Jan 29, 2017 - overnight until the residual pressure is 0.1 Pa (Marsh, 1989). ...... the two chambers never exceeded 0.2 Pa. ...... Radius of a pit hole [m]. R.
Downloaded from orbit.dtu.dk on: Jan 29, 2017
Disintegration of beech wood char during thermal conversion
Hindsgaul, Claus; Qvale, Einar Bjørn; Henriksen, Ulrik Birk; Jensen, Anker Degn
Publication date: 2007 Document Version Publisher's PDF, also known as Version of record Link to publication
Citation (APA): Hindsgaul, C., Qvale, E. B., Henriksen, U. B., & Jensen, A. D. (2007). Disintegration of beech wood char during thermal conversion. Technical University of Denmark.
General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
MEK-ET-PHD-2006-02
Disintegration of beech wood char during thermal conversion
4
_-__—-I-—
‘
Ph.D. Thesis Claus Hindsgaul
[Qq |\/|EK
Department of Mechanical Engineering Department of Chemical Engineering Technical University of Denmark (DTU)
August 2006
Bibliograpic data: Ph.D. Thesis by Claus Hindsgaul Title: Disintegration of beech wood char during thermal conversion Danish title: Nedbrydningen of bogetraes/co/is under terinisk oniscetning MEK-ET-PHD-2006-02 ISBN: 817475-337-1
Cover images: Background: SEM (Scanning Electron Microscope) image of a longitudinal section of beech Wood char gasified in CO2 to a degree of conversion of 10% at 650 °C. The image covers a section of 0.22>1100 C
6
Tar reduction
1
Exhaust
2
Engine
3 5
Fixed bed gasification
4 40 C
Gas
800 C
90 C D.H.
Water
D.H.
Ash Air preheat
Particles
Figure 0.1.: Simpli ed diagram of the two-stage gasi cation plant Viking at DTU. Typical temperatures are shown.
14
Contents
Contents
causes on the hot grate supporting the xed bed. The latter is especially a concern when upscaling the plant, since the grate then has to span a greater area. The violent and unpredictable variations in the xed bed pressure drop, which is sometimes observed, increase wear on the other components in the system, and may impact the stability of the whole process. It is therefore desirable to be able to predict and hopefully control this pressure drop. Computer ow models have shown that local variations in xed bed permeabilities can cause dead zones and channelling in the reactor (Jensen et al., 2002; Keyser et al., 2006). Experimental investigations have shown that large particle sizes and narrow size distributions result in higher permeabilities of coal and char beds (Hindsgaul and Henriksen, 1999; Standish and Mellor, 1980). Thus, understanding the way char particles disintegrate may be the key to predicting and controlling the pressure drop of xed char beds. In addition, the way particles disintegrate during conversion in both uid bed and xed bed processes determines which particles or particle fragments escape. This aects the carbon loss the amount of carbon that is lost unconverted from the reactor. Also, the physical strength of a xed bed itself is limited by the strength of its individual particles. The way char disintegrates during conversion also aect other parameters relevant to combustion processes. For example, the development of char reactivity during conversion depend on the treatment history of the char as well as how the physical structures are aected by the conversion. In this thesis, the structural changes occurring in slowly pyrolysed wood chars will be investigated. Char from beech wood (Fagus sylvatica) will be used as basis material for the present investigations. Beech is a very common wood species in Northern Europe, and beech char has already been subject to several combustion related studies (Ehrburger and Lahaye, 1982; Gøbel, 1999; Mouchot et al., 2000). Focus is put on the description of changes in the physical structure of the char as well as the development of its gas transport properties during conversion. The gas permeability and diusion resistance determine the transport of gaseous reactants and products during diusion-limited conversion, and may therefore strongly in uence the participation of dierent structural parts in the process. In addition, changes in gas transport properties that indicate structural changes inside the material, will be investigated.
15
Contents
Contents
The structure of this thesis The present thesis consist of ve main chapters divided into subsections. Larger subsections are followed by a summary.
• Chapter 1 describes common experimental methods that have been applied in the coal and char research, and reviews the theoretical background and current knowledge on materials coal and char and changes occurring during their thermal conversion. • Chapter 2 describes the experimental methods applied in the present work. • Chapter 3 presents the experimental results. • Chapter 4 documents a computer model built to describe diusion-limited gasi cation of beech char slabs, and discusses the results of simulations using this model. • Chapter 5 contain a summary of the results, and a conclusion. The common nomenclature used throughout this thesis is listed on page 182, followed by the bibliography.
16
1. Theory In this chapter, common methods to determine the properties of porous media such as wood char are described, and prior results on char and coal reported in the literature are presented. The available literature on coal and coal char is much more extensive than it is on wood char. Since coal shares many of the properties of wood char, including its biological origin, much relevant information has been gained by consulting past coal research.
• The rst section describe methods used to determine the physical structure of porous media, such as geometry, pore sizes, and density, followed by a description of the structures of coal and wood char. • In the second section, gas transport theory is described generally, followed by a review of the present knowledge on gas transport in coal and wood char. • The third section is a brief description of heat transfer in char. • The fourth section is on char gasi cation reactions, reactivity, and structural changes during reactions. • The fth section describes the strength of wood and char as well as fragmentation mechanisms.
1.1. Physical structure In this section, the most important methods used to investigate the physical structure of porous solids such as chars are described. Emphasis is put on features and problems speci c to the analysis of coals and chars. It is followed by a review of morphology of coal chars and wood chars. The IUPAC1 convention divide pore sizes into:
• micropores (d 20, the thermal wave regime , where drying and pyrolysis appeared simultaneously in the same moving reaction front. Figure 1.24 shows the thermal conductivity of wood perpendicular to the bres at temperatures up to 1100 ◦ C reported by Knudson and Schniewind (1975). Note that
67
1.4. CHAR REACTIONS
CHAPTER 1. THEORY
Figure 1.24.: Transverse thermal conductivity of wood and wood char at high temperatures (Knudson and Schniewind, 1975). it is based on a rather questionable extrapolation of a char conductivity value at room temperature assuming that char conductivity is proportional to temperature, as had been observed with wood (at much lower temperatures). Nevertheless, this correlation is still cited and used in the area of re protection (Lie, 1992). The thermal conductivity along wood bres is 2.02.8 times the perpendicular value (White, 1988). The speci c heat of charcoal is reported as constant 690 J/kg K above 350 ◦ C (Lie, 1992).
1.4. Char reactions The reaction rate of carbon depends heavily on temperature, gas concentrations, and the density of reactive sites on the carbon. If conversion of a particle is limited mainly by the external and internal gas transfer, it is said to be diusion-limited , while it is kinetically limited if it is in uenced mainly by the kinetic reaction rates. Diusion-limited conversion is dominated by large gas concentration gradients and restricts the reactions to near the outer surface of the particle, since reactants are consumed before they can travel deeper into the particle. For kinetically limited conversion, the gases penetrate the whole particle, and the local reactivity of the particle determines the reaction rate.
1.4.1. Coke and wood char reactivity The steel industry has established two measures for coke samples suitability in a blast furnace: the coke reactivity index (CRI) and the coke strength after reaction (CSR). The CRI is de ned as the relative mass loss of crushed coke lumps (19.0 by 22.4 mm) after
68
CHAPTER 1. THEORY
1.4. CHAR REACTIONS
reaction with CO2 for 2 hours at 1100 ◦ C under the conditions described in ASTM (1993). Subsequently the reacted coke lumps are placed in a cool drum tester and tumbled for 30 minutes to determine the CSR. The CSR is de ned as the mass percentage of the reacted and tumbled coke lumps, which cannot pass through a 9.5 mm sieve. In Japan the DI values from the similar drum test is used in place of CSR: A sample of 10 kg coal with sizes over 50 mm are tumbled 30 or 150 revolutions in a drum. The percentage of 150 particles still exceeding 15 mm de nes the DI30 15 and DI15 correspondingly. Despite their wide use, experience is inconsistent as to the importance of coke CSR, CRI and DI in real blast furnaces (Best and Burgo, 2002). Additionally it is di cult to translate these values into physical properties (Easler et al., 1985).
