Some of the five equations (reactions R1-R5) are endothermic while some are exothermic. The overall heat balance of reacting char particles is known from a balance of a particle’s heat generation and heat loss to the gas by conduction and radiation.

where Cpc is the specific heat of the char, AHk is the heat of reaction of the kth reaction at the char surface at temperature Ts, ep is the emissivity of the char particle, Xg is the thermal conductivity of the gas, and a is the Stefan-Boltzmann constant.

A similar heat balance for the gas in an element dz in length can be carried out as

— [hcom(Tg — Tw ) + ewo(Tg — TW)] kDr

where A|k is the extent of the gas-phase kth reaction with the heat of reaction, AHk (Tg); hconv is the gas-wall convective heat transfer coefficient; and Dr is the reactor’s internal diameter.

The first term on the right of Eq. (5.91) is the net heat absorption by the gas-phase reaction, the second is the heat transfer from the gas to the char particles, and the third is the heat loss by the gas at temperature Tg to the wall at temperature Tw.

The equations are solved for an elemental volume, AdLr, with boundary conditions from the previous upstream cell. The results are then used to solve the next downstream cell.

Symbols and Nomenclature

A = cross-sectional area of bed or reactor (m2)

A0 = pre-exponential coefficient in Eq. (5.42) (s-1)

Ab, Aw = pre-exponential coefficients in Eqs. (5.44) and (5.47), respectively (bar-" s-1) Aj = total number of atoms of element j entering the reactor (-) a, = number of atoms of jth element in Ith species (-) ajk = mass of jth gas, required for the kth reaction (kg)

Cl = molar concentration of ith gas (mol/m3)

Cpc = specific heat of char (kJ/kg. K)

Cpg = specific heat of the bulk gas Dr = internal diameter of the reactor (m)

Dgj = diffusion coefficient of the jth gas in the mixture of gases (m2/s) db = diameter of the bubble (m)

E = activation energy (kJ/mol) ep = emissivity of char particle (-)

Fgl0 = initial flow rate of the gas (mol/s)

Fgl = molar flow rate of the Ith gas (mol/s)

Gtotal = total Gibbs free energy (kJ) g = acceleration due to gravity, 9.81 (m/s2)

AHk = heat of reaction of kth reaction at char surface (kJ/mol)

AH = enthalpy change (kJ)

H0, Щ = heat of formation at reference state (kJ)

hconv = gas-wall convective heat transfer coefficient (kW/m2K)

hm = mass-transfer coefficient (kg carbon/m2.bar2.s)

k = first-order reaction rate constant (s-1)

k0 = pre-exponential factor (s-1)

kiiq = rate constant for the liquid yield of pyrolysis (s-1)

kBE = bubble-emulsion mass exchange coefficient (m/s)

kc = rate constant for the char yield of pyrolysis (s-1)

kg = rate constant for the gas yield of pyrolysis (s-1)

kj = rate constant of three primary pyrolysis reactions taken together (s-1)

K = number of element in Eq (5.77)

kw1, kw2, kw3 = rate constants in Eq (5.47) (bar-1 s-1)

Ksk = surface reaction rate constant for kth reaction, mol/m2.barn Ke, Kequlbbnum = equilibrium constant (-) l = number of gaseous reactants (-)

Lr = length of the reactor (m)

L = Lagrangian function (-)

mb = mass of the biomass in the primary pyrolysis process (kg) m0 = initial mass of the biomass (kg)

mc = mass of the biomass remaining after complete conversion (kg) m = reaction order with respect to carbon conversion in Eq. 5.42 (-)

m, n, p, q = stoichiometric coefficients in Eqs. 5.27-5.29 n = reaction order with respect to the gas partial pressure, Eq. 5.44 (-)

N = number of species present (-)

Nc = number of char particles in unit gas volume (-)

Nor = number of orifices in a bed of area (Ar)

Pi = partial pressure of the species i (bar)

