Experimental Investigation And Modeling Of Gasification Of Sewage Sludge In The Circulating Fluidized Bed

Chemical Engineering and Processing 44 (2005) 717–736

Experimental investigation and modeling of gasification of sewage sludge in the circulating fluidized bed I. Petersen, J. Werther∗ Technical University Hamburg-Harburg, Denickestr. 15, D-21073 Hamburg, Germany Received 31 October 2003; received in revised form 1 September 2004; accepted 1 September 2004 Available online 12 October 2004

Abstract Experiments of sewage sludge gasification were performed in a circulating fluidized bed of pilot plant scale (15 m height, 0.1 m i.d.). For the examination of the influence of the air ratio, gasification temperature, feeding height and fluidization velocity several screening tests were conducted. To understand better the results from the screening experiments, axial profiles of the gas composition were measured. As the most influencing factor for the heating value of the gasification gas the air ratio was found. Additionally, a low feeding height is recommended for good gas quality. While feeding into the lower dense zone of a circulating fluidized bed (CFB), mixing of the fuel particles is better. With low feeding ports, high velocities are attainable and therefore high fuel throughput can be achieved. In a second step a model of the CFB gasifier was developed. The fluid dynamics of a CFB were included as well as the complete reaction network of gasification. With the measured axial profiles of gas composition during pyrolysis, and gasification with air and a CO2 /N2 -mixture kinetic rate expressions for sewage sludge gasification under fluidized-bed conditions were determined which may now be used for reactor scale-up calculations. © 2004 Elsevier B.V. All rights reserved. Keywords: Gasification; Circulating fluidized bed; Reaction kinetics; 1.5-dimensional model

1. Introduction Combustion was the primary method of generating heat and also power (by a using the heat from the combustion in a steam turbine) from renewable fuels. More recently, gasification of wood, as well as wastes and also sewage sludge has come into the discussion. The efficiency of the gasification process is better, in principle, because the produced gas can be used directly in a power generation process. The only drawback to date for this technology is the high tar and dust content of the synthesis gas produced. Typical tar content for wood gasification is in the range of 1–30 g/m3 STP [1]. For the use in gas-motors or gas-turbines a tar content of only 50 mg/m3 STP is permitted [2,3].

∗

Corresponding author. Tel.: +49 40 428783039; fax: +49 40 428782678. E-mail address: [email protected] (J. Werther).

0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.09.001

In Germany nowadays the sewage sludge on one hand is used energetically in mono-combustion plants; it is cocombusted in coal fired power stations and in municipal solid waste combustion. On the other hand, sewage sludge is used as landfill and in agriculture [4]. From 1 June 2005 on, use as landfill will no longer be permitted. Only pre-treated wastes can be deposited. The facilities for pre-treatment have only sufficient capacity for the “normal” wastes. Additional treatment of sewage sludge is problematic [5]. But agricultural recycling of sewage sludge is controversial. In some German states, a ban is being drawn up. Agricultural recycling will probably cease by 2020 [6]. Therefore operators of wastewater treatment plants are looking for new and reliable disposal paths for the sewage sludge having high acceptance by the population and also by the operators of co-combustion facilities. In Germany utilization of biomass as renewable energy source is regulated by the German government in the

718

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

Renewable Energy Law (EEG) and the Biomass Ordinance (BiomasseV). The objective of the EEG was to increase the contribution of renewable energies for the total power consumption, and consequently to reach the goal set by the European Union to double the contribution of renewable energies for the total power consumption until the year 2010. The definition of “biomass” according to the EEG is given in the Biomass Ordinance (BiomasseV). The possible processes to generate power from biomass are also fixed in the BiomasseV. Sewage sludge itself is not accepted as “biomass” according to the BiomasseV. But in the processes, which are defined in the ordinance to be possible for power generation from biomass, it is allowed to add synthesis gas from sewage sludge gasification to a portion of up to 10% of the total energy content. In this case a gas with as high as possible energy content is to be produced in the gasification plant rather than a real tar-free gas. But besides the use of sewage sludge as renewable energy, gasification of sewage sludge is also interesting for cocombustion in fossil-fired power generation facilities [7]. The addition of sewage sludge directly to the combustor is sometimes problematic due to the high ash content of the sludge and the high amount of contaminants (e.g. heavy metals) in its ash. If sewage sludge gasification is performed before cocombusting the produced gas in the utility burner, the coal ash bed is prevented from being polluted by the sewage sludge ash. In this case, too, the tar amount in the low calorific value gas from gasification is unimportant as are some unconverted char particles from the gasifier. Some coal is replaced by sewage sludge, and additionally the entering gas from the gasifier produces a reburning-effect, which results in a reduction of nitrogen oxides (NOx ) [8,9]. The objective of the present paper is the examination of sewage sludge gasification. The circulating fluidized bed was chosen as the gasification reactor, because fluidized beds are already used mostly in sewage sludge mono-combustion plants due to the good gas-solid contact, mixing and its flexibility as far as the fuel composition and condition is concerned. To understand more deeply the reactions in the gasification of sewage sludge and to prove the feasibility of sewage sludge gasification in the circulating fluidized bed, an experimental examination was carried out at the circulating fluidized bed pilot plant (0.1 m riser diameter, 15 m high) at TUHH. To get information about the drying and pyrolysis, experiments in an inert atmosphere (only nitrogen present) were performed. CO2 gasification and air gasification were examined thereafter at different operating conditions. From these measurements supported by a 1.5-dimensional mathematical model of a fluidized-bed gasifier, the kinetics of pyrolysis and the main gasification reactions were determined based on kinetics available in the literature. An equilibrium calculation for the whole gasification reaction network in the temperature range commonly used in fluidized-bed combustion and gasification technology was also performed. A major goal of the present work was to derive a quantitative description of the gasification kinetics which should

be applicable under fluidized-bed conditions since a major drawback of kinetic informations about gasification reaction networks available in the literature is that they have been obtained from single-particle or fixed bed reactor experiments. Since heat and mass transfer in a fluidized bed are quite different and since furthermore it is well known from pyrolysis experiments that the pyrolysis gas yield and the composition of the pyrolysis gas are strongly dependent on the heating rate it is highly desirable to obtain information about the gasification kinetics directly from fluidized-bed experiments. In the present work a set of kinetic equations is coupled with a fluiddynamic model of a circulating fluidized-bed riser. Numerical values of three kinetic parameters are then determined not by simply comparing measured and calculated reactor exit concentrations but by fitting the model to measured axial profiles of the species concentration over the full 15 m of height the gasification reactor. Although, admittedly, inaccuracies of the complex fluid-dynamical model will also affect the thus determined values it is believed that the fluidized-bed conditions are essential for the determination of reaction kinetics which are to be used for the simulation of fluidized-bed gasifiers.

2. Experimental Experimental examination was conducted on pyrolysis and gasification of sewage sludge in order to observe the kinetics and the mechanism of devolatilization and the reaction network. The facility used for the gasification experiments is the circulating fluidized bed at TUHH (Fig. 1). The circulating fluidized-bed riser is made of stainless steel (German material number 1.4841) without refractory lining for fast start-up of the facility. The inner diameters of the riser and downcomer are 100 and 80 mm, respectively. The riser has a total height of 15 m. The plant is heated electrically from the outside. The distributor plate is a bubble-cap distributor with one bubble cap. The fluidizing gas is preheated electrically before entering the windbox up to a maximum temperature of 800 ◦ C. The gas and some fly ash leaving the facility pass the final measurement position for the gas quality after the cyclone, and enter an after-burning chamber where the energy-gas is completely burned. The after-burning chamber has an inner diameter of 300 mm and a total length of 4.3 m and is heated by electrical radiation heating to 850 ◦ C. The residence time in the after-burning chamber is at minimum 3.3 s. The afterburning air can be preheated electrically, too. The plant is equipped with ports for temperature and pressure measurement. In addition there are several ports for inserting gas measurement probes. At four positions along the riser height there are ports for fuel feeding (positions: 1.75, 2.5, 3.5 and 4.6 m). The feeding system is a screw feeder. It is positioned next to the facility and connected to the plant by a tube into which the fuel particles are dosed. The tube is approximately 1.5 m long, and the particles enter the fluidized bed due to gravity with their falling velocity. On top

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

719

Fig. 1. Flowsheet of the gasification facility.

of the screw feeder the storage is located with enough space for fuel to operate the plant for one whole day. Temperature measurement is carried out with Ni–Cr–Ni thermocouples. Only in the after-burning chamber where higher temperatures were expected, Pt–Rh–Pt thermocouples were used. The riser pressure drop is measured with sensors for differential pressures. The mean total riser pressure drop during the experiments was held at 7000 Pa. The operation of the fluidized bed as a gasifier is controlled with gas composition measurements. The complete combustion of the synthesis gas in the after-burning chamber is also controlled by gas concentration measurement. In the after-burning chamber an air ratio of λ = 1.23 was chosen.