1.4.2. Micro- mesopore development Reactions in char and coke often do not happen uniformly in the material. The pore sizes and orientations as well as ash particles inside the carbon structures lead to non-uniform reactivity in the particle (Hurt et al., 1991a). The relevant reactions with carbon char depend on the active sites or active surface area, but there is no general agreement in the literature on the location of active sites (Liu et al., 2000). Several authors have reported that reactivity is correlated with the surface area of pores larger than 1.52 nm. For coal and coal char, Dutta and Belt (1977) found that even though a greater part by far of the surface area measured by adsorption methods in coal and char is located in the micropores, the reactivity with CO2 was correlated with the surface area in pores larger than approximately 1.5 nm (6100% of the total surface area) rather than the total surface area. Hurt et al. (1991b) found that gasi cation of sub-bituminous coals with CO2 preferentially took place outside the micropores (>2 nm). As mentioned in Section 1.1.3.2, pore condensation in micropores during adsorption measurements may cause misleading and overestimated surface areas, which may explain why these authors were unable to correlate micropore surface area to the reactivity. The amount of active surface area can change signi cantly during conversion. It is increased by new pores formed during conversion, while it decreases when pores merge. The resulting development of active surface area may or may not increase initially before it decreases as pore merging dominate (Morell and Park, 1990). Murrell et al. (1988) observed the development of a very distinct characteristic pore size of 3.9 nm during gasi cation of a variety of petroleum cokes and chars from peat and animal bone, suggesting that gasi cation preferentially attacked structures of this size. A similar characteristic pore size of approximately 2.0 nm in cokes from wood and lignite has been found by several authors (Dubinin, 1983). Rist and Harrison (1985) measured the development of the pore size distribution during steam gasi cation of slowly pyrolysed lignite coke with 8% steam at 800 ◦ C. They measured the pore size distribution from the nitrogen desorption isotherm. The resulting pore size distributions are shown in Figure 1.25. Initially most of the surface area was located in the macropores. At 5% conversion the surface of micropores (>1.5 nm) had increased signi cantly, but at a degree of conversion of 15% conversion, a surface peak appeared for ∼2.2 nm mesopores. This peak became dominant and increased sharply until the last measurement at a degree of conversion of
69
1.4. CHAR REACTIONS
CHAPTER 1. THEORY
Figure 1.25.: BJH pore distribution development during steam gasi cation of lignite. At a degree of conversion of 36%, the total surface area was 436 m2 /g. From Rist and Harrison (1985), char degree of conversion annotations added.
70
CHAPTER 1. THEORY
1.4. CHAR REACTIONS
48% (after 8 hours of gasi cation). The micro/mesopore volume in the 0.83.5 nm range increased nearly linearly from 0.00 to 0.20 cm3 /g, while the macropore volume (730 nm) increased marginally from 0.02 to 0.04 cm3 /g. Rodriquez-Reinoso et al. (1984) studied the micropore development in chars from olive stones and almond shells during reaction with air at 350 ◦ C, and observed the initial presence of very small micropores. The volume of 0.40.7 nm micropores was constant at 0.3337 cm3 /g for degrees of conversion 030% followed by an almost linear decrease to 0.130.15 cm3 /g at 71% conversion, which may be due to pore merging. It is interesting that the observed distinct increase of surface area in 2.03.9 nm mesopores during gasi cation occur in the same size range as the cellulose micro brils in woods of approximately 2.53.5 nm (White, 1988; Jakob et al., 1995). This may indicate that the cellulose char is attacked during the initial gasi cation, so that open mesopores replace the micro brils inside the cell walls. This is further supported by the observations cited from Rist and Harrison (1985) of a linear increase in pore volume during gasi cation for the micropores, while macropore volume only increased marginally. On the contrary, the steam reactivity of pure cellulose char is lower or equal to that of pure lignin (see Table 1.8), and the diusion through these mesopores would be slow, as the original cell wall structure does not seem to oer short pathways into the micro bril pores unless the lignin-hemicellulose structure is opened for diusion during pyrolysis. Murrell et al. (1988) observed similar mesopore development in chars of animal bone, which does not contain cellulose. Instead, bone and many other biological tissues contain large amounts of collagen micro brils of very similar sizes as the cellulose micro brils in plants (Fratzl, 2003), which may explain the similar mesopore development in bone. Another explanation could be that the mesopores were already produced during the pyrolysis by removal of the cellulose micro brils. Table 1.3 shows that pure cellulose volatilise at lower temperatures than lignin, and that the char yield after pyrolysis of pure cellulose is as low as 19%, thus most of the cellulose micro bril material may already be removed during the pyrolysis. Polymerised tars on the macropore walls and/or in the mesopores themselves, may have blocked the access the these micro brils. During gasi cation, these blockages were removed, resulting in the reappearance of the micro bril voids. During fast pyrolysis, such blockages may be insigni cant, and the rapid volatilisation of the may even induce breakage of the lignin structures in order for the gas to escape. Since low rank coals are formed by alteration of the biopolymers of the original biomass, they may have retained structural reminiscents of the micro brils. It can be speculated that the micro/mesopore development during gasi cation of lignite shown in Figure 1.25 is caused by the micro brils in the original biomass.
1.4.3. Ash catalytic eect Inorganic ash particles can catalyze the reactions and produce channels in the char (Ranish and Walker, 1990). In the nal stages of high temperature combustion of coke, minerals can have an inhibiting eect on the reactivity, because they reduce the oxygen diusion and may cover the reactive carbon surface. Hurt et al. (1991a) developed
71
1.4. CHAR REACTIONS
CHAPTER 1. THEORY
a model of pore development for carbon gasi cation considering three types of nonuniformity: uniform pore widening, large pores widening and channel production. They found that channelling by ash particles produced pores in the mesopore or macropore regime, which severely decreased the surface area of microporous chars, but increased the surface area of chars, which had low initial surface areas. Using the model of channelling and restricting reactions to surface areas of pores >2 nm (approximately 10% of the total surface area), they could explain the measured pore development during kinetically limited CO2 gasi cation of coal char at 860 ◦ C from Murrell et al. (1988). The catalytic eect of inorganic species on carbons can be very pronounced. Turkdogan and Vinters (1972) found that a content of 2.1% Fe in graphite can increase its reactivity in CO2 by a factor of 106 at 800 ◦ C and by a factor of 2000 at 7001000 ◦ C with less than 0.01% Fe. They found that transition metals (introduced by soaking small graphite particles in an aquatic salt solution then reduced by H2 treatment) enhanced the graphite reactivity in air. The catalytic eect of Ni, Co and Fe were higher for oxidation in CO2 than in air, while Ag, Cu, Zn and Cr had virtually no eect on graphite oxidation in CO2 . Xie and Lie (1994) reported that calcium oxide (CaO) catalysed the gasi cation of coal in CO2 at 5001100 ◦ C, while the catalytic eect during gasi cation with H2 O was less pronounced. These ndings are summarized in Table 1.7.
