found in industry due to the complicated interaction of heat and mass transport to and from catalyst particles, adsorption, desorption and chemical reaction.
The first paper on some of the above problems, published in 1918 by Liljenroth ( 5 ) and entitled "Starting and stability phenomena of ammonia oxidation and similar reactions", is purely qualitative by nature and did not stimulate activities in this field. Much later, in the 1950's,the problem was taken up again by Van Heerden (6), who showed the presence of statically stable and unstable operating conditions of chemical reactors. But only during the last decade substantial progress has been made in the theoretical analysis of mathematical models, from simple basic model equations up to very complex sets of differential equations. This remarkable increase in the use of mathematical reactor models became possible only after the simultaneous development of large and fast digital computers and efficient mathematical techniques.
Although the simulation of the transient behaviour of packed-bed reactors has received widespread attention, the results of model calculations are often not checked with experimental data. (of. Beek (7), Froment ( 2 ) and Ray ( S ) ) , presumably because reliable measurements on transient reactor behaviour are much more difficult to perform, costly and time-consuming than computer calculations. In particular, problems arise with small laboratory reactors when
concentration and/or temperature profiles must be determined: the presence of instruments to measure these quantities in the packed bed often disturbs the phenomenon which is being studied.
The aim of the work reported in this thesis is to contribute to the theoretical and practical knowledge of the transient behaviour of fixed-bed catalytic reactors by investigating the fixed-bed adiabatic methanator.
1.2 M e t h a n a t i o n of c a r b o n o x i d e s
Several papers have been published on the methanation of carbon oxides in concentrations between 20 and 70 vol. %, where the object is to produce methane-rich fuel gases (,9,10,11,12,13,14^15). Very little is known, however, about the methanation of small amounts of carbon oxides with hydrogen over a supported nickel catalyst, which is a necessary purification step in the process sequence for the. manufacture of hydrogen and ammonia synthesis gas by hydrocarbon/
steam reforming or partial oxidation of hydrocarbons. As an
illustration figure 1-1 shows a diagram of a naptha/steam reforming process.
Air
Crude hydrogen 1^^ Reformer CO Convertor Methanator
2hd Reformer CO2 Removal
The gas produced in the second reformer contains approximately 12 vol % C0„ and about equal amounts of CO. Most of the CO is converted
into CO. by reaction with steam in the CO-shift convertor according to:
CO + H O t CO + H (AH° = - 9.8 kcal.mol"') = -41.1 kJ.mol"'
The next step is the removal of CO., e.g. by washing with an aqueous alkanol amine solution. These operations leave residual amounts of CO and CO. in the gas, the concentration being about 0.1-0.5 vol % each. Since even such small amounts of carbon oxides cause poisoning of catalysts in subsequent process steps like ammonia synthesis, CO and CO. are hydrogenated in an adiabatic methanator, usually over a supported nickel catalyst. The stoichiometric equations involved are:
CO + 3H. ->• CH, + H.O (AH° = - 49.3 kcal.mol"') 2 4 2 ^ r
= -206.1 kJ.mol CO, + 4H. -> CH, + 2H.0 (AH° = - 39.4 kcal.mol"')
2 2 4 2 r
= -164.7 kJ.mol
The dynamic behaviour of an adiabatic fixed-bed methanator can be important when the inlet concentration of CO. suddenly increases because of failure or misoperation of the CO. absorber. The
possibility of an upset in the CO. removal system is probably higher during the initial start-up than at any later time (iff ). It is then necessary to know how soon the temperature in the reactor increases to the critical value where catalyst activity declines. A fast-acting control system is required; an example is given in figure 1-2
(adapted from (17)). When the temperature in the reactor becomes too high the feed to the methanator is shut off by a fast butterfly valve and the product stream of the CO. absorber vented.
Additional reasons why the methanation of carbon oxides are attractive test reactions are:
., l l o r e ^-^ T Butterf 4 ' 1> Butterfly volve From CO2 absorber -*• to synthesis loop
Figure 1-2 Methanator control (TA-temperature alarm, BVC=butterfly valve closing)
- supported nickel catalysts having high activity and stability can be obtained commercially;
- pure and relatively cheap reactant gases are available;
- there are no consecutive or side reactions at these very low carbon oxide concentrations when using supported nickel catalysts;
- it is possible to determine the dynamic behaviour of the reactor from changes in the axial temperature profile since the large heats of reaction cause a considerable eixial temperature gradient over the catalyst bed, complete conversion of 1 vol % CO or CO. in H„ giving an adiabatic temperature rise of 70 C or 56 C, respectively.
1.3 O u t l i n e of t h e s i s
As stated above the aim of this work is to compare experimental data on transient behaviour with theoretical predictions by means of calculations with a mathematical model. Therefore, chapter 2
deals with general aspects of reactor modelling and presents a strategy to select the best possible model for describing fixed-bed catalytic reactors.
Since such reactor models always contain terms for the kinetics of the chemical reaction, a kinetic investigation into carbon oxide methanation was made; results are given in chapter 3. The laboratory methanator used in this work operates at atmospheric pressure; consequently, most measurements were made at substantially atmospheric hydrogen partial pressure. The kinetics are described with Langmuir-Hinshelwood-type equations. Some work was also done at hydrogen partial pressures below 1 atm.
In chapter 4 a model for the methanator is developed, the question whether heat and mass transport phenomena should be taken into
account in the model being answered on a basis of theory and experimental data. At the end of this chapter the model equations are presented and the method of solution is discussed.
Measurements on methanator dynamics are described and compared with model calculations in chapter 5. After a discussion of the results with feeds consisting of CO or CO. in hydrogen, data are given on the methanation of mixtures of CO and CO. in hydrogen.
Chapter 6 summarizes the investigation reported in this thesis and applies the results to the dynamics of industrial methanators.
CHAPTER 2
THEORY OF FIXED-BED REACTOR MODELLING
2.1 Introduction
A mathematical model can be defined as an equation (or set of equations) describing the system to which it applies. Such a model should be based on a mathematical interpretation of the physical and/or chemical processes taking place; every parameter contained in the model must be physically identifiable and obtainable from accepted correlations or independent measurements. When dealing with chemical reactors such models usually consist of mass and heat balances, and, less frequently, a momentum balance.
The description of a catalytic fixed-bed reactor may call for a very complex model because of heat and mass transport between the
two phases and within each phase, as well as chemical reaction in one or more phases or at the phase boundary; further complications may arise from the different temperature dependency of the rates of physical transport and chemical reaction. A complete description of such a system can result in a very complex set of equations, in which especially the exponential relation between temperature and rate of reaction complicates the method of solution very much.
However, it is not always necessary to take all the phenomena into account and often a rather simple model can be used. In general one will choose the simplest possible model which still gives a sufficiently accurate description of the phenomena investigated. The description is never better than the assumptions made in deriving the model and the quality of the parameter values substituted in it, e.g. those of the chemical rate equation.