Two basically different sampling locations were used: The measurement ports along the riser height enable gas sampling from inside the riser to probe the axial profile of the gas composition. In order to separate the sample gas from the fluidized-bed particles, the gas sampling probe is equipped with a ceramic filter at the tip of the probe. This ceramic filter prevents the particles from entering the probe. The ceramic filter is located inside a stainless steel tube to save the filter from erosion. The measured gas concentration is a mean average concentration for the cross section. The other measurement position is directly after the cyclone at the exit of the plant. Because the particles are already separated from the gas flow by the cyclone, only some fly ash particles are

720

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

Fig. 2. Sampling probes for use inside the riser (left) and for position the measurement after cyclone (right).

expected. Therefore the gas sampling probe is designed differently. It is just a stainless steel tube with an inner diameter of 4 mm (suction velocity 4–20 m/s). The fly ash that is sucked out is separated from the sample gas by a small measurement cyclone. So at this measurement position not only a gas sample is taken but also a sample of the fly ash is withdrawn. To prevent the particles not separated by this small measurement cyclone from plugging the adjacent gas sampling line, an additional filter is positioned behind the measurement cyclone. The measurement cyclone and filter are heated to 250 and 200 ◦ C, respectively. In Fig. 2 both sampling probes are shown. Directly after the gas sampling probe and cyclone plus filter, respectively, is the tar trap. Following the tar trap is the gas sampling line (Fig. 3). The gas sampling duct is made of Teflon-tubing, which is electrically heated from the outside to a temperature of 160 ◦ C to prevent the temperature inside from dropping below the dew point of water. The analyzers are fed via a membrane pump. The analyzer for the water content does not need any more pretreatment of

the sample gas. For the rest of the analyzers, a tar condenser with glass wash bottles in an ice bath is put in this place. Afterwards, the gas passes a cooler and the dry gas is distributed to the analyzers. The flow to the analyzers is adjusted to one liter per minute. The analyzers are supplied in series (Fig. 3). All the main components, which are O2 , CO, CO2 , H2 , CH4 , C2 H4 , and H2 O, could be measured online. The oxygen analyzer measures with the paramagnetic effect. The analyzers for CO, CO2 , CH4 , C2 H4 , and H2 O have a non-dispersive infrared (NDIR) detector. The instrument for the measurement of the H2 concentration has a thermal conductivity detector (TCD) with cross compensation for CH4 , CO, and CO2 . The solid materials used in the experiments were the fuel and silica sand as bed material. No additional catalyst or limestone was used in the riser. The fuel examined was dried pelletized sewage sludge from a municipal waste-water treatment plant. In Table 1 the composition (proximate and ultimate analysis) is given. The particle size distribution was measured before and after the feeder. The mean particle diameter before was x3,50 = 2.9 mm. After the feeder the mean particle diameter was slightly reduced to x3,50 = 2.8 mm. The density of the sewage sludge was experimentally determined by helium pycnometer to 1728 kg/m3 . As bed material silica sand was used. This sand was available with two different particle size distributions. The 50% value of the cumulative mass distribution was found to be Table 1 Proximate and ultimate analysis of the dried sewage sludge Mean

Fig. 3. Gas measurement system.

Proximate analysis Volatiles, wt% (waf) Combustibles,a wt% (raw) Water, wt% (raw) Ash, wt% (raw)

83.4 50.6 7.3 42.1

Ultimate analysis C, wt% (waf) H, wt% (waf) O,a wt% (waf) S, wt% (waf) N, wt% (waf)

50.5 6.6 34.5 1.2 7.1

Lower heating value (LHV), MJ/kg (raw)

10.0

a

By difference.

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

x3,50 = 180 ␮m and x3,50 = 203 ␮m, respectively. In most of the experiments finer sand was used. After each experiment, the sand from the facility was completely retained. For the next experiment a mixture of this retained activated bed material and new sand was used at the start. The retained bed material to be reused in the next experiment was sieved to have particle diameters smaller than 70 ␮m only. The density of the bed material was experimentally determined by helium pycnometer as 2687 kg/m3 . The minimum fluidization velocity umf was determined as 4.4 cm/s for the original sand, and 6.5 cm/s for the mixture of fresh and activated bed material under ambient conditions with air. In the experiments the following factors were examined: • As fluidizing agent air, a CO2 /N2 -mixture, and pure N2 were used, respectively. • The temperature was varied between 1023 and 1123 K. • To determine the influence of the air ratio, experiments with λ = 0.3 and λ = 0.6 were carried out. • As superficial gas velocities 3.5 and 5 m/s were adjusted, respectively. • As feeding height 2.5 and 4.6 m, respectively, above the distributor plate were examined. In several screening tests the gas composition was measured at the measuring position directly after the cyclone at the exit of the riser. For each of the four influencing factors, which are air ratio, temperature, feeding height, and superficial gas velocity, two conditions were chosen (two-level factorial design [10,11]), and experiments with all 16 combinations (24 = 16) were run. For the air ratio λ = 0.3 and λ = 0.6 were chosen, the desired temperature was adjusted to 750 and 850 ◦ C, the superficial gas velocity at the top of the riser was 3.5 and 5 m/s, respectively, and as feeding height the ports on 4.6 and 2.5 m were examined. These parameters are also listed in Table 2. To find the reasons for the influences discovered during the screening tests, for some selected operating conditions axial profiles of the gas composition were measured. Especially the conditions inside the riser near the distributor and around the fuel feeding port were examined. It was of great interest whether the fuel fed at higher positions reached the bottom zone or was carried away by the gas flow, in particular at high gas velocities. Answers were also expected with regard to the extension of the combustion region in air gasification. Up to which height is oxygen detectable? In contrast to the screening test experiments where more than one condition can be tested during one experimental day, for the axial profile measurements the plant was operated at one chosen set of operating parameters for the whole day. This is also some kind of long-term feasibility test for the Table 2 Low and high value for screening tests Factor

λ

Level Value

− 0.3

T + 0.6

− 750 ◦ C

utop + 850 ◦ C

− 3.5 m/s

hfeed + 5 m/s

− 2.5 m

+ 4.6 m

721

operation of the gasifier at the chosen condition. Because sewage sludge has a high ash content and the ash tends to bake in the course of time and to form agglomerates which lead to defluidization, the higher temperatures where omitted and the axial profile measurements were carried out at 1023 K only. An axial profile of gas concentration was also measured using only N2 as fluidizing gas. Therefore only the pyrolysis gas composition was measured, although some homogeneous gas phase reactions will also occur. The pyrolysis experiment is interesting especially with regard to the carbon oxides. Is carbon monoxide the only product of devolatilization or will carbon dioxide be released as well to a certain extent? In order to examine the CO2 -reforming reactions in gasification, axial profile measurements were carried out with a fluidizing agent mixed from N2 and CO2 . Both of them were supplied from separate gas cylinders containing 100% of carbon dioxide and nitrogen, respectively. They were mixed directly below the distributor plate. The amount of carbon dioxide in the mixture was desired to be the same as the oxygen in air, so that a switch from air gasification conditions to the CO2 /N2 -mixture was just a replacement of the oxygen in the gasifying agent by carbon dioxide. At first, it was intended to measure additionally the gas composition with a H2 O/N2 -mixture as gasifying agent, but as the heat of evaporation must also be supplied by the electrical heating, this idea has been dropped. This is not too bad because there was no great difference expected between fluidizing with nitrogen and with a CO2 /N2 - or H2 O/N2 mixture, respectively, since Kersten [12] has shown that in a conventional non-catalytic atmospheric CFB gasifier, operated below 1000 ◦ C, carbon dioxide gasification and steam reforming reactions do not proceed to a significant extent. Therefore the measurement of the axial profile of gas composition in gasification with a CO2 /N2 -mixture is just an experiment to verify that Kersten’s statement is also true for sewage sludge gasification.

3. Modeling It was intended to develop a mathematical model for the simulation of the gasifier. As it was intended not only to include the fluid dynamics of the circulating fluidized-bed system but also to model the reaction network for gasification, the main gasification reactions have to be considered. Additionally a choice had to be made whether these reactions can be modeled by equilibrium consideration or with a kinetic approach. It was decided to include kinetic rate expressions in the simulation program; nevertheless, an equilibrium calculation of gasification was also performed. Kinetic rate expressions for the gasification reactions included in the model were chosen from the literature. With the axially measured gas composition, it should be possible to adjust the kinetic rate constants measured for coal or biomass to sewage sludge behavior.

722

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

The reaction network chosen for the modeling part consists of the devolatilization reaction and the homogeneous and heterogeneous oxidation and gasification reactions. The drying process was assumed to occur in parallel with the devolatilization. For modeling purposes it is important to know the mass fraction of the initial fuel, which is pyrolyzed. It is assumed that the total yield of volatiles equals the volatile content of the parent fuel determined by the proximate analysis. Subsequently the composition of the volatiles becomes interesting. For the sake of simplification it was assumed that the char consists of pure carbon. The released volatiles could be assumed to decompose according to the following stoichiometrically consistent equation:

The release flux of the gaseous species H2 S, N2 , CO, CH4 and H2 (and CO2 , C2 H4 , C6 H6 ) are only fractions of the total mole flux. The heterogeneous reactions occurring during gasification are char reacting with oxygen, water vapor or carbon dioxide, respectively. The two reactions with oxygen can be expressed in one equation, as can the two possible reactions with water vapor:

Cvc Hvh Ovo Svs Nvn

1 ≤ ␣ ≤2

(2’)

C + CO2 → 2CO

(3’)

→ vs H2 S +

1 2 v n N2

+ ξCO vo CO +

− 2(1 − ξC2 H4 − 4.5ξtar )vc + (ξCO + 1)vo

− vs ]H2 + ξC2 H4 vc C2 H4 + ξtar vc C6 H6

(1)

