Mass Transfer in Multiphase Systems and its Applications Part 13 ppt

Conclusion Therefore, the physical-mathematical model of heat and mass transfer and condensation capture of fine dust in scrubbers was formulated, and its efficiency was determined.. So

Condensation Capture of Fine Dust in Jet Scrubbers 469 The condition of vapor condensation on particles follows from the equation of mass transfer, for instance, (5'): ρ ρ1− 1p> 0, then dmpf dτ> 0 This condition can be written at τ=0 in the

p p

d

K d , d 1p is moisture content determined

by temperature at chamber inlet Т00, the condition for the beginning of liquid vapor condensation on particles takes form

0

d >

1−

a K

For instance, for steam and air at B=101325 Pa, Т00=333 К (60 0С), Р 1p=0.199·105 Pa,

К=18/29=0,621 Then, а=0.1964 and d0 > 0.152 kg/kg of dry air Therefore, condition (32) should be taken into account at realization of the above problem

3 Comparison of calculation results with experimental data

Results of model implementation for the experimental data on soot capture in the jet scrubber

by the method of methane electric cracking from cracked gases are shown in Fig 4 On the basis of data from (Uzhov & Valdberg, 1972), we managed to determine approximately the physical parameters of cracked gases through the comparison with the molecular weights of the known gases: M g=11 24 kg kmole is molecular mass; с g=2 4 kJ kg K⋅ is specific heat capacity at constant pressure; coefficients of dynamic viscosity are

1,7 6 06,47 10

1,7 2 0

coefficient of steam diffusion in cracked gases is:

3 2 6 0

013,1 10− ⎛ ⎞

⎝ ⎠

T D

- inlet velocity of vapor-gas flow – U0=0 25, m/s;

- irrigation coefficient – q=7 1 10, ⋅ − 3 m3/m3;

0 1 72 / 2 8 /

- outlet soot concentration – ρpout =ρp( )H =0 356 / g m3(0 425 / g m normalconditions3( ) );

- inlet water temperature – 0

0 20

θ = С;

- scrubber diameter – D=3 m;

- scrubber height – H=12 75, m;

- water pressure on jets (evolvent) –P f =300kPa;

- jet nozzle diameter –d n=12 mm;

- density of cracked gases under normal conditions –ρg=0 51, kg m normalconditions/ 3( ) Approximated calculation of the size of irrigating fluid droplets by (Uzhov & Valdberg,

1972)gives the values of mean-mass diameter δ d0=700 μm and initial velocity of droplets

Let’s determine the efficiency values by the ratio of mass flow rates of particles at the scrubber outlet and inlet by formula (15) with consideration of dependence (9):

and inlet, and temperatures Т(H) and Т00 are assumed average from data presented

The theoretical value of efficiency for the given version of calculation is η=89.3 %, and the

diagrams in Fig 4 prove that

Calculation results on parameters described by the suggested model are shown in Fig 4 According to the diagrams, the “spread” density (mass concentration) of dry particles increases drastically at first, then it starts decreasing slowly An increase is caused by a fast reduction in velocity of the vapor-gas flow because of a significant withdrawal of vapors via their condensation of droplets and particles; then particles with condensation on the surface are entrapped by droplets and dust concentration in the flow decreases In this case the size

of particles increases by the factor of 3.5; i.e., their mass increases by the factor of 43

Condensation Capture of Fine Dust in Jet Scrubbers 471 Calculated outlet gas temperatures differ significantly from the experimental ones, and we suppose that this is connected with uncertainty of assignment of initial moisture content and averaging of temperature within 200 С from the measured values

1 2 3 4

295 300 305 310

350 400 450

350 400 450

Fig 5 Comparison of model with experimental data under isothermal conditions for

Venturi scrubber: η was determined by formula (15) and ηe – by formula (37)

To assure additionally efficiency of the model, the process of dust capture on water droplets

from air was calculated with the use of this model under the isothermal conditions (at t=20