P = total pressure of the species (bar)

Q = char gasification rate (kg carbon/m2.s)

Qualification, Qconv, Qrad, and Qmass = energy transfer due to gasification, convection, radia­tion, respectively (kW/m3 of bed)

R = gas constant (8.314 J/mol. K, or 8.314 x 10-5 m3.bar/mol. K)

Rc = chemical kinetic reaction rate (kg carbon/m2.bar2s)

Rm, gj = rate of production or consumption of gas species j (kg/m3s)

Ті = reaction rate of the ith reaction (s-1) rc = char particle radius (m)

T = temperature (K)

Ts = surface temperature of char particles (K)

Tg = gas temperature (K)

Tw = wall temperature (K) t = time (s)

ug = superficial gas velocity in Eq. 5.80 (m/s)

U = fluidization velocity (m/s)

UB = bubble rise velocity (m/s)

Umf = minimum fluidization velocity (m/s)

X = fractional change in the carbon mass of the biomass (kg)

y = mole fraction of a species (-)

yt = mole fraction of gas in the bulk (-)

yls = mole fraction of gas on the char surface (-)

z = height above grid or distance along a reactor from fuel entry (m)

alk = stoichiometric coefficient for lth gas in kth reaction (-)

В = partition coefficient (-)

X = Lagrangian multiplier (-)

Xg = thermal conductivity of gas (kJ/m. K)

О = Stefan-Boltzmann constant (5.67 x 10-8 W m-2 K-4)

AG, AG° = change in Gibbs free energy (kJ)

AG° = change in Gibbs free energy of formation of species i (kJ)

A^k = extent of gas-phase kth reaction (-) pj = density of jth gas (kg/m3)

Emf = voidage at minimum fluidization condition pg = density of the bulk gas AS = entropy change (kJ/K)

Because the gas residence time in an entrained-flow reactor is very short— on the order of a few seconds—to complete the reactions, the biomass particles must be ground to extremely fine sizes (less than 1 mm). The residence time

requirement for the char is thus on the order of seconds. Section 6.9.1 describes some important considerations for entrained-flow gasifier design.

Although an entrained-flow gasifier is ideally a plug-flow reactor, in practice this is not necessarily so. The side-fed entrained-flow gasifier, for example, behaves more like a continuous stirred-tank reactor (CSTR). As we saw in Figure 6.15, at a certain distance from the entry point, fuel particles may have different residence times depending on the path they took to arrive at that section. Some may have traveled a longer path and so have a longer residence time. For this reason, a plug-flow assumption may not give a good estimate of the residence time of char.

Metal surfaces are generally protected by a oxide layer that forms on them and guards against further attack from corrosive elements. This protective layer can be destroyed through chemical or electrochemical dissolution.

In chemical dissolution, the protective layer is removed by a chemical process using either an acidic or an alkaline solution depending on the pH value in the local region. In electrochemical dissolution, depending on the electro­chemical potential, the metal can undergo either transpassive or active dissolu­tion. All forms of electrochemical corrosion require the presence of aggressive ionic species (as reactants, products, or both), which in turn requires the exis­tence of an aqueous environment capable of stabilizing them.

Stainless and nickel-chromium alloys experience high corrosion rates at supercritical pressure but subcritical temperatures because of transpassive dis­solution (Friedrich et al., 1999), where the nickel or iron cannot form a stable insoluble oxide that protects the alloy. Under supercritical conditions, the acids are not dissociated and ionic corrosion products cannot be dissolved by the solution because of the solvent’s low polarity. Consequently, corrosion drops down to low values.

