Effect of Pressure Drop Due to Grate–Bed Resistance on the

ARTICLE pubs.acs.org/EF

Effect of Pressure Drop Due to Grate
Bed Resistance on the Performance of a Downdraft Gasifier Pawel Donaj,†,* Mohammad Reza Izadpanah,†,‡ Weihong Yang,† and Wlodzimierz Blasiak† †

Division of Energy and Furnace Technology, Department of Materials Science and Engineering, Royal Institute of Technology (KTH), Brinellvagen 23, SE-100 44 Stockholm, Sweden ‡ Department of Materials Science and Engineering, College of Engineering, Shahid Bahonar University, Kerman, Iran ABSTRACT: The grate
bed resistance coefficient appears to be an important operating parameter with a strong influence on overall performance during downdraft fixed-bed gasification. It directly affects the velocity profile, temperature distribution, and height of the bed. To date, no information on the pressure drop as a result of the grate
bed resistance has been found. The objective of the present investigation is to propose a correlation that can predict the total effect of pressure drop through a grate of a certain surface porosity covered by the porous bed. The term related to the grate
bed resistance is based on the effective grate porosity, which combines surface bed porosity with geometrical criteria of the grate. On the basis of these criteria, a new term has been integrated into the Ergun equation. The prediction has been validated against the experimental results and conducted on a 0.7 MWth downdraft, fixed-bed gasifier that was fueled with wood pellets of a feeding rate 50
100 kg/h. Three types of grates of different porosities (0.6, 0.2, and 0.04) and thicknesses (2 mm and 10 mm) of an orifice diameter of 6 mm each have been tested under various operating conditions. The oxidizer (air or mixture of air and steam) was preheated over 1000 °C and supplied with a rate of 60
110 kg/h. The predicted values are in agreement with the experimental results. Although lower grate porosity, higher conversion of fuel, and heating value of the gas is produced, the stability of the process is disturbed. Therefore, a grate porosity reduction below 20% is not recommended.

1. INTRODUCTION Conversion of biomass and waste using highly preheated gasifying agents (over 1000 °C) is advantageous in terms of achieving higher conversion rates, higher hydrogen yields, and cleaner gas.1
5 On the other hand, many technological challenges have emerged in the move toward better utilization of preheated agents to ensure the optimal use of the system. Gasification in a downdraft mode is well-known for the production of gas with lower tar content.6
8 To avoid instability during the operation (i.e., clogging, rapid pressure, and temperature changes), the downdraft gasifier requires an effective system for separating the solid materials from the resulting syngas. Because the intake of biomass and feeding gas flow in the same direction, clogging the reactor might result in hot gases escaping through the feeding system, which would lead to serious consequences. Some technological solutions, such as moving conical grates, have been proposed to overcome some of these problems.6 The solid material (fuel) that accumulates on the grate causes an increase in resistance to the flow, resulting in a pressure drop. Several researchers have presented a number of predictions for pressure drop due to bed resistance.8
12 The pressure drop along the porous bed can be predicted using the Ergun equation.9
12 This equation enables the prediction of pressure drop with regard to the summing of the two forces—inertia and viscous—which is calculated over a wide range of Reynolds numbers. Although the Ergun equation has some limitations in predicting the pressure drop in beds consisting of large particle size distribution, it gives a reasonable approximation for monodispersive beds.10
12 Another source of pressure drop is due to resistance created by the grate, which restricts passage, in contrast to an open column. r 2011 American Chemical Society

Many investigators13
15 have performed studies of the resistance coefficient for a perforated plate in packed beds. The reduction of the passage area of a grate or screen increases the hydrodynamics of the system, which has a direct effect on the orifice velocity profile as well as the pressure drop. The system becomes more complicated when the reactor is charged with biomass/char. In this case, a bed of biomass with a certain void fraction is formed on the grate, covering its free passage. Thus, because the resistance of the grate and the resistance of the bottom-layer of the bed are in contract with the grate, they have to be somehow interconnected. Moreover, they should affect significantly the velocity profile and pressure gradient inside the reactor. This, in turn, would influence the process performance (temperature distribution inside the reactor, conversion of biomass, and gas composition) and stability of the operation (blocking/clogging of the reactor and unsteady operation). Thus, the determination of an effective open area for the flow and prediction of total pressure drop (through bed resistance and grate
bed resistance) is of high importance. Although the grate
bed resistance coefficient appears to be an important operating parameter with a strong influence on the overall performance during downdraft, fixed-bed gasification, no information on the pressure drop due to the grate
bed resistance has been found in the literature. The aim of the present investigation is to study systematically the mechanism of pressure drop in a 0.7 MW downdraft, fixed-bed Received: August 16, 2011 Revised: October 6, 2011 Published: October 10, 2011 5366

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gasifier fueled with wood pellets in a wide range of flow rates, temperature distributions, and pressure drops. Subsequently, a model is presented that is capable of predicting the pressure drop in downdraft, fixed-bed gasifiers fueled with wood pellets. The presented model then is confronted with experimental data. In addition, the effect of pressure drop on overall performance with an emphasis on the temperature distribution inside the reactor, conversion of biomass, and gas composition will be discussed.

