This section briefly discusses how kinetic models can be applied to the three major gasifier types.

5.6.1 Moving-Bed Gasifiers

A basic moving-bed or fixed-bed gasifier can use the following assumptions:

• The reactor is uniform radially (i. e., no temperature or concentration gradi­ent exists in the radial direction).

• The solids flow downward (in a updraft gasifier) as a plug flow.

• The gas flows upward as a plug flow.

• The interchange between two phases takes place by diffusion.

The mass balance of a gas species, j, can be written (Souza-Santos, 2004, p. 134) as

where ug is the superficial gas velocity, z is the distance, pgJ is the density of the jth gas, and DgJ is the diffusivity of the jth gas. Rm, j, the production or consumption of the jth gas element, is related to Qgasificati0n heat generation or absorption.

Similarly, an energy balance equation can be written for a dz element as

where, Qgasification, Qconv, Qrad, and Qmass are the net heat flow into the element due to gasification, convection, radiation, and mass transfer, respectively. These terms can be positive or negative. pg, Cpg, and Xg are the density, specific heat, and thermal conductivity of the bulk gas, respectively.

Equations (5.79) and (5.80) can be solved simultaneously with appropriate expression for the reaction rate, RmJ.

As we saw in Figures 6.4 and 6.6, the cross-sectional area of a downdraft gasifier may be nonuniform; it is narrowest at the throat. The hearth load is, therefore, based on the cross-sectional area of the throat for a throated gasifier, and for a throatless or stratified downdraft gasifier, it is based on the gasifier cross­sectional area. The actual velocity of gas is, however, significantly higher than the designed space velocity because much of the flow passage is occupied by fuel particles. The velocity is higher in the throat also because of the higher tempera­ture there. Table 6.6 gives some characteristic values of these parameters.

In a downdraft gasifer, the gasification air is injected by a number of nozzles from the periphery (refer to Figure 6.6). The total nozzle area is typically 7 to 4% of the throat area. The number of nozzles should be an odd number so that the jet from one nozzle does not hit a jet from the opposite side, leaving a dead space in between. To ensure adequate penetration of nozzle air into the hearth, the diameter of a downdraft gasifier is generally limited to 1.5 m. This naturally restricts the size and capacity of a downdraft gasifier.

TABLE 6.6 Hearth Load for Downdraft Gasifiers Maximum Values Based on Throat Area
Plant	Gasifier Type	Medium			Superficial Velocity at Throat (m/s)	Hearth Load* (MW/m2)
Gengas	Imbert	Air	0.15	0.3	2.5	15
Biomass Corp.	Imbert	Air	0.3	0.61	0.95	5.7
SERI	Throatless	Air	0.15		0.28	1.67
Buck Rogers	Throatless	Air	0.61		0.23	1.35
Buck Rogers	Throatless	Air	0.61		0.13	0.788
Syngas	Throatless	Air	0.76		1.71	10.28
Syngas	Throatless	Oxygen	0.76		1.07	12.84
SERI	Throatless	Oxygen	0.15		0.24	1.42
*Based on throat	area.
Source: Data compiled from Reed and Das, 1988, p. 36.

Table 6.7 lists typical sizes for the Imbert-type downdraft gasifier and shows the relation between throat size and air nozzle diameter.

A feedstock preheater is the second most important part of an SCW gasifier system. The heat required to preheat the feedstock (water and biomass) is a significant fraction of the potential heating value of the product gas. Without efficient recovery of heat from the product gas, the external energy needed for gasification may exceed the energy produced, making the gasifier a net energy consumer. The feedstock should therefore obtain as much of its enthalpy as possible from the sensible heat of the product. This is one of the most important aspects of SCW plant design.

Figure 7.10 compares the capital costs of different components of an SCWG plant. We can see that the heat-recovery exchanger represents 50 to 60% of the total capital cost of the plant, which makes it a critical component.

Efficient heat exchange between the feed and the product is the primary goal of an SCWG heat-recovery system. However, for supercritical water intended for hazardous waste reduction (SCWO) or synthesis reaction (SCWS), it may not be all that important since the primary purpose of these systems is the production of chemicals, not energy as in a supercritical gasifier.

The heat-exchange efficiency, h, defines how much of the available heat in the product stream can be picked up by the feed stream.

h и

product-out product-in

n h — H V /

feed-in product-in

where H is the enthalpy, and the subscripts define the liquid it refers to.

Theoretically, the heat-exchange efficiency can be 100% if no heat of vapor­ization is required to heat the feed and an infinite heat-exchange surface area is available. Of course, these conditions are not possible. Figure 7.11 shows variations in heat-exchange efficiency with changes in tube surface area and water pressure.

The specific heat of water rises sharply close to its critical point and then drops equally sharply as the temperature increases (Figure 7.2). Thus, around

Amos Amos (PSA) FZK Matsumura Gen. Atomics

□ purification ed reactor № heat exchanger ■ feed preparation

20 [6] [7]

Г Л TABLE 7.5 Sample Data for VERENA Pilot Plant Product-to-Feed Heat Exchanger Flow Rate (kg/h) Product Product Feed Feed Reactor (Methanol %) in (°C) Out (°C) In (°C) Out (°C) Temperature (°C) 100 (10%) 561 168 26 405 582 90 (20%) 524 155 22 388 537 Note: Heat-exchanger surface area: 1.1 m2; heat-transfer coefficient: 920 W/m2C (Boukis et al., 2005). v________________________________________________________ 9

the critical point we may expect a modest temperature rise along the heat — exchanger length.