Most models for fixed-bed reactors, usually a set of differential equations, must be solved numerically because they are non-linear. This is possible nowadays with high-speed computers, even for very complex models, using advanced mathematical techniques. Although
very good numerical methods are available there is still a need for faster algorithms, since the consumption of computer time is often too high to permit extensive model analysis. This is particularly so in non-stationary model analysis, since almost always partial
differential equations must be solved.
To test the validity of the description by a model adopted, it is always necessary to compare results of calculations with measured data, which are in general much more difficult to obtain than calculated data.
2.2 Approach to modelling of fixed-bed catalytic reactors
Many mathematical fixed-bed reactor models of varying complexity have been presented in the literature. Although the parameter space
investigated is not always of practical interest, these analyses produce useful information on the conditions that must prevail in reaction systems to neglect the often secondary effects such as local mixing, resistance to mass and heat transport between phases, etc. The work done in the field of fixed-bed reactors has been reviewed recently by Froment (2,3 ) for stationary models and by Ray ( S ) for dynamic models. These two reviewers use the
classification given in table 2-1. The models are divided in six
A. Pseudo-homogeneous models
^fluid " ^solid
'^in fluid " "^in catalyst pores
Al . Plug flow (1-dimensional) A2. Axial dispersion
(1-dimensional) A3. Radial dispersion
(2-dimensional)
B. Heterogeneous models
''^fluid '' '''solid c ^ c
in fluid in catalyst pores
Bl. External resistance only
B2. External and internal resistance
B3. Radial mixing
classes, viz. three types of pseudo-homogeneous models in which the reactor contents are considered as a continuum, and three
heterogeneous model types, in which variables like temperature and concentrations differ in the two phases, catalyst and fluid. The disadvantage of this classification is that the differential
equations of models of the same class are quite different in character depending on the specific properties of the system considered.
Furthermore, it is not clear which phenomena are incorporated in a specific type of model.
Another systematic approach was followed by Slin'ko et al. ( 18,19,20) who divide a fixed-bed catalytic reactor into three levels, each level describing a subsystem inside the reactor. Each successive level is a subsystem of a higher order:
St
1 level : The kinetic model. The elements of this level are: - the catalytically active surface
- the adsorbed molecules of reactants, products and reaction intermediates, if present.
- reactant and product molecules above the surface. The mathematical description of this system is the kinetic equation.
2 level : The -porous catalyst pellet. The elements of this level are:
I St , ,
- 1 level
- reactants and products in the pores - the solid material
The mathematical description of this subsystem is the set of differential equations describing heat and mass transport inside the pellet.
3 level : A layer of catalyst. The elements of this level are: - The single porous pellet, i.e. level 2
- The assembly of solid particles
Processes occurring at this level are described by the set of equations for mass and heat transport and, if necessary,transport of momentum.
The second and the third level are connected via the boundary conditions on the external pellet surface.
In this thesis a non-stationary mathematical model for an adiabatic methanator was developed using a similar level concept, but now
considering five different levels. The subsystems are defined as outlined in figure 2-1. Each of the levels is studied separately to assess the importance of the various possible physical or chemical phenomena. LEVEL I LEVEL II LEVEL III LEVEL IV LEVEL V
Separate stages of chemical change
Transfer processes inside catalyst pellet Heat Mass
Transfer processes in a film layer Heat Mass
Transfer processes in a layer of catalyst Heat Mass
Interaction with the environment adiabatic non-adiabatic
Figure 2-1 Level scheme for model development
The philosophy behind this scheme is to consider the reactor initially as a distributed parameter system by treating each level separately, but it does not imply at all that the description of the reactor obtained in this way is always a distributed parameter model. From the discussion below it will become clear that often
several simultaneous mechanisms can be described with one lumped parameter giving an overall description of the processes observed.
LEVEL I contains the same elements as the first level of the Slin'ko scheme: the catalytically active surface and the molecules on and near this surface. The chemical reaction together with heat production or consumption for exothermic or endothemic systems, respectively, proceeds at the surface. Usually reaction rate equations are based on the Langmuir-Hinshelwood adsorption theory and are expressed in terms of partial pressures of the components. This theory is further discussed in chapter 3, where the kinetic models for the hydrogenation of CO and CO. are derived.
At LEVEL II the catalyst pellet can be considered as being
quasi-homogeneous since at any point in the pellet the temperature of the gas in the pores and the adjoining solid is equal. The heat of reaction generated or absorbed at the internal surface is distributed over adsorbed molecules, surface atoms or molecules of the catalyst, desorbing molecules and molecules in the gas phase. The large number of collisions guarantees a very good temperature equilibration. Another reason why the pellet may be regarded as a continuum relative to the concentration is that the average pore diameter is much smaller than the particle diameter. Consequently, the mass transport within the particle, mainly by diffusion, is described with an effective diffusivity, i.e. a combination of the molecular diffusion coefficient and the Knudsen coefficient, taking the pellet porosity and the tortuosity of the pores into account. Heat transport is
characterized similarly by an effective thermal conductivity. Thus, a lumped description of a catalyst particle applies. Mass and heat balances for several pellet models are discussed by Amundsen (21). When it follows from considerations at this level that the rate of mass transport in the catalyst pellet influences the overall process rate, an effectiveness factor can be used which lumps level I and II; an example is given by McGreavy and Cresswell (22).
At LEVEL III the system is extended to include the film layer around the catalyst pellet and special attention is now paid to heat
and mass transfer processes through this layer. From a theoretical analysis of several models for catalyst pellets with the surrounding film layer Hansen (23) concluded that the external resistance to heat transport is somewhat higher than the internal heat transport resistance; nevertheless, the two resistances appear to be of the same order of magnitude. The external resistance to mass transport is usually lower than the corresponding internal resistance because the presence of pores reduces the surface through which reactants can diffuse into the particle. The tortuosity of the pores adds to the pore diffusion resistance. When it follows from considerations at this level that the concentrations and temperature at the outer catalyst surface and in the adjoining gas phase do not differ, and when transport resistances within the particle are not present, a
quasi-homogeneous model description is valid.
Up to this level it makes no difference whether one uses a model based on differential equations or a so-called finite-stage or cell model, as proposed by Deans and Lapidus (24,25). In the latter type of model, the voids between the particles are regarded as a structure of perfect mixers. Depending on the pellet model (level I through III) pseudo-homogeneous stages are also possible. Finite-stage models are discussed by Amundsen (21) and Valstar (26) in studies of
stationary models of this type. Recently Berty et al. (27) and Rhee et al. (28) have used such models in work on transient behaviour of fixed-bed reactors. In this thesis attention will be paid to continuum models based on differential equations only.
The number of mass transport mechanisms added at LEVEL IV is limited: convective mass transport, "eddy" transport and bulk diffusion. The later two are usually lumped together as dispersion
in axial or radial direction.
Heat transfer is the result of (29,30): 1. mechanisms independent of flow, viz.:
1.1 thermal conduction through the solid particle
1.2 thermal conduction through the contact point of two particles 1.3 radiant heat transfer between the surfaces of two adjacent
pellets (gas-solid system)
2. mechanisms depending on the fluid flow, viz.:
2.1 thermal conduction through the fluid film near the contact surface of two pellets.