On the basis of the ultimate analysis of the tested biomass samples, it is possible to derive an average chemical formula (on a molar basis) for the tested wood pellets that can be expressed as CH1.46O0.65. From this formula, an equivalent ratio can be defined, taking to account a given amount of oxygen (deriving both from air (nO2) and steam (mH2O)) and the stoichiometric amount required for the complete combustion (nO2*). Hence,

2. METHODOLOGY

ER ¼

2.1. Materials. The properties of feedstock are presented in Table 1. The wood pellets with a diameter of 8 mm and an average ratio of length to diameter l/d = 4 were manufactured by BooForssj€o Energi AB.

Table 1. Characterization of the Wood Pellets Proximate Analysis moisture at 105 °C

8%

ash cont. at 550 °C

0.4
0.5% (dry)

LHV

17.76 MJ/kg (as received)

volatile matter

84% (dry)

pellet bulk density

630
650 kg/m3 Ultimate Analysis (Dry Basis)

sulfur, S

0.01
0.02%

carbon, C

50%

hydrogen, H

6.0
6.2%

nitrogen, N

1400 °C

corner round off, ST hemisphere, HT

1400
1500 °C 1500 °C

flow, FT

1500
1550 °C

n O2 þ m H2 O n O2 

ð1Þ

2.2. Test Rig. Figure 1 shows the test facility used in the present investigation. The system consists of four integrated parts: a biomass feeding system, preheater, gasifier, and afterburner. A detailed description of the gasification system can be found elsewhere.3
5 The biomass, transported from the feeding tank by means of screw conveyors, is fed from the top of the gasifier to the feeding section (FE) using four vertical water-intercooled feeding channels. The preheated gas (air or mixture of air and steam), which is generated in the preheater, is introduced into the wind-box section (WB) from the side. Both hot gases and biomass travel concurrently downward until they meet the grate. The grate stops biomass/char resulting in a bed, thus forming a fixed-bed of particles (BP). The grate also provides the passage of gases and fine particles. These particles are collected in the slag-box section (SB), and the raw producer gas (syngas) is sucked from the gas part and particles section (GPP) to the afterburner/combustor by means of an induced draft fan. The gas and tar sampling ports are located on the pipe transporting producer gas from the gasifier to the afterburner. 2.3. Experimental Procedure and Data Reduction. After the feedstock container was filled, biomass was introduced into the gasifier through feeding screws at FE. The preheated gasifying agent was then transferred into the wind-box section where it was mixed with the moving biomass. The flow rates were kept constant, and the mixture was allowed to flow for two hours. The

Figure 1. Continuous HTAG test facility in downdraft configuration at KTH/Energy and Furnace Technology. 5367

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Table 2. List of Experimental Conditions grate type • equiv. grate diam. • free passage surface • porosity

biomass feed rate,

mass flow rate of feed gas,

mass frac. air, xair,

mass frac. steam, xH2O

ER

pre-set,

mFG [kg/h]

[kg/kg]

[kg/kg]

[mol/mol]

TFG [°C]

• thickness

case

mF [kg/h]

grate I: perforated sheet

exp. 1.1

60

100

1

0

0.30

1100

• de1 = 0.3098 m

exp. 1.2

75

100

1

0

0.24

1100

• A1 = 0.0754 m2

exp. 1.3

90

100

1

0

0.20

1100

grate II: drilled disk

exp. 2.1

50

62.5

1

0

0.23

970

• de2 = 0.0805 m

exp. 2.2

50

43.8

1

0

0.16

970

grate III: drilled disk • de3 = 0.1793 m

exp. 3.1 exp. 3.2

60 60

106.3 75

0.53 0.33

0.47 0.67

0.43* 0.45*

1030 1030

• A3 = 0.0253 m2

exp. 3.3

100

75

0.33

0.67

0.27*

1030

• A1/A0 = 0.6 • l = 2 mm • d01 = 6 mm • n01 = 2667

• A2 = 0.0051 m2 • A2/A0 = 0.04 • l = 10 mm • d02 = 6 mm • n02 = 180

• A3/A0 = 0.2 • l = 10 mm • d03 = 6 mm • n03 = 895

Figure 2. Distribution of thermocouples along the vertical axis of reactor.