Thermal conductivity in SCW is lower than that in subcritical water because SCW’s intermolecular space is greater than that in liquid. A slight increase in conductivity is noticed as the fluid approaches the critical point. This increase is due to an increase in the agitation of molecules when the change from a liquidlike to a gaslike state (SCW) takes place. Above the critical point, thermal conductivity decreases rapidly with temperature.

The heat-transfer coefficient varies with temperature near its pseudo-critical value (see Section 7.2) because of variations in the thermophysical properties of water. As the temperature approaches the pseudo-critical value, conductivity and viscosity decrease but specific heat increases. The drop in viscosity and the peak of specific heat at the pseudo-critical temperature overcome the effect of decreased thermal conductivity so as to increase the overall heat-transfer rate.

As the temperature further increases, beyond the pseudo-critical point, the specific heat decreases sharply; the drop in thermal conductivity continues as well, and therefore the heat-transfer coefficient reduces. For a given heat flux, the wall temperature rises for the drop in heat-transfer coefficient. Generally, for high heat flux and low mass flux, the heat transfer deteriorates, leading to hot spots in the tube.

The two main routes for production of syngas from biomass or fossil fuel are low-temperature (~<1000 °C) and high-temperature gasification (~>1200 °C).

Low-temperature gasification is typically carried out at temperatures below 1000 °C. In most low-temperature gasifiers, the gasifying medium is air, which introduces undesired nitrogen in the gas. To avoid this, gasification can be carried out indirectly by one of the following means:

• An oxygen carrier (metal oxide) is used to transfer the oxygen from an air oxidizer to another reactor, where gasification takes place using the oxygen from the metal oxide.

• A combustion reaction in air is carried out in one reactor and heat-carrier solids carry the heat to a second reactor, where this heat is then used in gasification.

• Dilution of the product gas by nitrogen is avoided by the use of steam or oxygen as the gasifying medium.

Low-temperature gasification produces a number of heavier hydrocarbons along with carbon monoxide and hydrogen. These heavier hydrocarbons are further cracked, separated, and used for other applications. High-temperature gasification is carried out at temperatures above 1200 °C, where biomass is converted mainly into hydrogen and carbon monoxide. Primary gasification is often followed by the shift reaction, as described in the next section, to adjust the hydrogen-to-carbon monoxide ratio to suit the downstream application.

In any case, the product gas must be cleaned before it is used for synthesis reactions. Special attention must be paid to clean the syngas of tar and other

catalyst-poisoning elements before it is used for Fischer-Tropsch synthesis, which uses iron — or cobalt-based catalysts.

Shift Reaction

For a reaction like Fischer-Tropsch synthesis that produces various gaseous and liquid hydrocarbons, a definite molar ratio of CO and H2 in the syngas is neces­sary. This is done through the shift reaction that converts excess carbon mon­oxide into hydrogen:

The reaction can be carried out either at higher temperatures (400-500 °C) or at lower temperatures (200-400 °C). For high temperatures, the shift reaction is often catalyzed using oxides of iron and chromium; it is equilibrium limited. At low temperatures, the shift reaction is kinetically limited; the catalyst is composed of copper, zinc oxide, and alumina, which help reduce the CO con­centration down to about 1%.

Here, water or an appropriate scrubbing liquid is sprayed on the gas. Solid particles and tar droplets collide with the drops, forming larger droplets because of coalescence. These larger droplets are easily separated from the gas by a

demisterlike cyclone. The gas needs to be cooled until it is below 100 °C before cleaning. The tar-laden scrubbing liquid may be fed back into the gasifier or its combustion section. Alternatively, it may be regenerated by stripping the tar away.

Some commercial methods, such as the OLGA and TARWTC technologies, use proprietary oil as the scrubbing liquid. The tar liquid is then reinjected into the gasifier for further conversion (Knoef, 2005, p. 196). Scrubbers have a high (>90%) collection efficiency, but the efficiency drops sharply below 1-micron­sized particles. They consume a large amount of fan power owing to the large (~50-inch water gauge) pressure drop across the scrubber. While their operating cost is high, their capital cost is much less than that for ESPs.

A system with a tar removal scrubber produces cleaned gas with a lower outlet temperature and a higher energy content, but it contains tars that are more difficult to remove. The main challenge of tar removal is the formation of “tar balls,” which are long-chained hydrocarbons that have a tendency to agglomer­ate and stick together, fouling equipment in the initial stages of tar condensing and collecting.

The tar-laden stripper gas, if fed into the gasifier, lowers its dewpoint well below that of water. This allows condensation of the tar, while flue gas contain­ing tar vapor can be recycled back to the combustion section of the gasifier for combustion.

A downdraft gasifier is a co-current reactor where air enters the gasifier at a certain height below the top. The product gas flows downward (giving the name downdraft) and leaves through a bed of hot ash (Figures 6.4 and 6.5). Since it passes through the high-temperature zone of hot ash, the tar in the product gas finds favorable conditions for cracking (see Chapter 4). For this reason, a downdraft gasifier, of all types, has the lowest tar production rate.

Air from a set of nozzles, set around the gasifier’s periphery, flows down­ward and meets with pyrolyzed char particles, developing a combustion zone (zone III shown schematically in Figure 6.5 and described in the discussion of throatless downdraft gasifiers that follows) of about 1200 to 1400 °C. Then the

gas descends further through the bed of hot char particles (zone IV), gasifying them. The ash produced leaves with the gas, dropping off at the bottom of the reactor.