O2 CO2
Ag ** 0
Ca† **
Co * **
Cr ** 0
Cu ** 0
Fe * ***
Ni * **
Zn * 0
Table 1.7.: Catalytic eect of inorganic compounds on graphite on oxidation in O2 or CO2 . The number of stars indicate the degree of catalytic eect. Rough summary of Turkdogan and Vinters (1972) †: Reactivity on coal Xie and Lie (1994)) Zekel and Krasnobaeva (2003) found that sublimated metal hydroxide vapours catalysed the gasi cation process of coke in steam at 800 ◦ C by up to 29%. The catalytic eect was increasing in the order: NaOH100† 4.4 600 >100† 6.5 870 900 0.25 76.9 900 0.25 56.4 20 1.5 600 4 0.31.2 1200 4 23.5 1200 30 11.7
E [GPa] Source a a a 629 b 9.0 c 8.5 c d d d d
Table 1.10.: Strength measurements of coal, coal char, form coke and wood (longitudinal direction) in the literature. Sources: a: Chirone and Massimilla (1989); b:Easler et al. (1985); c: Byrne and Nagle (1997a); d:Kumar et al. (1999). †: Pyrolysed in a uid bed. Figure 1.10 lists strength measurements of coal, coal char, form coke and the longitudinal direction of wood char found in the literature. No strength measurements were found in the literature in the radial or tangential directions of wood char. Kumar et al. (1999) measured the longitudinal crushing strength of pyrolysed acacia and eucalyptus wood samples. After pyrolysis (4 K/min) of 1530 mm long cubic wood samples, the resulting char was placed in a standard strength test machine at room temperature, and compressive force was applied in the longitudinal direction until fracture occurred. The strength of chars of both species were very similar, approximately 1.5 MPa, which is approximately 2% of the strength of eucalyptus wood. They had a strength minimum (0.31.2 MPa) when pyrolysed to approximately 600 ◦ C. When pyrolysed to elevated temperatures of 10001200 ◦ C, the strength increased to approximately 23.5 MPa. Chars pyrolysed at a high heating rate (30 K/min) had a lower strength than similar samples pyrolysed at the low heating rate (4 K/min). Chars pyrolysed fast to 1000 1200 ◦ C had approximately half the strength of samples pyrolysed slowly pyrolysed to the same temperature. Inspection in a SEM microscope revealed cracks and broken bres in the fast pyrolysed chars, which may explain the lower strength of these chars. Slow pyrolysis can produce very strong chars. Byrne and Nagle (1997a) produced what they called wood monoliths by pyrolysing woods at ultra slow heating rates of 515 K/h (0.080.25 K/min) to temperatures between 4002500 ◦ C. The compressive
80
CHAPTER 1. THEORY
1.5. STRENGTH
strength of a poplar char monolith pyrolysed to 900 ◦ C at 15 K/h was 76.9 MPa, which was 28% higher than that of the original wood. The Young's modulus of stiness of this char was 9.0 GPa, which was 37% lower than that of the wood. If the cellulose micro brils are volatilised before the lignin matrix during pyrolysis, as suggested in Section 1.4.2, it is possible that the pressure of escaping vapours caused the rupture in the lignin matrix as observed by Kumar et al. (1999). Very low heating rates would allow the vapours to escape at lower pressures, causing less damage to the lignin matrix. This may be the reason for the lower strength of wood chars produced at medium to high heating rates, and the good preservation of strength at extremely low heating rates observed by Byrne and Nagle (1997a).
1.5.5. Rupture and fragmentation 1.5.5.1. Primary fragmentation Fragmentation due to high thermal stress and internal pressure inside the particles caused by devolatilisation of the particle is called primary fragmentation . As an example of primary fragmentation, Zhang et al. (2002) experimented with a batch uid bed reactor (FB) uidised with air. Ten Chinese coals and seven particle diameters in the range 0.637 mm was uidized at temperatures of 500900 ◦ C. The particle distribution was measured after dierent retention times, t, and a fragmentation index, Sf , was calculated as follows:
Sf (t) =
N0 ·
Nt Pn i=1
Xt,i di d0
were d0 is the initial diameter of the particles, Xt,i is the fraction of particles having diameter di at time t. N0 and Nt are the total number of particles initially and at time t. They found that Sf initially increased until a peak, Sf,max at t=1.56 s presumably due to thermal stress and increased inner pressure from volatiles in the heating particles. As it would be expected, coals with a low volatile content had markedly lower Sf,max , and reached it faster than coals with high volatile contents. In addition, higher temperatures were demonstrated to cause higher Sf,max . After the peak, Sf decreased due to reduced volatile pressure, thermal stress as well as burnout of small particles. Above a certain initial particle size (d0 '45 mm), Sf,max increased greatly with increasing d0 . Finally it was shown that if nitrogen was used as uidising medium instead of air, Sf,max decreased because fewer very small particles ( nes ) were produced. This was explained by the presence of secondary fragmentation (see Section 1.5.5.2) in the air case due to combustion reactions, but increased thermal stresses would add to this trend. A stochastic model of particle fragmentation was developed by Chen et al. (1994). They divided particles into discrete classes, i, based on their volume. One constant αi for each class denoted the probability that one particle would break into exactly two new particles during a given time period. Mass conservation of the particles were assumed. Experimental data from Chirone and Massimilla (1989) was used to recursively t values
81
1.5. STRENGTH
CHAPTER 1. THEORY
for αi 's to match the resulting number of particles keeping their initial size as well as the particle multiplication rate. The experiments were carried out in a laboratory uid bed combustor with coals having initial sizes of 15.5, 10.5, 8.5, and 5.5 mm reacting at temperatures up to 600 ◦ C. The resulting αi s increased with decreasing particle sizes. The ratios appeared to be inversely proportional with the square of the particle radii, αi ∝ r12 . The authors suggested that this indicated that heat transfer was the i limiting factor. They suggested that particle fragmentation occurred when the particle core reached temperatures where volatilisation would increase the pressure inducing fragmentation.
1.5.5.2. Secondary fragmentation Secondary fragmentation describe fragmentation caused by external forces or fatigue.
1.5.5.2.1. Surface fragmentation Iwanaga (1991) gasi ed coke beds in steam and
CO2 , which were subject to controlled mechanical vibrations. Temperatures ranged from 11001500 ◦ C and coke particle sizes were 10, 20 and 30 mm. They found that when the mechanical impact exceeded a critical value, coke nes with high ash content were emitted from the reactor. The amount of nes increased with temperature and mechanical impact. They concluded that the particles were converted from the outside causing 'micro-cracks' in the surface so that particle nes eventually escaped. Fines generation without mechanical impact or attrition was observed by Feng and Bhatia (2000). They observed partially combusted coal particles with sizes around 100 µm in the diusion-limited regime with optical microscopy. After a certain conversion (decreasing with increasing temperature), nes fell from the coal particles. The size distribution of the nes was independent of the combustion temperature (400600 ◦ C) as well as the overall conversion rate and amount of nes. The average ne size was 1.6 µm
Broken part (S > Sc )
P
Figure 1.29.: Contact breakage Recently Yamaoka and Nakano (2003) developed a contact breakage model to model surface breakage of coke in physical contact to external surfaces. The contact breakage
82
CHAPTER 1. THEORY
1.5. STRENGTH
theory is based on the Hertzian contact theory, which describes the deformation when two elastic particles (approximated as spheres) are forced together. It is assumed that the radius of contact, a is much smaller than the particle radii, R1 and R2 . The compressive stress distributions inside the spheres and deformations are calculated. The contact breakage theory assumes that any volume of the particle, which compressive stress exceeds its compressive strength will break and leave the particle as small fragments. The roughness of the particle surface is modelled as convexes, and it is assumed that all convexes in contact with the external surface will break entirely. By evaluation of the energy needed for fragmentation, the friction forces can be calculated, and good agreement with friction measurements in simple shear tests was obtained. This model was applied to predict the contact breakage in drum tests (DI determination) (Yamaoka and Suyama, 2003; Yamaoka et al., 2003). The coke was modelled as a compound of ve dierent coke textures: Isotropic, inertinite, mosaic, brous and lea et. Both reactivity and strength were calculated as weighted averages of the values for pure textures. During conversion, texture concentrations changed due to dierences in reactivities resulting in decreasing development of the compressive strength of the coke. Good agreement was obtained for the modelled CRI, CSR and nes generation for cokes with dierent texture compositions.