system then was left to stabilize for about one hour before any reading was taken. Finally, the data acquisition system was switched on to record flow rates, temperatures, and pressure drops. The biomass and gasifying agent flow rates were subsequently varied and kept constant. Then, the above procedure was

followed for the new conditions. All experiments were repeated for the three different grates, the specifications of which are given in Table 2. The range of the experimental parameters covered in this investigation is also summarized in Table 2. 2.3.1. Temperature and Pressure Measurements. Temperatures were measured using thermocouples (types K, B, S) located along the reactor’s height, according to the schematic drawing presented in Figure 2. However, the transverse temperature distribution was assumed flat. The total pressure difference was measured with an uncertainty level of (0.5 mm H2O ((5 Pa), which refers to the precision of readings from the u-tube manometer. The pressure differences above and below the grate were measured by a u-tube manometer. The induced draft flue gas fan provides a suitable draft in the outlet gas section. 2.3.2. Gas Measurement. The producer gas was sampled at the outlet of the gasifier. The noncondensable part of the gaseous mixture was analyzed continuously for process control (O2, CO, and CO2) using an online gas analyzer (an O2 paramagnetic detector and a CO and CO2 nondispersive infrared (NDIR) detector). A micro-gas-chromatograph Varian CP-4900 coupled with a thermal conductivity detector (TCD) was used to measure the H2, CO, CO2, N2, O2, and CH4 concentrations in the producer gas. Gas chromatography (GC) was used only during steady-state operation. Each gas measurement consists of three injections, which were sampled automatically every 90 s by the GC instrument. The values were processed and averaged when the oscillations of the mean value in the gas composition between the subsequent injections were not greater than (3%. 5368

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Figure 3. Average temperature gradient along the vertical reactor’s axis. Points T0 to T10 represent the distribution of thermocouples.

To calculate densities and viscosities of the gas mixtures (feeding gas and raw producer gas (syngas) at the given temperature, Aspen Plus software was employed using the NRTL (nonrandom two liquid) mode.

3. RESULTS AND DISCUSSION 3.1. Process Performance. Exp. 1 was carried out using a perforated steel plate characterized by a total free passage surface A = 0.075 m2, and a grate porosity of Ω0 = 0.6. The preheated agent temperature and volume flow rate were constant along the whole run, while the biomass throughput was changed from 60 kg/h to 75 kg/h to 90 kg for exp. 1.1, exp. 1.2, and exp. 1.3, respectively. The increase in the biomass feeding rate decreased the equivalence ratio (ER), thus reducing the contribution of the combustion process. The operation was stable for all experimental cases. Exp. 2 was performed to intensify the process and improve the gas quality (LHV, H2 content). To achieve this, the grate was redesigned, and the airflow was reduced to increase the residence time of hot gases above the grate. The total openings area was A = 0.005 m2, and the grate porosity was Ω0 = 0.04, indicating that the gas flow from the bed was significantly restricted. The preheated gas temperature was around 970 °C, which was lower than in exp. 1. In this case, the biomass flow rate was kept constant at 50 kg/h (reduced with respect to the previous experiment), while the airflow rate was an adjustable parameter. The process was unstable and difficult to control, and it was difficult to reach a steady-state condition. However, two experimental periods, for ER = 0.19 and 0.15, were considered completed. During this run, pressure constantly built up in the reaction chamber above the bed and the grate seemed to clog by the char deposition, which reduced flow ability. In case of exp. 3, the drilled grate from exp. 2 was cut further to increase the open area from 0.005 to 0.025 m2 and to obtain a porosity of Ω 0 = 0.2. This reconstruction was also intended to avoid damage to the feeding system caused by a sudden pressure

rise resulting from the choking bed. In addition, for this case, steam was added to check its possible effects. The operation was stable, but difficulties in bed formation were observed. Some portion of the biomass was lost through the grate before the reaction was completed. 3.1.1. Temperature Profile. Figure 3 shows the temperature distribution profile along the height of the gasifier. Level “zero” represents the temperature at the bottom of the bed section 5 mm above the grate surface. Very fast gas quenching could be seen just after its entrance into the gasifier. Quenching of the inlet gas temperature was observed for all cases. A temperature reduction of about 300 °C was observed. Reasons for the temperature drop in this region include the following: (1) heat losses from the top of the reactor where the cooling system for biomass feeding pipes is installed and (2) the expansion of the incoming gases. Subsequently, the sensible heat exchange between the hot gas and cold biomass occurred, which is responsible for the extraction of another part of energy. This process initiates endothermic reactions, that is, drying and devolatilization of the biomass even before it reaches the fixed bed. After an initial loss of energy, the gasifying agent and fuel moved concurrently downward to reach the bed surface. The vertical temperature gradient in that region was relatively small, and thus, the temperature difference between T7 and T4, corresponding to about 1500 mm (see Figure 3), was about 100 °C and exhibited a linear drop with average rates from 48.5 °C/m for exp. 2 to 95 °C/m for exps. 1 and 3. In exps. 1 and 3, the temperature profiles reached a plateau from T5 to T2, indicating that, at this particular region of the reactor, the bed had not yet formed. Meanwhile, the temperature curve in exp. 2 reached a minimum at T5 and then started rising again until it reached T2. Afterward, the temperature indicated at T1 and T0 started rising (except in exp. 2.2) as the gases passed through the bed and grate, initiating partial oxidation of the bed material. In exp. 2.2, this process occurred earlier in a higher part of the reactor, but because of the lower amount of oxygen, the temperature fell as the 5369