Downdraft gasifiers work well with internal-combustion engines. The engine suction draws air through the bed of fuel, and gas is produced at the end. Low tar content (0.015-3 g/nm3) in the product gas is another motivation for their use with internal-combustion engines. A downdraft gasifier requires a shorter time (20-30 minutes) to ignite and bring the plant up to working tem­perature compared to the time required by an updraft gasifier.

There are two principal types of downdraft gasifier. The throatless (or open core) type is illustrated in Figure 6.5. Reactions in different zones and at dif­ferent temperatures are plotted on the right. The throated (or constricted) type is shown in Figure 6.4.

The startup of a fluidized-bed gasifier is similar to the startup of a fluidized bed combustor. The inert bed materials are preheated either by an overbed burner or by burning gas in the bed. Once the bed reaches the ignition temperature of the fuel, the feed is started. Combustion is allowed to raise the temperature. After that, the air/oxidizer-to-fuel ratio is slowly adjusted to switch to gasifica­tion mode.

One major problem with fluidized-bed gasifiers is the entrainment (escape) of fine char with the product gas. The superficial velocity in a fluidized bed is often sufficiently high to transport small and light char particles, contributing to major carbon loss. A tall freeboard can reduce the problem, but that has a

cost penalty. Instead, most fluidized-bed gasifiers use a cyclone and a recycle system to return the entrained char particles back to the gasifier.

Entrained-Flow Gasifier

The startup procedure for an entrained-flow gasifier takes a long time because a startup burner must heat up the reactor vessel wall. During this time, the reactor vessel is not pressurized. Once oil or gas flame heats up the thick refrac­tory wall to ~1100 °C, the startup burner is withdrawn and the fuel is injected along with the oxidizer (Weigner et al., 2002). The hot reactor wall serves as an igniter for the fuel, which once ignited continues to burn in the combustion zone, consuming the oxygen. For this reason, the fuel injector in an entrained — flow reactor is also called the burner. The reactor is pressurized slowly once the main fuel is ignited.

The gasifying medium is rarely premixed with the fuel. The fuel and the medium are often injected coaxially, as in a pulverized-coal (PC) burner in a boiler or furnace. They immediately mix on entering the reactor. The operation of a gasifier “burner” is similar to that of conventional burners, so design methods for PC or oil burners can be used for a rough and an initial sizing. The use of a separate startup burner involves replacing it with a fuel injector. This is especially difficult for water-cooled walls because their lower thermal inertia cannot hold the wall temperature long enough. Integration of the startup burner in the existing fuel injector is the best option.

Tar Cracking

Several options for tar control and destruction are available; these were dis­cussed in Chapter 4. In fixed-bed gasifiers, thermal cracking or burning has been used with success. In one such design, as shown in Figure 6.24, the air entering the gasifier passes through an aspirator that entrains the tar vapor. The mixture is then burnt in the combustion zone. The aspirator can be outside or inside the gasifier.

Symbols and Nomenclature

Ab = cross-sectional area of the fluidized bed (m2)

ASH = fractional of ash in the fuel in dry basis (-)

C = fractional of carbon in the fuel in dry basis (-)

Ci = volumetric specific heat of gas i (kJ/nm3.K)

Co = initial carbon in the biomass (kg)

Cp = specific heat of the gas (kJ/kg. C)

Ea = activation energy (kJ/mol)

EA = excess air coefficient (-)

ER = equivalence ratio (-)

F = amount of dry fuel required to obtain 1 Nm3 of product gas (kg/nm3)

F[C] = char feed rate into the gasifier (kg/s)

Fuel FIGURE 6.24 Gasifier with an aspirator for cracking tar. Fresh air picks up the tar from the gasifier and injects it into the high-temperature combustion zone.

H = fractional of hydrogen in the fuel in dry basis (-)

HHV = higher heating value (kJ/kg)

HHVd = higher heating value of biomass on dry basis (MJ/kg)

HHVa = higher heating value of biomass on dry ash-free basis (MJ/kg)

Hbed = height of the bed (m)

Hg = enthalpy of steam at gasification temperature (kJ/kg)

Hin = heat of the input gas (kJ)

[H2O] = concentration of steam (-) k = rate constant (A1)

k0 = pre-exponential constant in the Arrhenius equation (A1)

LHVbm = lower heating value of the biomass (MJ/kg)

LHVdaf = lower heating value of biomass on dry ash-free basis (MJ/kg)

LHVf = lower heating value of the solid fuel (MJ/Nm3)

LHVg = lower heating value of the produced gas (MJ/Nm3) m = mass-flow rate of carbon or char (kg/s)

mth = theoretical air requirement for complete combustion of a unit of biomass (kg/kg) Ma = amount of air required for gasification of unit mass of biomass (kg/kg)

M = fractional of moisture in the fuel (-)

Mdaf = moisture based on dry ash-free basis Mf = fuel flow rate (kg/s)

M)h = quantity of steam (kg/s)

Mg = gas produced (kg/s) n = order of reaction (-)

П = number of moles of species i (-)

N = fractional of nitrogen in the fuel in dry basis (-) nMai = total number of moles

O = fractional of oxygen in the fuel in dry basis (-)

Pc = amount of char produced per nm3 of product gas (kg/nm3) qc = heating value of char (kJ/kg)

Q = power output of the gasifier (MWth)

Qext = external heat addition to the system (kJ/Nm3)

Qg = Lower heating value of the product gas from gasification (MJ/Nm3)

