Propagation of reaction fronts in exothermic heterogeneous noncatalytic systems solid-solid and solid-gas

Chemical

P&ted

Science,

Engineering

Vol. 41, No. 4. pp. 877-882, 1986. @

in Great Britain.

PROPAGATION OF REACTION FRONTS IN EXOTHERMIC HETEROGENEOUS NONCATALYTIC SYSTEMS SOLID-SOLID AND

V.

Hlavacek,

J.

Puszynski*,

Department of State University Buffalo, New *Technical

J.

Degreve

and

S.

ooo9-2509186$3.00 + 0.00 1986. Pergamon PressLtd.

SOLID-GAS

Kumar

Chemical Engineering of New York at Buffalo York 14260, U.S.A.

University,

Wroclaw,

Poland

ABSTRACT Exothermic heterogeneous noncatalytic reactions of the type solid-solid and solid-gas can be efficiently used to produce new type of materials. The idea of the process is based on the selfpropagating reaction waves in the reactant mixture. Modeling of the process is suggested. comparison of experimentally observed phenomena with theoretical supercomputer calculation is presented. KEYWORDS Exothermic

noncatalytic

reaction;

synthesis

of

ceramic

materials;

supercomputer

calculation.

INTRODUCTION There exists an important class of heterogeneous noncatalytic reactions of the type solid-gas and solid-solid which are accompanied by a substantial generation of heat. The most important are oxidation of metals and nonmetallic compounds, direct reaction of nitrogen or hydrogen with certain metals, synthesis of carbides, borides, sulfides or sllicides of metals (from pure comporeduction of metallic oxIdes by carbon or aluminum, nents), synthesis of intermetallic compounds (e.g. Ni-Al), combustion of solid propellants and many others. In this paper, we will address ourselves to reactions occurring without gas phase formation. Many of these reactions are of major technological importance. Unique properties of various boron, carbm and nitrogen ceramics will lead to increased or new applications in the area of refractories, abrasives, E-M windows, anti reflection coatings, electronic devices, nuclear materials, bearings, military ceramics, heat engines and energy storage. The exothermic noncatalytic reaction can proceed through the reacting mixture in a uniform way and the concentration of the components at any instant is almost the same everywhere (kinetic or "sintering" regime). However, if the system was locally ignited by external means, a steep reaction front can propagate through the mixture. the latter phenomenon is closely Evidently, related to flame propagation in gaseous mixtures and is frequently referred to as the selfpropagating regime. Synthesis of borides and carbides of transition and rare earth metals can be performed both in sintering and self-propagating regimes. The synthesis in the sintering regime requires a substantial energy input, high reaction temperature and a long reaction time. On the other hand, the self-propagating synthesis calls only for a short range initial energy input. The reaction is self-sustaining owing to the high values of the activation energy and heat of reaction. MODEL An

assumption S(s)

or

between

and

that

+

S and S(s)

Following

FORMULATION is made

the

+

M(s)

+

gaseous A(g)

reaction

physical

that

+

a heterogeneous

reaction

occurs

between

two

solid

materials,

S and

M.

P(s) A P(s)

rate

can

assumptions

be

described

have

been

by

an

integer

power

kinetics.

made:

A heterogeneous mixture of solid powders S and M behaves as an isotropic homogeneous system. 1) The temperature dependence of the reaction rate constant can be expressed in the Arrhenius 2) form. 3) Heat conduction in the solid phase can be described in terms of the Fourier law. Mass diffusion of the solid reactants or products does not occur. 5) All physical properties 4) heat capacity, (density, effective thermal conductivity) are assumed constant. 6) The reaction

x77

V. HLAVACEK

878

is not accompanied by melting effects. play an important role. Heat loss from force. 8) The reactant M is in excess first order with respect to S.

et al.