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Table 3. Average Registered Pressure Difference above and below the Bed for an Empty and Loaded Reactor As Well As the Height of the Bed during Gasification of Wood Pellets in a Downdraft Operation exp. 1.1

exp. 1.2

exp. 1.3

exp. 2.1

exp. 2.2

exp. 3.1

exp. 3.2

grate type ΔPempty_grate, Pa ΔPloaded_reactor, Pa

I 0.98 59

I 0.13 78

I 0.2 88

II 38.4 1570

II 17.1 638

III 4.2 265

III 1.8 128

III 1.7 108

l, m

0.14

0.17

0.21

0.43

0.35

0.15

0.16

0.1
0.2

reductive atmosphere was built. This also roughly indicated that the height of the bed was higher for exp. 2 than for exps. 1 and 3. Figure 3 also shows that the output gas temperature T9 was always higher than the bed temperature, indicating partial combustion of the resulting combustibles (gas and tar). Furthermore, it confirms that some amount of unreacted oxygen was still present after passing through the bed and grate. However, T9 values varied strongly with different grates, and this variation indicated that the available oxygen concentration was also varied. The outlet gas temperature denoted the highest values for the whole group of exp. 1 (grate I) as a result of a higher contribution of partial combustion of producer gas and a larger porosity of the grate. At this point, some of the oxidizer could bypass the solid bed and react with the resulting products below the grate. In this case, a descending order in temperature profile was observed in exps. 1.1, 1.2, and 1.3 as a result of the reduced equivalence ratio from 0.3 to 0.24 and 0.20, respectively. This also confirms that the grate with a large passage surface has a rather low impact on process performance, and the system is mainly sensitive to air-to-fuel ratio. Meanwhile, in the case of exp. 2, the output gas temperature was particularly low (around 700
800 °C). At this time, the bed temperature at T1 and T0 was approximately 100 °C higher than that in exp. 1, despite the higher initial gas temperature in the first case. This indicates that the use of the grate with the most restricted passage significantly affected the process performance, which was reflected in the temperature profiles and height of the bed. As a result of the restriction of the flow caused by the resistance of the grate covered with the bed material, the combustion zone moved up above the grate, which is depicted by the increasing order of the temperature curves from T5 to T1, which are shown in Figure 3 for exp. 2. It is clearly seen that most of the gas reactions occurred above the grate (in and above the bed of biomass). In this case, a smaller portion of reaction products was oxidized and the consumption of the oxidizer for char gasification was intensified, which is depicted by the outlet gas temperature (T9) for exps. 2.1 and 2.2. The outlet gas temperature was significantly lower than in case of the experiments with the grate of high flow permeability. Although the temperature profile for exp. 2 suggests a higher conversion of biomass, the process is difficult to control and to operate in steady conditions because of the pressure pulsation inside the reactor chamber above the grate. The results from exp. 3 indicate that the extent of the steam reaction was highly limited because the temperature profile was very similar to that of exp. 1, in which only air is used. The expected additional reduction of temperature (especially in the fixed-bed region T1 and T0) due to an endothermic carbon
steam reaction had not been observed. Hence, a low influence of steam on conversion and gas yield is expected. In this case, most probably the biomass was not retained by the bed, but was passed through the grate and, still partially unreacted, ended up in the ash collector section. This means that only a small part (the upper layer) of a newly formed bed deposited on the bottom

exp. 3.3

of the reactor could react with hot gases. This hypothesis is supported by the results of temperatures registered for T9. 3.1.2. Pressure Drop. Table 3 gives the absolute pressure difference measured between PB and GPP sections of the gasifier (see Figure 1) for an empty and loaded reactor as well as the average height of the bed. As anticipated, the porosity of the grate made a significant contribution to the pressure drop due to head-loss of the velocity profile upon reaching an orifice. However, this effect is enhanced further when the grate is filled with a bed. For exp. 1, where the grate of the largest open area was used, the pressure difference between PB and GPP was at the level of 60
90 Pa. The increasing trend of pressure difference contributed mainly to the increasing height of the bed due to the increasing feeding rate of the fuel. An enormous difference is observed for the pressure drop registered for exp. 2. Despite nearly a 2-fold reduction in the feed gas and biomass flow rate, the pressure drop rose to 10
18 times, for the grate of lowest porosity. Here, in exp. 2.2, compared with the result for exp. 2.1, the height of the bed was almost two times larger than those in exps. 1 and 3. For exp. 2.2, the velocity of gas was reduced, which explains the difference in pressure drop and the bed height with respect to exp. 2.1. At the same time, grate III, which was used in exp. 3, resulted in intermediate values of pressure drop. Although in exp. 3.3 the input flow rates of gas and fuel were the highest with respect to all experiments, the pressure loss was not significant and the height of the bed was varied. This suggests that some of the fuel bypassed the grate before the reaction had been completed. Because the height of the bed was in the order of the same range, the difference in pressure drop between the experimental cases must have contributed to the grate resistance, or more precisely, to the grate
bed resistance. 3.1.3. Gas Composition. Figure 4 illustrates the gas composition with a lower heating value as well as the gas yield (expressed as the volume flow rate of generated gas to the mass flow rate of fuel). As a consequence of reducing the ER for exp. 1, the content of CO, H2, and CH4 increased while CO2 remained constant. This increased the heating value of the gas. The H2-to-CO ratio was 0.8, which is a typical value for air gasification.3,6
8 Although the volume of gas increased, the yield of gas linearly decreased, which is depicted by the trend line in Figure 4. The reason for that is the reduced conversion rate, which is the effect of both increasing the feeding rate of the fuel and reducing the amount of available oxygen due to the constant supply of air. This effect is also in line with the observation of the temperature profile for exp. 1. Exp. 2 generated higher amounts of CO and CH4, a slightly higher amount of H2 (see Figure 4 for exp. 2.1 and exp. 2.2, respectively), and a similar amount of CO2 compared with those achieved in exp. 1. Moreover, exp. 2.1 and exp. 1.2 had nearly the same ER (though the flow rate was reduced), but the lower heating value of gas was 50% higher, reaching 6.5 MJ/Nm3. The 5370