QSasifiCaa<,n = heat supplied to gasify 1 mol of biomass (kJ/mol)

Qioss = heat loss from the gasifier (kJ/Nm3) r = steam gasification reaction rate (kg/s)

R = universal gas constant (0.008314 kJ/mol. K)

S = fractional of sulfur in the fuel in dry basis (-)

SC = steam to carbon molar ratio (-) t = time (s)

T = temperature (K)

Tf = gas temperature at the exit (°C)

Tg = gas temperature (°C)

T0 = gas temperature at the entrance (°C)

Ug = fluidizing velocity (m/s)

V = volume of the fluidized bed (m3)

Vbed = volume of the bed (m3)

Vdaf = volatile based on dry mass-free basis Vg = gas generation rate (m3/s)

Vg = volumetric flow rate of product gas (Nm3/s)

V = volumetric fraction of gas species i (-)

W = total steam needed in Eq. 6.22 (kg/s)

Win = rate of the char moving in (kg/s)

Wout = rate of the char moving out (kg/s) xchar = weight of the reacting char (kg)

X = fraction of char in the feed converted (-)

Xc = fixed carbon fraction in the fuel (kg carbon/kg dry fuel)

Xchar = char fraction in bed (-)

Xg = fraction of steam used up in gasification Є = voidage of the bed (-)

AI = Lagrangian multiplier for species i (-)

pg = density of air at the opening temperature and pressure of the gasifier (kg/m3) в = residence time of char in bed or reactor (s) pb = bed density (kg/m3) ps = density of bed solids (kg/m3)

Hgef = gasifier efficiency (-)

HCf = cold gas efficiency (-)

Hcg = cold gas efficiency of the gasifier (-)

Hhg = hot gas efficiency of the gasifier (-)

H„et = net gasification efficiency of the gasifier (-)

AHT = heat of formation at temperature T (kJ/mol)

A typical biomass energy system comprises farming, collection, transportation, preparation, storage, feeding, and conversion. This is followed by transmission of the energy produced to the point of use. The concern here is with the handling of biomass upstream of the conversion system—that is, a gasifier in the present context. Biomass farming is a subject by itself and is beyond the scope of this chapter.

Biomass fuel can be procured from the following sources:

• Energy crop or forestry

• Ligno-cellulose wastes that are from forestry, agriculture, wood, or other industries

• Carbohydrates such as fat, oil, and other wastes

Chemicals

Pulp mill/chemical plant

FIGURE 8.1 Biomass is used for the production of energy or for commercial products such as paper or chemicals.

Biomass has two major (Figure 8.1) applications: (1) energy production through gasification or combustion, and (2) production of chemicals and fiber-based items (e. g., paper).

The collection methods for biomass vary depending on its type and source. Forest residues are a typical ligno-cellulose biomass used in gasification plants. They are collected by various pieces of equipment and transported to the gas­ification plant by special trucks (or rail cars in some cases). There, the biomass is received, temporarily stored, and pretreated as needed. Sometimes the plant owner purchases prepared biomass to avoid the cost of onsite pretreatment. The treated biomass is placed in storage bins located in line with the feeder, which feeds it into the gasifier at the required rate.

Biomass typically contains only a small amount of ash, but it is often mixed with undesirable foreign materials. These materials require an elaborate system for separation. If the plant uses oxygen for gasification, it needs an air — separation unit for oxygen production. If it uses steam, a steam generator is necessary. Thus, a biomass plant could involve several auxiliary units. The capacity of each of these units and the selection of equipment depend on a large number of factors. These are beyond the scope of this chapter.

Forestry and agriculture are two major sources of biomass. In forestry, large trees are cut, logged, and transported to the market. The logging process involves delimbing, and taking out the large-diameter tree trunks as logs. The processes involved in biomass harvesting, such as delimbing, deburking, and chipping, produce a large amount of woody residue, all of which constitutes a major part of the forest residue. The entire operation involves chopping the tree into chips and then using those chips to make fuels or feedstock for pulp industries.

Biodiesel, ethanol, and biogas are transport fuels produced from biomass that are used in the transportation industry. The composition of biodiesel and biogas may not be exactly the same as their equivalence from petroleum, but they perform the same task. Ethanol derived from biomass is either used as the sole fuel or mixed with gasoline in spark-ignition engines.

There are two thermochemical routes available for the production of diesel and gasoline from syngas: (1) gasoline, through the methanol-to-gasoline (MTG) process; and (2) diesel, through the FT process. The two biochemical means for production of ethanol and diesel are

• Diesel, through the transesterification of fatty acids

• Ethanol, through the fermentation of sugar

It may be noted that in both schemes part of the syngas’s energy content (30-50%) is lost during conversion into liquid transport fuel. It is apparent from Table 9.4 that this loss in conversion from biomass to methanol or ethanol can be as high as 50%, and further loss can occur when the methanol is converted into a transport fuel like gasoline. For this reason, when we con­sider the overall energy conversion efficiency of a car run on biogas and compare that with an electric car, the former shows a rather low fuel-to-wheel energy ratio.

Stoichiometric calculations can help determine the products of reaction. Not all reactions are instantaneous and completely convert reactants into products. Many of the chemical reactions discussed in the preceding sections proceed at a finite rate and to a finite extent.

To what extent a reaction progresses is determined by its equilibrium state. Its kinetic rates, on the other hand, determine how fast the reaction products are formed and whether the reaction completes within the gasifier chamber. A review of the basics of chemical equilibrium may be useful before discussing its results.