1.5.5.2.2. Percolative fragmentation Percolative fragmentation, the loss of connectivity among the phases within the particle, of coal was investigated by Feng and Bhatia (2000). Here the term phase was used for a solid with no bonds to other parts of the material. They used the electrical resistivity of a bed of small (30) from the pyrolysed beech stick with a scalpel, and identifying the pieces with the least curved surfaces in the desired direction with a microscope. The thickness of these particles were reduced to 0.2 MPa. Failure occurred near one of the nuts at a stress of σL =1.15 MPa. Since only one specimen was tested, it may or may not have been caused by a local weakness. Thus, the true longitudinal tensile strength is at least 1.15 MPa,
106
CHAPTER 3. RESULTS
3.3. STRENGTH TEST
0.15 0.13
Strain [%]
0.10 0.08 0.05 0.03 0.00 -0.03 -0.05 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Stress [MPa] Figure 3.2.: Measured strain curves for longitudinal tensile strength test of unconverted beech wood. Dashed lines: extensometers, Thick solid lines: vertical strain gauges, Thin solid lines: horizontal strain gauges.
107
3.4. PORE SIZE DISTRIBUTIONS
CHAPTER 3. RESULTS
but may exceed this value. The measured tensile strength for beech char was similar to the values reported for compressive strenghts of acacia and eucalyptus wood chars prepared under the same conditions (pyrolysis to 600 ◦ C at 4 K/min) by Kumar et al. (1999) (Table 1.10).
3.4. Pore size distributions Figure 3.3 shows the pore size distributions as derived from the adsorption isotherms by BJH theory, and from mercury porosimetry. Both methods showed very small dierences between the 0% and 10% converted samples, while the volumes of several pore sizes appear to have increased signi cantly in the 46% converted sample. The limitations and spurious features inherent in these curves are discussed in the following sections.
3.4.1. Mercury porosimetry Figure 3.4a shows the mercury pressure vs. cumulated intrusion volume for the 0% converted char sample. Just as was reported for coal by Toda and Toyoda (1972) (see section 1.1.2), the curve was almost linear for pressures 10100 MPa, but above 150 MPa the volume was nearly constant (the coal measurements by Toda and Toyoda did not exceed 100 MPa). This indicated that bulk compression and/or crushing might have been the dominating eect in this pressure range, corresponding to pore sizes of 9130 nm in the measured distribution. Similar linear parts on the intrusion curve existed for the other samples. The extrusion curve was very at. This has been observed before for mercury porosimetry of wood chars by Mermoud et al. (2006), who attributed this to potential irreversible crushing of the sample. Other explanations could be inkbottle eects or signi cant viscoelastic properties similar to that found in coal char (see Section 1.1.2). The position of a potential hysteresis loop could not be established, as no repeated intrusion was made in the present investigation. After analysis, visual inspections of the 10% converted sample indicated no apparent structural changes caused by the high pressures during analysis; No changes in the particle size of number were noted in the samples after analysis, and in an optical microscope (see Figure 3.4), the microscopic features (>1 µm) of the char structure were unaltered except for the mercury droplets left in the structure. Limited shrinkage of the structure and crushing of submicron structures may have occurred, but had not left the samples signi cantly more fragile; the particles were still hard to crush with the ngers after analysis. Unfortunately, the 46% converted sample was disposed after the analysis, so it was not inspected after the analysis. The initial steep part of the curve at sub-atmospheric pressures (not covered by extrusion) was well explained by the vessel cells of the wood, and was not likely to represent signi cant crushing.
3.4.1.1. Bulk compression In order to estimate the eect of bulk compression, the elastic bulk modulus, κ, is estimated from the elastic properties of the char determined in section 3.3. If orthotropic
108
CHAPTER 3. RESULTS
3.4. PORE SIZE DISTRIBUTIONS
1.5 0.5
1.0
0% (adsorption) 10% (adsorption) 46% (adsorption) 0% (desorption) 10% (desorption) 46% (desorption)
0.0
dV/dlog(D) [(cm3/g)/log(D)]
2.0
BJH volume distribution
0.002
0.005
0.01
0.02
0.05
0.1
Pore size [µm]
(a) Nitrogen BJH porosimetry
2.0
Hg porosimetry, beech char
1.0 0.0
0.5
dlog(mg/l)/dr
1.5
0% (intrusion) 10% (intrusion) 46% (intrusion) 0% (extrusion) 10% (extrusion) 46% (extrusion)
0.01
0.1
1
10
100
Pore size [µm]
(b) Hg porosimetry
Figure 3.3.: Pore size distributions from nitrogen adsorption and Hg porosimetry of beech char converted 0%, 10% and 46%. Both adsorption/intrusion (thick lines) and desorption/extrusion (thin lines) curves are shown.
109
3.4. PORE SIZE DISTRIBUTIONS
!
Bulk compression
Extrusion
CHAPTER 3. RESULTS
sion
u Intr
(a) Cumulated Hg intrusion volume vs. pressure, 0% converted sample
(b) Optical microscope image of 10% converted char sample after Hg porosimetry
Figure 3.4.: Mercury pressure vs. cumulated intrusion volume for mercury pressures 0250 MPa, 0% gasi ed sample. The dashed line indicates the suspected linear bulk compression. (b): Char sample after Hg porosimetry.
materials are subjected to hydrostatic stress, p, the stress-strain relationship can be written for the three orthogonal directions L, R, and T:
µ
²L ²R ²T
¶ 1 νLR νLT = − − ·p EL ER ET µ ¶ 1 νT R νLR = − − ·p ER ET EL µ ¶ 1 νLT νLR = − − ·p ET EL ER
(3.1)
For isotropic materials, bulk and Young's modules are equal in all directions. Since the elastic properties were only determined for one direction, the bulk modulus will be estimated by assuming that the elastic properties were isotropic. So: ¶ µ ν ν 1 − − ·p (3.2) ²L = ²R = ²T = E E E p (1 − 2ν) (3.3) = E p κ = (3.4) ²L + ²R + ²T
110
CHAPTER 3. RESULTS
=
3.4. PORE SIZE DISTRIBUTIONS
E 3(1 − 2ν)
(3.5)
The longitudinal tensile Young's modulus and Poisson's ratio from section 3.3 was EL =1.0 GPa and (assuming νL = νLR = νLT ), νL =0.29. Therefore, the bulk modulus estimate from the strength test was:
κchar '
1.0 GPa = 0.8 GPa 3 · (1 − 2 · 0.29)
(3.6)
The slope dV /dp in the pressure range 10100 MPa in Figure 3.4 is 0.0022 cm3 /(g·MPa). So (1.5) gives:
1 MPa · cm3 κ · ρs = − dV = 458 g dP
(3.7)
The apparent skeleton density from the mercury porosimetry measurement (1.4) was ρs =0.87 g/cm3 , which is signi cantly lower than the values of 1.42.0 found by helium pycnometry for wood char in the literature (see Figure 1.14). The low value for ρs was likely caused by overestimation of the sample volume at high pressure due to the bulk shrinkage. So the density reported by Byrne and Nagle (1997a) for 600 ◦ C pyrolysis temperature, ρs =1.5 g/cm3 will be assumed in the following. Assuming pure hydrostatic compression, (1.5) estimates the bulk modulus to κ=0.31 GPa. These values of κ are of the same magnitude as the estimate based on the tensile strength test of κ=0.8 GPa in (3.6). This indicate that most or all of the intruded pore volume in the range 13130 nm in Figure 3.3 is not real, but caused by compression of the solid matrix. As mentioned in Section 1.1.2, the viscoelastic properties of chars can explain the lack of extrusion volume as lack of (immediate) relaxation of the structure. Similar estimates of the bulk modulus from the mercury intrusion curves for the 0%, 10% and 46% converted samples gives κ estimates of 0.31 GPa, 0.27 GPa and 0.22 GPa.