2.2 heat transfer by convection, solid-fluid-solid 2.3 heat conduction within the fluid
2.4 heat transfer by lateral mixing.
Mechanism 1.2 can usually be neglected (30,31). According to an experimental and theoretical study by Vortmeyer et al. (32,33,34) with a one-dimensional quasi-homogeneous model the contribution of radiation to the total heat flow is important at temperatures above 400°C. This is confirmed by others (21,27). Below this temperature the various mechanisms of heat transport are usually described by a lumped parameter, the effective thermal conductivity coefficient, except for heat transport by convection. Correlations for axial heat conductivity coefficients have been developed by Yagi et al.
(30,35), by Kunii and Smith (31,36) and more recently by Votruba et al. (37). Vortmeyer and Schaeffer (38) described heat transfer in packed beds with one and two-phase models. The authors were able to characterize axial thermal conduction with a pseudo-homogeneous model containing an effective heat conductivity coefficient which dependson the flow conditions in the bed, and attribute this dependence to a dispersion effect caused by the resistance against heat transfer between solid and fluid. With heterogeneous models containing a term for heat transfer between the phases a flow-independent heat conductivity coefficient can be used.
Dynamic models taking axial conduction into account have been studied by Eigenberger (39,40) for heat conduction in the catalyst phase only, and also by Gilles and Zeits (41). For this purpose Lubeck (42) and Venkatachalam et al. (44) use a pseudo-homogeneous model containing an effective thermal conductivity coefficient. Lubeck (43) studied the influence of heat conduction on the transient behaviour of fixed-bed reactors by computer simulation with a number of models, viz.: pseudo-liomogeneous as well as heterogeneous equations.
At LEVEL V the system is extended to interactions with the environment. Heat exchange is possible when the reactor is cooled but also when heat is exchanged between catalyst bed and fluid flow as is done in an autothermal reactor, such as is used in ammonia synthesis. Both types of reactors require very complicated models when the radial temperature gradients and the resulting radial concentration gradients are so large that they cannot be neglected. A two-dimensional model should then be used and radial conductivity and heat transfer coefficients at the tube wall taken into account.
The influence of the reactor wall may be important even for an adiabatic reactor when it operates non-stationarily. This is illustrated by Hoiberg et al. (45) who compared experimental data with calculations and found that the heat capacity of the reactor wall considerably influences reactor response. Eigenberger (46,107) noted that even the response of a homogeneous tubular reactor to a step change in inlet temperature changes from fast and steep to slow and smooth when the heat capacity of the reactor wall is taken into account. Wall effects are particularly important in studies with pilot plant fixed-bed reactors, since the heat
capacity of the wall may be of the same order of magnitude as that of the catalyst bed, or even higher. It thus appears that in real systems it is incorrect to neglect the heat capacity of the reactor wall. Nevertheless, the wall influence is assumed to be negligible in most theoretical studies. A similar conclusion applies to axial heat conduction along the reactor wall. In a recent paper (47), Lunde shows, experimentally and by simulation, that this heat conduction can also be important.
The preceding discussion refers to but a small fraction of the published literature; many papers have been published in this field, especially during the last decade. Favourite subjects are transient behaviour, multiplicity and stability of single particles, and multiplicity and stability of fixed-bed reactors. Since these
subjects have been reviewed exhaustively by Ray (8), the above discussion was limited to those papers which are of direct interest
in connection with the level approach followed here. Further mention of papers will be made in chapter 5, where the results of this work are compared with relevant literature.
C H A P T E R 3
K I N E T I C S OF C A R B O N O X I D E H Y D R O G E N A T I O N
3.1 I n t r o d u c t i o n
Adequate kinetic expressions are needed for the rate of CO and CO. hydrogenation to perform calculations on the dynamic behaviour of the methanator. In the literature little attention has so far been paid to the methanation of CO and CO.; very few of the papers published to date deal with the use of these reactions for the removal of traces of CO and CO. such as practiced for hydrogen production. Accordingly, a study was made of the kinetics of CO and C0» methanation on a supported nickel catalyst in the range of carbon oxide concentrations up to 2.5 vol %. Results of this work are discussed below.
When hydrogenating CO on nickel Vlasenko (48) found a zero order dependency of the rate on the partial pressure of CO between 135 and
175 C, at concentrations below 0.3 vol % CO in hydrogen and a total pressure of I atm. Schoubye (49), on the other hand, found a negative order in CO which decreases from zero to -0.5 with increasing CO concentration. His experiments were carried out under the following conditions: 0.1-20 vol % CO in H., 160-300°C and a total pressure of 1-15 atm. He described his results with the equation:
k .exp(-E/RT) p"
r =
(I+K .exp(16650/RT) - S I ) °*^
" Pu " 2
E varies from 18 to 28 kcal.mol , depending on the type of catalyst. A typical value for n is 0.15.
Vlasenko (50) also studied the kinetics of hydrogenation of low concentrations of carbon dioxide at atmospheric pressure and found a first order dependency in CO. when varying the temperature from 125
to 325°C and the concentration from 0.05 to 0.4 vol % CO in hydrogen. Pour (51) investigated the kinetics of CO. hydrogenation on a nickel on chromia catalyst at a total pressure of 1 atm. temperature range 160-220 C and concentration range 0.1 to 1.2 vol %. The hydrogen concentration, which was varied by dilution with nitrogen at a total pressure of 1 atm., has no influence on the reaction rate except at hydrogen concentrations lower than 25 vol %, where the rate decreases.
Vlasenko et al. (52) have published data on the hydrogenation of mixtures of CO and CO. on nickel. Their qualitative conclusion is that CO. does not influence the hydrogenation of CO whereas CO is a strong poison for the hydrogenation of CO.. This is confirmed by Campbell et al. (53) who report that concentrations of CO above
200-300 ppm inhibit the hydrogenation of CO.. Rehmat and Randhava (54) use this fact to methanate CO selectively in the presence of CO.. According to Fischer and Pichler ( 9 ) such inhibition also occurs when hydrogenating gas mixtures of almost stoichiometric composition.
Vlasenko et al. found no influence of the reaction products, CH, and H.O, on the hydrogenation rate of CO and CO.. A similar
conclusion was reached by Pour (51) when adding 0.6 to 2.13 vol % H.O or 0.5-2.0 vol % CH, to the reaction mixture.
z 4
3.2 Kinetic measurements.
In general, three methods are available to obtain rate data from conversions measured in a flow reactor:
(i) differential method (ii) integral method (iii) initial rate method
The differential method assumes the rate to be constant throughout the catalyst bed and interprets it as the rate corresponding to the average composition in the bed, which is a reasonable approximation for conversions up to 10 %.
For the integral method an accurate relationship between conversion and reciprocal space velocity, W/F, is required, which implies that
many data points are needed t-o obtain reliable values of the
derivative at some points of the C versus W/F plot. Both methods have the disadvantage that reaction products are present.