5.4.1 Chemical Equilibrium

Let us consider the reaction:

nA + mb kfor > pC + qD (5.27)

where n, m, p, and q are stoichiometric coefficients. The rate of this reaction, r1, depends on CA and CB, the concentration of the reactants A and B, respectively.

R = kforCnACS (5.28)

The reaction can also move in the opposite direction:

pC + qD —kback > nA + mB (5.29)

The rate of this reaction, r2, is similarly written in terms of CC and CD, the concentration of C and D, respectively:

R2 = kback CC CD (5.30)

When the reaction begins, the concentration of the reactants A and B is high. So the forward reaction rate r1 is initially much higher than r2, the reverse reac­tion rate, because the product concentrations are relatively low. The reaction in this state is not in equilibrium, as r1 > r2. As the reaction progresses, the forward reaction increases the buildup of products C and D. This increases the reverse reaction rate. Finally, a stage comes when the two rates are equal to each other (r1 = r2). This is the equilibrium state. At equilibrium,

• There is no further change in the concentration of the reactants and the products.

• The forward reaction rate is equal to the reverse reaction rate.

• The Gibbs free energy of the system is at minimum.

• The entropy of the system is at maximum.

Under equilibrium state, we have

k cm = k CP CQ

for A В back C D

Reaction Rate Constant

A rate constant, ki, is independent of the concentration of reactants but is dependent on the reaction temperature, T. The temperature dependency of the reaction rate constant is expressed in Arrhenius form as

к = A) exp (^-Rf j (5.32)

where A0 is a pre-exponential constant, R is the universal gas constant, and E is the activation energy for the reaction.

The ratio of rate constants for the forward and reverse reactions is the equi­librium constant, Ke. From Eq. (5.31) we can write

The equilibrium constant, Ke, depends on temperature but not on pressure. Table 5.4 gives values of equilibrium constants and heat of formation of some gas­ification reactions (Probstein and Hicks, 2006, pp. 62-64).

f Л

TABLE 5.4 Equilibrium Constants and Heats of Formation for Five

Gasification Reactions

Heat of Formation Equilibrium Constant (log10K) (kJ/mol) Reaction 298 K 1000 K 1500 K 1000 K 1500 K C + /2o2 ^ CO 24.065 10.483 8.507 -111.9 -116.1 C + O2 ^ CO2 69.134 20.677 13.801 -394.5 -395.0 C + 2H2 ^ CH4 8.906 -0.999 -2.590 -89.5 -94.0 2C + 2H2 ^ C2H4 -11.940 -6.189 -5.551 38.7 33.2 H2 + >$02 ^ H2O 40.073 10.070 5.733 -247.8 -250.5 Source: Data compiled from Probstein and Hicks, 2006, p. 64. )

Gibbs Free Energy

Gibbs free energy, G, is an important thermodynamic function. Its change in terms of a change in entropy, AS, and enthalpy, AH, is written as

AG = AH — TAS (5.34)

The change in enthalpy or entropy for a reaction system is computed by finding the enthalpy or entropy changes of individual gases in the system. It is explained in Example 5.2. An alternative approach uses the empirical equations given by Probstein and Hicks (2006). It expresses the Gibbs function (Eq. 5.35) and the enthalpy of formation (Eq. 5.36) in terms of temperature, T, the heat of formation at the reference state at 1 atmosphere and 298 K, and a number of empirical coefficients, a’, b’, and so forth.

AG-0 ,r = ДА0И — a’T ln (T) — b’T2 — [ у j T3 — (у] T4

+ (2r) + F’ + 8’T k^/m°l

The values of the empirical coefficients for some common gases are given in Table 5.5.

The equilibrium constant of a reaction occurring at a temperature T may be known using the value of Gibbs free energy.

Ke = exp j (5.37)

Here, AG is the standard Gibbs function of reaction or free energy change for the reaction, R is the universal gas constant, and T is the gas temperature.

Example 5.2

Find the equilibrium constant at 2000 K for the reaction

co2 ^ co + /2o2

Solution

Enthalpy change is written by taking the values for it from the NIST-JANAF ther­mochemical tables (Chase, 1998) for 2000 K:

AH = (hf + Ah)ro + (hf + Ah)0i — (H° + Ah)C02

= 1 mol (-110,527 + 56,744) J/mol +1/2 mol (0 + 59,175) J/mol — 1 mol (-393,522 + 91,439) J/mol = 277,887 J

The change in entropy, A5, is written in the same way as for taking the values of entropy change from the NIST-JANAF tables (see list that follows on page 140).

TABLE 5.5 Heat of Combustion, Gibbs Free Energy, and Heat of Formation at 298 K, 1 Atm, and Empirical Coefficients from Eqs. 5.35 and 5.36 HHV (kj/mol) AfG293 (kj/mol) AfH298 (kj/mol) Empirical Coefficients Product a’ b’ c d’ e’ f S’ C 393.5 0 0 CO 283 -137.3 -110.5 5.619 x 10~3 -1.19×1 0~5 6.383 x 10"9 -1.846 x 1043 -4.891 x 103 0.868 -6.131 x 10-3 о и 0 -394.4 -393.5 -1.949 x 1 0~3 3.122 x 10~5 -2.448 x 10~8 6.946 x 10~13 -4.891 x 103 5.27 -0.1207 сн4 890.3 -50.8 -74.8 -4.62 x 1 0~3 1.1 3 x 1 0~5 1.31 9 x 1 0~8 -6.647 x 1043 -4.891 x 103 14.11 0.2234 с, н4 1411 68.1 52.3 -7.281 x 10~3 5.802 x 10~5 -1.861 x 10~8 5.648 x 10~13 -9.782 x 103 20.32 -0.4076 СНзОН 763.9 -161.6 -201.2 -5.834 x 10~3 2.07 x 10~5 1.491 x 1 0~8 -9.614 x 10 43 -4.891 x 10 3 16.88 -0.2467 н, о (steam) 0 -228.6 -241.8 -8.95 x 1 0~3 -3.672 x 10“6 5.209 x 10"3 -1.478 x 10~13 0 2.868 -0.0172 н, о (water) 0 -237.2 -285.8 о. 0 0 0 Н, 285.8 0 0 Source: Adapted from Probstein and Hicks, 2006, pp. 55, 61.