Electrochemical corrosion requires the presence of ionic species like halides, nickel-based alloys, and compounds. These show high corrosion rates, which decrease at higher temperatures. High-pressure water in an SCW reactor pro­vides favorable conditions for this, but once the water enters the supercritical domain the solubility and concentration of ionic species in it decrease, although the reaction rate continues to be higher because of higher temperatures. The total corrosion reduces because of decreased concentration of the reacting species. Thus, corrosion in a plant increases with temperature, reaching a peak just below the critical temperature, and then reduces when the temperature is supercritical. The corrosion rate increases downstream, where the temperature drops into the subcritical region.

At a relatively low supercritical pressure (e. g., 25 MPa), the salt NaCl is not soluble. Thus, in an SCW a reaction that produces NaCl, the salt can pre­cipitate on the reactor wall. Sometimes water and brine trapped between the salt deposit and the metal can create a local condition substantially different from conditions in the rest of the reactor in terms of corrosion. This is known as underdeposit corrosion.

In general, a reaction environment that is characterized by high density, high temperature, and high ion concentration (e. g., acidic) is most conducive to cor­rosion in an SCW reactor. Rather than the severity of corrosion in terms of whether the flow is supercritical or subcritical, the density of the water should be the major concern.

Bio-oil is a hydrocarbon similar to petrocrude except that the former has more oxygen. Thus, most of the chemicals produced from petroleum can be produced from bio-oil. These include:

• Resins

• Food flavorings

• Agro-chemicals

• Fertilizers

• Levoglucosan

• Adhesives

• Preservatives

• Acetic acid

• Hydroxyacetaldehyde

Transport Fuel Production

Bio-oil contains less hydrogen per carbon (H/C) atom than do conventional transport fuels like diesel and gasoline, but it can be hydrogenated (hydrogen added) to make up for this deficiency and thereby produce transport fuels with a high H/C ratio. The hydrogen required for the hydrogenation reaction nor­mally comes from an external source, but it can also be supplied by reforming a part of the bio-oil into syngas. This method is practiced by Dynamotive, a Canadian company.

The typical moisture content of freshly cut wood ranges from 30 to 60%, and for some biomass it can exceed 90% (see Table 2.9). Every kilogram of mois­ture in the biomass takes away a minimum of 2260 kJ of extra energy from the gasifier to vaporize water, and that energy is not recoverable. For a high level of moisture this loss is a concern, especially for energy applications. While we cannot do much about the inherent moisture residing within the cell structure, efforts may be made to drive away the external or surface moisture. A certain amount of predrying is thus necessary to remove as much moisture from the biomass as possible before it is fed into the gasifier. For the production of a fuel gas with a reasonably high heating value, most gasification systems use dry biomass with a moisture content of 10 to 20%.

The final drying takes place after the feed enters the gasifier, where it receives heat from the hot zone downstream. This heat dries the feed, which releases water. Above 100 °C, the loosely bound water that is in the biomass is irreversibly removed. As the temperature rises, the low-molecular-weight extractives start volatilizing. This process continues until a temperature of approximately 200 °C is reached.

A circulating fluidized-bed (CFB) gasifier has a special appeal for biomass gasification because of the long gas residence time it provides. It is especially suitable for fuels with high volatiles. A CFB typically comprises a riser, a cyclone, and a solid recycle device (Figure 6.10). The riser serves as the gasifier reactor.

Although the HTW process (Figure 6.9) appears similar to a CFB, it is only a bubbling bed with limited solid recycle. The circulating and bubbling fluid­ized beds are significantly different in their hydrodynamic. In a CFB, the solids are dispersed all over the tall riser, allowing a long residence time for the gas as well as for the fine particles. The fluidization velocity in a CFB is much

Uniflow cyclone

Reactor

Biofuel feed

Product gas at 650-750 °C

Cooling… -…… water

Bottom ash-cooling screw Bottom ash

FIGURE 6.10 Circulating fluidized-bed gasifier. (Source: Adapted from Foster Wheeler.) higher (3.5-5.5 m/s) than that in a bubbling bed (0.5—1.0 m/s). Also, there is large-scale migration of solids out of the CFB riser. These are captured and continuously returned to the riser’s base. The recycle rate of the solids and the fluidization velocity in the riser are sufficiently high to maintain the riser in a special hydrodynamic condition, known as fast fluidized bed. Depending on the fuel and the application, the riser operates at a temperature of 800 to 1000 °C.