In Eq. (1) vi is the mole fraction of component i (i = C, H, O, S, N) in the volatiles. Eq. (1) assumes that • All nitrogen is released as N2 . Additionally NH3 could be taken into account as primary product of devolatilization, as van der Drift et al. [13] and Kurkela [14] found that about 60% of the fuel-bound nitrogen is converted to NH3 , but for simplicity reasons the component NH3 is neglected here. • All sulfur is released as H2 S, because in gasification oxygen is scarce and sulfur will be released as H2 S and not as SO2 . • The oxygen might be released as CO only, or as a mixture of CO and CO2 . • The rest of the carbon in the volatiles results in the products CH4 , C2 H4 and an additional tar component (C6 H6 ). • The hydrogen not consumed by H2 S and hydrocarbons will decompose as H2 . Thus, one has to introduce three splitting factors: • one parameter for the part of the oxygen reacting to CO (␰CO ); • one parameter for the fraction of carbon reacting to tar (␰tar ); • finally, one parameter for the fraction of carbon reacting to C2 H4 (ξC2 H4 ). The total flux of volatiles in mol/s depends on the fuel feed rate m ˙ fuel and the composition only: n˙ vol =

1 ≤ ␣ ≤2

(1’)

C + ␤H2 O → (2 − ␤)CO + (␤ − 1)CO2 + ␤H2 , where

1 2 (1 − ξCO )vo CO2

+[(1 − 2ξC2 H4 − 6ξtar )vc − 21 (ξCO + 1)vo ]CH4 + [ 21 vh

␣C + O2 → 2(␣ − 1)CO + (2 − ␣)CO2 , where

m ˙ vol m ˙ fuel xvol,raw = Mvol v c M C + v h M H + v o M O + v s MS + v n M N (2)

The splitting factor α in the combustion reaction determines the ratio of produced carbon monoxide to carbon dioxide. There are empirical correlations available for the prediction of α. The correlation given by Linjewile and Agarwal [15] was used in the present model giving, e.g. α = 1.3 for T = 1023 K and α = 1.2 at T = 1123 K. In the steam gasification or so-called heterogeneous water gas shift reaction (reaction (2 )), the splitting factor β as introduced by Matsui et al. [16] will be adopted in the model with the value β = 1.2. As long as oxygen is present combustion of the gaseous species CH4 , H2 and CO will take place: CH4 + 21 O2 → CO + 2H2

(4’)

H2 + 21 O2 → H2 O

(5’)

CO + 21 O2 → CO2

(6’)

If all oxygen is consumed, carbon monoxide and hydrogen could take part in the well-known water-gas shift reaction: CO + H2 O ↔ CO2 + H2

(7’)

The water-gas shift reaction is an equilibrium reaction. Depending on temperature, the equilibrium is on the side of the products or the educts. So the reaction can be driven in both directions. As reaction (7 ) is a reaction with constant volume, pressure will not influence the equilibrium. A very pressure sensitive reaction is the reaction of water vapor with methane (steam reforming): CH4 + H2 O ↔ CO + 3H2

(8’)

Also a CO2 -gasification of methane (CO2 reforming) could be considered. As product gases only CO and H2 are taken into account: CH4 + CO2 ↔ 2CO + 2H2

(9’)

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

In this study of gasification reactions it was not intended to model the complete reaction scheme of nitrogen and sulfur compounds especially as biomass fuels do not contain as much sulfur as coal does. Therefore the nitrogen and sulfur contained in the fuel was modeled to be released as volatile N2 and H2 S, respectively (Eq. (1)). 3.1. Equilibrium calculation To solve simultaneously the equilibrium of the nine reaction equations, two possible strategies can be pursued. One is the calculation of the equilibrium composition by minimizing the Gibbs free energy (or Gibbs free enthalpy) [17]. The second possibility is to solve the reaction scheme with the so called relaxation method [18,19]. The relaxation method was chosen to calculate the equilibrium composition in the present paper. In this method it is assumed that each reaction takes place in a separate reactor and reacts to equilibrium. This equilibrium composition enters the next reactor, and the next reaction can reach equilibrium. Leaving the last reactor, the composition enters again the first reactor and the chain of equilibrium calculation starts a second time. So the equilibrium composition for all reactions is found iteratively. The procedure can be stopped when the molar amount of each component does not change any more before and after a reactor cascade. All reaction equations defined above were considered. The Gibbs free enthalpy of reaction and the equilibrium constant was calculated according to Eqs. (3) and (4), respectively.
0 0 gR = vi gf,i (3)   0 gR (4) K = exp − RT The data for the Gibbs free energy of formation for each component was taken from the JANAF thermochemical tables [20]. The data is given for several temperatures in steps of 100 K. The temperature range from 800 to 1300 K was chosen, and the calculated equilibrium constants were fitted to a function of the Arrhenius type to find the equilibrium constant for each temperature in-between the given temperature steps. 3.2. Kinetic rate expressions For all kinetic rate expressions r in the model, the unit used is mol/(m3 s). The gas concentrations are all given in mol of the model compound and are based on m3 reaction volume. When in the literature different units were used, the expressions were modified to fit this unit. r=

dci dt

(5)

The amount of the reaction rate is related to the reaction equations formulated above. In order to determine the con-

723

sumption of the components, the reaction rate has to be multiplied by the stoichiometric coefficient νij of that component i given in the reaction equation j. The reaction rates used in the present paper are simplified overall-reaction rates and account for all mechanisms. This is of course a simplification, but the gasification process is controlled by the chemical reaction [21], and the particle size as well as the initial char mass has no significant effect. As the reactions rates are in mol/(m3 s), for the solids the reaction rates have to be multiplied with the molar mass of the solid species for the balance equations. 3.3. Model equations As the facility used for the experiments is very tall, and horizontal mixing was complete, the first model presented in the present paper is a 1.5-dimensional or “pseudo twodimensional” model. Although concentration changes were only considered in the axial direction, the model somewhat describes two dimensions, because the riser was divided horizontally into different phases. The model is unsteady-state and semi-empirical. Conservation equations for solids and gas are based on the semi-empirical model by Kruse et al. [22]. To model the circulating fluidized-bed gasifier, the riser was cut axially into three zones, the bottom zone, upper dilute zone and exit zone. As done in Kruse and Werther [23], the fluid-dynamic behavior of the bottom zone is considered to be similar to that of a bubbling fluidized bed. Therefore, in the bottom zone the two-phase theory of fluidization [24] was used. In the upper dilute zone a core-annulus model was applied. The exit zone was modeled as continuous stirred tank reactor for gas and solids. The solid material in the fluidized bed is composed of inert bed material and fuel. The fuel consists of volatiles, water, carbon and ash. To be able to describe the drying, the devolatilization, and the carbon gasification separately, the components of the fuel were treated as independent “pseudo solids”. So four different solid species were considered: carbon, ash (or inerts), volatiles, and the solid-bound water. Nine components in the gas were chosen to represent the gasification gas, namely oxygen (O2 ), carbon dioxide (CO2 ), carbon monoxide (CO), methane (CH4 ), hydrogen (H2 ), water (H2 O), nitrogen (N2 ), hydrogen sulphide (H2 S), and a hydrocarbon representing the tar (C6 H6 ). Benzene was chosen as the model compound for the tar because it was determined earlier as the major single component in the producer gas representing 60–80% of the total tar [25]. In the bottom zone the bubble phase was believed to be particle free. The suspension contains particles and gas and was believed to be in minimum fluidization state. Gas flows in plug flow in both the bubble and suspension phase. The solids are evenly distributed and are transported by dispersion only. Gas–solid reactions occur in the suspension phase only. Homogeneous gas reactions take place in the bubble and in the suspension phase. Because of the reaction the change in

724

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

volume of gas results in a higher velocity. The suspension phase gas stays at minimum fluidization, only the bubble phase gas velocity is increased. Thus, there is a net flow according to Yan et al. [26] that considers the production or reduction of gaseous volume by reaction. This net flow is directed from the suspension phase to the bubble phase. In addition, there is exchange of gas between these two phases. The conservation equation for the gaseous component i in the bubble phase in the bottom zone reads as follows: εb

∂cgb,i ∂(ub cgb,i ) + ∂t ∂z = −Kbs (cgb,i − cgs,i ) + εb




vi,j rb,j + ∆bz n˙ net flow,i

j(g–g)

(6) In the suspension phase the gas is transported by dispersion and convection with minimum fluidization velocity. The conservation equation reads: ∂cgs,i ∂2 cgs,i − (1 − εb )εmf Dg,ax ∂t ∂z2 ∂cgs,i + (1 − εb )umf ∂z
vi,j rsusp,j = Kbs (cgb,i − cgs,i ) + (1 − εb )εmf j(g–g)
+ cv,bz vi,j rsusp,j − ∆bz n˙ net flow,i j(g–s) (1 − εb )εmf

(7)

The solids in the bottom zone were calculated with transport by dispersion only. So the mass balance equation for the component i of the fuel particle is the following. ∂xsbz,i ∂2 xsbz,i − cv,bz Ds,ax ρs ∂t ∂z2
=m ˙ ˙ vi,j rsusp,j Return,i + cv,bz Mi Feed,i + m j(g–s)

cv,bz ρs

(8)

Because the reaction rate is in mol/(m3 s) it has to be multiplied by the molar mass of the solid component i here, since the balance for the solids is in kg/m3 . The boundary conditions for the mass balance equations in the bottom zone are the following. For gas in the bubble phase it holds cgb,i |h=0 = cgb,i,IN for gas in the suspension phase  ∂cgs,i  −(1 − εb )εmf Dg,ax ∂z z=0 = +(1 − εb )umf (cgs,i,IN − cgs,i ),