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Figure 4. Gas composition, lower heating value, and yield.

Figure 5. Mass balance of species based on output/input molar flow: [kmol/h detected in producer gas]/[kmol/h fed in with fuel + oxidizer].

lower heating value of gas in exp. 2.1 reached 6.25 MJ/Nm3, but in this case, the conversion rate was lower, thus lowering the yield of gas. The lower conversion of biomass is attributed to a lower ER, as a result of the reduced amount of oxygen available for the reaction. The higher values of LHV and CH4 might be the direct effect of pressure increase in the reactor above the grate, which was a result of the restricted flow ability through the grate II compared with grate I. Exp. 3 generated gas of a composition and heating value similar to that generated in exp. 1. This indicates that the reaction of char with steam was marginal, and most of the products, which correspond to the amount of air, were injected with the feeding gas. This can be seen particularly in the last two experiments

where steam was added at 83 wt % to the feeding gas. Furthermore, the additional cuts in grate III could have caused the bypass of some of the unreacted biomass through the grate, which accumulated at the bottom of reactor, reducing significantly the conversion rate. 3.1.4. Mass Balance. Carbon conversion, which is expressed as the amount in the producer gas/introduced with the fuel, is limited to only those species detected by GC, namely, H2, N2, O2, CO, CO2, and CH4. Carbon conversion indicates what portion of fuel has been converted into producer gas, and it underestimates the real, mean fuel conversion, as tar and solid particles are not included. The total conversion of fuel can be better estimated following the molar content, because no oxygen was 5371

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contribution because of the existence other variables affecting the reaction rate. Nevertheless, it can be observed that the decreasing porosity of the grate leads to the intensification of the process. Although increasing the area of the grate passage surface is beneficial for preventing undesired pressure increase, it causes a negative effect on the overall efficiency of the process. On the other hand, if the passage area is too large, some of the bed material (especially the one that comes from the erosion of particles) can penetrate the grate before the reaction is completed. 3.1.5. Superficial Velocity Distribution along the Height of the Reactor. Figure 6 shows the various superficial velocity distributions along the reactor height extracted from the experimental cases. Each point on the graphs corresponds to the actual measured gas parameters, taking into account composition, temperature, viscosity, and density, as well as locations along the height of the gasifier. Four characteristic locations were chosen across the section of the reactor (uFG_in; uFG_grate; uSG_grate; and uSG_out) and one across the open area of the grate (uOR). The trends of the velocities are similar for all cases. As the temperatures of the entering hot gases drop, the densities of the gases decrease. This is a reducing factor on the superficial velocity profile. However, the evolving syngas increases the amount (mass flow rate) of the gases, which compensates for the effect of the axial drop in the temperature. Therefore, the variation in superficial velocity between the feeding gas and syngas is not high, and the distribution velocities are quite flat (see uFG_in; uFG_grate; uSG_grate; and uSG_out in Figure 6). On the other hand, a sharp increase in the velocity of the gas is observed for the flow using different grates, as a result of a reduced passage surface. Moreover, the velocity in the open area of the grates varies significantly for the cases. These discrepancies explain the observed differences in process performance described before, but they have even more important consequences for the pressure drop estimation. The pressure drop is proportional to the second power of the velocity; thus, an effect of the variation in grate effective porosity (which is the grate porosity reduced by the covering layer of biomass/char) is of high importance. 3.2. Modeling of the Pressure Drop. The pressure drop can be estimated as the sum of pressures related to the resistance of the porous bed and the resistance due to head-loss caused by the fluid passing through a grate of the restricted passage. These terms are represented as ΔPT ¼ ΔPbed þ ΔPgrate ¼ ΔPbedv iscous þ ΔPbedi nertial þ ΔPgrate

Figure 6. Distributions of velocities along the reactor’s height for three types of grate.