The hot gas from the gasifier passes through a cyclone, which separates most of the solid particles associated with it, and the loop seal returns the par­ticles to the bottom of the gasifier. Foster Wheeler developed a CFB gasifier where an air preheater is located in the standpipe below the cyclone to raise the temperature of the gasification air and indirectly raise the gasifier tempera­ture (Figure 6.10).

Many commercial gasifiers of this type have been installed in different countries. At the time of writing, the biggest among these is a 60-MWth unit in a coal-fired and natural-gas-fired power plant in Lahti, Finland, to provide a cheap supplementary fuel by gasifying waste wood and refuse-derived fuels (RDFs). Several manufacturers around the world have developed versions of the CFB gasifier that work on the same principle and vary only in engineering details.

Transport Gasifier

This type of gasifier has the characteristics of both entrained-flow and fluidized — bed reactors. The hydrodynamics of a transport gasifier is similar to that of a fluid catalytic cracking reactor. A transport gasifier operates at circulation rates, velocities, and riser densities considerably higher than those of a conventional circulating fluidized bed. This results in higher throughput, better mixing, and higher mass and heat-transfer rates. The fuel particles are also very fine (Basu, 2006) and as such it requires a pulverizer or a hammer mill. A comparison of typical hydrodynamic operating conditions in a transport gasifier and in a fluid catalytic cracking unit is given in Table 6.3.

A transport gasifier consists of a mixing zone, a riser, a disengager, a cyclone, a standpipe, and a J-leg. Coal, sorbent (for sulfur capture), and air are injected into the reactor’s mixing zone. The disengager removes the larger carried-over particles, and the separated solids return to the mixing section through the J-valve located at the base of the standpipe (Figure 6.11). Most of the remaining finer particles are removed by a cyclone located downstream, from which the gas exits the reactor. The reactor can use either air or oxygen as the gasification medium.

Use of oxygen as the gasifying medium avoids nitrogen, the diluting agent in the product gas. For this purpose, air is more suitable for power generation, while oxygen is more suitable for chemicals production. The transport gasifier has proved to be effective for gasification of coal, but it is yet to be proven for biomass.

Twin Reactor System

One of the major problems in air gasification of coal or biomass is the dilution of product gas by the nitrogen in the air used for the exothermic combustion

reaction necessary in a self-sustained gasifier. To avoid this, oxygen is used instead, but oxygen gasification is expensive and highly energy intensive (see Example 6.5 later in chapter). A twin reactor (e. g., a dual fluidized bed) over­comes this problem by separating the combustion reactor from the gasification reactor such that the nitrogen released in the air combustion does not dilute the product gas. Twin reactor systems are used for coal and biomass. They are either externally circulating or internally circulating.

This type of system has some limitations; for example, Corella et al. (2007) identified two major design issues with the dual fluidized-bed system:

• Biomass contains less char than coal contains; however, if this char is used for gasification the amount of char available may not be sufficient to provide the required endothermic heat to the gasifier reactor to maintain a tempera­ture above 900 °C. External heating may be necessary.

• Though the gasifier runs on steam, only a small fraction (<10%) of the steam participates in the gasification reaction; the rest of it simply leaves the gas­ifier, consuming a large amount of heat and diluting the gas.

The Technical University of Vienna used the externally circulating system to gasify various types of biomass in an industrial plant in Gussing, Austria.

The system is comprised of a bubbling fluidized-bed gasifier and a circulating fluidized-bed combustor (Figure 6.12). The riser in a CFB operates as a com­bustor; the bubbling fluidized bed in the return leg operates as a gasifier. Pyrolysis and gasification take place in the bubbling fluidized bed, which is fluidized by superheated steam. Unconverted char and tar move to the riser through a nonmechanical valve. The riser is fluidized by air.