Д5 = lxSco +12XSo2 -1 XSco2

= (1 mol x 258.71 J/mol K) + (1/2 mol x 268.74 J/mol K)

— (1 mol x 309.29 J/mol K)

= 83.79 J/K

From Eq. (5.34), the change in the Gibbs free energy can be written as AG = AH — TAS

= 277.887 kj -(2,000 Кx83.79 J/K) = 110.307 kj The equilibrium constant is calculated using Eq. (5.37):

AC ( 110,307 )

K2000K = e~w = e-о.00831 4*2°°°/ = 0,001315 (5.38)

Kinetics of Gas-Solid Reactions

The rate of gasification of char is much slower than the rate of pyrolysis of the biomass that produces the char. Thus, the volume of a gasifier is more depen­dent on the rate of char gasification than on the rate of pyrolysis. The char gasification reaction therefore plays a major role in the design and performance of a gasifier.

Typical temperatures of the gasification zone in downdraft and fluidized-bed reactors are in the range of 700 to 900 °C. The three most common gas-solid reactions that occur in the char gasification zone are

Boudouard reaction: (R1:C + CO2 ^ 2CO) (5.39)

Water — gas reaction: (R2: C + H2O о CO + H2) (5.40)

Methanation reaction: (R3: C + 2H2 о CH4). (5.41)

The water-gas reaction, R2, is dominant in a steam gasifier. In the absence of steam, when air or oxygen is the gasifying medium, the Boudouard reaction, R1, is dominant. However, the steam gasification reaction rate is higher than the Boudouard reaction rate.

Another important gasification reaction is the shift reaction, R9 (CO + H2O о CO2 + H2), which takes place in the gas phase. It is discussed in the next section. A popular form of the gas-solid char reaction, r, is the nth-order expression:

1 dx -—

(1 — X)m dt ^ ’

where X is the fractional carbon conversion, A0 is the apparent pre-exponential constant (1/s), E is the activation energy (kJ/mol), m is the reaction order with respect to the carbon conversion, T is the temperature (K), and n is the reaction

order with respect to the gas partial pressure, Pt. The universal gas constant, R, is 0.008314 kJ/mol. K.

Boudouard Reaction

Referring to the Boudouard reaction (R1) in Eq. (5.6), we can use the Lang — muir-Hinshelwood rate, which takes into account CO inhibition (Cetin et al.,

2005)

to express the apparent gasification reaction rate, rb:

where PCO and PCO2 are the partial pressure of CO and CO2, respectively, on the char surface (bar). The rate constants, kh are given in the form, A exp(-E/ RT) bar-ns-n, where A is the pre-exponential factor (bar-n. s-n). Barrio and Hustad (2001) gave some values of the pre-exponential factor and the activation energy for Birch wood (Table 5.6).

When the concentration of CO is relatively small, and when its inhibiting effect is not to be taken into account, the kinetic rate of gasification by the Boudouard reaction may be expressed by a simpler nth-order equation as

_ e_

rb = Abe^P£o2s-_ (5.44)

For the Boudouard reaction, the values of the activation energy, E, for biomass char are typically in the range of 200 to 250 kJ/mol, and those of the exponent, n, are in the range of 0.4 to 0.6 (Blasi, 2009). Typical values of A, E, and n for birch, poplar, cotton, wheat straw, and spruce are given in Table 5.7.

The reverse of the Boudouard reaction has a major implication, especially in catalytic reactions, as it deposits carbon on its catalyst surfaces, thus deac­tivating the catalyst.

2CO ^ CO2 + C -172 kJ/mol (5.45)

TABLE 5.6 Activation Energy and Pre-Exponential Factors for Birch Char Using the Langmuir-Hinshelwood Rate Constants for CO2 Gasification
Langmuir-Hinshelwood Rate Constants (s-1 bar-	Activation Energy, ’) E (kJ/mol)	Pre-Exponential Actor, A (s-1 bar-1)
kbi	165	1.3 x 105
kb2	20.8	0.36
kb3	236	3.23 x 107
Source: Adapted from Barrio.	and Hustad, 2001.

Char Origin	Activation Energy, E (kJ/mol)	Pre-Exponential Factor, A (s-1 bar-1)	Reaction Order, n (-)	Reference
Birch	215	3.1 x 106 s-1 bar-038	0.38	Barrio and Hustad, 2001
Dry poplar	109.5	153.5 s-1 bar-1	1.2	Barrio and Hustad, 2001
Cotton wood	196	4.85 x 1 08 s-1	0.6	DeGroot and Shafizadeh, 1984
Douglas fir	221	19.67 x 108 s-1	0.6	DeGroot and Shafizadeh, 1984
Wheat straw	205.6	5.81 x 106 s-1	0.59	Risnes et al., 2001
Spruce	220	21.16 x 106 s-1	0.36	Risnes et al., 2001

r ; л TABLE 5.7 Typical Values for Activation Energy, Pre-Exponential Factor, and Reaction Order for Char in the Boudouard Reaction

The preceding reaction becomes thermodynamically feasible when (PC20/ PCo2) is much greater than that of the equilibrium constant of the Boudouard reaction (Littlewood, 1977).