0С) without mass transfer in a standard Venturi tube (Uzhov & Valdberg, 1972) Calculation

results are compared in Fig 5 with the experimental data described by the known

dependence of fractional efficiency on Stokes number (Uzhov & Valdberg, 1972)

Stk18

at q=0.5·10-3 m3/m3, b=1.5 (b is constructive parameter: b=1.25-1.56 (Uzhov & Valdberg, 1972,

Shilyaev et al., 2006)) Difference in a wide range of Stokes numbers Stk does not exceed 2 %

In calculations velocity of the vapor-gas flow was determined by formula

2 0

where U0 is velocity of the vapor-gas flow in the throat of tube with diameter D min , D х is the

current diameter of diffuser:

2 tg2

α

х min

α is diffuser angle, and х is coordinate along the tube axis The size of fluid droplets, fed into

the tube throat, was calculated by formula of Nukiyama-Tanasava (Shilyaev et al., 2006,

Shvydkiy & Ladygichev, 2002):

Condensation Capture of Fine Dust in Jet Scrubbers 473

0 45

1 5 0

0

0 585 σ 53 4 μδ

where σ f is coefficient of surface tension of fluid (for water σ f =0.072 N/m), ρ f is fluid density

(for water ρ f=103 kg/m3), μ f is coefficient of dynamic viscosity of fluid (for water μ f=10-3 Pa·s

at t=20 0С), V r0=V g−V d0 , V g is gas velocity in the throat of Venturi tube, and V d0 is velocity

of droplets in the throat of Venturi tube, assumed equal to 4-5 m/s The density of particles was taken conditionally ρ0p=103 kg/m3 The diameter of tube throat was taken D min=0.1 m,

length of diffuser part was l=1 m, and angle was α=60

4 Condensation effect of single particle enlargement in irrigation chamber

Results of model (Shilyaev et al., 2008) implementation together with mass transfer equation for a single submicron droplet (5') under the condition of fluid vapor condensation on it (32)

are shown in Figs 6-9 for the air-water system (calculations have been carried out at Т00=333

К, δd0 =500 μm, q=0.001 m3/m3, Θ0=293 К, U0=3 m/s, V d0 =12 m/s; q is coefficient of

irrigation; V ,U , d0 0 Θ0,T00 are inlet velocities and temperatures of irrigating fluid droplets and vapor-gas flow; δd0 is initial size of irrigating fluid droplets; δ0 is initial size of submicron

droplet; d0 is moisture content at the inlet to the chamber; and l is chamber length) The

effect of collision between submicron droplet and irrigating fluid droplet was not taken into account

According to Figs 6 and 7, at high moisture contents the condensation effect is very strong and inverse to initial size δ0 The droplet size for δ0=0.1 μm increases by the factor of 450 up

to 45 μm, for δ0=0.01 μm it increases by 4500 times up to the same size These formations can

be efficiently captured even independently in vortex drop catchers

Fig 6 Condensation of fluid vapors in a vertical chamber in direct flow on droplet with size

δ0=10-7 m: l=2 m, d0=3 kg/kg of dry air

Results of calculations under outstanding conditions of condensation (32) are shown in Fig

8 In this case critical value is d0=0.15 kg/kg of dry air According to the figure, the droplet

with initial size δ0=0.1 μm evaporates along the whole chamber and disappears almost at the chamber inlet

0

δ δ

Fig 7 Condensation of fluid vapors in a vertical chamber in direct flow on droplet with size

0.7 l it disappears turning to vapor

Therefore, condensation processes in irrigation chambers under some certain conditions can effect positively the efficiency of submicron particle capture, but these conditions can be achieved only on the basis of adequate mathematical models similar to the suggested one including model equations (Shilyaev et al., 2008) combined by mass and heat balance, heat and mass transfer equations of particles under the conditions of their absorption by fluid droplets at the motion along the chamber

0

δ δ

Condensation Capture of Fine Dust in Jet Scrubbers 475

Fig 9 Condensation is evaporation of a droplet in the vertical chamber at direct flow:

ρπ

ρv is the average vapor density on distance l near the droplet surface calculated by its

temperature equal to the temperature of saturation; δ0 and δd are initial and final diameters of droplet; ρf is droplet density; δ is average size of a droplet on distance l

Time is Δ = l / U , where U is velocity of the vapor-gas flow along the chamber axis τ

If we assume δ= δ δd 0, from (40) we can obtain

2 0

16

ρδ

δd = , δ02=10 μm−2 , δd2=17μm; 2

02170

=

v v

w

Relationship (45) proves the fact that the diffusion mechanism of small particle deposition

on large droplets is insignificant because of small diffusion velocities of vapors at condensation on their surfaces, and it can be neglected; simultaneously it is very important for small droplets This conclusion correlates with formula of B.V Deryagin and S.S Dukhin (Uzhov & Valdberg, 1972)

According to calculations by formula (46), at δ0<<δd the efficiency of submicron dust deposition is low (Shilyaev et al., 2006)

5 Parametrical analysis of condensation capture of fine dust in Venturi

scrubber

The Venturi scrubber (VS) is the most common type of wet dust collector for efficient gas cleaning from dust particles even of a micron size Together with dust capture the absorption and thermal processes can occur in VS The VS is used in various industries:

Condensation Capture of Fine Dust in Jet Scrubbers 477

ferrous and non-ferrous metallurgy, chemistry and oil industry, production of building

materials, power engineering, etc The construction of VS includes combination of irrigated

Venturi tube and separator (drop catcher) The Venturi tube has gradual inlet narrowing

(converging cone) and gradual outlet extension (diffuser) A pinch in cross-section of

Venturi tube is called a “throat” The operation principle of VS is based on catching of dust

particles, absorption or cooling of gases by droplets of irrigating fluid dispersed by the gas

flow in Venturi tube Usually the gas velocity in the throat of scrubber tube is 30-200 m/s,

and specific irrigation is 0.1-6.0 l/s3 In the current section we are considering optimization

of possible application of Venturi scrubber for fine dust capture under condensation

conditions on the basis of the suggested physical-mathematical model

Results of calculation on the basis of suggested model for VS are shown in Figs 10 and 11

According to Fig 10, at low moisture contents (almost dry air) with a rise of initial particle

concentration the efficiency of their capture increases slightly and with an increase in

moisture content it decreases (Fig 10а) At that high efficiency of dust capture can be

achieved al low particle concentrations and high moisture contents at the VS inlet (Fig 10b)

Dependence of dust capture efficiency on diffuser angle of Venturi tube α is shown in Fig

11а, and it is obvious that for the given case the optimal is α ≈ 7.7 0 For any other case this

optimal angle can be calculated by the model

а) b) Fig 10 Effect of initial particle concentration and moisture content on dust capture

efficiency: V0=5 m/s, Θ0=293 К, ρ0p=103 kg/m3, q=0.5⋅10-3 m3/m3, U0= 160 m/s, Т00=333 К,

α=60, l=1m, δ0=10-7 m

Dust capture efficiency vs relative diffuser length is shown in Fig 11b, and it can be seen

that the optimal length of diffuser tube, which provides the required dust capture efficiency,

can be determined with the help of the model Thus, for this case at required efficiency η=99

% the length of diffuser should be l=1 m

According to Fig 12, efficiency depends significantly on the flow velocity in the tube throat

and irrigation coefficient Calculations were carried out for diagram а) at following

parameters: l=1 m, V d0 =5 m/s, δ=0.1 μm, Θ0=293 К, α=60, ρ p0=1 g/m3, ρ0p=103 kg/m3, q=2

l/m3, U0= 80 m/s, Т00=303 К, d0=0.01193 kg/kg of dry air

а) b) Fig 11 The effect of diffuser angle (а) and diffuser length (b) on dust capture efficiency:

V0=5 m/s, Θ0=293 К, ρ0p=103 kg/m3, q=10-3 m3/m3, U0= 80 m/s, Т00=333 К, ρ p0=1 g/m3,

d0=0.5 kg/kg of dry air, δ0=10-6 m

Fig 12 Calculation results: а) distribution of particle concentration along the diffuser; b)

efficiency of particle capture depending on irrigation coefficient: 1 - U0= 80 m/s, d0=0.01193

kg/kg of dry air; 2 - U0= 100 m/s, d0=0.01193 kg/kg of dry air; 3 - U0= 100 m/s, d0=0.5 kg/kg

of dry air, other parameters are the same as for Fig а)

6 Comparison of direct-flow and counter-flow apparatuses of condensation

capture of fine dust

It is interesting to compare specific power inputs for gas cleaning from fine dust under the

conditions of condensation of particle capture on fluid droplets in the direct-flow and

counter-flow apparatuses as well as their sizes under the same conditions For this purpose

let’s compare the counter-flow jet scrubber (CJS) and Venturi scrubber (VS) under the same

flow rates of cracked gases cleaned from soot particles, corresponding to experimental data

of (Uzhov & Valdberg, 1972) for CJS

%

,

η

Condensation Capture of Fine Dust in Jet Scrubbers 479

Comparative calculations were carried out for the following data For CJS: q=7.1·10-3 m3/m3,

δd0 =700 μm, V d0=24.5 m/s, Θ0=293 К, Т00=443 К, d0=0.93 kg/kg of dry air, U0=0.25 m/s,

δ0=0.12 μm, ρ p0=1.72 g/m3, D=3.0 m, Н=2; 3; 6; 9; 11; and 12.5 m For VS the diameter of tube throat D min was determined from the equilibrium equation for volumetric flow rates of the

vapor-gas flow at the inlets of the compared apparatuses Thus, at U0=80 m/s D min=0.17 m,

at U0=160 m/s D min =0.12 m Angle α was varied as well as scrubber length l Initial size of droplets δ d0 for VS was calculated by Nukiyama-Tanasava formula (39) depending on (U0 –

Vd0), fluid density ρf , q, coefficient of fluid surface tension σ f (for water σf=0.072 N/m); the

value of initial velocity of droplets in tube throat V d0 was set 4.0 m/s

Calculation results are generalized in Figs 13 and 14 for optimal angle α=7.70, corresponding to maximal efficiency of dust capture According to the figures, with an increase in the relative length of Venturi tube and relative height of CJS, the efficiency increases significantly, but the higher l D min and H D , the less expressive is this growth

According to Fig 13b, the efficiency growth is caused firstly by enlargement of “formations” (particles with condensate on their surface) Deceleration of efficiency growth depending on converging cone length and scrubber height is caused by a decrease in particle concentration

in the flow and reduction in probability of collisions between “formations” and fluid droplets The suggested model provides a possibility to determine the optimal length of

Venturi tube l or scrubber height Н for the required efficiency of dust capture

Fig 13 Results of calculations by the model for Venturi scrubber: q=7.1·10-3 m3/m3, V d0=4.0

m/s, Θ0=293 К, Т00=443 К, d0=0.93 kg/kg of dry air, U0=80 m/s, δ0=1.2⋅10-7 m, ρ p0=1.72 g/m3,

Dmin =0.17 m, α=7.70

Calculation results on the relative size of “formations” and CJS efficiency under the same conditions as for VS, corresponding to experimental data for CJS on soot capture from cracked gases (Uzhov & Valdberg, 1972), are shown in Fig 15 depending on the initial

temperature of droplets The height of experimental CJS was Н=12.7 m, and diameter was

D=3 m It can be seen from the figure that with a decrease in droplet temperature at the inlet

Θ0 efficiency increases significantly Thus, an increase in Θ0 from 293 К (20 0С) to 278 К (5

0С) increases efficiency by 8 % This important result proves the fact that the same

experimental efficiency η≈90 % can be obtained at significantly less height of the scrubber Thus, according to calculations, at Θ0=278 К (5 0С) this value of efficiency can be achieved at

height Н≈4-5 m instead of 12.7 m, what reduces the dimensions and specific quantity of

metal of the whole construction The point in Fig 15b indicates the experimental value of efficiency, and this means that model operability is proved well by the experiment