The advantages of both the differential method and the integral method are combined in the initial rate method, viz, measuring several conversions at a number of space velocities and extrapolating the plot of C versus W/F to the origin. The reaction rate corresponding to feed conditions is then calculated from the slope in the origin:
e.
r L _ (3-1)
(W/F).For CO hydrogenation the plots of C versus W/F are straight up to conversions of 99 % (cf. also 3.7) whereas plots for CO. hydrogenation show a slight curvature. Here, measured conversions above 60 % were not used because these points were no longer in the linear region according to visual inspection. A straight line through the origin was fitted to the data points using the least squares criterion. For
the best slope one can derive: ^ C.(W/F). '
I (W/F)?
(3-2)
1
This was done for the ranges of temperature and initial concentrations of carbon oxides representative of methanator conditions.
3.3 Modelling of kinetic data.
It is possible to derive kinetic equations known as Langmuir-Hinshelwood kinetics, as Eley-Rideal or Hougen-Watson models assuming Langmuir-type adsorption on the catalyst. A number of simplifying assumptions is made:
(i) adsorption occurs on equivalent active sites, i.e. the sites are distributed homogeneously over the surface.
(ii) only one molecule or atom is adsorbed per site, and there is no interaction between adsorbed species; this means that
adsorption and desorption rates and the heat of adsorption are independent of the surface coverage.
(iii) one step is rate-determining.
Several of these assumptions are rarely valid, such as the homogeneity of the surface, but nevertheless the simple kinetic equations obtained from the above assumptions often give a satisfactory description of measured rate data,
Following the approach of Hougen and Watson (56) and of Yang and Hougen (56) the general form of the kinetic equation for a
heterogeneous catalytic reaction can be written as:
k^.exp(-E/RT).g(p),(l-6)
r = = (3-3) (l+f(p,T))ni
The driving potential term, (1-6), expresses the deviation from thermodynamic equilibrium. Calculation of the equilibrium composition shows that at equilibrium the conversion of CO as well as of CO. is complete up to 400 C (10). This means that the value of 6 for the methanation reactions is so small that it can be neglected. g(p), the purely kinetic term, is only a function of the partial pressures of hydrogen and the carbon oxide provided that the effects of the reaction products need not be taken into account (48,50,61,57). This is
obviously true when initial rates are considered, i.e. when reaction products are absent.
In the pilot plant experiments described in this thesis (chapter 5) the hydrogen partial pressure is always close to 1 atm. and very large compared to that of carbon oxides. In such cases g(p) is a function of the carbon oxide-concentration only. However, when studying the
kinetics at hydrogen partial pressures below 1 atm., the above assumption is no longer valid and the hydrogen partial pressure must be incorporated in the kinetic term. As for the denominator, f(p,T) originates from the coverage balance over the active sites and m is the number of sites involved in the rate-determining step. If the hydrogen partial pressure equals 1 atm. the contribution of H to the denominator can be neglected. When one supposes that CO, CO , CH, and
H O do not adsorb dissociatively a simplified rate equation is obtained: k.p (3-4) ( ' " • ^ C P C - ^ ^ , 0 - P H , 0 * V ' C H > " 2 2 4 4
in which p is the partial pressure of the carbon oxide. With initial rate data only reactants are present and (3-4) becomes:
k.p
r = (3-5) (1 + K^.p^)«
Rate constant k depends on the temperature according to the Arrhenius relation:
k = k^^.exp (-E/RT) (3-6)
This is the first step in building kinetic models, the qualitative modelling based on Langmuir assumptions and using other special features of a particular reaction. The second step is to develop this qualitative model into a group of equations having the desired
properties. The various equations of this group differ in that different values of m are taken or one or more terms neglected. The equations are then fitted to the rate data by non-linear regression using the F-test of the variance of fit to determine which model(s) give(s) an "equal" description of the measurements from a statistical point of view: it seldom happens that only one model applies to the data. The sum of squares that must be minimized can be written as:
f^ 2
Q = . \ ('^obs.-'^calc.) (3-7)
1=1 1 1
in which r , is the i observed rate and r , is the i
obs. calc. calculated rate.
The final step is to descriminate between the remaining models by studying physical properties incorporated in the model such as the
apparent activation energy as a function of surface coverage, etc. If a special trend is not noticeable in the measured data one should always use the simplest model.
3.4 Catalyst
The supported nickel catalyst used in this work was Girdler G-65 obtained from Girdler Sildchemie, Munich. Table 3-1 contains data on this catalyst. The procedure used for reductive activation of the
Composition AZ^Oj NiO CaO ^^2°3 CuO MgO SiO^ Cr^Oj MnO^
«2°
wt. Z 53.4 33.6(=25 1.2 0.09 0.04 1.3 0.06 0.004 0.16 2.5 wtZ Ni) particle diameter : particle density : particle porosity : ^BET •hi
average pore diam.: max.temp, without loss of activity : sintering temperature : 0.35-0.42 mm 2750 kg.m"-' 0.46 42.4 m^.g"' 8.8 m^.g"' 100 A 800°C > 137a°C
Table 3-1 Data on G-65 catalyst
catalyst is outlined in table 3-2. When hydrogen containing CO or CO was fed to freshly reduced G-65 catalyst, deactivation was observed (cf. figure 3-1). With feeds containing CO the activity became constant after a relatively short processing period, but with mixtures of CO and hydrogen the activity continued to decrease during a considerable period of time. Consequently, the catalyst was always conditioned prior to kinetic measurements. When CO-containing feeds had to be used a correction for deactivation was applied by frequently measuring the CO conversion under the standard conditions of table 3-2 and normalizing observed conversions to the catalyst activity observed after 100 hours. Details can be found in table 3-2,
Reduction
temperature pressure
reducing gas space velocity
rate of heating to reduction temperature reduction time Conditioning with H„ containing CO CO concentration space velocity temperature pressure time CO conversion
with ff. containing CO^ CO, conversion space velocity temperature pressure time CO, conversion 350°C 1 atm. "2 4000 h"' 60°C.h-' 16 h 1.0 vol % 12000 h"' 200°C 1 atm. 60 h figure 3-1 1.4 vol % 12000 h"' 220°C 1 atm, 10 h figure 3-1
Table 3-2 Catalyst reduction and conditioning
o COg X CO ^ J " " — c%oo 0—0 o 0—0-J I I I 1 0 2 0 40 6 0 8 0 ^— t Ch)
Figure 3-1 Conversion as a function of time under deactivation conditions (cf. table 3-2)
1 O
3 . 5 E x p e r i m e n t a l
The measurements of conversion versus reciprocal space velocity were carried out in a continuous flow apparatus. A flow sheet is shown
in figure 3-2. The feed gases were fed from bottles, dried with molecular sieves 3A and metered with Brooks ELF precision flow controllers. The flows were measured by means of the pressure drop over stainless steel capillaries placed in thermostat C O - After mixing the gases were passed over active copper on silica ("B.T.S, catalyst") to remove traces of oxygen C^j. The tubular reactor, volume 4 ml, was placed in a fluid bed of glass spheres acting as a
thermostatic bath Cs), The temperatures in reactor and fluid bed were
H2 COj
0
• ^ li-i**©
Q
i — *-u
©
VENT VENTk
©
®
H2Figure 3-2 Simplified flow sheet of the k i n e t i c equipment
measured with chromel-alumel thermocouples. The r e a c t o r was charged with 0.5-2.4 g of crushed G-65 c a t a l y s t , sieve f r a c t i o n 0.32-0.42 mm,
if necessary d i l u t e d with quartz p a r t i c l e s of the same s i z e . The length of the r e a c t o r was about 125 times the p a r t i c l e size and the
diameter about 25 times, which is sufficient to satisfy the conditions for plug flow. With valve ( 4 ) samples of feed and product gases could be injected into on-line gas chromatograph T s ) , The components were separated over a 6-m active carbon column using hydrogen as carrier gas and detected by means of a katharometer. The peak surface was electronically integrated and recorded. After reduction and
conditioning of the catalyst the conversion to methane was measured at several temperatures and flow rates. The conversion was calculated from the CO/CH, or CO„/CH/ ratio in the product gas. The mass balance was checked by analysis of the feed.