(9)

 ∂cgs,i  =0 ∂z z=Hbz

(10)

for the solids in the suspension phase of the bottom zone  ∂xsbz,i  =0 (11) ∂z z=0  ∂xsbz,i  −cv,bz Ds,ax ρs ∂z z=Hbz  −fd cvd vd ρs (xsd,i − xsbz,i ) = −(1 − fd )cvl vl ρs (xsl,i − xsbz,i )

(12)

The feeding of gas and solids (feed and return) was described by an ousting model instead of absolute mass flow rates. Doing this, it is taken into consideration that for example during feeding the solid volume concentration can increase or decrease in case the solids present are ousted by solids with lower volume concentration. The distribution is approximated with the Gaussian error-function (ferf ).   xsbz,i Gs ferf (13) m ˙ Return,i = 1 − xReturn,i   xsbz,i m ˙ = 1 − (14) m ˙ Feed ferf Feed,i xFeed,i In the upper dilute zone a core-annulus model with heightdepending core radius is used. The gas flow across the boundary between the core and the annulus is described by an exchange flow, and the change in volume again is modeled by a net flow. The change in solids across the boundary is due to convective compensation because of the enlarging or shortening of the core and the annulus region. Additionally, because there will be entrainment of downfalling particles by the gas stream at the boundary from core to annulus phase, an exchange flow for the solid phase was defined. The fraction of the dense phase, i.e. the annulus region, of the total cross-sectional area is described by the variable fd . The solids volume concentration in the two regions is contained in cv with the index l or d for lean and dense phase, respectively. For the velocity of gas the variable u and for the velocity of solids v is used. As in the dense phase the flow is downward, the velocities are defined negative. It follows for the balance for gas in the dense phase of the upper dilute zone for component i: ∂[fd cgd,i ] ∂[fd cgd,i ] + (1 − cvd )ud ∂t ∂z ∂fd cgl,i − Kdl,g (cgd,i − cgl,i ) = (1 − cv,d )ud ∂z 
+ fd (1 − cvd ) vi,j rdense,j j(g–g) 
+ cvd vi,j rdense,j  − ∆ud n˙ net flow,i j(g–s)

(1 − cvd )

(15)

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

the balance for gas in the lean phase for component i: ∂[(1 − fd )(1 − cvl )cgl,i ] ∂[(1 − fd )(1 − cvl )ul cgl,i ] + ∂t ∂z ∂fd = −(1 − cvd )ud cgl,i + Kdl,g (cgd,i − cgl,i ) + (1 − fd ) ∂z  

× (1 − cvl ) vi,j rlean,j + cvl vi,j rlean,j  j(g–g) j(g–s)

725

∂cgez,i Hez ∂t = (−uez + fd (1 − cvd )ud )cgez,i + (1 − fd )(1 − cvl )ul cgl,i  

+ (1 − cv,ez ) vi,j rez,j + cv,ez vi,j rez,j  Hez j(g–g) j(g–s) (23)

(1 − cv,ez )

at z = Hbz :

the balance for solids in the exit zone for component i: ∂xsez,i Hez cv,ez ρs ∂t = −Gs,i + fd ccv vd ρs xsez,i + (1 − fd )cvl vl ρs xsl,i
+cv,ez Mi (24) vi,j rez,j Hez j(g–s) The variables, which are not yet known, are defined according to the following closure laws. In the mass balances above the gas and solids velocities (umf , ub , ud , ul , uez , vd , vl ) have yet to be determined, as well as the void fractions (εmf , εb ) and solid volume concentrations (cv,bz , cvl , cvd , cv,ez ) and the fraction of the dense zone from the cross sectional area (fd ). The solid density is assumed to be constant ρs = 2600 kg/m3 . The solids circulation rate Gs as well as the solid volume concentration in the bottom zone and in the exit zone, respectively, are input parameters for the model and are taken from measurements. The minimum fluidization void fraction εmf and velocity umf have to be determined for the bed material and are input parameters of the model. The velocity of gas in the dense phase is assumed to be constant and was set to −0.75 m/s according to optical probe measurements by Schoenfelder [28]. The solids volume concentration in the dense phase cvd was assumed to be constant over the riser height. cvd was set to 0.25 according to the findings of Schoenfelder. In the bottom zone it holds

(1 − fd )(1 − cvl )ul cgl,i = −fd (1 − cvd )ud cgl,i + ub cgb,i

cv,bz = (1 − εb )(1 − εmf )

+ ∆ud n˙ net flow,i

(16)

the balance for solids in the dense phase of the upper dilute zone for component i:

∂ fd xsd,i ∂ fd xsd,i cvd ρs + cvd vd ρs ∂t ∂z
∂fd = cvd vd (17) ρs xsl,i + fd cvd Mi vi,j rdense,j ∂z j(g–s) the balance for solids in the lean phase for component i:

∂ (1 − fd )cvl xsl,i ∂ (1 − fd )cvl vl xsl,i ρs + ρs ∂t ∂z
∂fd vi,j rlean,j ρs xsl,i + (1 − fd )cvl Mi = −cvd vd ∂z j(g–s) (18) The boundary conditions for these four equations for the gas in the dense phase: at z = Hap − Hez : cgd,i = cgez,i

(19)

for the gas in the lean phase:

+(1 − εb )umf cgs,i

(20)

for the solids in the dense phase: at z = Hap − Hez : xsd,i = xsez,i

(21)

for the solids in the lean phase: at z = Hbz : (1 − fd )cvl vl xsl,i = −fd cvd vd xsd,i + (fd cvd vd +(1 − fd )cvl vl )xsbz,i

(22)

The exchange coefficient Kdl,g is dependent on the fraction of the dense phase of the total cross sectional area fd , as described by Schoenfelder et al. [27]. The exit zone was modeled as a continuous stirred tank reactor. The balance for gaseous component i in the exit zone is obtained as

(25)

This relationship defines the solids volume concentration in the bottom zone, which is the fraction not occupied by the gas phase. The solids volume concentration in the bottom zone was assumed to be constant and was set to cv,bz = 0.3. Thus Eq. (25) allows us to determine εb . The gas velocity in the dense phase can be determined using the following equation used by Schoenfelder [28]:   1 − cvd nRZ −1 umf ud − vd = (26) 1 − εmf 1 − εmf For the remaining unknowns the same amount of linear independent equations is necessary. In this model as in the great majority of gasification models in fluidized beds [29], an empirical correlation to describe the fluid dynamics inside the reactor is used. Thus the need to solve the momentum equations is avoided. The mean solids volume concentration for each height of the riser contains the

726

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

two parts of solids volume concentration in the dense and in the lean phase:

At the bottom (z = 0) the incoming gas flow V˙ IN is distributed on the two phases,

c¯ v = (1 − fd )cvl + fd cvd

z = 0 : V˙ IN = (ub + (1 − εb )umf )At

(27)

This mean solids volume concentration can be determined from axial pressure measurements and can be fitted to the following empirical exponential equation according to Kunii and Levenspiel [30]: c¯ v = cv,ez + (cv,bz − cv,ez ) exp(−αcv (z − Hbz ))

(28)

The solids circulation rate Gs results from the upwards flowing solids in the lean phase and the downwards flowing solids in the dense phase (remember vd to be negative!). Gs = fd cvd vd ρs xsd + (1 − fd )cvl vl ρs xsl

(29)

The solids velocity in the lean phase vl is contained in an approach given by Martin [31] for the settling velocity of single particles.  2 1√ Re = 18 1 + Ar − 1 (30) 9 This equation is valid for 0 < Re < 105 , with the Reynolds and the Archimedes number defined by dp (ul − vl ) Rep = vG

(31)

gdp3 ρs Arp = 2 vG ρ g

(32)

From Eq. (30) it follows  2 vG 1√ vl = ul − 18 1+ Ar − 1 dp 9

(35)

In the upper dilute zone the homogeneous and heterogeneous reactions in both core and annulus regions contribute to the velocity in the lean phase, because the velocity of gas in the dense phase is assumed to be constant. The axial profile of the gas velocity in the lean phase can be expressed by (1 − fd )(1 − cvl )

∂ul ∂z

  

RT   vi,j rlean,j  = (1 − fd )(1 − cvl ) P i j(g–g)  

 + (1 − fd )cvl vi,j rlean,j  i j(g–s)  

 + fd (1 − cvd ) vi,j rdense,j  i j(g–g)  

 + fd cvd vi,j rdense,j  i j(g–s)

(36)

With the condition at the boundary to the bottom zone: ub + (1 − εb )umf |z=Hbz = fd (1 − cvd )ud + (1 − fd )(1 − cvd )ul

(33)

The axial velocity profile in the riser is determined by the homogeneous and heterogeneous gasification reactions. In the bottom zone heterogeneous reactions occur only in the suspension phase. Solids are consumed and gas is produced. As it is assumed that the suspension phase stays in minimum fluidization state, the surplus gas contributes to the velocity in the bubbles only. Thus, we get the following differential equation for the velocity profile in the bubble phase of the bottom zone:     ∂ub RT  

= εb vi,j rb,j  ∂z P i j(g–g)   

 + (1 − εb )εmf  vi,j rsusp,j  i j(g–g)   

 + cv,bz  (34) vi,j rsusp,j  i j(g–s)

(37)

The gas velocity in the exit zone is uez = fd (1 − cvd )ud + (1 − fd )(1 − cvd )ul   