G-l

7) The radiation effects inside the porous layer do not the system can be described by an effective linear driving so that the reaction process can be considered of the

Gas-solid noncatalytic reactions of the type S(s) + A(g) + P(s) can be handled in a similar way if diffusion effects are unimportant. This is satisfied for high pressure systems and thin layers of S. The gas-solid reaction will be studied in two configurations: a) flow system, b) filtration regime. (See Fig. la and lb.) In a flow system the gas flows over the powdered material, and the reaction is ignited at the reactor inlet. Initially the reaction front propagates in the same direction as the flowing gas. For a filtration regime arrangement, gas is filtered towards the reaction zone and initially the front propagates against gas flow direction. Filtration regime is important for synthesis of ceramic materials which can melt during the exothermic process. The governing partial differential equations of parabolic-hyperbolic type are described elsewherel. Because of high values of both heat of reaction and activation energy very steep reaction fronts may occur. Within the reaction front the solution varies rapidly over a vary thin region. The corrugated "boundary layers" on concentration and temperature profiles represent a very difficult numerical problem. High-order compact finite-difference scheme with automatic time step control was adopted. The calculations were performed on supercomputers Gray-1 (Los Alamos) and Cyber CDC 205 (Univ. Purdue). The results were processed by a color graphic package DI-3000. Typical

values

of

physical

chemical

parameters

are

reported

in

Table

1.

EXPERIMENTAL Experiments were performed in a vacuum chamber which was equipped with leadthroughs for thermocouples, vacuum gages, inert gas valve, electrodes and resistor holding assembly, sample supporting rod and exhaust valve. The thermocouple wires are connected to a microcomputer through an analog to digital convertor interface to record the temperature during ccxnbustion of the samples. The electrodes are attached to a transformer-rheostat combination to generate and control a high current. The experiments involved igniting ccmpact reactant pellets at one end with a high Axial temperatures in a sample current and monitoring the propagating fronts by a video assembly. The velocity of a constant pattern propagating wave was deterwere recorded by thermocouples. The velocity and temperature data are used to estimate mined by analyzing video recorded data. kinetic parameters. RESULTS

AND

Solid-solid

DISCUSSION Systems

Constant pattern profiles are traveling waves propagating through the system with constant velocity. For adiabatic conditions, Fig. 2 displays a system featuring constant pattern profiles. After one end of the cylindrical sample was brought to a sufficiently high temperature, There is a heating-up time the exothermic reaction generates enough heat to be self-sustaining. For associated with an insignificant degree of conversion of the solid reactants (cf. profile A). profiles are steeper; for low values higher values of the activation energy E, the concentration The ccmstant pattern profile regime can also exist for a wave degenerates. of E, the propagating With the increasing value of the external cooling parameters, both the velocity nonadiabatic case. of the front and the hot spot temperature decrease. For high values of the cooling parameter the but far enough from the external energy source an extinction reaction can still be ignited, process occurs. For supercritical conditions oscillatory fronts can be observed. A typical behavior in this region is shown in Fig. 3. The temperature can overshoot the adiabatic temperature and at these high temperatures the solid material is completely burned. This is the onset of the cooling cycle, the temperature drops well below the adiabatic temperature and the fresh unreacted material is slowly After the temperature of the fresh material reaches certain critical value, a new preheated. ignition process occurs and the temperature in the reaction front exceeds again the adiabatic the profiles become very steep. temperature, etc. With increasing value of the activation energy, For low values of an extinction of the oscillatory regime may occur. In the nonadiabatic case, oscillations show similar behavior to that for the adiabatic situation. the heat loss parameter, the maximum temperature in the reaction front can be signifor the nonadiabatic case, However, This can be easily explained since there is a lower conversion in the preheating ficantly higher. zone so that at the moment of ignition more solid material can react in the very narrow reaction Oscillation and extinction phenomena are highly undesirable in practical applications front. because of nonuniform product properties resulting from melting effects and/or thermal stresses. the solid mixture should be preheated and ignited. To avoid these phenomena, An oscillatory multiplicity of propagating fronts has been found. For a two-dimensional model, We will front can exist which does not show any symmetry breaking in two other space dimensions. if the front hits a local irregularity, However, call this wave a ZD-piston front (see Fig. 4). the one-dimensional character of the front is lost and several two-dimensional (or threeFor a case of a transverse traveling wave at dimensional) corrugated reaction fronts may appear. If a transverse traveling wave exists at the reacthe reaction front a fingering wave results. For identical parameter tion interface a spinning (or helical) wave can be observed (cf. Fig. 5). values and boundary and initial conditions, different kind of fronts (piston, fingering, rotating,