3.6 H y d r o g e n a t i o n of C O ^
3.6.1 h y d r o g e n partial p r e s s u r e equal to 1 atm.
As has been pointed out in 3.4 the activity of the catalyst for CO. methanation becomes constant after a few hours of deactivation. Thus, no correction had to be made for loss of activity. Table 3-3 lists the ranges of temperature and CO. concentration in which the reaction rates were measured. The graph of conversion versus reciprocal space
Temperature Concentration Total pressure 200 215 230°C 0.22-2.38 vol % CO in H 1 atm.
Table 3-3 Experimental conditions for CO hydrogenation
velocity, W/F^o.. shows a definite curvature for large conversions (cf. figure 3-3). Therefore only points below C = 0.6 were used when calculating initial rates according to 3-2; figure 3-4 shows the initial rates as a function of the partial pressure of CO . The results indicate a change from first order dependency below 0.004 atm. to zero order dependency at partial pressures above 0.015 atm.; they can be
1 0 as n • ^ — * ^'^""^ 1 " 4 2 3 0 ' C x 2 1 5 ' C • 2 0 0 ' C 100 2 0 0 » - W / F C O 2 (gh/nnol. COa)
Figure 3-3 Example of measured conversions as a function of the reciprocal space v e l o c i t y (p -0.015 atm.) 0 010 0 0 0 5 -0 -01 PC02 ^otf") 0 0 2
Figure 3-4 I n i t i a l rates of CO, methanation (points measured,
l i n e s calculated from model I)
described with a Langmuir-type r a t e equation l i k e 3 - 5 , m being equal to 1. Transformation of t h i s equation g i v e s :
1/r = 1/kp + K /k (3-8)
To test the applicability of 3-8 a regression analysis was made for 1/r as a function of 1/p It appears that a linear relation gives the best description at the three temperatures (cf. figure 3-5).
100 200
••"Pcoa (atm-1)
400
Figure 3-5 Plot of 1/r
reciprocal partial pressure 1/p
From t h e s l o p e of t h e l i n e s t h e v a l u e s of k and Kj,^ can be c a l c u l a t e d (cf. t a b l e 3 - 4 ) . I t follows t h a t r a t e c o n s t a n t k i s s t r o n g l y
t e m p e r a t u r e - d e p e n d e n t but t h a t K^^ can be c o n s t a n t . Therefore t h e
T (°C) 200 215 230 (mol.g k ' . h - ' 2 . 0 4 . 4 7 . 7 . a t m - ' ) K " 2 (atm"') 8.4 * 10^ 9.4 * 10^ 6.7 * 10^
Table 3-4 Values for the reaction rate constant and the adsorption equilibrium constant for CO,
e q u a t i o n used to d e s c r i b e a l l the d a t a p o i n t s i s :
k . e x p ( - E / R T ) . p
(1+K .p ) CO2 co^
(3-9)
With a non-linear regression routine the best values of the parameters were then determined, minimizing the sum of squares of the deviations between the measured rates and the values calculated from 3-7.
More complicated models were also tested. The first extension of equation 3-9 was the introduction of temperature dependency of the adsorption constant T^coy'
k .exp(-E/RT)p II (1+K .exp(-AH/RT)p ) °° CO-CO 2 (3-10)
In a third model the value of the exponent of the denominator was allowed to vary:
III
k^, exp(-E/RT)p^
(l+K_^,exp(-AH/RT),p )'"
The use of this model can give some idea about the sensitivity towards m. Of course only integer values can have a physical meaning,
The results of the regression calculations on the above three models are given in table 3-5, Since the differences in the variances are not significant it is concluded -from a statistical point of view that it is impossible to say that one of the models describes the data best, Therefore model III can be discarded because apparently a variable value for m does not improve the regression significantly and, more-over, the value found is close to unity.
k. ^ \ ^ model ^-^^ parameter\^^ k E K K AH m sum of squares of residuals variance about regression I 1.71 * 26.1 7.02 * -I 2.8 * 1.6 * lo'^ 10^ 10-^ 10-' II 3.96 * 10'° 22.3 -8.58 -4.37 1 2.8 • 10-^ 1.7 • IQ-' III 9.58 .10'° 23.5 -18.1 -3.10 1.11 2.6 » IQ-^ 1.7 * IQ-' Dimensions mol C0..h .g .atm. kcal.mol atm. atm. kcal.mol
-Table 3-5 Results of regression on reaction rates for CO
The initial rates were calculated using the maximum conversion level of 0,6, which can cause low estimates of some reaction rates, especially for the measurements at 230 C, In order to eliminate these errors another regression analysis was made on the measured conversion points for the analytically integrated models I and II, The minimum was sought of the sum of squares of the differences between calculated and measured conversions. The results of these calculations are given in table 3-6. From these calculations it follows that the difference
i\^_^ model
^^\^
p a r a m e t e ? \ ^ k E K AH sum of squares of residuals variance about regression I 1.36 * 25.3 1.27 * -1.07 * 1.56 * io'2 10^ 10-' 10-3 II 7.87 » lo'* 31.6_
2.51 * 10* 7.45 1.04 * IQ-' 1.53 . IQ-^ Dimensions mol CO^.h-'.g-' kcal.mol-' atm.-'-atm.-' kcal.mol .atm.-'Table 3-6 Results of regression on CO. conversion data
2 2
between s, and s is again not significant, although model II has the smallest variance. Model I is preferred because of its physical simplicity. Since regression on measured conversions is more realistic than regression on initial rates, the equation chosen as the best description of the kinetics contains the parameters found by the
former method;
1.36*10'^ exp (-25.3/RT)p
(1 + 1270 p )
mol.h .g (3-12)
The calculated rates (curves) are shown in figure 3-4; the points represent measured rates,
Finally it was tested whether the values of the apparent activation energy, Ea, calculated from the models agree with those found from the measured rates. The apparent activation energy is defined (58) as:
3 In (r(p)] ^a (P>
3 1/T
When this operation is applied to equation 3-11 a relation between the apparent activation energy and the surface coverage is found:
K ,exp(-AH/RT)p E = E
-a .m,AH = E - m.e .AH (3-14)
1+K .exp(-AH/RT)p
For model I, which can be interpreted as model III with AH equal to zero and m equal to 1, E must be independent of coverage and there-fore independent of temperature and pressure. The apparent activation energy was calculated from the measurements for one value of the partial pressure of carbon dioxide by finding the values of A and E that minimize:
.1^ rj(p)-A,exp(-Ea/RTj) (3-15)
Since only three points are used for each calculation a high accuracy cannot be expected. The results of these calculations are shown in figure 3-6 along with the lines obtained from models I and II. It follows that the activation energy does not depend very strongly, if at all, on the experimental conditions.