RT   + cv,ez vi,j rez,j  P i j(g–s)  

 + (1 − cv,ez ) vi,j rez,j  Hez i j(g–g)

(38)

Not only the velocity but also the concentration of each component i in the gas changes because of reaction. Yan et al. [26] pointed out the significance of a ‘net flow’. So their calculation of the net flow is adopted in this model. The total net flow in the bottom zone is 

(1 − εb )εmf ∆bz n˙ vi,j rsusp,j net flow = i j(g–g) 
(39) + cv,bz vi,j rsusp,j  j(g–s)

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

And the net flow of each component i in the bottom zone can be calculated from 

c gs,i (1 − εb )εmf ∆bz n˙ vi,j rsusp,j net flow,i =  i cgs,i i j(g–g) 
+ cv,bz vi,j rsusp,j  (40) j(g–s) The corresponding equation for the upper dilute zone for the total net flow is 

fd (1 − cvd ) vi,j rdense,j ∆ud n˙ net flow = i j(g–g) 
(41) + fd cvd vi,j rdense,j  j(g–s) and for the gas species i in the upper dilute zone it holds 

c gs,i fd (1 − cvd ) ∆ud n˙ vi,j rdense,j net flow,i =  i cgs,i i j(g–g) 
+ fd cvd vi,j rdense,j  (42) j(g–s)

It is obvious that the parameter with the highest influence is the air ratio λ. This is not surprising and in agreement with previous literature [13,32,33]; and the chosen higher value of λ = 0.6 is the upper limit for an operation condition which can be called gasification. Vriesmann et al. [34] even stated that the lower heating value of gas produced at air ratios higher than 0.45 is not very useful for combustion purposes. The parameter temperature shows the trend that with higher temperature the heating value of the gas increases. This can certainly be understood looking at the tar cracking and the other endothermal gasification reactions, which will perform better at higher temperatures. For the feeding height, if one looks at the lower heating value of the gas, no clear trend is obvious. For high velocity and low air ratio the heating value becomes better the lower down the fuel is fed into the riser. The parameter gas velocity has the least influence on the product gas composition. Therefore, neither a final statement about the best feeding height nor about the optimal gas velocity can be made. In general, it should be stated here that the feasibility of sewage sludge gasification in a circulating fluidized bed has been proven with these experimental findings. The lower heating value obtained in the experiments, and also the overall efficiency of the process, fits well with the range known for gasification of for instance wood, as these were reported in the literature. An efficiency for the gasification process, ηeff =

4. Results and discussion 4.1. Screening experiments With screening experiments the influence of the air ratio, gas velocity, temperature, and the feeding height on the product gas composition and lower heating value was examined. The higher and lower levels chosen for these parameters were given in Table 2. In Fig. 4 all the measured results are shown. The concentration of the combustible components H2 , CO, CH4 and C2 H4 are given as well as the concentration of carbon dioxide and the lower heating value of the synthesis gas. All the values refer to dry gas at standard temperature and pressure (STP). The two left columns of diagrams in Fig. 4 refer to the experiments at the lower velocity (3.5 m/s), the two right columns of diagrams show the results for the higher velocity (5 m/s). For each of the velocities there is one column of diagrams for the measurements with the higher feeding port (4.6 m, left column of the two), and one for the lower feeding port (2.5 m, right column of the two). In all diagrams on the abscissa the temperature (750 and 850 ◦ C) is shown, and in all diagrams the results for the two air ratios (λ = 0.3, λ = 0.6) are given. On the ordinate the gas concentration and the lower heating value in weight percent and kJ/m3 on a water-free basis are given, respectively.

727

V˙ g LHVg (J/m3 ) m ˙ s LHVs (J/kg)

(43)

of 58% for λ = 0.3 and 35% for λ = 0.6 was obtained. The efficiency given in the literature ranges from 46% to 63% for biomass like barley, grass and miscanthus [35] to about 68–87% for wood [12,36–38]. The produced gas from the sewage sludge gasification performed in this work had on average a lower heating value of 4.7 MJ/m3 from the experiments at λ = 0.3 and 1.9 MJ/m3 for λ = 0.6. This compares well with the lower heating value given by Kersten [12] who measured 3–5.8 MJ/m3 STP in air gasification of wood (λ = 0.4–0.2). The carbon conversion in the present study was calculated from the carbon detected in the gas (without tar) and was about 96% for the λ = 0.6 experiments, and at λ = 0.3 it was 85% on average. In the literature, a carbon conversion of 97% [35,38] or even complete carbon conversion [39] is often given for wood and other biomass fuels. But, if the amount of carbon in the tar is excluded from the balance given by Kersten [12], a conversion of 87% at λ = 0.3 is obtained, which agrees with the calculated value in this work. 4.2. Axial profile measurements Axial profile measurements of the gas composition have been performed to better understand the results of the screening tests. Especially the influence of the feeding height, which

728

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

Fig. 4. Results of screening tests: influence of λ, T, utop and hfeed .

Fig. 5. Axial profile of gas composition measured at λ = 0.6, utop = 5 m/s, and hfeed = 2.5 m (H2 O calculated from O-mass balance).

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

729

Fig. 6. Axial profile of gas composition measured at λ = 0.6, utop = 5 m/s, and hfeed = 4.6 m (H2 O calculated from O-mass balance).

showed no uniform trend for different gas velocities, needed more explanation. To further examine the influence of the feeding height, in Figs. 5 and 6 the results from axial profile measurements at λ = 0.6 with a gas velocity at the top of 5 m/s and a feeding height of 2.5 m and 4.6 m, respectively, are shown. As measurements at λ = 0.3 were restricted to the temperature of 750 ◦ C because of ash agglomeration problems, the following diagrams all refer to this latter temperature. The height of the measurement position above the distributor is given on the abscissa, and the gas concentration is on the ordinate. For convenience an arrow points at the feeding location. In case there were repeated measurements at one measurement port, as for example at the position after the cyclone in Fig. 5, the single symbols were shifted to the sides so that the repeatability of the measurement is visible. The concentrations given are all based on the raw gas state. All gases but the water content were measured as dry gas and were then calculated to the raw gas condition by the water content. Because in some cases the water content had not been measured, the H2 O-concentration used is calculated from the oxygen mass-balance. This method was used earlier in case a water measurement has not been carried out [40], and a comparison to the measured values showed good agreement in the present work.

Obviously, in the experiments with the high superficial gas velocity, the particles entering at the upper feeding location did not reach the bottom zone to react there. Pyrolysis products such as hydrogen, methane and ethylene were only measured above the feeding point (cf. Fig. 6). Narva´ez et al. [33] found already that for a bubbling fluidized bed feeding near the bottom is recommended for gas of good quality. Because the gas quality from the experiments with λ = 0.6 is poor, the same axial profiles were intended to be measured at λ = 0.3. But operation of the plant at λ = 0.3 was not easy with the higher feeding port. With the higher velocity steady state operation could not be held long enough for axial profile measurement, because possibly many unreacted particles were entrained from the riser and reacted further in the downcomer, which lead to blocking. Therefore, it can be stated that a feeding port in the upper section, even though possible, is not advisable. To examine the influence of the velocity, axial profiles were measured with a superficial gas velocity of 3.5 and 5 m/s, respectively, at λ = 0.3 with feeding at the 2.5 m position. The results are shown in Figs. 7 and 8. Comparing the results from the experiments with the same feeding height but different gas velocities, it is obvious that at the higher gas velocity the hydrogen concentration is higher while the CO concentration remains roughly constant, and

Fig. 7. Axial profile of gas composition measured at λ = 0.3, utop = 3.5 m/s, and hfeed = 2.5 m.

730

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

Fig. 8. Axial profile of gas composition measured at λ = 0.3, utop = 5 m/s, and hfeed = 2.5 m (H2 O calculated from O-mass balance).

therefore not only a lower feeding height but also a higher velocity is recommended. 4.3. Pyrolysis and CO2 -gasification experiment The measurements of the gas composition from pyrolysis and with a CO2 /N2 -mixture, respectively, have been conducted to get information on the direct pyrolysis components, and also to test the kinetic rate expressions taken from literature. Using the 1.5-dimensional model of the CFB, the kinetic constants from different authors were applied and adjusted if necessary to simulate the axial profiles measured during the experiments. In Table 3 the average exit gas composition from the two experiments are given, respectively. Looking first at the results from pyrolysis, it is obvious that carbon dioxide is a primary product of the decomposition reaction. Because no oxygen is added to the reaction chamber, the oxygen in the CO2 can only result from the fuel particles. Therefore the splitting factor ξ CO is not equal to one. What else can be seen from Table 3 is that the addition of CO2 to the nitrogen in the fluidizing gas does not lead to increased carbon conversion. The water gas shift reaction is influenced, however, resulting in slightly lower hydrogen content and increase in the water concentration, whereas a change in the amount of carbon monoxide could not be detected. The reason will certainly be the low temperature in the experiments. At these temperatures the Boudouard reaction does not proceed to a significant extent, as already reported by Kersten [12]. Also the CO2 -reforming of methane does not seem to proceed because although the methane concentration is decreasing, the hydrogen and carbon monoxide values do not increase. The results might be compared with the pyrolysis gas composition given by Schuller and Brat [41] (Table 4). The concentrations given by the authors are on a nitrogen-free

basis, but qualitative agreement is good: The carbon dioxide and carbon monoxide concentration detected in the gas are nearly equal and the hydrogen content is approximately twice that of the carbon monoxide. Only the methane concentration obtained by Schuller and Brat is lower. 4.4. Results from the equilibrium calculation The calculations were carried out for the composition of the dried sewage sludge used in the experiments. The devolatilization products were calculated as presented above and were taken as input concentrations. The chosen air ratio for the equilibrium calculation was λ = 0.3. The resulting equilibrium compositions were computed. In Fig. 9 the concentration for the main components are shown. They are given Table 4 Pyrolysis gas composition according to Schuller and Brat [41] in volume percent Component

vol%N-free

H2 CO CO2 CH4

21.8–40.9 15.55–44.05 18.4–41.0 5.9–14.5

Table 3 Exit gas composition from pyrolysis and CO2 -gasification experiments vol% raw

CO2

CO

H2

CH4

C2 H 4

H2 O

Pyrolysis CO2 -gasification (ψCO2 = 0.2)

4.0 16.6

4.8 4.8

8.1 6.1

4.7 3.6

1.8 1.5

4.7 5

Fig. 9. Results from equilibrium calculations. Main components, composition in vol% at different temperatures.