Propagation

G-l

erratic) may regime depends

result,

if strongly,

of reaction

different perturbations among other factors,

on

have the

879

fronts

been imposed. heterogeneity

The selection of the system.

of

a prevailing

The exothermic solid-solid reaction is supposed to occur in a porous cylinder, initially comuosed suddenly increased of the powders of S and M. At the time t = 0, the initial temperature To is at the end of the cylinder to Tie This temperature is high enough to ignite the mixture. Different reaction fronts, experimentally observed for various systems, are shown in a color movie. Following fronts have been found: constant pattern profiles, oscillatory fronts, rotating fronts and erratic behavior. Extinction and ignition processes are also shown in the movie. Gas-solid

Systems

Constant pattern profile regime is a typical regime arising for flow gas-solid systems2. The reaction front propagates downstream and consumes completely all solid material. Under certain cirumstances the temperature in the reaction zone keeps increastng with time as the front propagates downstream. This effect is caused by a dynamic feedback of heat towards the incoming gas. Similar effects were also observed for a rapidly deactivating bed3. Dynamic overshooting of adlabatic temperature results in melting of the solid reactants and such regime should be avoided. Complicated wave pattern results for systems with reacting gas shortage (Fig. 6). Preheating temperature wave propagates downstream and reaction is ignited at the reactor exit. The reaction front propagates upstream, however, the solid material is not completely consumed because of shortage of reacting gas. After the reaction front reaches the reactor inlet, a new downstream propagating wave occurs which completes the reaction process. Similar consume part of

situations the solid the solid

can be reactant reactant

observed for a filtration completely, and a forward (cf. Fig. 7).

regime. moving

The wave

backward appears

moving front consuming the

does not unreacted

BEFERENCES 1.

Puszynsky. Conference

2.

Olson,

K.

E.,

3.

Blaum,

E.

(1974).

TABLE1

J., J. Degreve, (Ithaca). D.

Luss Chem.

Physico-chemical

and

S..Kumar

J.

R.

Engng.

and

Amundson Sci.,

Parameters E(kJ/mol)

29, of

V.

Hlavacek

(1968).

IEC

(1985).

Proc.

Proc.

Des.

of

the

Devel.,

Sumner

7,

AMS-SIAM

99.

2263.

Certain

Exothermic

(-AH)(kJ/kg)

Noncatalytic

Reactions

AT,d(K)

B

S-S

+

2B+TiB2

318.4

1034.9

2700

0.091

0.10

Hf

+

2B+HfB2

398.1

1676.0

3520

0.08

0.087

238.8

1915.5

3950

0.138

0.140

+

N2+2HfN

Here E is activation sionless heat release

energy, (-AH) heat of reaction, AT,d adiabatic parameter, 8 dimensionless activation energy.

temperature

S-G

Y

Ti

2Hf

and

rise,

Y dimen-

880

V.

HLAVACEK

6

a

Fig. 1. a-reactor,

Reaction between solid 3-reaction product,

Fig.

2.

phase and 4-unreacted

Solid-solid

G-l

etal.

gas a) flow-system b) component. 5-reaction

reaction.

Constant

pattern

filtration regime; l-gas, zone, &heating element.

profiles.

8. 0

4.

R

-4.

-8.

,,,n

Fig.

Solid-solid reaction. 3. Oscillatory lD-fonts.

Fig.

4.

Solid-solid reaction. ZD-piston front.

882

V.

Gas-solid Fig. 7. profiles of temperature,

HLAVACEK

et

G-l

al.

Filtration reaction. concentration, density

regime. and pressure.