28 2 5 -22
-- / •
/ •
•-—
•
•
1 • ^ I ^ I • 0 01 0 0 2Figure 3-6 Apparent activation energy,Ea as a function of p^oo (points calculated from measurements, lines calculated from models I and II)
3.6.2 I n f l u e n c e of the hydrogen partial p r e s s u r e
To study the influence of the hydrogen partial pressure measurements were carried out using feeds diluted with helium. Table 3-7 gives the parameter space in which the initial rate measurements were done. The total pressure was always 1 atm.
Temperature Concentration Hydrogen partial pressure
200 215 230°C
0,2-2.38 vol % CO2 in H2/He 0.5 0.25 0.1 0.05 atm.
Table 3-7 Experimental conditions
The shape of the plots of the conversion, E,, versus the reciprocal space velocity W/F^.^., was similar to those found in 3.6.1 (cf. figure 3-3). As an example the initial rate of CO2 hydrogenation as a function of the partial pressure of carbon dioxide is given in figure 3-7 for pjj =0.1 atm. for comparison, the broken line is added, which represents the
c^ 0 u 0 t u a £ ^-CM 0 U 0 010 -•005 0 0 0 5 0010 - ^002 * ° * ' " ' 0 015 0 0 2 0 0 0 2 5 Figure 3-7 I n i t i a l r a t e s of C02methanation for pjj, = 0. 1 atm. ( p o i n t s measured, l i n e s c a l c u l a t e d from equation 3-12 for P y , ' ! atm)
initial rate for pu = 1 atm. calculated from equation 3-12.
It appears that the shape of the curve of r^-j, as a function of
Pco9 does not change when the hydrogen partial pressure is
lowered from about 1 to 0.1 atm: a similar change of the
apparent reaction order, from first to zero, with increasing
c?
0 010 C7t Jc CM 8 0 0 0 5.
1 0 Ar.
t
{
3 t O j " 0.002 atm • 200'C ^ — • — • X 215 -C ^ . j - - ' ' * ^ A * 230 -C x _ X-* ^
1 1 0 5 1 0-,
O.s
0 010 0 006 0 < PcOj = 0 005 atm i^,.-- * * • 200 •€ y ^ X 215 'C J A 230 -C X ^ , - ' ' 1J--^
1 1 3 0 5 1 0 ^^m- nH<-i fntm)Figure 3-8 Initial rates of CO, methanation as a function of p„
4>oints measured,lines calculated from model I; p^g, " 0.002 atm.)
Figure 3-9 Initial rates of CO, methanation as a function of pjj (points measured,lines calculated
from model I; p^o, = 0.005 atm.)
<5',
E
I' O O 0 005 / ^f
r
A ^ ^x--• PcOg A 1 = 0 0 2 a t m A • 2 0 0 ' C X 2 1 5 - C A 2 3 0 • € x 1 1 0 5 • pH2 <atm)Figure 3-10 Initial rates of CO^ methanation as a function of pjj (points measured,lines calculated from model I; p^,;, = 0.02 atm.)
partial pressure is found. However, the hydrogen partial pressure does have an influence on the rate of CO. hydrogenation; this can be seen best in plots of r^Q versus pjj at constant Pcoo' Figures 3-8 to 3-10 show such curves for three different values of the carbon dioxide partial pressure. These data are consistent with the following form of the dependency of the rate on the hydrogen partial pressure:
r V ^ = e„ (3-16) '^°2 1 + K n^ "
^ '
S-\
Dissociative adsorption of H. on Ni is assumed here (69). The simplest equation describing all the measurements can be derived from 3-9 and 3-16:
k .exp (-E/RT).p .p^
I r = . — (3-17)
(' ^^co2-Pco2>(' '^-4^^
This equation, in which the adsorption equilibrium constants are taken to be independent of the temperature, was fitted to the data points, minimizing the sum of squares of the deviations between the measured rates and the rates calculated with equation 3-17.
The adsorption equilibrium constant for CO. was found to be constant in the temperature range investigated (cf. 3.6.1). However, the question remains whether the adsorption equilibrium
constant of hydrogen depends on the temperature; to answer it a more complicated model was also tested:
k„.exp(-E/RT).p p j
II r = r (3-18) ( ' ^ ^ o ^ - P c o ^ ) ^ ' +K„^.exp(-AH^/RT).p^^)
Several authors state (51 , 60) that carbon dioxide adsorbs dissociatively on nickel. If this is true, the power of the CO. partial pressure should be 0.5. To check this supposition a third
model was tested:
k^.exp(-E/RT)
^J.,J
III r = 1
^^—r
(3-19)
( ' ^ '^co^-PcoJX' . K ^ . p , J )
The results of non-linear regression calculations with the above three models are given in table 3-8.
The data of table 3-8 show that the description of the measurements does not improve when introducing the temperature
dependency in the adsorption equilibrium constant for hydrogen. Since models I and III describe the data about equally well from a
statistical point of view model I is selected because of its physical
simplicity ^ ^•\^ model ^"^^^ paramete^\^^
K
E '^°2 •Si sum of squares of residuals variance about 1 regression I 8.2 • l o " 2.2 * 10* 3.4 * 10^ 4.9 -2.1 • IQ-^ 2.7 * lO"' II 2.7 • 1.9 • 1.5 * 0.55 2.1 * 2.1 » 2.7 • lo'" 10* 10* 103 10-5 10-^ III 4.6 • lo' 2.1 * 10* 4.7 -2.1 . 10-5 2.7 * lO"' Dimensions mol C0,.h .g .atm. -1 kcal.mol atm. atm.-' atm. kcal.molTable 3-8 Results of regression on reaction rates at p„ < 1 atm. "2