Tar and gas produced during pyrolysis are combusted in the riser’s combus­tion zone. Heat generated by combustion raises the temperature of the inert bed material to around 900 °C. This material leaves the riser and is captured by the cyclone at the riser exit. The collected solids drop into a standpipe and are then circulated into the bubbling fluidized-bed reactor to supply heat for its endo­thermic reactions. The char is gasified in the bubbling bed in the presence of steam, producing the product gas. This system overcomes the problem of tar by burning it in the combustor. In this way, a product gas relatively free of tar can be obtained.

The Rentech-Silvagas process is also based on the externally circulating principle. Here, both the combustor and the gasifier work on circulating fluid — ized-bed principles. In the internally circulating design, the fluidized-bed

reactor is divided into two chambers and connected by a window at the bottom of the division wall separating them. The chambers are fluidized at different velocities (Figure 6.13), which result in their having varying bed densities. As the bed height is the same in both, the hydrostatic pressure at the bottom of the two chambers is different. The biomass and sand thus flow from the higher — density chamber to the lower-density chamber, creating a continuous circulation of bed materials similar to the natural circulation in a boiler. This helps increase the residence time of solids in the fluidized bed.

Such an arrangement can provide a more uniform distribution of biomass particles in the reactor, with increased gasification yield and decreased tar and fine solids (char) in the syngas (Freda et al., 2008). A special feature of the twin reactor is that more air or oxygen can be added in one part of the bed to encourage combustion, and more steam can be added in another part to encourage gasification.

The following are two broad routes for the production of energy or chemical feedstock from biomass:

Biological: Direct biophotolysis, indirect biophotolysis, biological reac­tions, photofermentation, and dark fermentation are the five major biologi­cal processes.

Thermochemical: Combustion, pyrolysis, liquefaction, and gasification are the four main thermochemical processes.

Thermal conversion processes are relatively fast, taking minutes or seconds to complete, while biological processes, which rely on enzymatic reactions, take much longer, on the order of hours or even days. Thus, for commercial use, thermochemical conversion is preferred.

Gasification may be carried out in air, oxygen, subcritical steam, or water near or above its critical point. This chapter concerns hydrothermal gasification of biomass above or very close to the water’s critical point to produce energy and/or chemicals.

Conventional thermal gasification faces major problems from the forma­tion of undesired tar and char. The tar can condense on downstream equip­ment, causing serious operational problems, or it may polymerize to a more complex structure, which is undesirable for hydrogen production. Char residues contribute to energy loss and operational difficulties. Furthermore, very wet biomass can be a major challenge to conventional thermal gasification because it is difficult to economically convert if it contains more than 70% moisture. The energy used in evaporating fuel moisture (2257 kJ/kg), which effectively remains unrecovered, consumes a large part of the energy in the product gas.

Gasification in supercritical water (SCWG) can largely overcome these shortcomings, especially for very wet biomass or organic waste. For example, the efficiency of thermal gasification of a biomass containing 80% water in conventional steam reforming is only 10%, while that of hydrothermal gasifica­tion in SCW can be as high as 70% (Dinjus and Kruse, 2004). Gasification in near or supercritical water therefore offers the following benefits:

• Tar production is low. The tar precursors, such as phenol molecules, are completely soluble in SCW and so can be efficiently reformed in SCW gasification.

• SCWG achieves higher thermal efficiency for very wet biomass.

• SCWG can produce in one step a hydrogen-rich gas with low CO, obviating the need for an additional shift reactor downstream.

• Hydrogen is produced at high pressure, making it ready for downstream commercial use.

• Carbon dioxide can be easily separated because of its much higher solubility in high-pressure water.

• Char formation is low in SCWG.

