Modeling and analysis of filtration combustion for synthesis of transition metal nitrides

0009-2509/90 $3 .00+0 .00 J 1990 Pergamon Press plc

Chemical Engineering Science, Vol . 45, No . 8, pp . 2 49 9-2504, 1990 . Printed in Great Britain .

Modeling and Analysis of Filtration Combustion for Synthesis of Transition Metal Nitrides

Hemant W. Dandekar, Christos C. Agrafiotis, Jan A. Puszynski and Vladimir Hlavacek

Laboratory for Ceramic and Reaction Engineering Dept. of Chemical Engineering, SUNY at Buffalo Buffalo, New York 14260 USA

ABSTRACT Refractory nitrides can be synthesized from their elements in the combustion regime . This process is self sustaining given the highly exothermic nature of synthesis reactions . Non-isothermal measurements of combustion parameters were used to calculate the activation energy for the reaction between tantalum and nitrogen . A two dimensional pseudo-homogenous, unsteady state model of the process was solved numerically, employing a twodimensional moving adaptive mesh . Reasonable agreement between experimental observations and numerical predictions was reached . KEYWORDS Filtration Combustion, Modeling, Kinetics, Simulation, Ceramics . INTRODUCTION Self-propagating high-temperature synthesis (SHS) is a unique method for the preparation of advanced ceramic materials and has recently received considerable attention as an alternative to conventional ceramic processing technology . Some of the synthesis reactions for the production of ceramic materials from their elements, are characterized by very high heats of reaction and high activation energies . These thermal effects can be utilized to run the reactions in a self - sustaining mode . Once ignited, a sharp combustion front is formed, which propagates through the system, separating un-reacted material from products . Self-sustaining mode has been achieved in gas-solid, solid-solid and solid-liquid systems . In this work, we will concentrate on solid-gas reactions (transition metals- nitrogen) for the synthesis of transition metal nitrides . The metal reactant is often in the form of loosely packed powder inside a container exposed to a gaseous environment. The resident gas in the pores is quickly consumed by the chemical reaction . This creates a pressure gradient between the surrounding atmosphere and the combustion front . Fresh gas is filtered through the packed bed , due to the pressure gradient, sustaining the combustion front . The process is known as filtration combustion . Various configurations have been proposed in the past, leading to co- current, counter-current, or cross-current flow of gas relative to the direction of the propagation of the combustion front . These configurations are shown in Fig . 1(Kumar,1988) . The cross-flow configuration provides for shorter filtration path for the gaseous reactant, thus enabling a lower pressure of operation compared to the coor counter -current configurations . This makes it suitable for scale-up to industrial scale . Experimental studies using cold pressed metal specimens in the form of pellets were presented by Merzhanov and co-workers (1972,1973) . Experimental studies in counter-flow configuration have been presented by Kumar (1988), and a a theoretical study can be found in Dandekar et al (1990) . These were exploratory studies and helped define and understand the various regimes of operation. The present work consists of a detailed experimental investigation of the effects of various physico-chemical parameters on the combustion characteristics, and an attempt to evaluate the kinetics of nitridation of transition metals based on combustion measurements . These kinetics were utilized in simulating of the filtration combustion process using a two-dimensional pseudo-homogeneous model . The predictions from the simulations were then compared with experimental observations to test the accuracy of the model .

EXPERIMENTS Combustion reactions between transition metals and gaseous nitrogen occur very fast and generate very high temperatures (2000 - 3500 °C ) . These conditions make the traditional approach of isothermal kinetic measurements unsuitable . However, the macrokinetic parameters of combustion reactions 2499



2500

El

HEMANT W . DANDEKAR et al.

can be extracted from experimental measurements of the combustion parameters, namely velocity of propagation, combustion temperature, and degree of conversion (Merzhanov, 1973) . In this respect, non - isothermal measurements have the unique advantage of providing information about the kinetics of fast reactions at elevated temperatures and pressures, information which is very difficult to obtain in traditional ways.