3.4.2. Adsorption isotherms Figure 3.5 shows the nitrogen adsorption isotherms measured for the beech char samples. They covered the relative pressure range 0.010.1µm)
0,8 0,7 0,6
0,4
Missing data
0,5
Missing data
Volume per gram [cm³/g]
0,9
(b) Relative lengths and
0,3 0,2
q
m m0
Figure 3.9.: Pore, mass and size development during conversion beech char relative to 0,1 char pyrolysed to 600 ◦ C. All measurements were done at room temperature. 0,0
600°C 0% conv.
600°C 10% CO2
600°C 20% CO2
750°C 0% conv.
Sample 118
ple
Relative mass and size 100%
750°C 48% H2O
CHAPTER 3. RESULTS
3.4. PORE SIZE DISTRIBUTIONS
10% onversion in CO at 600 C
48% onversion in H O at 750 C
2
◦
Pure shrinkage of stru ture
Further shrinkage + pore widening
Figure 3.10.: Illustration of the shrinkage and pore widening concluded from Vs and Vp . while the L length did not change at all. At 462 ◦ C signi cant shrinkage occurred in all directions, but the mass decreased even more, indicating that the bulk density was now signi cantly lower than that of the dry beech sample, which was to be expected. Vs had become nearly equal to Vp , so the change in pore volume from dry beech of pores >0.1 µm could be explained by pure shrinkage rather than pore widening. Signi cant pore volume in smaller pores must have formed in order to for the density to decrease. Such micro/mesopore development was also detected by Ehrburger and Lahaye using helium pycnometry density measurements. The dierence between the relative L, R, and T lengths shows that the pure shrinkage had not been isotropic, as shrinkage had been most severe in the T direction and weakest in the L direction. At 600 ◦ C, Vs was smaller than Vp by 24%, indicating that the pore volume had decreased signi cantly faster than could be explained by pure shrinkage. That is, wall thickening or swelling of the structures between pores >0.1 µm. It must be stressed that the calculation of Vs from this point relies on the assumption that the pore volume of dry beech measured by Ehrburger and Lahaye was representative for the beech used in the present study. It is possible that the pore volumes of the dry beech in the two studies diered by 24%, in which case no such swelling has actually occurred. The fact that the relative mass apparently increase from 462 ◦ C to 600 ◦ C was expected, as the experiments up to 462 ◦ C represent fast pyrolysis (a very thin sample was inserted in a preheated oven), while the 600 ◦ C pyrolysis in the present study was performed at a slow heating rate of 4 K/min. This experimental dierence also means that it is not possible from the present data to establish at which temperature the potential swelling during slow pyrolysis could have occurred, except that it must be below 600 ◦ C. If real, such swelling may be related to deposition of volatiles on the pore walls during pyrolysis or to the physical transition and relaxation of the structure caused by the removal of non-covalent bonds in coals in the temperature range 200280 ◦ C reported by Yun and Suuberg (1993).
119
3.4. PORE SIZE DISTRIBUTIONS
CHAPTER 3. RESULTS
(a) Mercury pore volume per gram dry wood. Actual (Vp ) and caused by pure shrinkage (Vs ).
Pore volumes per gram dry wood Vp (>0.1µm) Vs (>0.1µm)
0,6 0,5
0,3 0,2
Missing data
0,4
Missing data
Volume per gram [cm³/g]
0,7
(b) Sizes and cubic root of masses relative to dry wood.
0,1
Figure 3.11.: Pore, mass and size development during conversion of beech wood to char 0,0 relative to dry wood. Samples 20C†462C† were pyrolysed by rapid in20°C 192°C 302°C 462°C 600°C 600°C 600°C 750°C 750°C in an oven0% 10% 20% 0% 48% (Ehrburger and Lahaye, troduction at the given temperatures conv. CO2 CO2 conv. 1982), while the last ve samples (this work) H2O were pyrolysed at 4 ◦ C/min Sample and then gasi ed to a degree of conversion of 1048% in CO2 or H2 O. All measurements were done at room temperature.
elative to dry wood
Relative mass and size 100% 90%
120
Size L Size R Size T (m/m0)^(1/3)
80% 70% 60%
CHAPTER 3. RESULTS
3.5. DIFFUSION
The development in the rest of the samples was discussed in relation to Figure 3.9. One additional point worth noting is that the relative T length follows the mass curve closely for all samples except the two with the highest degree of conversion. Unlike the L and R directions, no pores are aligned in the T direction of the wood. It may be that the lack of such reinforcement allows the cell walls to shrink relatively unconstrained, and it can thus be speculated that the preferred q shrinkage of cell walls tangentially to the cell direction is to shrink proportionally to 3 mm0 . If this is generally the case, tensile stresses will build up in longitudinal cell walls parallel to the ray cells, and ray cell walls parallel to the longitudinal cell direction. These stresses must by counteracted by compressive stresses in the length direction of all cell types.
3.5. Diusion To illustrate the progress of a diusion experiment, Figure 3.12 on the following page shows the measured diusive ows during the diusion measurements for one longitudinal sample (Figure 3.12a) and a 20% gasi ed radial sample (Figure 3.12b). The x-axes are the time in hours, while the y -axes are the diusive ows FA and FB through the sample calculated from the gas analyser data (corrected for cross sensitivity) and ows by (2.1). The dierent time scales illustrate a large dierence in response times for the two samples; the longitudinal sample reached a steady diusive ow within a number of minutes, while the radial sample required hours to reach stability. The longitudinal experiment started with the N2 -CO gas pair, where stability was reached within approximately 5 minutes. After 30 minutes, N2 was replaced by CO2 , which generally required more time to reach a steady diusion rate. Each time a gas ow was changed, the ows were redirected to the bubble ow meter for a few minutes, which causes a discontinuity in the gas reaching the gas analysers. This is why the diusion ow curves peak during ow transitions. After approximately 15 more minutes, the gas ow rates into the chambers were reduced by 50%. This should double the gas concentrations at the gas analysers, since the diusive ow through the sample would be almost unaected. While the NO diusive ow rate stayed at the same level, the CO2 ow rate increased a little. After a total of 1 hour, both ingoing gas ows were changed to nitrogen. As the curve indicates, the CO2 concentrations always decayed much slower than CO. The radial experiment (Figure 3.12b) was carried out using a sample with a larger cross sectional area and half the length compared to the longitudinal sample in order to increase the diusive ow, because the diusivity was expected to be much lower. The test started out with the CO-CO2 gas pair for approximately 17 hours. As the curve clearly illustrates, the diusive CO ow stabilised much faster than the CO2 ow. This may be caused by CO2 adsorption in the sample. When the ingoing ow then was reduced 50%, the measured diusive ows stayed at the same levels and were steady. This supports the hypothesis that the slow CO2 response may be due to adsorption in the sample, since at this point, the sample was already saturated. Additionally, Grahams law predicts that the diusive ow of the heavier CO2 gas (44 g/mol) should be lower
121
3.5. DIFFUSION
CHAPTER 3. RESULTS
Diffusion experiment 12% gasified longitudinal 0.09
Diffusion [cm³/s]
0.08 CO diffusion
0.07
CO2 diffusion
0.06 0.05 0.04 0.03 0.02 0.01 0.00 0
0.5
N 2 CO
Half flow
CO 2 CO
1
Time [hours]
N 2 purge
1 1 Diffusion experiment, 20% gasified radial sample (a) Longitudinal N2 -CO diusion test for 2 hours. Then 2 hour of CO2 -CO test at two
dierent ows followed by N2 purge. (sample L5) 0.005
Half flow
Half flow CO diffusion NO diffusion CO2 diffusion
Diffusion [cm³/s]
0.004
0.003
0.002
0.001
0.000 0
5
CO 2 CO
10
15
Time [hours]
20
25
N 2 CO NOCO
(b) Radial CO2 -CO diusion test for 16 hours (plus 12 hour using half inlet ows). Then 3 hours of N2 -CO test and 3 hours NO-CO. (Sample R7-1)
Figure 3.12.: Examples of diusion measurement curves of the diusive ows (Fi , Fj ) vs. time. Note the dierent time scales.