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

731

Table 5 Kinetic rate constants valid for sewage sludge gasification Reaction (1 )

αC + O2 → 2(α − 1)CO + (2 − α)CO2

Kinetic rate expression, (mol/m3 s) kinetic constants

Reference

r(1) = k(1) cO2 f(1)

[45]

f(1) = 0.05

(2 )

C + βH2 O → (2 − β)CO + (β − 1)CO2 + βH2

  (J/mol) 6 k(1) = 5.957 × 102 (m/s K)Tp exp − 149,440 dp  RTp −3 r α = 1+2f exp 37,737RT(J/mol) 1+fr with fr = 4.72 × 10 p

[15]

r(2) =

[16]

k(2) cH2 O

(2)

(2)

(2)

1+Kk H O cH2 O +Kk H cH2 +Kk CO cCO 2 2

f(2)

f(2) = 2

  (J/mol) ρchar k(2) = 2.39 × 102 (m3 /s mol) exp − 129,000 RT MC (1 − X)   (2) 30,100 (J/mol) −2 3 Kk H2 O = 3.16 × 10 (m /mol) exp − RT   (2) Kk H2 O = 5.36 × 10−3 (m3 /mol) exp − 59,800RT(J/mol)   (2) Kk CO = 8.25 × 10−5 (m3 /mol) exp − 96,100RT(J/mol) β = 1.2 X = 0.5 (3 )

C + CO2 → 2CO

r(3) =

(3)

k(3) cCO2

(3)

1+Kk CO cCO2 +Kk CO cCO 2

f(3)

[46,47]

f(3) = 1

  (J/mol) k(3) = 4.89 × 107 (m3 /s mol) exp − 268,000 RT (3) CO (3) Kk CO

Kk

ρchar MC (1 − X)

= 6.60 × 10−2 (m3 /mol)

  = 1.2 × 10−1 (m3 /mol) exp − 25,500RT(J/mol)

X = 0.35 (4 )

CH4 + 21 O2 → CO + 2H2

0.7 0.8 r(4) = k(4) cCH c f(4) 4 O2

[48]

f(4) = 100 0.75

k(4) = 1.58 × 1010 ((m3 ) (5 )

(6 )

H2 + 21 O2 → H2 O

CO + 21 O2 → CO2

  (J/mol) /s mol0.75 ) exp − 202,641 RT

r(5) = k(5) cO2 cH2 f(5) f(5) = 0.001   (J/mol) k(5) = 1.08 × 1010 (m3 /mol s) exp − 125,525 RT

[49]

0.5 0.25 r(6) = k(6) cCO cH c f(6) 2 O O2

[48]

f(6) = 1

(7 )

CO + H2 O ↔ CO2 + H2

  0.75 (J/mol) k(6) = 1.78 × 1010 ((m3 ) /s mol0.75 ) exp − 180,032 RT   cCO cH r(7) = k(7) cCO cH2 O − K 2 2 f(7)

[50]

(7)eq

f(7) = 0.1

(8 )

CH4 + H2 O ↔ CO + 3H2

  k(7) = 2.778 (m3 /mol s) exp − 12,560RT(J/mol)   4 (J/mol) K(7)eq = 0.022 exp 3.473×10 RT   3 cCO cH r(8) = k(8) cH2 O cCH4 − K 2 cS f(8) f(8) = 0.1   k(8) = 4.916 × 10−10 T 2 (kg m4 /s mol2 K2 ) exp − 36,150RT(J/mol)   5 (J/mol) 2 K(8)eq = 3.106 × 1014 (mol/m3 ) exp − 2.088×10 RT

(9 )

CH4 + CO2 ↔ 2CO + 2H2

Neglected (does not proceed, too slow)

(10 )

C2 H4 + O2 → 2CO + 2H2

1.18 r(10) = k(10) cC0.92 H4 cO f(10) 2

f(10) = 1 1.08

k(12) = 3.71 × 1012 ((m3 ) (11 )

C6 H6 + 3O2 → 6CO + 3H2

[51]

(8)eq

r(11) = k(11) ctar cO2

1 MC ρchar dp

[52]   (J/mol) /s mol1.08 ) exp − 209,205 RT

  (J/mol) k(11) = 1.58 × 1012 (m3 /s mol) exp − 202,641 RT

732

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

in vol% based on the raw gas for temperatures in the range from 800 to 1300 K. There is a big change in composition from 800 to 900 K. At temperatures above 1000 K the composition does not change significantly. The main products are H2 and CO in nearly the same amount; the H2 :CO ratio is around one. This ratio stays the same for all temperatures, but from 800 to 1000 K the H2 - and CO-concentration doubles, respectively. The CH4 - and CO2 -content at higher temperatures is astonishingly low (nearly zero). The equilibrium concentration of water is nearly unaffected by a change in the temperature (around four volume per cent). Looking at the experimentally determined composition of a gasification gas given in the literature or measured in this work, it can be stated that there must be strong kinetic influence that affects the composition because during gasification with air there are considerable amounts of carbon dioxide present, and it has not

been reported that the hydrogen and carbon monoxide concentrations calculated above were ever measured in air gasification. The same deviation between measured synthesis gas composition and the concentrations predicted by equilibrium calculation has been detected by Li et al. [17] and Kersten [12]. Therefore the kinetic approach was chosen to model the reaction network in the program. The pseudo two-dimensional model was used to check the kinetic rate expressions taken from the literature, whether they are also valid for sewage sludge gasification, and whether they are applicable for gasification in circulating fluidized beds, too. To adjust the kinetics for some reactions of the complete reaction network separately from the others, the measurements of the gas composition along the riser height during pyrolysis and CO2 /N2 gasification were taken, respectively. The best fit for the splitting factor for the distribution of the oxygen-content in

Fig. 10. Axial profiles of measured gas composition in (a) pyrolysis, (b) CO2 -gasification, and (c) air-gasification experiments and modeling results from pseudo two-dimensional model.

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

the fuel to CO and CO2 was obtained for ξ CO = 0.3. With nitrogen as the only fluidizing gas in the pyrolysis experiments, the heterogeneous gasification reactions can perform only with the steam released during drying and with the carbon dioxide from the devolatilization. These take part in the water-gas shift reaction, too; and gasification reactions of the hydrocarbons (reaction (8 ) and (9 )) might also play a role. But especially the CO2 -gasification experiments showed that a higher amount of carbon dioxide present in the gasifier did not significantly alter the gas composition in comparison to the pyrolysis experiment. This has also been detected by Garc`ıa et al. [42] who achieved only higher conversion and higher CO-concentration in their experiments with pine sawdust in a fluidized-bed gasifier at 700 ◦ C with higher amounts of catalyst in the reactor. As the amount of carbon dioxide strongly influences the equilibrium of the water-gas shift reaction, it can be stated that the water-gas shift reaction is nearly unaffected and must therefore be far from equilibrium. Chamberland and Labrecque [40] also found that the final composition of the synthesis gas is not that expected from the equilibrium constants but depends far more on the pyrolysis reactions. So the assumption often made in gasification modeling that the water-gas shift reaction reaches equilibrium is obviously wrong. Hamel [43] also reported that equilibrium of the water-gas-shift reaction in fluidized bed is seldom attained. This is why, although the kinetic rate expression is formulated as a rate equation for reversible reactions according to Franks [44] with the equilibrium constant, the kinetic constant for the reaction is smaller than one. A kinetic rate constant smaller than one signifies that the attainment of the equilibrium is slowed down. The reactions, which have already been presented above, are listed again in Table 5. They are given together with the kinetic rate expressions, which are valid for sewage sludge gasification. As has been discussed already, the carbon dioxide reforming reaction does not proceed to a significant extent and was therefore omitted. For the partial combustion of the tar compound (e.g. benzene) a rate expression of second order with a kinetic rate constant similar to the one for the methaneoxidation was used (see reaction (11 ) in Table 5). In Table 5 the reactions (10 ) and (11 ) are the partial combustion of ethylene and tar, respectively. C2 H4 + O2 → 2CO + 2H2

(10’)

C6 H6 + 3O2 → 6CO + 3H2

(11’)

For the adjustment of the oxidation reaction kinetics, different measurements of axial gas composition profiles were available. In Fig. 10 the measured axial profiles from the pyrolysis, CO2 -gasification and one of the air-gasification experiments are shown, together with the modeling results. For the air-gasification experiment simulation, the measurement at λ = 0.3 with a superficial gas velocity at the top of utop = 3.5 m/s at the temperature of T = 750 ◦ C was chosen,

