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).