Gm

Gas

Fig 1 : Various configurations for filtration combustion . In the filtration combustion experiments three processes can be rate -controlling : i) Filtration of the reactant gas through the porous solid ii) Diffusion of the gas inside the individual metal particles iii) Intrinsic chemical reaction between the solid and the gas . The latter two can be combined in the form of a phenomenological rate expression

ry = ry (T, 77, P, dP)

(1)

The conversion of the solid reactant ?7 and the gas pressure P are related to the concentrations of the metal and the gaseous reactant, respectively. The dependence on temperature is usually an 'Arrhenius - type' one . Experiments at various combustion temperatures can be performed by changing the solid phase dilution . I

4 I ---1 - I i System _ Tantalus'. - Nitrogen

0

7 0 .75 0 0 .50 i W 0 .25

(b)

P. size . 200 mtcrona P . size 84 microns B .5 microns P . size

0 .00 0

Fig. 2 : SEM Micrographs of tantalum a) 20O p b) 8 .5 p

1 I I 40 50 60 10 20 30 Pressure (atm)

Fig 3. : Effect of particle size and pressure on velocity

'70

80

El

2 50 1

Modeling and analysis of filtration combustion

The effect of the particle size depends on the rate - controlling step on the particle level (intrinsic chemical reaction, diffusion of the gaseous reactant through the layer of solid product) . Experiments with various metal particle sizes will determine the form of this dependence and suggest the rate - controlling step . Given the high temperatures generated during combustion reactions, melting of either the reactant or the product might occur, further complicating the analysis . In order to simplify matters, the system Ta - N2 was chosen for study, due to the fact that the reaction between tantalum and nitrogen is known to proceed without the formation of any liquid phase . Metal particles of average sizes of 200, 85 and 8 .5 microns were used . SEM photographs of coarse (200 ,urn) and fine (8 .5 pm) particles (Fig . 2) show that the former are highly porous as opposed to the latter . A plot of the velocity of propagation as a function of particle size (Fig . 3) indicates that the velocity is not affected by neither the size nor the porosity of the particles .

1 .75

-8 System

Tantalum

-

Nitrogen

1 .50 -10 1-25 Ip.

1 .00 0 .75 0 .50 -16 0 .25 0 .00 0

20

40 60 Pressure (atrn)

Fig . 4: Effect of dilution, pressure on front velocity

so

-18 3 .5

1

4 .0

1

4 .5 104/TS

1

5 .0

5 .5

Fig. 5: Plot for evaluation of activation energy

The effects of pressure and solid phase dilution on the velocity of propagation are shown in Fig . 4, for particles of 85 microns in diameter . Particles of diameters 200 and 8 .5 microns also exhibited the same trend . At low pressures, the velocity increases almost linearly with increasing pressure, but at higher pressures, it becomes independent of the gas pressure, for all the values of solid phase dilution used . The transition from a pressure- dependent to a pressure-independent speed of propagation (the latter case being typical for solid-solid systems) suggests that at high pressures, filtration of the gas is not a limiting factor anymore . Therefore, experiments in this region of high pressures, can be used for the evaluation of the macrokinetic parameters . Experimental results when plotted in the form of In{( T )2F(7,)} vs . should generate a straight line from which the activation energy can be calculated . Details of this T, derivation can be found in Merzhanov (1977) . This kind of plot is shown in Fig . 5 . The 'grain' model (Szekely et al, 1976) was applied for the description of the reaction rate on the particle level, in order to explain the independence of the combustion parameters from the particle size . Thus, results from coarse and fine particles were plotted together. From this plot, the apparent activation energy of this system was calculated as 32,400 cal/mol . MODELING AND SIMULATION Due to the extreme exothermicity of these synthesis reactions, the system manifests complex process dynamics, which are difficult to predict a priori . Detailed modeling and numerical simulations are necessary to understand the various front propagation characteristics and to predict the effect of various operating parameters (bed height, pressure, dilution etc .) on the final conversion of reactants to products . The cross-flow configuration is shown in Fig . 1d . The model for the cross-flow configuration consists of a set of parabolic partial differential equations representing the heat, mass and momentum balance for the filtration combustion process . The model equations are simplified on the basis of the following assumptions:



El

HEMANT W . DANDEKAR et at

2502

• The model is pseudo-homogenous, and two dimensional (no variation in the direction of width) . • Physical properties of the solid (specific heat and density) and gas (specific heat) are assumed constant. • No dissociation of formed products occurs . • Gas flow is governed by Darcy's Law. • Porosity variation due to volumetric expansion is considered . • Bed thermal conductivity is taken as a linear function of porosity . • The permeability dependence on porosity is given by the Kozeny Carman equation . Based on these assumptions the dimensionless governing equations are : Mass balance on the gas phase a«Ep9 a(aEpg vs ) ae = a; . T-

-

a(ae 9 vv ) ay

_ 7 _1

(2)

R,

Heat balance on the system

8(ad 1Ep' 9 + 1 - 77 + d2 1)0 _ 8 A` 80 8 80 ae + at as as ay ay 8(ab1EP9 i5 9) 8(a61EPgvy©) + [( 1 + 61 - b2)(a71 - + 7- 2 1 RA a~ ay 1

(3)

Equation of state _ P9 (1 + 00) (1+QB,)

(4)

Darcy's law Or U,,

=

-W-

v- y = -

497r

(5) Wa y

Reaction rate expression 8

1Rs u =7-)r t 1 + pe A number of dimensionless parameters appear after dimensionalization . They are : 8n = 7-1fi7)exP(

(6)

4

a

cop2o

PPRo - RT. l3 b1 =

IfJ PoP R.CR AR _ CRRT2

W =

=

Ea

PCR Cg

(1 + u)CP -2 =

CR

The boundary conditions for the system involve impermeable boundaries at all sides except the top which is open to the gaseous atmosphere . Convective heat losses are assumed from all sides, and radiation heat losses are accounted for only at the top . For a certain time the boundary at left is heated to the adiabatic temperature, to ignite the system, after which normal heat losses are assumed from this boundary . The parameters j3 and y represent the dimensionless activation energy and heat of reaction respectively. Parameter a represents the fraction of stoichiometric quantity of gas initially present in the pores . The parameter w is the dimensionless permeability coefficient representing the ratio of heating zone length and the filtration zone length . The model partial differential equations are coupled, highly non-linear and have solutions exhibiting moving steep spatial gradients in time . Use of a two-dimensional moving adaptive grid is made, as an equi-spaced grid would require a phenomenally large number of points for resolution of these steep gradients . Separate adaption was performed for x and y directions every ten time steps . Details are available elsewhere (Degreve, 1987) . The space derivatives are approximated using finite differences and fully implicit time integration scheme is used for time integration . The resulting matrix is solved iteratively at each step by successive over relaxation . Typically, 60-80 minutes of CPU time was required on a CRAY X-MP/48 .

Modeling and analysis of filtration combustion

El

Table I Dilution Ta-TaN Wt % 100-0 80-0

2 50 3

Comparison of Experimental and Predicted Velocities T. K 2990 2451

-y

Vj (experiment)

Vj (simulation)

0.2283 0.1534

103 x m/s 13.75 7 .0

10, x m/s 11 .521 6 .653

13

0 .1827 0.1498

The kinetic parameters obtained from experimental measurements were used in a series of numerical simulations for the tantalum-nitrogen system . The activation energy used was 32,400 cal/mole, and the heat of reaction is 59,950 cal/mole . The values of -y ranged from 0 .1534 to 0.2283 and the ,8 values ranged from 0 .1498 to 0 .1827 . Typical profiles are shown in Fig. 6. It can be seen that the combustion front initially travels along the upper layers of the bed . As the front travels along the length of the bed, the layers along the depth progressively become involved in the reaction . This form of afterburning was also observed experimentally. Table I lists the velocity of front propagation as observed experimentally and as predicted by the numerical simulations .