Water-Gas Reaction

Referring to the water-gas reaction, the kinetic rate, rw, may also be written in Langmuir-Hinshelwood form to consider the inhibiting effect of hydrogen and other complexes (Blasi, 2009).

where Pi is the partial pressure of gas i in bars.

Typical rate constants according to Barrio et al. (2001) for beech wood are

kw1 = 2.0 x 107 exp (-199/RT); bar-1s-1

kw2 = 1.8 x 106 exp (-146/ RT); bar-1s-1

kw3 = 8.4 x 107 exp (- 225/ RT) bar-1s-1

Most kinetic analysis, however, uses a simpler nth-order expression for the reaction rate:

_ e_

rw = A^P^oS-1 (5.47)

Typical values for the activation energy, E, for steam gasification of char for some biomass types are given in Table 5.8.

Hydrogasification Reaction (Methanation)

The hydrogasification reaction is as follows:

C + 2H2« CH4 (5.48)

With freshly devolatilized char, this reaction progresses rapidly, but graphitiza- tion of carbon soon causes the rate to drop to a low value. The reaction involves volume increase, and so pressure has a positive influence on it. High pressure and rapid heating help this reaction. Wang and Kinoshita (1993) measured the rate of this reaction and obtained values of A = 4.189 x 10-3 s-1 and E = 19.21 kJ/mol.

Steam Reforming of Hydrocarbon

For production of syngas (CO, H2) direct reforming of hydrocarbon is an option. Here, a mixture of hydrocarbon and steam is passed over a nickel-based catalyst at 700 to 900 °C. The final composition of the product gas depends on the fol­lowing factors (Littlewood, 1977):

• H/C ratio of the feed

• Steam/carbon (S/C) ratio

• Reaction temperature

• Operating pressure

The mixture of CO and H2 produced can be subsequently synthesized into required liquid fuels or chemical feedstock. The reactions may be described as

C. H.+—H=o « EHJ. CH,+CO

CH4 + H2O « CO + 3H2 (5.50)

CO + H2O « CO2 + H2 (5.51)

The first reaction (Eq. 5.48) is favorable at high pressure, as it involves an increase in volume in the forward direction. The equilibrium constant of the first reaction increases with temperature while that of the third reaction (Eq. 5.51), which is also known as the shift reaction, decreases.

Kinetics of Gas-Phase Reactions

Several gas-phase reactions play an important role in gasification. Among them, the shift reaction (R9), which converts carbon monoxide into hydrogen, is most important.

R9: CO + H2O kf°r > CO2 + H2 — 41.1 kJ/mol (5.52)

This reaction is mildly exothermic. Since there is no volume change, it is rela­tively insensitive to changes in pressure.

The equilibrium yield of the shift reaction decreases slowly with tempera­ture. For a favorable yield, the reaction should be conducted at low temperature, but then the reaction rate will be slow. For an optimum rate, we need catalysts. Below 400 °C, a chromium-promoted iron formulation catalyst (Fe2O3 — Cr2O3) may be used (Littlewood, 1977).

Other gas-phase reactions include CO combustion, which provides heat to the endothermic gasification reactions:

R6: CO + l/2O2 kpr > CO2 — 284 kJ/mol (5.53)

These homogeneous reactions are reversible. The rate of forward reactions is given by the rate coefficients of Table 5.9.

TABLE 5.9 Forward Reaction Rates, r, for Gas-Phase Homogeneous Reactions
Reaction	Reaction Rate (r)	Heat of Formation (m3.mol-1.s-1)	Reference
H2 + xo2 ^ H2O	K ChCCo,	51.8 T’5 exp (-3420/7)	Vilienskii and Hezmalian, 1978
CO + 1 O2 ^ CO2	k C C 0.5c 0.5 K cCOcq2 cH2O	2.238 x 1 012 exp (—167.47/R7)	Westbrook and Dryer, 1981
CO + H2O ^ CO2 + H2	K CC0CH20	0.2778 exp (—12.56/R7)	Petersen and Werther, 2005
Note: Here, the gas constant,	R, is in kJ/mol. K.

For the backward CO oxidation reaction (CO + >2 O2 < kbact— CO2), the rate, kback, is given by Westbrook and Dryer (1981) as

кЬаЛ = 5.18 x 108 exp (-161.41/ RT) Cco2 (5.54)

For the reverse of the shift reaction (CO + H2O < kbact— CO2 + H2), the rate is given as

кЬаск = 126.2exp(-41.29/RT)Cco2Ch2 mol. m-3 (5.55)

If the forward rate constant is known, then the backward reaction rate, kback, can be determined using the equilibrium constant from the Gibbs free energy equation:

k (-AG0 ^

Kequilibrium =-^- = exp I at 1atm pressure (5.56)

kback V RT )

AG° for the shift reaction may be calculated (see Callaghan, 2006) from a simple correlation of

AG0 = -32.197 + 0.031T -(1774.7/ T), kJ/mol (5.57)

-0.2896 0.008314 [2] [3]1100

where T is in K.