found in the producer gas. This indication is closer to the real conversion. The material balance, based on the molar output/ input data of C, H, and O, is presented in Figure 5. The results were normalized against the ratio of kmol/h of N2 fed in with the air and the kmol/h of N2 output detected by GC. The results presented in Figure 5 demonstrate that the highest conversion based on oxygen consumption was obtained for exp. 2.1 at around 68% following exp. 1 and exp. 2.2 at around 52
55%. Finally, the poorest conversion is associated with experiments using steam (exp. 3.1
3.3, respectively, from 40% to only 25
15%). This suggests that the conversion rate of biomass is somewhat related to the pressure resistance across the thickness of the grate and porous bed, but it is difficult to conclude a direct

ð2Þ

Pressure drop across the porous bed can be predicted using the Ergun equation:9
12 ΔPbed ð1
εÞ2 μu ð1
εÞ Fu2 ¼ 150 2 þ 1:75 3 ε3 dp Φ L ε ðdp ΦÞ

ð3Þ

The above equation is valid for the Reynolds particle numbers in the range 0.4 < Rep < 1000, which is defined as Rep = udpFμ.9
11 The pressure drop across the perforated plate/screen is given as the following:13 ΔPgrate ¼ k

u2 F 2

ð4Þ

where k is a head-loss resistance coefficient as a function of grate porosity, orifice Reynolds number, friction factor, and l/deff [
]. 5372

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For ReOR > 105 and l/deff < 0.015, k can be obtained using the following relation:13 l k0 þ λ def f k¼ , for l=deff < 0:015 ð5aÞ Ωef f 2

If the particles are separated by a distance, S, and a packing angle, ϕ, then the volume of empty space can be calculated as a difference of the total volume of a lattice S3 and the volume of the spherical particle (Vp = πdp3/6),12,14 which gives: V0 ¼ S3 ð1
cos ϕÞ

and

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½0:707 1
Ωef f þ ð1
Ωef f Þ2 , for l=deff > 0:015 k¼ Ωef f 2 ð5bÞ

where Ωeff is the effective grate porosity, which is defined as Aeff/ A0, and λ is a friction factor of ReOR and the relative roughness of the duct. Its values for different ReOR are the following λ¼

64 for ReOR < 2100 ReOR

ð6aÞ

and 1:325

λ¼2


5

4ln 4:5  10 def f

3 5 !2 3 for 4  10 < ReOR < 10 5:74 5 þ ReOR 0:9

ð6bÞ

From which, S can be calculated: dp S ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 2 cos ϕ 3 6ð1
cos ϕÞ ð1
εÞ π

Ωb ¼ 1


þ 3:3854ðl=deff Þ3 þ 0:4687ðl=deff Þ2
0:7975ðl=deff Þ þ 1:35

ð8Þ

For 30 < ReOR < 105 and all l/deff values, the head-loss coefficient can be calculated from13 klaminar ¼

kf þ Ck Ωef f 2

ð9Þ

where kf is a function of grate porosity and the orifice Reynolds number, and C is a function of the orifice Reynolds that has been interpolated with a regression parameter r2 = 1 from ref 13 as follows: C ¼
0:0164ðlogðReOR ÞÞ3 þ 0:1904ðlogðReOR ÞÞ2 0:5145ðlogðReOR ÞÞ þ 0:7973

ð10Þ

Subsequently, kf can be computed from the interpolation with the regression parameter r2 = 0.921 as kf ¼
4:4501C2 þ 7:144C
2:734

ð11Þ

Thus, the key parameter to be estimated in order to find the resistance (head-loss) coefficient is the grate effective porosity. Porosity of the unloaded grate is defined as Ω0 ¼

A nd2 d2 ¼ 2i ¼ e2 A0 D D

ð12Þ

ð14Þ

πdp2 Ap π ¼ 1
¼ 1
2 4S sin ϕ AT 4AT

ð15Þ

Assuming that S = dp to 1.5dp; ϕ = 60° to 90°; Ωb = const; di > dp; and Fp = const, then eq 14 will yield dp S ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi π ð1
Ωb Þ 4 sin ϕ

ð7Þ

τ ¼ 7:5521ðl=deff Þ5
11:719ðl=deff Þ4

ð13Þ

Equation 14 gives the relation among the bed porosity and particle size, packing angle, and distance between the particles. To simulate a covering effect of particles on a grate of certain porosity, a simple model of 2D-arrays is considered. Assuming a uniform particle distribution, incompressible and solid particles for a monolayer spherical particles of diameter dp, which occupy an area, A0, the model can be represented as

Now, a new parameter, k0, can be defined as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k0 ¼ ð0:5 þ τ 1
Ωef f Þð1
Ωef f Þ þ ð1
Ωef f Þ2 where τ is a function of l/deff, which has been interpolated with a regression parameter r2 = 1 from Table 2.1 of ref 13.