122
CHAPTER 3. RESULTS
3.5. DIFFUSION
than that of CO (28 g/mol), but the opposite is clearly the case. This was consistently the case in all experiments involving CO2 . The test ended with the NO-CO gas pair, which did not reach stability within the time frame of the test. Figure 3.13a shows the diusion coe cient ratios for this sample calculated from each measurement point as a function of the inlet ow (Fi,in and Fj,in ). It clearly illustrates the observation, that diusion coe cients derived from measurements of CO2 , ³ general ´ Deff , were signi cantly higher than those derived from other gas pairs or even D CO2 ´ ³ Deff from the CO gas ux of the CO-CO2 gas pair . Figure 3.13b shows the D CO permeability measurements for the same sample, illustrating the general features that the uncertainty was lower at high ows, due to the better relative determination of the gas ow, and that there was no signi cant discrepancy between measurements using dierent gases.
3.5.1. Diusion and permeability D
Figure 3.14 shows the diusion ratios Deff found in the diusion measurements with the gas pairs NO-CO and N2 -CO (Figure 3.14a) and CO2 -CO (Figure 3.14b). All measurements with the same sample and gas pair were combined into one data point using maximum likelihood estimates (see Appendix C.4.7). The results produced with the CO2 -CO gas pair failed validation with Grahams law, as the CO2 ux was much higher than would have been expected. These measurements were not used, and will be discussed in section 3.5.4. The trend lines from the NO-CO graph were copied to the CO2 -CO for easy comparison. The trend lines were least square polynomial ts ³ graph ´ Deff to ln D , and are expressed like this:
L: 0.48 Deff R: 0.00126 e9.31x = D 2 T: 0.00062 e6.0x+4.8x
(3.10)
D
The assessed relative measurement uncertainties of Deff for each sample were 1721% except for the radial and tangential samples at 0% conversion, which had measurement uncertainties up to 40% (See Appendix C.4). For reference, Figure 3.15 on page 126 shows the apparent tortuosities τ assuming negligible Knudsen diusion using (1.53) and the porosities of the best matching analysed samples in Figure 3.8:
τ=
Dij · φ Dij · φ ' Dij,eff Dij,eff
(3.11)
The permeability results (one point per sample) are summarised in Figure 3.16 and Table 3.4. The relative measurement uncertainties were below 9%. The values range
123
3.5. DIFFUSION
CHAPTER 3. RESULTS
Diffusion measurements, sample R7−1 CO2 − CO N2 − CO NO−CO
0.025
CO2
D eff D
0.020
0.015
0.010
0.005
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Inlet flow [l/min]
(a) Radial diusion measurements, dierent carrier gas ows and gases. The two high results are CO2 data points. The other measurements are at the same level, in the lower part of the plot. Hollow symbols represent the rst species in the gas pair, while lled symbols represent the second species.
Permeability measurements, sample R7−1
1.5
Permeability, Φ [mD]
1.4 1.3 1.2 1.1 1.0 0.9
N2 CO2 0.1
0.2
0.5
1.0
Superficial velocity [mm/s]
(b) Permeability measurements, dierent ows. ¦: N2 ; ×:CO2
Figure 3.13.: Diusion and permeability measurements for sample R7-1 (Radial, 20% conversion) 124
CHAPTER 3. RESULTS
3.5. DIFFUSION
Diffusivity NO−CO & N2 − CO 0.5 L 0.2 0.1
D eff D
0.05 0.02 0.01 R
0.005 0.002
Longitudinal Radial Tangential
T
0.001 0.0005 0.0
0.1
0.2
0.3
0.4
0.5
Degree of conversion, x
(a) Diusion results with gas pairs NO-CO and N2 CO. ¤ ◦ 4: NO; ¥ • N: CO. Diffusivity CO2 − CO 0.5 L 0.2 0.1
D eff D
0.05 0.02 0.01 R
0.005 0.002 0.001
Longitudinal Radial Tangential
T
0.0
0.1
0.2
0.3
0.4
0.5
Degree of conversion, x
(b) Gas pair CO2 -CO. ¤ ◦ 4: CO2 ; ¥ • N: CO.
Figure 3.14.: Results of uni-axial diusion measurements along the three major orientations in beech wood char assuming pure ordinary diusion and using NO-CO (a) and CO2 -CO (b). The trend lines in both graphs are identical and based on the NO-CO and N2 -CO measurements.
125
3.5. DIFFUSION
CHAPTER 3. RESULTS
Apparent tortuosity 1000
Tangential Radial Longitudinal
T
500 200 100
R
τ
50 20 10 5 L
2 1 0.0
0.1
0.2
0.3
0.4
0.5
Degree of conversion, x Figure 3.15.: Apparent tortuosities calculated from the NO-CO diusion measurements using (3.11), along the three major orientations in beech wood char. Based on eective diusion coe cients of NO (4 ◦ ¤) and CO (N • ¥)
126
CHAPTER 3. RESULTS
3.5. DIFFUSION
Permeability, beech char
Permeability, Φ [mD]
10000
Longitudinal Radial Tangential
L
1000
100 R 10
1
T
0.0
0.1
0.2
0.3
0.4
0.5
Degree of conversion, x (a)
Figure 3.16.: Results of uni-axial permeability measurements in the three major orientations in beech wood char with nitrogen gas.
127
3.5. DIFFUSION
CHAPTER 3. RESULTS
from below 1 mD, which correspond to that of very ne sand or layered clay to nearly 105 mD, which correspond to that of sand and gravel and very permeable peat. The trend lines in Figure 3.16 were least square polynomial ts to ln (Φ), and expressed like this (except longitudinal permeability which is given as a constant):
L:16000 mD 2 R: 0.226 e8.56x+9.3x mD Φ= 2 T: 0.720 e−2.51x+16.2x mD
(3.12)
The assessed relative measurement uncertainties of Φ where 10% except for the radial and tangential samples at 4650% conversion, which had measurement uncertainties up to 15% (See Appendix C.4).
Diusion ratios, x 0.00 0.100.12 0.180.20 0.460.50
Deff, D
Direction L R T 0.484 0.0013 0.00064 0.484 0.0063 0.0024 0.112 0.0457
Table 3.3.: Average diusion coe cient ratios from CO-NO and CO-N2 diusion measurements on beech char at dierent degrees of conversion.
Permeabilities, Φ [mD] x 0.00 0.100.12 0.180.20 0.460.50
Direction L R T 18800 0.24 0.70 15700 1.17 0.83 126 159
Table 3.4.: Average permeabilities for N2 viscous ow at dierent degrees of conversion in milliDarcies (1 mD=10−15 m2 ). The measured permeability and diusivity generally followed the same trends: they increased with increasing degree of conversion and the values for the longitudinal orientation were approximately 3-4 orders of magnitude higher than for the other orientations in the pyrolysed sample. But the relative values of the radial and tangential orientation were dierent for low degrees of conversions; at low conversions the radial diusivity was higher than the tangential, while the opposite was true for the permeability.