Part (b). At equilibrium, the rate of the forward reaction will be equal to the rate of the backward reaction, or KequiBt>rium = 1. So, using the definition of the equilibrium constant, we have

K _ Pco2 pH

Kequilibrium

Pco Ph2O

where p denotes the partial pressure of the various species. In this reaction, nitrogen stays inert and does not react. Thus, 1 mole of nitrogen comes out from it. If x moles of CO and H2O react to form x moles of CO2 and H2, then at equi­librium, (1 — x) moles of CO and H2O remain unreacted. We can list the com­ponent mole fraction as:

Species	Mole	Mole fraction
CO	(1 — x)	(1 — x) / 3
H2O	(1 — x)	(1 — x) / 3
CO2	x	x/3
H2	x	x/3
N2	1	1/3

The mole fraction y is related to the partial pressure, p, by the relation yP = p, where P stands for total pressure.

Substituting the values for the partial pressures of the various species,

p)(Ї)

(¥ p)(¥ p)

Solving for x, we get x = 0.5. Thus, the mole fraction of CO2 at equilibrium =

(1 — x)/3 = 0.5/3 = 0.1667.

Part (c). To determine if this reaction is exothermic or endothermic, the standard heats of formation of the individual components are taken from the NIST-JANAF thermochemical tables (Chase, 1998).

AH = (hf )COi + (hf )H2 -[(hf )co + (hf )H20 ]

AH = -393.52 kj/mol — 0 kj/mol -[-110.53 kj/mol — 241.82 kj/mol]

AH = -41.1 7 kj/mol

Since 41.17 kJ/mol of heat is given out, the reaction is exothermic.

Part (d). This reaction does not depend on pressure, as there is no volume change. The equilibrium constant changes only with temperature, so the equilib­rium constant at 100 atm is the same as that at 1 atm, for 1100 K. The equilibrium constant is 0.9688 at 100 atm, for 1100 K.

5.4.2 Char Reactivity

Reactivity, generally a property of a solid fuel, is the value of the reaction rate under well-defined conditions of gasifying agent, temperature, and pressure.

Proper values or expressions of char reactivity are necessary for all gasifier models. This topic has been studied extensively for more than 60 years, and a large body of information is available, especially for coal. These studies unearthed important effects of char size, surface area, pore size distribution, catalytic effect, mineral content, pretreatment, and heating. The origin of the char and the extent of its conversion also exert some influence on reactivity.

Char can originate from any hydrocarbon—coal, peat, biomass, and so forth. An important difference between chars from biomass and those from fossil fuels like coal or peat is that the reactivity of biomass chars increases with conversion while that of coal or peat char decreases. Figure 5.3 plots the reactivity for hardwood and peat against their conversion (Liliedahl and Sjostrom, 1997). It is apparent that, while the conversion rate (at conversion 0.8) of hardwood char in steam is 9% per minute, that of peat char under similar conditions is only 1.5% per minute.

Effect of Pyrolysis Conditions

The pyrolysis condition under which the char is produced also affects the reactivity of the char. For example, van Heek and Muhlen (1990) noted that the reactivity of char (in air) is much lower when produced above 1000 °C compared to that when produced at 700 °C. High temperatures reduce the number of active sites of reaction and the number of edge atoms. Longer resi­dence times at peak temperature during pyrolysis also reduce reactivity.

Effect of Mineral Matter in Biomass

Inorganic materials in fuels can act as catalysts in the char-oxygen reaction (Zolin et al., 2001). In coal, inorganic materials reside as minerals, whereas in biomass they generally remain as salts or are organically bound. Alkali metals, potassium, and sodium are active catalysts in reactions with oxygen-containing species. Dispersed alkali metals in biomass contribute to the high catalytic activity of inorganic materials in biomass. In coal, CaO is also dispersed, but at high temperatures it sinters and vaporizes, blocking micropores.

Inorganic matter also affects pyrolysis, giving char of varying morphologi­cal characteristics. Potassium and sodium catalyze the polymerization of vola­tile matter, increasing the char yield; at the same time they produce solid materials that deposit on the char pores, blocking them. During subsequent oxidation of the char, the alkali metal catalyzes this process. Polymerization of volatile matter dominates over the pore-blocking effect. A high pyrolysis tem­perature may result in thermal annealing or loss of active sites and thereby loss of char reactivity (Zolin et al., 2001).

Intrinsic Reaction Rate

Char gasification takes place on the surface of solid char particles, which is generally taken to be the outer surface area. However, char particles are highly

porous, and the surface areas of the inner pore walls are several orders of magnitude higher than the external surface area. For example, the actual surface area (BET) of an internal pore of a 1-mm-diameter beechwood char is 660 cm2 while its outer surface is only 3.14 cm2. Thus, if there is no physical restriction, the reacting gas can potentially enter the pores and react on their walls, resulting in a high overall char conversion rate. For this reason, two char particles with the same external surface area (size) may have widely different reaction rates because of their different internal structure.

From a scientific standpoint, it is wise to express the surface reaction rate on the basis of the actual surface on which the reaction takes place rather than the external surface area. The rate based on the actual pore wall surface area is the intrinsic reaction rate; the rate based on the external surface area of the char is the apparent reaction rate. The latter is difficult to measure, so some­times it is taken as the reactive surface area determined indirectly from the reaction rate instead of the total pore surface area measured by the physical adsorption of nitrogen. This is known as the BET area (Klose and Wolki, 2005).