Fig 14 Results of calculations for CJS: q=7.1·10-3 m3/m3, δ d0=7⋅10-4 m, V d0 =24.5 m/s, Θ0=293

К, Т00=443 К, d0=0.93 kg/kg of dry air, U0=0.25 m/s, δ0=1.2⋅10-7 m, ρ p0=1.72 g/m3, D=3.0 m

Fig 15 Results of calculations by the model for CJS: H=12.75 m, q=7.1·10-3 m3/m3, δ d0=7⋅10-4

m, V d0 =24.5 m/s, Т00=443 К, d0=0.93 kg/kg of dry air, U0=0.25 m/s, δ0=10-7 m, ρ p0=1.72 g/m3 According to analysis, for similar required efficiency, the direct-flow dust catchers (in this case they are VS), despite their advantage by dimensions over the counter-flow apparatuses, require higher power inputs for gas cleaning, determined by pressure drops in apparatuses Actually, for VS the coefficient of hydraulic resistance can be estimated by formula (Shilyaev

Condensation Capture of Fine Dust in Jet Scrubbers 481 Substituting these data into (47), we obtain ξt v=6 9, Hence, at U0=80 m/s the pressure drop

on the Venturi tube is

2

0 77282

ξ ρ

Δ t v= t v =

U

Р Pa, and at U0=160 m/s ΔР t v=30912Pa

This resistance exceeds the resistance of CJS, where the main part of energy is spent for fluid spraying, and hydraulic resistance is low (as usual, the velocity of cleaned gas does not exceed 1 m/s) At that, the same energy is spent for fluid spraying in Venturi tube Thus, specific energy spent for fluid spraying is

All the above mentioned proves the fact that the counter-flow schemes of condensation dust capture are in preference to the direct-flow ones

7 Conclusion

Therefore, the physical-mathematical model of heat and mass transfer and condensation capture of fine dust in scrubbers was formulated, and its efficiency was determined The suggested model can be used for preliminary calculations and estimation of the most rational determining parameters of apparatuses, which provide efficient gas cleaning

Shilyaev, M.I., Khromova, E.M (2008) Simulation of heat and mass transfer in spray

chambers Theoretical Foundations of Chemical Engineering, Vol 42, No 4, P 404-414

Shilyaev, M.I., Khromova, E.M., Tumashova, A.V (2008) Physical-mathmatical model of

heat and mass transfer process in jet irrigation chambers at high moisture contents

Izv Vuziv Stroitelstvo, No 6, P 75-81

Shilyaev, M.I., Shilyaev, A.M., Grischenko, E.P (2006) Calculation Methods for Dust Catchers

– Tomsk: Tomsk State University of Architecture and Building

Shilyaev, M.I., Shilyaev, A.M., Khromova, E.M., Doroshenko, Yu.N (2008) About

condensation mechanisms of dust capture intensification in CJS and DC Izv Vuzov

5, P 526-530

Vitman, L.A., Katsnelson, B.D., Paleev, I.I (1962) Liquid Spraying by Jets –

Moscow-Leningrad: Gosenergoizdat

21

Mass Transfer in Filtration Combustion Processes

David Lempert, Sergei Glazov and Georgy Manelis

Institute of Problems of Chemical Physics of Russian Academy of Sciences

Russian Federation

1 Introduction

Wave combustion is one of wide-spread regimes of chemical reactions progress in the systems with the enthalpy excess Combustion waves in porous medium have some special features, that let consider them as especial kind of combustion processes Usually one denominates the filtration combustion (FC) as the oxidation of any solid combustible at gaseous oxidizer filtration The presence of two phase states, intensive heat- and mass exchange between these two phase states, a constant countercurrent flow of solid and gas phases complicate considerably theoretical description of FC wave, as well as experimental results explication In such systems one has to consider not only heat and concentration fields, but also the gas flow dynamics and heterogeneous reactions peculiarities Besides it a huge difference between densities of components provides the necessity of common consideration of processes with appreciably different characteristic rates Anyway due to some peculiarities filtration combustion waves remain very attractive objects for industrial application