3.7 Hydrogenation of CO
3.7.1 Hydrogen partial pressure equal to 1 atm.
The r a n g e s of c o n c e n t r a t i o n s and t e m p e r a t u r e s i n which t h e i n i t i a l r a t e s of carbon monoxide h y d r o g e n a t i o n were determined a r e g i v e n i n t a b l e 3 - 9 . Temperature Concentration Total pressure 170 180 190 200 210°C 0.22-2,38 vol % CO in H^ 1 atm,
Table 3-9 Experimental conditions for CO hydrogenation
The c o n v e r s i o n , E,, was measured a s a f u n c t i o n of t h e r e c i p r o c a l space v e l o c i t y a t 17 d i f f e r e n t c o n c e n t r a t i o n s w i t h i n the r e g i o n l i s t e d above. In f i g u r e 3-11 t h e r e s u l t s for 0.65 v o l % CO i n H a r e g i v e n as an example. The p l o t s a r e s t r a i g h t up t o c o n v e r s i o n s of 0 . 9 5 . Such e x c e l l e n t l i n e a r i t y was found for a l l c o n c e n t r a t i o n s
W/Fco (Q h/mol CO) — Pco (at"i)
Figure 3-11 Example of measured ' Figure 3-12 I n i t i a l r a t e s of CO conversions as a function of the methanation(points measured, l i n e s r e c i p r o c a l space v e l o c i t y (p - c a l c u l a t e d from model I )
which suggest zero order kinetics. If however, the slopes of the lines are plotted as a function of the partial pressure of carbon monoxide it appears that the rate varies with the partial pressure of CO. The presence of a maximum at CO partial pressures between 0.002 and 0.005 atm. is quite evident (cf. figure 3-12). Regression of 1/r as a function of 1/p does not give satisfactory results because a polynomial of at least the third degree is needed to describe the measured rates.
The appearance of a maximum rate is rather intriguing and the question arises whether equation 3-5 can indeed describe the presence of this extremum. There are two conditions that must be fulfilled:
3r
3P.
0 for (3-20)
Differentiation of equation 3-5 leads to:
3r 3P. (1+K .p )" CO '^co m.K .p CO CO 1-1+K .p CO CO (3-21)
The second condition of 3-20 is invariably satisfied since m is always positive. The first condition produces a relation for p
(3-22) max (m-1).K
It appears from 3-22 that a maximum occurs only when m ^ 1. This is in line with the fact that neither the rate data nor the rate equation for CO. hydrogenation, where 1.0 was found to be the right value for m, show a maximum. Apart from one, two is an obvious choice for m, which means that a dual-site step should control the reaction rate:
k.p^
" (1-K .p )2 CO "^co
The relation can be written as:
(k)
i
(k)J •
(3-24)
Regression analysis of the left hand side as a function of p^^ showed that, for three of the five temperatures, a first degree polynominal gives the best fit and that the other two are described quite satisfactorily by a first degree polynominal. The values for k and K can be calculated from the coefficients. K can also be calculated
C O
from the position of the maximum rate with 3-22, although this procedure gives less accurate results. Table 3-10 lists the results of these
calculations. It is concluded that the rates can be described by CO T o
c
170 180 190 200 210from linear regression
k K CO
-1 -1 -1 -1 (mol.g '.h .atm ) (atm. ')
0.94 405 1.89 365 2.92 315 4.66 250 4.32 165
from maximum rate
K p CO CO _] "ax (atm. ) (atm.) 330 0.003 330 0.003 500 0.002 250 0.004 160 0.006
Table 3-10 Values of reaction rate constant and adsorption equilibrium constant of CO
equation 3-23 and that both parameters are strongly temperature-dependent. This points to a model l i k e :
k^.exp(-E/RT).p_
(l+K„.exp(-AH/RT).p^^)2
Two adjacent models were also tested: k^.exp(-E/RT),p_ II and; III (1+K .p )' ^ CO CO k^.exp(-E/RT).p^^ (l+K„.exp(-AH/RT).p_)" (3-26) (3-27)
The results of the regression calculations are shown in table 3-11, in which the models are placed in the order of increasing complexity. The
'"^v^ model parametei^v^^ k E K K AH m sum of squares of residuals variance about regression 11 2.66 • 25.6 2.28 * -2 8.1 * 1.1 * .o'2 10^ 10-^ 10-' I 2.09 * 10^ 10.1 -4.56 * IQ-* -12.4 2 5.8 * 10-* 7.7 * 10"^ III 8.26 * 10* 9.17 -2.31 * lO"* -13.2 1,93 5.8 • lo"* 7.8 * 10-^ Dimensions
mol CO.h .g .atm. kcal.mol
atm. atm.-' kcal.mol
-Table 3-11 Results of regression on reaction rates for CO
difference in the variances of model II and model I being significant at the 90 % level, model II is excluded as it is too simple. Since the difference in variances between model I and model III is not
significant in a statistical sense, model I is selected as the best model on physical grounds. The fact that the value of the power in model III is very close to 2 supports this choice. The predicted rates calculated from this model are shown as lines in figure 3-12.
The c a l c u l a t e d p o s i t i o n of pVn i s i n d i c a t e d by t h e broken l i n e . The a p p a r e n t a c t i v a t i o n e n e r g y was c a l c u l a t e d b o t h from t h e models and from t h e e x p e r i m e n t a l d a t a w i t h e q u a t i o n s 3-14 and 3 - 1 5 , r e s p e c t i v e l y . The r e s u l t s ( f i g u r e 3-13) show t h a t Ea v a r i e s q u i t e s t r o n g l y w i t h p . Model I d e s c r i b e s t h i s v a r i a t i o n q u i t e w e l l . 30 25 ?0
~
• /
<
•
r
•
^
•
•
1•
•
• ^^^
1•
0 010 Pco tatm' 0 0 2 0Figure 3-13 Apparent a c t i v a t i o n energy, Ea, as a function of p ( p o i n t s c a l c u l a t e d from measurements, l i n e s c a l c u l a t e d from model I )
3.7.2 Influence of the hydrogen partial pressure
The influence of hydrogen partial pressures below 1 atm. was studied by making initial rate measurements in the parameter space of table 3-12. The total pressure was 1 atm. in all cases examined
Temperature Concentration Hydrogen partial pressure 180 190 200 210°C 0.02-2.1 vol % CO in H^/He 0.33 0.66 atm.
The excellent linearity of the C versus W/F plots was again observed. The measured initial reaction rates are given in figures 3-14 and 3-15 as a function of p for the different hydrogen
CO
partial pressures. When comparing these data with the results of Pjj = 1 atm. (cf. figure 3-12) it is at once apparent that the maximum in the reaction rate shifts to the left with decreasing hydrogen partial pressure. However, the rate of reaction at the maximum does not change much. This is discussed further in 3.10.