128
CHAPTER 3. RESULTS
3.5. DIFFUSION
In an attempt to understand why permeability in the T direction was nearly constant between degrees of conversion of 0% and 20%, while the diusion coe cient ratio more than tripled, the dependence of the permeability Φ and apparent diusion coe cient Di on the pore geometry was evaluated. In circular capillaries (See section 1.2.2 and equation (1.37)):
r2 8 r = 2 4 2 = · K0 hvi i = r hvi i 3 3
(3.13)
Φ = K0 ⇔ Di,K
(3.14) (3.15)
so Φ ∝ r2 , Di,K ∝ r, while the ordinary diusion coe cient Dij is independent of r. Therefore the apparent diusion coe cient is Di ∝ rα where α ∈ [0 . . . 1]. Since Φ has a stronger dependence on r than Di on the pore radius, simple pore widening does not explain why Φ was nearly constant in the T direction from 0% to 20% conversion, while Di more than tripled. One explanation could be an undetected aw in the 0% converted sample. Due to the very low permeability, even small cracks could in uence the measurements signi cantly. This can not be rejected, but the agreement of the permeability measurements between the two 0% converted T-samples (samples T1 and T5) was excellent, so undetected aws of very similar sizes would have to have been present in both of these samples. Another explanation could be that the applied pressure dierence during the permeability measurements 2 altered the microstructure of samples with low degrees of conversion, causing additional openings to appear or widening existing pores. These changes would have to be a reversible, since the permeability measurements were performed before the diusion measurements on each sample. No such structures were identi ed, and furthermore it will be noted in Section 3.6.3 that (in the absence of a pressure dierence) radial cell walls (obstructing the tangential gas transport) tend to be keep its structural stability better than the tangential cell walls during gasi cation.
3.5.2. Char microstructures and diusion The apparent tortuosity of the longitudinal orientation was essentially unity, indicating that the diusion through the vessel cells was nearly perfectly unobstructed ordinary diusion, only limited by the porosity. The apparent tortuosities (Figure 3.15) in the radial and tangential directions were extremely high. This was likely to be caused by the very multimodal pore structure, where diusion was delayed by bottlenecks, such as pits in the cell walls, rather than an excessively long distance through the char labyrinth. 2 Pressure
gradients up to approximately 100 mbar/mm were applied to low permeability samples in order be able to measure the gas ow.
129
3.5. DIFFUSION
CHAPTER 3. RESULTS
3.5.2.1. Knudsen diusion in L direction The pore structure in the L direction was assumed to be described well as straight circular pores following the L direction (τ =1). In the preceding calculations, it was assumed that Knudsen diusion could be ignored, i.e. the eective apparent diusion coe cient was assumed to equal the eective ordinary diusion coe cient, Di = Dij,eff . This assumption fails if pores below a certain size carry a signi cant amount of the gas ow. Recall the Bosanquet formula (1.50):
µ Di,eff =
1 Di,K,eff
+
¶−1
1 Dij,eff
If one of Di,K,eff or Dij,eff is signi cantly lower than the other, Di,eff will approach its value. So neglecting Knudsen diusion is equivalent to assuming that Di,K,eff is signi cantly higher than Dij,eff . This means that for a given measured value of Di,eff , the Knudsen diusion coe cient Di,K,eff must be approximately of the same order of magnitude or smaller in order to be signi cant. For long, cylindrical pores:
φ Di,K τ r 2 Ru T φ 4 = · r τ 3 π Mi φ = Dij τ
Di,K,ef f =
Dij,eff
(3.16) (3.17)
In order for Knudsen diusion to be responsible for lowering Di,eff by a factor of α (α < 1) compared to the case of pure ordinary diusion (where Di,eff = Dij,eff ), it must satisfy:
Di,eff =
1 DiK,eff
⇔ Di,K,eff
0.17, it can not be severely thermally thin. In steady state, the sum of energy produced by the reaction, qR , and the energy transport through the slab surfaces by way of conduction, qh , and radiation, qr , must be zero:
0 = qR + qh + qr
¡ ¢ ρs Vs R ∆H = A · h · ∆T + A σB Ts4 − T04 MC ¡ ¡ ¢¢ = A · h · ∆T + σB Ts4 − T04 ¡ ¢ −ρs R ∆H Vs ⇔ h · (Ts − T0 ) + σB Ts4 − T04 = · MC A −ρs R ∆H a b w ρs R ∆H · w = = MC 2ab 2 MC ³ ´ kg kJ −6 −451 m3 · 339 · 10 s · −136 kmol = kg 2 · 12 kmol K = 866 · w m ⇔−
(4.43) (4.44) (4.45) (4.46) (4.47)
· (w4.48) (4.49)
Solving for the surface temperature, Ts , given the ambient temperature 800 ◦ C (1073 K) and slab width w=9.7 mm, Ts is only 0.01 ◦ C below the ambient temperature. This is
163
4.6. RESULTS
CHAPTER 4. MODELLING
far less than was estimated from the experimental mass development of the 9.7 mm thick L-slab in Figure 4.2, which suggested a temperature dierence of T0 − Ts =800778=22 ◦ C. This indicates that any signi cant temperature gradients should be found inside the slab, so that the system is thermally thick. If the temperature gradient through the slab is assumed linear, a center temperature, TC , exist for which the mean reactivity matches that of a at temperature pro le with temperature Ts . Numeric calculations of the mean reactivity R assuming a linear temperature gradient through the slab from T0 =800 ◦ C at the surface to TC at the center, showed that TC should be approximately 751 ◦ C in order to match the mean reactivity from a at temperature pro le with Ts =778 ◦ C for all X ∈ [0 : 0.8]. In steady state, the sum of the reaction enthalpy of the reactant ux through a point in the slab and the heat ux must be zero. Heat transfer is assumed to occur only as heat transfer through the solid char. In pseudo-steady state, assuming constant Deff and thermal conductivity, kc,c , of the char:
∂T − Jr · (−∆H) ∂ξ ∂Cr ∂T − Deff · (−∆H) = kc,c ∂ξ ∂ξ
(4.50)
0 = kc,c
(4.51)
integration from the surface to the center gives:
Z
Z w ∂T ∂Cr kc,c = Deff · (−∆H) ∂ξ ∂ξ ξ=0 ξ=0 ⇔ kc,c · (Ts − TC ) = Deff · (−∆H) · (Cr,s − Cr,C ) kc,c ⇔ Cr,s − Cr,C = (Ts − TC ) · Deff · (−∆H) w
(4.52) (4.53) (4.54)
where Cr,s and Cr,C are the reactant concentrations at the surface and in the center of the slab, and ∆H is the reaction enthalpy. The eective diusion coe cient is found using (3.10) DH2 O-N2 = 2.43·10−4 m2 /s at 800 ◦ C (derived from the FSG relation):
Deff = 0.48 · DH2 O-N2 = 0.48 · 2.43 · 10−4
(4.55) m2 m2 = 1.17 · 10−4 s s
(4.56)
so,:
Cr,s − Cr,C = (800 K − 751 K) ·
0.15 mW ·K 2 m kJ 1.17 · 10−4 s · 136 kmol 164
(4.57)
Mole fraction
CHAPTER 4. MODELLING
= 0.462
4.6. RESULTS
kmol m3
(4.58)
This corresponds to a dierence in reactant mole fraction of 4% between the surface and the center of the slab, which seems plausible. In order to con rm this, the model was run with xed a linear temperature pro le from Ts = 800 ◦ C at the surface to TC = 751 ◦ C in the center. The resulting H2 O developments are shown in Figure 4.3.