733

where the feed was supplied at hfeed = 2.5 m above the distributor plate. Agreement of the measured gas composition with the calculation results from the pseudo two-dimensional model is good. The best fit was obtained for the splitting factor for the amount of ethylene with ξC2 H4 = 0.1, and for the one for the tar amount with ξ tar = 0.005. With this tar coefficient a benzene concentration of 1460 mg/m3 was calculated for the λ = 0.3 case. 5. Conclusions Combustion, pyrolysis and gasification of sewage sludge in the circulating fluidized bed were examined by both, experimental and modeling studies. In order to obtain information about the optimal operation parameters, several gasification experiments were performed with dried sewage sludge (>90% dry matter) in a pilot-scale circulating fluidized bed. The experimental program was subdivided into screening tests, axial gas composition measurements, and additional pyrolysis as well as CO2 -gasification experiments. The program for the screening tests was developed based on statistical methods and was conducted to determine the influence of the temperature, air ratio, feeding height, and superficial gas velocity. Axial profile measurements were performed to better understand the processes inside the riser; different gasification gases than air were used to learn about the devolatilization and reforming reactions and kinetics. From the experimental part, the following conclusions can be drawn: • The excess air ratio has the most significant influence on the produced gas composition. A value of λ = 0.3 is a good choice for the operation of a gasifier for sewage sludge. • Temperature has the second most important influence. At higher temperatures a more valuable gas is produced. But the choice of temperature in sewage sludge gasification is limited due to the risk of melting, agglomeration and sintering of the sewage sludge ash. • Although no clear trend is obvious for the optimal feeding height, for good gas quality a feeding port close to the bottom of the riser is recommended, because mixing of the fuel particles is better there. Feeding at higher locations leads to particle entrainment and incomplete carbon conversion. • With near-bottom feeding, high velocities are attainable and therefore a high fuel throughput can be achieved. • The extension of the combustion zone at the bottom of the riser is small. • In pyrolysis, in spite of the lack of oxygen in the surrounding gas, not only carbon monoxide is produced, but also carbon dioxide is a primary product of the devolatilization reaction. • CO2 -gasification reactions do not proceed to a significant extent at the low temperatures necessary to prevent ash sintering.

734

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

• The water-gas shift reaction does not reach equilibrium. Considering the diameter of 0.1 m and its height of 15 m the reactor can be described as one-dimensional. A 1.5dimensional model was developed, which contains the fluiddynamic characteristics of the circulating fluidized bed with gas and solids upflow in the center and downflow at the wall. A complete reaction network for pyrolysis, combustion and gasification was formulated. Most kinetic rate expressions were taken from the literature. Three open parameters are related to the devolatilization process, namely the splitting factor ξ CO which describes the part of the oxygen in the volatile matter which is released in the form of CO, the splitting factor ξC2 H4 for the fraction of carbon in the volatiles which is released as C2 H4 and the splitting factor ξ tar for the carbon fraction which is released as tar (and which is balanced as C6 H6 ), respectively. Since the composition of pyrolysis gas is strongly dependent on the heating rate of the fuel particles these latter parameters must be determined under fluidizedbed conditions. Numerical values of ξ CO , ξC2 H4 and ξ tar were therefore obtained by fitting the model calculations to three sets of measured axial profiles of the species O2 , CO2 , CO, H2 , CH4 , C2 H4 and H2 O which were taken under conditions of pyrolysis, CO2 -gasification and air-gasification, respectively. The model is seen to give a good description of the reactor behavior under any of these conditions. In particular, under air gasification conditions the model is seen to give a good description of the combustion zone near the bottom of the riser. The thus determined reaction kinetics can be used for simulation calculations of fluidized-bed gasifiers with different geometries [53].

Appendix A. Nomenclature Ar At c cS cv c¯ v dp D fd ferf f(No.) 0 gf,i G Gs h h0R H HHV i, j

Archimedes number cross-sectional area of reactor (m2 ) concentration (mol/m3 , kg/m3 ) char or carbon concentration in kinetic rate expression (kg/m3 ) solids volume concentration average solids volume concentration particle diameter (m, mm, ␮m) dispersion coefficient (m2 /s) volume fraction of the dense phase Gaussian error function fitting factor for the reaction specified standard Gibbs free energy of formation for component i (J/mol) Gibbs free enthalpy (J/mol) solids circulation rate (kg/(m2 s)) height in one zone (m) heat of reaction (J/mol) height of one zone (m) higher heating value (J/m3 , J/kg) counting variables

reaction rate constant (m3 /(kg s)) parameter for the calculation of the cv -profile (kcvl = 0.65) Kbs mass transfer coefficient between bubble and suspension phase in the bottom zone (1/s) Kdl mass transfer coefficient between dense and lean phase in the upper dilute zone (1/s) Kk adsorption constant according to Reed (1981) (1/atm) K, Kp , Keq equilibrium constant ((various units)) LHV lower heating value (J/m3 , J/kg) m ˙ mass flow (kg/s) m ˙ mass flow based on an area (kg/(m2 s)) mass flow based on a volume (kg/(m3 s)) m ˙ M molar mass (kg/mol) n molar amount (mol) n local cell number in the pseudo two-dimensional model n˙ molar flow (mol/s) nRZ Richardson–Zaki exponent (nRZ = 3) molar net flow (convection because of reaction) n˙ (mol/(m3 s)) P system pressure (Pa) Pe Peclet number r reaction rate (mol/(m3 s)) R ideal gas constant (J/(mol K)) Re Reynolds number t time (s) T temperature (K) ub volumetric gas flow in the bubble phase divided by the cross-sectional area of the reactor ud interstitial gas velocity in dense phase (upper dilute zone) (m/s) uez superficial gas velocity in the exit zone (m/s) ul interstitial gas velocity in lean phase (upper dilute zone) (m/s) umf minimum fluidizing velocity (superficial) (m/s) v velocity of solids (m/s) vi mole fraction of component i in volatiles) (i = C, H, O, S, N) (mol/mol) V˙ volume flow (m3 /s) w water (kg, mol) x mass fraction (kg/kg) x3,50 particle diameter of fifty percent mass fraction (mm, ␮m) X carbon conversion z coordinate in axial direction (m)

k kcvl

Greek letters α splitting factor for the reaction of carbon and O2 αcv coefficient for the fitting of the c¯ v (m−1 ) β splitting factor for the reaction of carbon and H2 O ε void fraction η dynamic viscosity (Pas) ηeff efficiency λ air ratio

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

µ νg νi,j ψ ρ ξ Indices a, ash ap ax b bz c, C d, dense eq ez g g–g g–s h, H hor i IN j l, lean max mf n, N o, O p s s, susp s, S st t ud vol waf

chemical potential (J/mol) cinematic viscosity of gas (m2 /s) stoichiometric coefficient of gas species i in reaction j volume fraction (e.g. of oxygen in air) density (kg/m3 ) splitting factor

ash apparatus (riser) axial direction bubble phase in the bottom zone bottom zone carbon dense phase in the upper dilute zone equilibrium exit zone gas homogeneous gas phase reaction heterogeneous gas-solid reaction hydrogen horizontal gas species inlet of reactor reaction number lean phase in the upper dilute zone maximum minimum fluidization state nitrogen oxygen particle solid phase suspension phase in the bottom zone in balance equation sulfur in fuel composition stoichiometric total upper dilute zone volatile water and ash free

References [1] R. Buehler, Internal Combustion (IC) Engines for Biomass Gasifiers: An Overview, IEA Thermal Gasification Seminar, in: Proceedings of the IC Engines for LCV Gas from Biomass Gasifiers, Zuerich, 28 October 1997, 1998, pp. 7–12. [2] S. Bajohr, R. Reimert, Katalytische Reinigung von Rohgasen aus der Pyrolyse und der Vergasung von Biomasse und Muell, Chemie Ingenieur Technik 71 (9) (1999) 1053. [3] O. Carsjens, Biogas - eine saubere Sache, UmweltMagazin 6 (2002) 73. [4] H. Friedrich, H. Hehrenbach, J. Giegrich, F. Knappe, Oekobilanz der verschiedenen Entsorgungswege des Klaerschlamms, Muell und Abfall 10 (2002) 558–568.