O O0O5 0010 0O15 0 0 2 0 0 0 2 5 o 0 0 0 5 0010 0 0 1 5 0 0 2 0 0 025 ^ — P ( ; Q ( a t m ) m^-~ P c Q ( a t m )
Figure 3-15 I n i t i a l rates of CO methanation. pg =0.33 atm.(points measured, lines calculated from model I)
Vhen d e r i v i n g a r a t e e q u a t i o n t o d e s c r i b e t h e measurements i t was assumed t h a t t h e s u r f a c e r e a c t i o n between adsorbed hydrogen and c a r b o n monoxide d e t e r m i n e s t h e r a t e . Again hydrogen was supposed to a d s o r b d i s s o c i a t i v e l y ; t h e f r a c t i o n of t h e s u r f a c e covered with hydrogen under c o n d i t i o n s of c o m p e t i t i v e a d s o r p t i o n of CO and H„ can be w r i t t e n a s (61):
Figure 3-14 Initial rates of CO methanation. pjj =0.66 atm. (points measured, lines calculated from model I)
For carbon monoxide one finds: K .p
e = £2_1£2 (3-29)
CO ( 1 + K„.p„^ + K .p ) 11 ^H- CO '^coIf only adsorbed species are involved in the rate determining step, the general rate expression is:
r = k'. e° . e" (3-30) H CO
in which m and n are most probably integers. Substitution of equations 3-28 and 3-29 into 3-30 results in:
, m/2 n k.p„ .p •^H '^co r = f (3-31) ( 1 + K .p + K „ .p„^)^""") CO "^co H "^H.
On the basis of the experimental evidence some values of m and n are impossible. The value of m cannot be zero because in that case an inverse relationship between the hydrogen partial pressure and the reaction rate should exist, which is not observed. Similarly, if m = 1 and n = 0, equation 3-31 does not yield the observed maximum. It is also possible to derive rate equations based on an Eley-Rideal mechanism, in which the rate-determining step is assumed to be a reaction between an adsorbed species and another species in the gas phase. However, it is still necessary to postulate competitive adsorption to explain the existence of maxima in the derived curves, and the reaction must involve a gas-phase species as well. The equation developed for Langmuir-Hinshelwood kinetics (3-31) and the rate equation for the two possible Eley-Rideal mechanisms differ only in the relationships among the exponents, as has been shown by
Levinson (62).
It should thus be possible to deduce the mechanism from the form of the kinetics. However, such conclusions must be regarded as inferences only because the Langmuir equation greatly oversimplifies the adsorption behaviour of most gases.
Starting from kinetic equation 3-25, which gives the best fit on the data for pjj = 1 atm. (cf .3.7 . 1), an obvious choice for m and n in equation 3-31 is m = 1 and n = 1. This points to:
1 k^.exp (-E/RT) p^^.pjj (3-32)
L2
(1 + K^ .exp(-AH/RT) p^^ + K^^ .p^^^) C O 2A somewhat more complicated model tested contains a temperature-dependent adsorption equilibrium constant for hydrogen:
k .exp (-E/RT) p .p ' °o CO H , II ( 1 + K .exp(-AH/RT) p + K .exp(-AH/RT)p„^) <» C O "f, H , CO H /
K2
(3-33)The exponents were allowed to vary in the third model:
k^.exp (-E/RT) P^,.P^^' III (1 + K^ .exp(-AH/RT) p^^ + K^-P^') CO 2 (m+n) (3-34)
The results of non-linear regression calculations on the reaction rates for pjj = 1 , 0.66 and 0.33 atm. are shown in table 3-13.
0 0 0 8 " 0 0 0 6 O 0 0 0 4 U 0 0 0 2 0
^
/
t
r
h
h
" ^ ^ - e ^ A^ T ^
P H 2 X •"•v A, ^
_ A ^ » l a t m o A*
A O A ^ - . . . ^ A - * 4•
V*
0 o A__»_^_
170 "C 160'C 190'C 200"C 210"C ^ o A A J 1 _ _ _ •^ A • A»
A O 00O5 0 010 0015 0 020 0025 ^ — Pj;o(atm)Figure 3-16 Initial rates of CO methanation, Pj^ = 1 atm. (points measured, lines calculated from model I)
The differences between the variances for the three models are not significant and it is impossible to distinguish between them from a statistical point of view. Therefore the simplest model, I, is selected. The description of the measured rates with this model can be read from figures 3-14 and 3-15 for pjj = 0 . 6 6 and 0.33 respectively, and from figure 3-16 for pjj = 1 atm. Comparison with figure 3-12 shows that the measurements for pjj. = 1 atm. are
described satisfactorily by the model containing terms for the dependency on the hydrogen partial pressure, equation 3-32.
^•v,^^ model ^ ~ ~ > . ^ , ^ parameter^"-.^^^ k E
Ho
AH CO •Si•s
^"H m+n sum of squares of residuals variance about regression I 2.4 • 10® 10.1 8.0 * lO"^ -14.2 27.0 -2 8.1 * 10-^ 1.1 . 10-7 II 8.9 * 7.2 1.2 * -12.7 0.2 4.4 2 5.8 * 7.7 * 10^ 10-2 10-^ 10-® III 2.0 • 10® 9.7 1.6 * 10-2 -13.2 -1.8 5.8 . 10-^ 7.8 • IQ-® Dimensions mol CO/(h.g.atm.) kcal.mol atm. kcal.mol atm.-' atm.-' kcal.mol-Table 3-13 Results of regression on reaction rates at pu < 1 atm.
3.8 Hydrogenation of mixtures of CO and COj,
The feed to an industrial methanator always contains carbon oxides as well as hydrogen; typical concentrations are 0.1 vol % CO and 0.3 vol % CO.. Some exploratory experiments were carried out at 200 C
to study the rate of hydrogenation in mixtures. Three CO/CO. ratios were used, viz. 0.22, 0.50 and 1.90. The total concentration varied
from 0.67 to 3 . 7 5 v o l %. I t soon became c l e a r t h a t t h e m e t h a n a t i o n of c a r b o n dioxide does n o t s t a r t u n t i l a v e r y high c o n v e r s i o n of CO i s a t t a i n e d . An example of t h e measured c o n v e r s i o n curves i s given i n f i g u r e 3-17. O f t e n c a s e s were encountered where, a t c o n c e n t r a t i o n s of b u t 200 ppm., t h e r a t e of m e t h a n a t i o n of CO, was not y e t m e a s u r e a b l e .
1 O 0 5 UJI 0 O 100 200 — W/F(co.C02) (g h/mol (C0tC02))
Figure 3-17 Example of measured conversions of CO and CO, in a mixture as a function of the r e c i p r o c a l space v e l o c i t y (p • 0.0069 atm, p = 0.0305 atm)
C O ,
Thus, one may conclude that the first part of the catalyst bed almost exclusively converts carbon monoxide to methane and that only the second part of the bed causes hydrogenation of carbon dioxide. If this is true, the initial rates for both reactions should be equal to the rates measured with single feeds. The rate for the hydrogenation of CO can be calculated as the quotient 5 /(W/F ) . For carbon dioxide
CO CO
a corrected space velocity must be used, because a fraction of the bed is not active for this reaction. The weight of this part of the bed should be substracted from the total weight of catalyst to find the corrected space velocity. The experiments were not accurate enough to permit exact calculation of the rate of CO, hydrogenation. From table 3-14 it appears that the values from the mixed feed correspond reasonably well with those of a single feed. The rates of the separate feeds were calculated from the rate equations.