Combustion regimes with heat accumulation occupy an especial place in wave combustion processes A typical example it is the combustion of a solid fuel at gas oxidizer filtration, when the combustion front direction coincides with the gas flow one (Aldushin et al., 1999; Hanamura et al., 1993; Salganskii et al., 2008) In coordinates, cohered with the combustion front (zone of the exothermic transformation) this process may be considered as the interaction of gas and condensed flows, coming from the opposite direction, passing through the chemical reactions zone, and being transformed in this zone with the change of both chemical content and physical-chemical properties (Fig.1)

The presence of high temperature area with an intensive interphase mass-transfer processes between counter-current phases flows forms a zone structure In each zone there are physical and chemical processes depending on corresponding conditions (temperature, medium properties, reagents concentration etc.) Space separation of zones supplies an accumulation of either, one or another substance in the definite zone accordingly to his physical-chemical properties, and provides possibility of some useful components extraction These peculiarities allow to realize some industrial processes in extremely effective and a low-price regime, basing on heat-effectiveness of combustion wave Examples of FC processes industrial application are known It is waste extermination using superadiabatic combustion (Manelis et al., 2000; Brooty & Matcowsky, 1991) underground oil recovery (Chu, 1965; Prato, 1969), metallurgical burden agglomeration (Voice & Wild,

processes are typical examples of FC with counter-current flow and superadiabatic overheat

We have to notice that in this paper we consider heterogeneous combustion only We do not consider the FC of gases where preliminary mixed gaseous fuel and oxidizer burns in porous heated medium (Babkin, 1993), because in these systems heterogeneous processes are not determinative

Due to the wave structure the heat, released in chemical reactions, transfers intensively to source materials with no use of outside heat-exchange devices, only because of extremally intensive interphase heat-exchange while gas filtration The heat accumulation may be so considerable that combustion temperature can exceed by several times the adiabatic temperature, when it calculated assuming that the initial temperature of any portion of reacting compounds is equal to the ambient temperature That is why sometimes one uses the terms «superadiabatic heating», «superadiabatic regime of filtration combustion», or simply «superadiabatic combustion»

The term «superadiabatic» seems disputable at first glance, however any heat recuperation from combustion products to initial substances can increase the adiabatic temperature (Wainberg, 1971) of the mixture Really due to an intensive interphase heat exchange in such system the temperature of initial interacting compounds is far higher than the ambient temperature and may approach the combustion front temperature Anyway the term

«superadiabatic» has been used during many years and we guess one should not replace it Just in superadiabatic regime the effectiveness of the heat recuperation may be maximally high, whereby namely when the solid combustible contains enough high amount of an inert material, and when the gaseous oxidizer contains enough high fraction of inert gas component (Salganskii et al., 2008) It is due to the FC process organization – inert components are very effective heat carriers, thus both combustible and oxidizer can be overheated maximally before they enter into the zone of chemical reactions Solid combustible is heated due to gaseous combustion products, while gaseous oxidizer – due to ash residue and solid inert material

The most interesting peculiarity of combustion waves in such systems is the independence

of the stationary combustion wave temperature on the value of the reaction heat release (if it

is a positive value) After ignition the temperature in the combustion front increases until the heat input (due to exothermic reactions) is equal to the side heat losses Minimizing side heat losses the thermal equilibrium is reached at very high temperature, enough for considerable increase of chemical reaction rates So, heat losses in FC processes play more important role than in case of classic combustion waves, because in the case of FC the heat losses determine to more considerable degree the temperature in the reaction zone Temperature profile of such combustion wave is shown schematically in Fig.2 Due to an intensive heat exchange between source reagents and combustion products the released energy is accumulated mainly close to the combustion zone If the mixture has a small heat release value (e.g a mixture of carbon with a high amount of an inert material) the FC process will accumulate the heat energy with a lower rate and therefore it will reach the stationary regime longer