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi πdp3 1 þ 2 cos ϕ
6

ð16Þ

Introducing the packing parameter, defined as P = S/dp, from eqs 15 and 17, the following relation between the surface porosity and a bed’s void fraction can be found: π 1
Ωb ¼ 2 4P sin ϕ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 6P ð1
cos ϕÞ 1 þ 2 cos ϕ 2  ð1
εÞ2 ¼ βðϕ, PÞ ð1
εÞ2=3 π ð17Þ The solution of eq 17 for P = 1 gives the minimal bed void fraction, ε(ϕ=90°) = 0.476 and ε(ϕ=60°) = 0.215, as well as the minimal surface porosity, Ωb(ϕ=90°) = 0.269 and Ωb(ϕ=60°) = 0.093, respectively, for octagonal and hexagonal packing patterns. Equation 16 enables for prediction of the surface porosity (or coverage factor) for a given void fraction and assumed distance and angle between the spherical particles. For nonspherical particles, the equivalent particle diameter using sphericity factor has to be included. Let the effective grate porosity used in eqs 5, 7, 9, and 11 be expressed as Ωef f ¼ Ωb Ω0 ¼ Ωb

A A0

ð18Þ

from which the effective hydraulic diameter can be computed as rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffi A Aef f def f ¼ ð1
ΩÞb D2 ¼ D ð19Þ A0 A0 Knowing the bed void fraction, geometry of the grate, and surface porosity makes it possible to calculate the head-loss coefficient, k, which allows the estimation of the pressure loss due to bed
grate resistance. Finally, the total pressure drop can be 5373

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Figure 7. Measured and calculated (using eq 20) values of the total pressure drop across the bed for a void fraction ε = 0.44.

calculated by summing the three terms: "

ð1
εÞ2 μu ð1
εÞ Fu2 ΔPT ¼ L 150 þ 1:75 ε3 d p Φ ε3 ðdp ΦÞ2 þ k

#

u2 F 2 ð20Þ

3.3. Prediction of the Total Pressure Drop and Validation with Experimental Results. All data for gas parameters

(velocity, density, viscosity, and temperature) were taken from the experimental results for the syngas temperature at the grate temperature. The height of the bed was taken from Table 3. The particle dimensions for determination of the Ergun equation were assumed as follows: dc = 0.008 m; hc = 0.015 m, dp = 0.011 m, Φ = 0.8, and ε = 0.44. The simulation was done by fitting packing ϕ and P (parameters reflecting distribution pattern of particles accordingly to eq 17). The dimensions of the grate are presented in Table 2. Figure 7 compares the measured values with the calculated values of the total pressure drop on the basis of eq 2. The predicted results are in agreement with measured values. In both cases, a massive pressure drop is observed for the case using the grate with the lowest porosity (see exp. 2 in Figure 7). The pressure drop is proportional to the second power of the velocity; thus, the effect of the reduced porosity of the grate is highly influential on the total pressure drop and hydrodynamics of the system. Moreover, after applying the concept of the effective grate porosity (see eq 5
7, 9, 18), which is the grate porosity reduced by the covering layer of biomass/char, the prediction of the pressure drop is valid for the whole range of experimentally measured cases. The average error of prediction was (7.10% with a standard deviation of mean value S = 5.3. The pressure drop was calculated as a sum of the Ergun equation, and the grate
bed pressure drop gave satisfactory results.

Figure 8 presents the contribution of each term in eq 20 to the total pressure drop. This figure shows the significance of each contribution to the total pressure drop. Usually, in fixed bed reactors most of the pressure drop is accounted for by the bed resistance, especially for the large heights of the bed. However, when the porosity of the grate is reduced below 20%, the pressure drop becomes the major factor to be considered. This occurs as a result of the additional restriction of the flow caused by the layer of bed in contact with the grate. In this case, the effective grate diameter or effective area of the grate is severely reduced. This causes the increase in the resistance coefficient, exponentially. Figure 9 shows the correlation between the resistance coefficient, k, and the effective grate porosity for two size of grate thickness. The correlation equations for two thicknesses of the grates are listed below: logðkg ¼ 2mm Þ ¼
1:0352 lnðΩeff Þ
0:157

ð21aÞ

logðkg ¼ 10mm Þ ¼
1:8735 lnðΩeff Þ
0:951

ð21bÞ

The presented results demonstrate that the grate effective porosity makes an enormously high contribution to the resistance coefficient. The lower value of packing parameter, P, the smaller bed void fraction, and grate effective porosity and, consequently, the lower hydraulic diameter are obtained. This increases the orifice Reynolds number calculated for the effective hydraulic diameter. The increase in the orifice velocity between the most open grate and the most restricted grate was around 60
70 times (see Figure 9). For the grate of highest passage area (exp. 1), the resistance coefficient for the bed porosity 0.44 and P = 1 was in the range of hundreds Pa. The grate of lowest free passage increased the grate
bed resistance coefficient by 6 orders of magnitude, comparing with the case of the grate with largest porosity. Moreover, the influence of the thickness of the grate exhibited the highest contribution to the resistance coefficient for the grate of the lowest porosity (see Figure 9). This shows that, in the case of using a grate with a low passage area, the 5374

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Figure 8. Simulated pressure drop across the bed of height given in Table 3, as a result of viscous, inertial, and hydraulic grate
bed losses using P = 1.1, ε = 0.44, and ϕ = 60°, respectively.