• Heteroatoms like S, N, and halogens leave the process with aqueous efflu­ent, avoiding expensive gas cleaning. Inorganic impurities, being insoluble in SCW, are also removed easily.

In a silo, the solids are withdrawn through chutes at the bottom. Previous dis­cussions examined solids flow through the silo. Now, we will look at the flow out of the silo through the chute, which connects the silo to the feeder. A proper chute design ensures uninterrupted flow from storage to feeder. Improper

design results in nonuniform flow. Figure 8.9 illustrates the problem, showing partial solids flow with a uniform-area chute and full solids flow with a properly designed chute. As the solids accumulate on the belt, their uniform flow through the hopper prevents them from accumulating at the chute’s downstream section. The chute’s expanded and lifted opening helps the solids spread well, allowing uniform withdrawal. For this reason, the modified design of Figure 8.9(b) shows the skirt on the chute to be lifted and expanded (in plan view) to facilitate uniform solid discharge from the hopper. These angles (slope and discharge) should be in the range of 3 to 5 degrees.

Figure 8.10 is another illustration of this phenomenon, this time with a rotary feeder. Here the design on the left (Figure 8.10a) is without the short vertical section like that on the right (Figure 8.10b). Solids are compressed in the direction of rotation and pushed up through the hopper. The design on the right uses a short vertical chute that limits this backflow only to the chute height, giving a relatively steady flow.

The two key requirements for chute design are: (1) the entire cross-section of the outlet must be active, permitting the flow of solids; and (2) the maximum discharge rate of the chute must be higher than the maximum handling rate of the feeder to which it is connected.

A restricted outlet, caused by a partially open slide gate, results in funnel flow with a small active flow channel regardless of hopper design. A rectangular outlet ensures that feeder capacity increases in the direction of the flow. With a belt feeder, the increase in capacity is achieved by a tapered interface. The

capacity increase along the feeder length is achieved by the increase in height and width of the interface above the belt.

Poor feeder design is a common cause of flow problems, as it prevents smooth withdrawal of solids. If the discharge rate of the chute is lower than the maximum designed feeding rate of the feeder, the feeder can be starved of solids and its flow control will be affected.

Generally, the oil burnt in a diesel (compression-ignition) engine is called diesel. If produced from petroleum, it is called petrodiesel, and if produced from biomass, it is called biodiesel. Mineral diesel (or petrodiesel) is made of a large number of saturated and aromatic hydrocarbons. The average chemical formula can be Ci2H23. Petrodiesel (also called fossil diesel) is produced from the fractional distillation of crude oil between 200 °C and 350 °C at atmospheric pressure, resulting in a mixture of carbon chains that typically contain between 8 and 21 carbon atoms per molecule (Collins, 2007).

According to the American Society for Testing and Materials (ASTM), biodiesel (B100) is defined as "a fuel comprised of mono-alkyl (methyl) esters of long chain fatty acids derived from vegetable oils or animal fats, and meeting

the requirements of ASTM D 6751.” Its characteristics are similar to those of petrodiesel, but not identical. Biodiesel, which can be mixed with petrodiesel for burning in diesel engines, has several positive features for use in engines, as listed in the following:

• Petrodiesel contains up to 20% polyaromatic hydrocarbon, while biodiesel contains none, making it safer for storage.

• Biodiesel has a higher flash point, making it safer to handle.

• Being oxygenated, biodiesel is a better lubricant than petrodiesel is and therefore gives longer engine life.

• Its higher oxygen content allows biodiesel to burn more completely. Biodiesel Production from Methanol

Biodiesel is generally produced from vegetable oil and/or from animal fats with major constituents that are triglycerides. It is produced by transesterification of vegetable oil or fat in the presence of a catalyst. Biodiesel carries the name fatty acid methyl (or ethyl) ester, commonly abbreviated as FAME. A popular production method involves mixing waste vegetable oil or fat with the catalyst and methanol (or ethanol) in appropriate proportion. A typical proportion is 87% oil, 1% NaOH catalyst, and 12% alcohol. Both acid and base catalysts can be used, but the base catalyst NaOH is the most common. Because NaOH is not recyclable, a “nongreen” feed is required to produce “green” biodiesel. Efforts are being made to produce recyclable catalysts and thereby make the product pure “green.”