At conditions of counter-current flows of combustible and oxidizer the combustion rate (that

is very important characteristic) is determined mostly not with the heat transfer rate, but with the rate of reagents supply into the combustion zone (that is with the filtration rate)

Mass Transfer in Filtration Combustion Processes 485 Besides, before the combustion zone (in Fig 1 and 2 - to the right of the high temperature area where the main chemical exothermic reactions run with highest effectiveness) the reducing zone exists with high amount of combustible and rather high temperature, that results in complete gaseous oxidizer consumption Behind the combustion zone (in Fig 1 and 2 - to the left of the high temperature area), contrariwise, there is a hot zone with high content of oxidizer, that provides the completeness of the material burning

In view of the aforesaid, it is obvious that the FC process is very attractive for industry, particularly when it is needed

• To burn cheaply a material containing small amount of combustible

• To obtain high combustion temperatures,

• To provide maximal fullness of solid fuel burning,

• To get space separation of zones (heating, pyrolysis, evaporation, oxidation, condensation, cooling etc.) in solid porous fuel

Hereby the energy outlay may be minimal due to effective heat recuperation in FC waves

Fig 1 Schema of combustion wave with superadiabatic heating The solid combustible material – small balls, while the inert material – big balls The solid material flow – right to left, the gas flow – left to right High-temperature zone – the area with more light

background

Fig 2 Temperature and concentration profiles of the combustion wave in case of equal heat capacities of the flows of condensed and gaseous phases

2.1 The simplest case of FC process

There are many possibilities to realize mass transfer in FC processes The simplest case in one-dimensional approximation is the chemical interaction of counter-current of solid fuel flow with gaseous oxidizer (being filtrating through the solid material) flow when a single combustion product forms We are expecting the presence of both inert material in the solid fuel and other gaseous components (that do not participate in chemical reactions, e.g nitrogen) in gaseous oxidizer Hereby, depending on the phase state of the combustion product, this product is added to the respective flow through the reaction zone For example, at carbon oxidation the combustion product is gaseous carbon dioxide, while at aluminum oxidation it is solid aluminum oxide So, we have an interphase mass transfer of either solid fuel to gaseous product (Fig 3b) or gaseous oxidizer to solid product (Fig 3b) In both cases the whole redox process and the summary heat release are concentrated in the single reaction zone

Fig 3 Mass flows through the reaction front in cases of: a) gaseous products (Pg) and b) solid products (Ps) Og and Ig – gaseous oxidizer and inert; Fs and Is – solid fuel and inert

substances, correspondingly

Let's presume that the temperature level in the reaction zone is enough high, it allows to consider this zone width being negligible small in comparison with the warming-up zone of the combustion wave Besides we presume that the interphase heat-transfer at the filtration process is so effective that the difference between temperatures of solid and gaseous phase

is negligible Then depending on real conditions (combustible concentration in the solid mixture and oxygen concentration in gaseous oxidizer) the heat structure of the FC wave may be either like the curve in Fig.4a (”reaction trailing” structure), or like the curve in Fig.4b (”reaction leading” structure) The type of the heat structure is determined with the ratio of heat capacities of counter-current solid and gas flows through the reaction front (Aldushin et al.,1999; Salganskii et al., 2008) The heat, released in combustion, is removed with the gas flow in the case of the reaction trailing structure, while in the case of the reaction leading structure it is removed with the solid material flow These two heat flows determine the type of the profile of the FC wave It is possible that two these heat flows are equal, it provides a symmetric profile of the combustion wave and maximal heat accumulation in the combustion wave [Aldushin et al.,1999] In this case the heat of

Mass Transfer in Filtration Combustion Processes 487 chemical reactions is removed with both solid material and gas In all considered cases an intensive interphase heat-transfer results in the accumulation of all released heat near the combustion front If the reactor is long enough, all products leave it at the initial temperature Continuous heat energy accumulation results in the expansion of the warming-up zone in the direction either of the solid material or gas flow depending on the type of the heat structure of the FC wave When side heat losses exist, a stationary profile

of combustion wave can form When side heat losses are negliglible, a stationary process is possible at uncompleted heat-transfer only, in this case either gas or solid material leaves at hot temperature