Figure 9. Correlation between the resistance coefficient, k, and the effective grate porosity for two size of grate thickness.

sensitivity of the process performance and pressure drop for any changing conditions is of great importance. The main reason for the uncertainties in determining the pressure drop using the method described in this paper is the following: It does not take to account the effect of changing the densities and sizes of particles as well as the motion of the bed during reaction. Moreover, this method cannot predict the effect of the fine particles that may block the orifices of the grate.

4. CONCLUSIONS The present work proposes a method for the prediction of a total pressure drop through a fixed-bed downdraft gasifier

equipped with a grate of certain porosity. The total pressure drop consists of two terms: first, the resistance of the bed given by the Ergun equation and, second, the head-loss resistance due to the grate of a reduced free passage area. This study introduced the new terms—effective grate porosity and effective grate hydraulic diameter—which enable calculation of the resistance that occurs due to the grate
bed interactions. The predicted values of pressure drop showed good agreement within the experimental results obtained in gasification of wood pellets in a continuous downdraft system. The uncertainty of prediction is (7.10. The significance of the prediction of the pressure drop due to the grate
bed resistance caused by the total pressure drop appeared lower than 20% for the grate porosity. 5375

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Energy & Fuels The resistance coefficient for the bed void was 0.44, and the close packing particle distribution was 100. The grate of lowest free passage, which was covered with the biomass layer, increased up to 6 orders of magnitude, which affects all the process parameters. The influence of the pressure drop/grate porosity on the overall process performance is important. It directly affects the velocity profile, temperature distribution, and the height of the bed. This influences the product composition and conversion rates. Lower grate porosity and a higher conversion of fuel and heating value of gas are produced. However, the stability of the process is disturbed; therefore, reducing the grate porosity below 20% is not recommended unless the system is designed to compensate for the consequences of the rising pressure inside the reactor.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Telephone: +46 8790 8366. Fax: +46 8 207 681.

’ ACKNOWLEDGMENT The authors would like to acknowledge the financial support of the grant on STEM project from the Swedish National Energy Administration (Energimyngiheten). The fruitful collaboration with Nippon Furnace, Kogyo Kaisha Ltd, Japan is very much acknowledged. Special thanks are directed towards Dr. Artur Swiderski and Dr. Sylwester Kalisz for technical supervision during the experimental work. We also would like to express our gratitude to all the collaborators from the Royal Institute of Technology, as well as the industrial partners involved in the project. ’ NOMENCLATURE A0 = cross sectional area of the gasifier, m2. A1, A2, A3 = area of the open surface of grates 1, 2, and 3, m2. C = constant in eq 9 being a function of ReOR. D = diameter of the gasifier, m. dc = diameter of a pellet, m. de1, de2, de3 = hydraulic equivalent diameter of the of grates 1, 2, and 3, m. di = diameter of a single orifice of the grate, m. dp = equivalent diameter of the particle, m. deff = effective grate diameter, m. ER = equivalence ratio. k, klaminar = head-loss coefficient for turbulent and laminar flow regime. kf, k0 = resistance coefficients. L = length (height) of the bed, m. LHV = lower heating value of gas, MJ/Nm3. l = thickness of the grate, m. lp = average length of a pellet, m. n = number of grate orifices (openings). mF = mass flow rate of fuel, kg/h. mFG = mass flow rate of feeding gas, kg/h. P = packing parameter. ΔPT = total pressure loss, Pa. ΔPbed, ΔPgrate = pressure drop along the bed, pressure drop due to grate
bed resistance, Pa. Re = Reynolds number across the section of the gasifier, uDF/μ. ReOR = orifice Reynolds number, udeffF/μ. Rep = particle Reynolds number, udpF/μ. S = distance between the centers of particles, m.

ARTICLE

u = superficial velocity. uair_in = superficial velocity of the feeding gas at the feeding gas temperature, m/s. uair_bed = superficial velocity of the feeding gas at temperature just above the bed temperature, m/s. uSG_grate = superficial velocity of the raw syngas at the grate temperature, m/s. uSG_out = superficial velocity of the raw syngas at the gas outlet temperature, m/s. uOR = effective superficial velocity at the grate temperature for an empty grate, m/s. Vp = volume of a particle, m3 Vp = free volume (void volume) or volume of fluid, m3. VFG = volume flow rate of feeding gas, Nm3/h. VSG = volume flow rate of syngas, (producer gas), Nm3/h. Greek Letters ε = bed void fraction, bed porosity. Φ = sphericity, ratio of the surface area of a sphere (with the same volume as the given particle) to the surface area of the particle. ϕ = packing angle, deg. λ = friction factor. μ = gas dynamic viscosity, Ns/m2. F = gas density, kg/m3. Fp = particle density kg/m3. τ = function of l/deff. Ω0 = grate porosity (A/A0). Ωb = bed surface porosity (layer of bed being in contact with grate). Ωeff = effective grate porosity.

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