735

[5] H. Alwast, J. Hoffmeister, H. Paschlau, 2005 oder “5 vor 12”, Muell und Abfall 1 (2003) 16–29. [6] K.J. Thom´e-Kozmiensky, Aufbereitungskonzepte fuer Ersatzbrennstoffe (Processing Concepts for Substitute Fuels), Aufbereitungs Technik 43 (4) (2002) 11–20. [7] K. Redepenning, A. Hellwig, Klaerschlammverwertung durch Vergasung in Kohlekraftwerken, Abfallwirtschafts J. 7 (1995) 442–445. [8] H. Anderl, A. Mory, T. Zotter, BioCoComb-Vergasung von Biomasse und Mitverbrennung von Gas in einem Kohlenstaubkessel, VGB Kraftwerks Technik 3 (2000) 68–75. [9] L.D. Smoot, S.C. Hill, H. Xu, NOx control through reburning, Prog. Energy Combust. Sci. 24 (1998) 385–408. [10] G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experimenters— An Introduction to Design, Data Analysis and Model Building, Part III: Measuring the Effects of Variables, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1978. [11] A. Nordin, L. Eriksson, M. Oehman, NO reduction in a fluidized bed combustor with primary measures and selective non-catalytic reduction—a screening study using statistical experimental designs, Fuel 74 (1) (1995) 128–135. [12] S.R.A. Kersten, Biomass Gasification in Circulating Fluidized Beds, Dissertation Twente University, Twente University Press, Enschede, Netherlands, 2002. [13] A. van der Drift, J. van Doorn, J.W. Vermeulen, Ten residual biomass fuels for circulating fluidized-bed gasification, Biomass Bioenergy 20 (2001) 45–56. [14] E. Kurkela, Formation and removal of biomass-derived contaminants in fluidized-bed gasification processes, PhD thesis, VTT Publications, Espoo, 1996, p. 287. [15] T.M. Linjewile, P.K. Agarwal, The influence of product CO/CO2 ratio on the ignition and temperature history of petroleum coke particles in incipiently gas-fluidized beds, Fuel 74 (1) (1995) 12– 16. [16] I. Matsui, D. Kunii, T. Fursuawa, Study of fluidized bed steam gasification of char by thermogravimetrically obtained kinetics, J. Chem. Eng. Jpn. 18 (2) (1985) 105–113. [17] X. Li, J.R. Grace, A.P. Watkinson, C.J. Lim, A. Erguedenler, Equilibrium modeling of gasification: a free energy minimization approach and its application to a circulating fluidized bed coal gasifier, Fuel 80 (2001) 195–207. [18] O. Teichmann, G. Saller, G. Funk, W. Krumm, Die Relaxationsmethode zur Bestimmung der Gleichgewichtszusammensetzung der Gase bei der Verbrennung von Kohlenwasserstoffen und Vergasung von Biomasse, Muell und Abfall 30 (3) (1998) 153–158. [19] J. Gmehling, B. Kolbe, Thermodynamik, second ed., VCH Verlagsgesellschaft mbH, Weinheim, 1992. [20] JANAF Thermochemical Tables, third ed., Part 1 + 2, New York, 1986. [21] J.M. Encinar, J.F. Gonz´alez, J.J. Rodr´ıguez, M.J. Ramiro, Catalysed and uncatalysed steam gasification of eucalyptus char: influence of variables and kinetic study, Fuel (2001) 80. [22] M. Kruse, H. Schoenfelder, J. Werther, A two-dimensional model for gas mixing in the upper dilute zone of a circulating fluidized bed, Can. J. Chem. Eng. 73 (1995) 620–634. [23] M. Kruse, J. Werther, 2D gas and solids flow prediction in circulating fluidized beds based on suction probe and pressure profile measurements, Chem. Eng. Proc. 34 (1995) 185–203. [24] R. Clift, J.R. Grace, Fluidization, in: Davidson, Clift, Harrison (Eds.), Continuous Bubbling and Slugging, second ed., London, Academic Press, 1985 (Chapter 3). [25] P. Simell, E. Kurkela, P. St˚ahlberg, Formation and catalytic decomposition of tars from fluidized-bed gasification, in: Bridgwater (Ed.), Advances in Thermochemical Biomass Conversion, vol. 1, 1993, p. 265. [26] H.-M. Yan, C. Heidenreich, D.-K. Zhang, Mathematical modelling of a bubbling fluidised-bed coal gasifier and the significance of ‘net flow’, Fuel 77 (9–10) (1998) 1067–1079.

736

I. Petersen, J. Werther / Chemical Engineering and Processing 44 (2005) 717–736

[27] H. Schoenfelder, M. Kruse, J. Werther, Two-dimensional model for circulating fluidized bed reactors, AIChE J. 42 (7) (1996) 1875–1888. [28] H. Schoenfelder, Modeling of Circulating Fluidized Bed Reactors, Dissertation TUHH, Shaker Verlag, Aachen, 1996. [29] F. Chejne, J.P. Hernandez, Modelling and simulation of coal gasification process in fluidised bed, Fuel 81 (2002) 1687–1702. [30] D. Kunii, O. Levenspiel, Fluidization Engineering, second ed., Butterworth-Heinemann, Boston, 1991. [31] H. Martin, Waerme- und Stoffuebertragung in der Wirbelschicht, Chem. Ing. Tech. 52 (3) (1980) 199–209. [32] C. Chen, M. Horio, T. Kojima, Numerical simulation of entrained flow coal gasifiers. Part II: Effects of operating conditions on gasifier performance, Chem. Eng. Sci. 55 (2000) 3875–3883. [33] I. Narva´ez, A. Or´ıo, M.P. Aznar, J. Corella, Biomass gasification with air in an atmospheric bubbling fluidized bed. effect of six operational variables on the quality of the produced raw gas, Ind. Eng. Chem. Res. 35 (1996) 2110–2120. [34] P. Vriesmann, E. Heginuz, K. Sjoestroem, Biomass gasification in a laboratory-scale AFBG: influence of the location of the feeding point on the fuel-N conversion, Fuel 79 (2000) 1371–1378. [35] H.W. Gudenau, H. Meyrahn, A. Bellin, W. Hahn, Vergasung nachwachsender Rohstoffe fuer die CO2 -neutrale Energiegewinnung mit Hilfe der Rheinbraun HTW-Vergasung, Final Report, Bundesministerium fuer Ernaehrung, Landwirtschaft und Forsten, Bonn, 1994. [36] F.G. van den Aarsen, Fluidised bed wood gasifier—performance and modelling, Dissertation TH Twente, University Publication, 1985. [37] M. Ising, U. Balke, C.A. Unger, Energetische Nutzung von Holz und Biomasse durch Vergasung in der zirkulierenden Wirbelschicht, Final Report, UMSICHT, 94 NR 140-F, Institute Publication, 1999. [38] P. Mehrling, R. Reimert, Entwicklung eines Verfahrens zur Vergasung von Biomassen nach dem Prinzip der Zirkulierenden Wirbelschicht, Final Report BMFT-FB-T 86-009, Lurgi GmbH, Frankfurt, 1986. [39] S.R.A. Kersten, W. Prins, B. van der Drift, W.P.M. van Swaaij, Principles of a novel multistage circulating fluidized bed reactor for biomass gasification, Chem. Eng. Sci. 58 (2003) 725–731. [40] A. Chamberland, R. Labrecque, Parametric study of an oxygenblown fluidised-bed reactor for wood gasification, in: Bridgwater, Kuester (Eds.), Research in Thermochemical Biomass Conversion, Elsevier Applied Science, London, NY, 1988, pp. 1125–1140.

[41] D. Schuller, B. Brat, Klaerschlammpyrolyse mit Rueckstandsvergasung, Chem. Ing. Tech. 65 (4) (1993) 401–449. [42] L. Garc´ıa, M.L. Salvador, J. Arauzo, R. Bilbao, Catalytic CO2 gasification of biomass in a fluidized bed reactor, Influence of catalyst weight/biomass flow rate and CO2 /biomass ratio, Fluidisation (II), Toulouse, France, 2000, pp. 657– 664. [43] S. Hamel, Mathematische Modellierung und experimentelle Untersuchung der Vergasung verschiedener fester Brennstoff in atmosphaerischen und druckaufgeladenen stationaeren Wirbelschichten, Dissertation Uni Siegen, Fortschritt-Berichte VDI Reihe, VDI Verlag, Duesseldorf, 6 (2001) 469. [44] R.G.E. Franks, Mathematical Modeling in Chemical Engineering— Chapter VI: Reaction Kinetics, John Wiley & Sons Inc., New York, 1967. [45] M.A. Field, D.W. Gill, B.B. Morgan, P.G.W. Hawksley, Reaction Rate of Carbon Particles, Combustion of Pulverised Coal, Cheney & Sons Ltd., Banbury, England, 1967 (Chapter 6). [46] I. Matsui, D. Kunii, T. Furusawa, Study of char gasification by carbon dioxide. 1. Kinetic study by thermogravimetric analysis, Ind. Eng. Chem. Res. 26 (1987) 91–95. [47] I. Matsui, D. Kunii, T. Furusawa, Study of char gasification by carbon dioxide. 2. Continuous gasification in fluidized bed, Ind. Eng. Chem. Res. 26 (1987) 95–100. [48] F.L. Dryer, I. Glassman, High-temperature oxidation of CO and CH4 , in: Proceedings of the 14th Symposium (Int.) on Combustion, Pittsburgh, Pansylvania, 1973, pp. 987–1003. [49] E.V. Kerinin, E.I. Shifrin, Mathematical Model of Coal Combustion and Gasification in a Passage of an Underground Gas Generator, Combustion, explosion and Shock Waves, Academy of Sciences, Russia, 1993, pp. 148–154. [50] V. B´ıba, J. Mac´ak, E. Klose, J. Malecha, Mathematical Model for the Gasification of Coal under Pressure, Ind. Eng. Chem. Process Des. Dev. 17 (1) (1978) 92–98. [51] Y. Wang, C.M. Kinoshita, Kinetic model of biomass gasification, Solar Energy 51 (1) (1993) 19–25. [52] R.A. Srinivasan, S. Siramulu, S. Kulasekaran, P.K. Agarwal, Mathematical modeling of fluidized bed combustion-2 combustion of gases, Fuel 77 (9–10) (1998) 1033–1049. [53] J. Petersen, J. Werther, Modeling three-dimensional effects in a circulating-fluidized-bed gasifier for sewage sludge, Chem. Eng. Sci., submitted for publication.