Fig 4 Temperature profiles of combustion wave in case of there is no heat losses: a) – reaction leading heat structure, b) – reaction trailing structure Hatchs indicate zones of chemical reactions

2.2 Attended processes of evaporation and condensation

The heat structure of the FC wave determines conditions of compounds heating at combustion wave propogation, and all accompanying physical and chemical processes For example, the presence of an additional volatile component in the solid fuel (besides the combustible itself and an inert material) results in the localization of the zone of this component concentration (evaporation – condensation) in the region of the fuel warming-up (Fig 5a) The main heat release, providing the existence of whole FC wave structure, takes place in the combustion front Evaporation process occurs due to convective heat flow from the combustion front Mass transfer of the vaporized component with the gas flow takes place before the area of condensation If the convective heat flow from the combustion front

is higher than heat losses for the evaporation, the zone of the accumulation of the vaporized component expands If there are side heat losses the expansion of this zone ends sooner or later, and further all processes set moves stationary as a batch

In the case of the reaction leading structure, the evaporation zone is situated near the combustion front, which determine and provide the FC wave structure Therefore considerable heat expenses for the evaporation may decrease the combustion front temperature, and surely it has an influence on all characteristics of FC waves In the case of reaction trailing structure, the heat expenses for the component evaporation decrease the temperature in the region of warming-up, not in the combustion front, therefore these heat expenses do not influence the value of heat release in the combustion front It is an extraordinary peculiarity of these regimes of the FC The zone of condensation of vaporized component is situated a bit farther along the gas flow The condensation process is accompanied with some heat release, therefore in this case there is not mass transfer only, but heat transfer from one zone to another one too

moisture does not prevent propagation of stable combustion wave (Salganskaya, 2008)

It is not necessary that the condensation of the vaporized component occurs always to its accumulation in the determined reactor zone For example, the water condensation occurs to

an aerosol forming The higher size of drops of the liquid, the easier they sediment on the initial solid material during the filtration process Temperature gradients in the FC wave may be very high In this case a high rate of the gas cooling occurs to forming very small drops (less than 10-6 m), which sediment badly under filtration and may be removed (as a fog) from the reactor with the gas flow Thus, it is rather simple to organize the extraction of

a volatile component from the source solid material

Fig 5 Heat structure of the FC wave, propagating through a porous solid fuel: (a) – in case

of an evaporating component, and (b) – in case of pyrolytic decomposition of the fuel

2.3 Peculiarities of filtration combustion of carbonic systems

Layer burning of carbonic fuel has been used long since, and many systems of gas generators, industrial furnaces work still using this process The combustion of porous burden containing solid carbonic fuel and incombustible material at air or another oxygen-containing gaseous oxidizer filtration is of great interest for industrial application in processes of solid fuel burning optimization, as well as for developing environmentally friendly methods for different combustible wastes recycling

Heterogeneous carbon oxidation is a complicated and multistage process The final product are carbon dioxide and monoxide There is no sure answer which one of these two oxides is the primary product of the carbon particles oxidation, and which one forms already in the gas phase It is so difficult to find out it because as soon monoxide forms it may be oxidized immediately to dioxide, while dioxide at rather high temperature may be reduced to monoxide above carbon surface Currently most part of researchers guess that in result of heterogeneous processes two oxides form together (Lizzio et al., 1990; Bews et al., 2001; Chao’en & Brown, 2001) Oxidation mechanism and the quantitative ratio of formed oxides depend on conditions (temperature, pressure etc.) as well as on properties of carbon particles surface

At the interaction of the main components of FC in counter-current flows of solid fuel and gaseous oxidizer, a zone structure forms, each zone differs from another one in temperature and reagents concentrations In the main zone of heat release (combustion front) carbon is