CONCLUSIONS Use of combustion theory has made it possible to calculate kinetic parameters from non-isothermal measurements . Experimental measurements under high pressures helped remove pressure dependence of the reaction rate expression, thereby simplifying the calculation procedure for determining activation energy of the reaction . A full simulation of a two dimensional pseudo-homogenous model was performed . Use of two dimensional adaptive meshes, and availability of fast vector computers made it possible for the simulation to be performed in a realistic time frame . As can be seen in Table I, good order of magnitude estimates of the velocity are obtained . We believe that the discrepancies between the experimental observations and theoretical predictions can be attributed to the following factors : a two-step mechanism might be involved (2Ta + 1/2N2 -* Ta 2 N + 1/2N2 --+ 2TaN) . This implies only a partial conversion at the combustion front . The simulation on the other hand requires full conversion at the front, thus predicting a lower combustion front velocity. Furthermore, the accuracy of the model can be enhanced by using experimental measurements of transport properties, rather than those predicted by correlations which are generally valid at low temperatures . Efforts are currently underway to take these factors into account in the hope of achieving better agreement between experiments and simulations .

(a) e E

0 i 0

a

Fig. 6: Perspective plots of system variables at time t = 11 .0 a) Temperature b) Conversion . c) Density d) Pressure .



2504

HEMANT W . DANDEKAR

et al.

El

ACKNOWLEDGEMENTS This work was supported in part by NSF grant CTS 89-15787 . The computations were performed using a CRAY XMP/48 at the National Center for Supercomputing Applications through NSF grant CBT 89-0018N .

LIST OF SYMBOLS Ps = P2/Pr-

PR PP

0 b1

62 E = E/£ 71 =

o

( Pixo - Pn)/Pfto

7

w 7r

= P/ Po

0 = (T - T<)Ea /RT. 2 CU

Dimensionless density of gas Bulks density of Solid Reactant kg .m -3 Bulks density of Solid Product kg .m -3 Dimensionless activation energy Ratio of specific heat of gas to solid reactant Ratio of specific heat of product to reactant Dimensionless porosity Conversion of solid Dimensionless heat of reaction Dimensionless effective thermal conductivity of the bed Stochiometric coefficient Dimensionless permeability of the medium Dimensionless pressure Dimensionless temperature Specific Heat of the solid reactant -J .kg -1 .K -1 Diameter of particle in the solid phase m Activation Energy cal.grnole-1 Heat of Reaction J.kg -1 Permeability Coefficient of the Bed m 3 .kg - ' .s Universal Gas Constant 1.98ca1 .grnolc' .K -1 Combustion temperature K Adiabatic temperature of the reaction K Velocity of front Propagation m .s-1

REFERENCES • Dandekar H . W, J .A. Puszynski , J . Degreve and V. Hlavacek,(1990) .Reaction Front Propagation Characteristics in Exothermic Non-Catalytic Gas-Solid Systems,Chem . Eng. Comm . (in press) . • Degreve J., P. Dimitriou, J. A. Puszynski and V. Hlavacek, (1987) .Use of 2-D Adaptive mesh in Simulation of Combustion Front Phenomena, Cornput . in Chem . Engng., 11, 749-755 . • Kumar S .,(1988) .Self Propagating High Temperature Synthesis of Ceramic Materials, Ph .D dissertation, SUNY at Buffalo . • Merzhanov A . G., Borovinskaya I . P and Volodin Yu . E.,(1972) . The Burning Mechanism of Porous Metallic Samples in Nitrogen, Dokl. Akad. Nauk SSSR,206, 905-908 . • Merzhanov A. G., Filonenko A . K. and Borovinskaya I. P.(1973).New Phenomena in Combustion of Condensed Systems," Dokl. Akad . Nauk SSSR, 208, 892-894 . • Merzhanov A . G.(1973) . Non - isothermal Methods in Chemical Kinetics Fiz. Gor. Vzr.

9, 4-36 .

• Merzhanov A. G.(1977). New Elementary Combustion Models of the Second Kind Dokl. Nauk SSSR, 233, 1130-1133 .

Akad.

• Szekely J .,Evans J. W. and Sohn H . Y (1976) . Gas - solid Reactions Academic Press, New York .

NOTE Since data in the literature suggests that low operating pressures might cause relatively poor conversion levels, all experiments reported in this study were restricted to operating pressures above 3 atmospheres . Numerical simulations on the other hand have been carried out only for 55 atmospheres for comparison with experimental observations .