Figure 9.5 shows the reaction for the conversion of triglyceride into bio­diesel (FAME) and its by-product, glycerol. Glycerol cannot be used as a transport fuel, and its disposal is a major issue.

An alternative noncatalytic conversion route for biodiesel is under develop­ment in which transesterification of triglycerides is by supercritical methanol (above 293 °C, 8.1 MPa) without a catalyst (Kusdiana et al., 2006). The metha­nol can be recycled and reused, but the process for this must be carried out at high temperatures and pressures. Efforts are also being made to use woody biomass (ligno-cellulose) instead of fats or oil to produce biodiesel using the supercritical method (Minami and Saka, 2006). The reaction is carried out in

a fixed or fluidized bed. The fluidized bed has the advantage of continuous catalyst regeneration and efficient removal of the heat of reaction.

In nonstoichiometric modeling, no knowledge of a particular reaction mecha­nism is required to solve the problem. In a reacting system, a stable equilibrium condition is reached when the Gibbs free energy of the system is at the minimum. So, this method is based on minimizing the total Gibbs free energy. The only input needed is the elemental composition of the feed, which is known from its ultimate analysis. This method is particularly suitable for fuels like biomass, the exact chemical formula of which is not clearly known.

The Gibbs free energy, Gtotai for the gasification product comprising N species (i = 1.. .N) is given by

where AG0,; is the Gibbs free energy of formation of species i at standard pres­sure of 1 bar.

Equation (5.73) is to be solved for unknown values of ni to minimize Gtotal, bearing in mind that it is subject to the overall mass balance of individual

elements. For example, irrespective of the reaction path, type, or chemical formula of the fuel, the amount of carbon determined by ultimate analysis must be equal to the sum total of all carbon in the gas mixture produced. Thus, for each jth element we can write

where ai, j is the number of atoms of the jth element in the ith species, and Aj is the total number of atoms of element j entering the reactor. The value of n should be found such that Gtotai will be minimum. We can use the Lagrange multiplier methods to solve these equations.

The Lagrange function (L) is defined as

Xai>ni — Aj kJ/mol

where Л is the Lagrangian multiplier for the jth element.

To find the extreme point, we divide Eq. (5.75) by RT and take the derivative,

£ > ° (576)

Substituting the value of Gtotal from Eq. (5.73) in Eq. (5.75), and then taking its partial derivative, the final equation is of the form given by

Kinetic Models

Gas composition measurements for gasifiers often vary significantly from those predicted by equilibrium models (Peterson and Werther, 2005; Li et al., 2001; Kersten, 2002). This shows the inadequacy of equilibrium models and under­scores the need of kinetic models to simulate gasifier behavior.

A kinetic model gives the gas yield and product composition a gasifier achieves after a finite time (or in a finite volume in a flowing medium). Thus, it involves parameters such as reaction rate, residence time of particles, and reactor hydrodynamics. For a given operating condition and gasifier configura­tion, the kinetic model can predict the profiles of gas composition and tempera­ture inside the gasifier and overall gasifier performance.

The model couples the hydrodynamics of the gasifier reactor with the kinet­ics of gasification reactions inside the gasifier. At low reaction temperatures, the reaction rate is very slow, so the residence time required for complete conversion is long. Therefore, kinetic modeling is more suitable and accurate

at relatively low operating temperatures (<800 °C) (Altafini et al., 2003). For higher temperatures, where the reaction rate is faster, the equilibrium model may be of greater use.

Kinetic modeling has two components: (1) reaction kinetics and (2) reactor hydrodynamics.