H2O mole fractions, linear temperature profile 800-751C 1
0.17 mm 1.00 mm 2.00 mm 3.00 mm 4.00 mm 5.00 mm
0.8
0.6
0.4
0.2 development in 10 mm L-slab with a linear temperature 0 Figure 4.3.: H2 O mole fraction ◦ ◦ at the surface C at the120 center. 0 20pro le from 40 800 C60 80 to 751100 Time [minutes]
It shows no signi cant concentration gradients. Indeed, the H2 O concentration at the center did not depart more than 0.01% from the ambient concentration. Thus, the expected dierence of 4% was not con rmed. The simpli ed calculations above could not point out if any temperature gradient would occur outside or inside the slab. Since a model slab temperature of 778 ◦ C tted the experimental mass developments of 10 mm thick L-slabs well, this temperature was used in the models to replicate the experiment conditions for 10 mm slabs. Choosing a xed temperature may introduce an error when the reaction rate changes, causing a temperature change. For example, if the reaction rate is lowered by signi cant diusion limitations in the R and T directions, the true slab temperature may increase, causing the reactivity to increase as well. Thus, in such cases, the model would generally
165
4.6. RESULTS
CHAPTER 4. MODELLING
underestimate the mass loss rate.
4.6.1.2. Knudsen diusion Figure 4.4 shows experimental and model results for 10 mm L-, R- and T-slabs gasi ed at ambient temperature 800 ◦ C (model temperature 778 ◦ C). Figure 4.4a assumed pure ordinary diusion, while Figure 4.4b assumed pure Knudsen diusion. In the experiments, the R- and T-slabs were converted signi cantly slower than the L-slab until a degree of conversion of approximately X = 0.3. For the ordinary diusion curve, this development was followed qualitatively but the quantitative dierence between the L, and R/T curves was much smaller than that found in the experiments. The assumption of Knudsen diusion led to an improved description of the R and T curves, supporting the conclusion in section 3.5.2.2 that diusion in these directions were limited by Knudsen diusion. The T model curve tted the experiments perfectly, while the R model curve was initially close to the experimental data, but overestimated the conversion rate and D ended up in the middle between the L and T experimental data. Since the values for Deff and Kτ0 φ in the R direction were approximately twice the values in the T direction, the observed dierence between the model results for the R and T directions was expected. A deviation by a factor of 2 from the slab experiments was considered satisfactory, D considering that the uncertainty of the Deff and Kτ0 φ measurements at low degrees of conversion was assessed to be 40%, and possible variations in properties of the beech wood used. It was concluded that with the assumption of Knudsen diusion in the R and T directions, the model described the slab experiments well, and in the following, In the following, diusion coe cients for simulations in the R and T directions will be calculated as pure Knudsen diusion.
4.6.2. Model variants The signi cance of some of the model assumptions were challenged by building model variants, where one assumption was changed at a time. Figure 4.5 shows the resulting mass developments. The model presented in Figure 4.4b was used as the basis, and reproduced in Figure 4.5a. The variants are described below:
Perpendicular pressure relief Figure 4.5b shows the results of eliminating pressure build-up, assuming that excess pressure would be relieved perpendicular to observed direction. In the experiments, the edges were covered with alumina silicate. If pressure could force gases through this coating, this model should give a better description. It was implemented P ∂Ci by always removing the amount of gas from each node that would = 0. The species were removed in proportion to their mole fraction keep ∂ξ in the node. The resulting mass development curves did not dier from the basis model. For the experimental conditions, perpendicular removal of gases would not change the results.
166
CHAPTER 4. MODELLING
4.6. RESULTS
Degrees of conversion, 10 mm slabs 1
Degree of conversion
0.8
0.6
0.4 Experiment L Experiment R Experiment T Model L Model R (a) Pure ordinary diusion Model T
0.2
0 0
20
40
60 80 Time [minutes]
100
120
Degrees of conversion, 10 mm slabs, Knudsen 1
Degree of conversion
0.8
0.6
0.4 Experiment L Experiment R Experiment T Model L Model R (b) Knudsen diusion in R and T directions Model T
0.2
0 0
20
40
60
80
100
120
Figure 4.4.: Experimental results of gasi cation for 10 mm R, T and L-slabs at 800 ◦ C Time [minutes] in 50% H2 O, and model results at 778 ◦ C, assuming pure ordinary diusion (a) and pure Knudsen diusion in the R and T directions (b).
167
4.6. RESULTS
CHAPTER 4. MODELLING
Model results with no pressure buildup 1
0.8
0.8 Degree of conversion
Degree of conversion
Degrees of conversion, 10 mm slabs, Knudsen 1
0.6
0.4 Experiment L Experiment R Experiment T Model L Model R Model T
0.2
0 0
20
40
(a) Basis
60 80 Time [minutes]
100
0.6
0.4 Experiment L Experiment R Experiment T Model L Model R Model T
0.2
0 120
0
1
0.8
0.8
0.6
0.4 Experiment L Experiment R Experiment T Model L Model R Model T
0.2
0 0
40
60 80 Time [minutes]
40
60 80 Time [minutes]
100
120
100
0.6
0.4
0.2
(c) Negligible viscous ow resistance
20
(b) Perpendicular pressure relief
Model results with same properties for XR>L. This was supported by measurements of the macro porosity by mercury porosimetry and by the fact that the measured eective gas diusion coe cients in all directions of beech char were similar to values for beech wood reported in the literature. Images produced during direct observation of the microstructures of beech char during gasi cation in CO2 in a heating stage microscope (HSM) were presented in Section 3.6 on page 142. Until a degree of conversion of X =0.1, pure shrinkage of the structure was observed. This was consistent with the changes in pore sizes observed by mercury porosimetry for 10% converted char. At X =0.1, visible thinning of the macropores was initiated. Signi cant wall thinning was con rmed in chars with X =0.5 by mercury porosimetry. Cotton-like CaO containing structures developed on the sample surface, increasingly obscuring the view. Despite this, it was possible to con rm reports in the literature, that even for X exceeding 0.6, the general wood structure was intact. At high X , a sudden collapse occurred. Chars of wood and other materials of biological origin often contain large volumes of micro- or mesopores with a very narrow size distribution around a few nanometres. During gasi cation, the volume of these pores measured by gas adsorption methods generally increase. This was also observed for beech char in the present study. It was suggested in section 1.4.2 on page 71, that these pores may be related to the cellulose micro brils in the biological structures of the original biomasses. Volatilisation of the micro brils during the early stages of pyrolysis may leave voids of the observed geometry. Unless pyrolysis occur at a very low heating rate, the pressure caused by these gases
175
CHAPTER 5. SUMMARY AND DISCUSSION may cause rupture of the lignin matrix. Severe rupture of cell walls during fast pyrolysis of wood has been reported in the literature. It is also consistent with the higher initial reactivities of chars from fast pyrolysis, which is otherwise attributed to changes in macroporosity and the lack of tar polymerisation on the char surfaces occurring at lower heating rates. Finally, volatilisation of micro brils could oer an explanation for the lower strengths of chars from fast pyrolysis. In particular, it could explain observations in the literature that extremely slow pyrolysis (0.8)=re(x=0.8) Ru k1 k2 k3 k4 k5
= = = = = =
8.3144; # [J/(mol*K)] 7.531E7*exp(-2.11E5./(Ru*T)); 3.270E8*exp(-2.48E5./(Ru*T)); 3.282E6*exp(-1.52E5./(Ru*T)); 2.016E8*exp(-2.17E5./(Ru*T)); 2.458E7*exp(-2.14E5./(Ru*T));
# # # # #
[1/(s*atm)] [1/(s*atm)] [1/(s*atm)] [1/(s*atm)] [1/(s*atm)]
f = (378.10*x.^6 -707.17*x.^5 +504.22*x.^4 -166.33*x.^3 +25.333*x.^2 -0.61855*x +0.44280); # Low H2O, high H2 expression # f = (32.174*x.^6 -57.172*x.^5 +46.096*x.^4 # -16.043*x.^3 +2.924*x.^2 -0.2972*x +0.5286); denominator=(1+(k1./k5).*pH2O+(k2./k5).*pCO2 \ +(k3./k5).*pH2+(k4./k5).*pCO); R_beech.H2O=f.*(k1.*pH2O) \ ./denominator; # 1/s R_beech.CO2=f.*(k2.*pCO2) \ ./denominator; # 1/s endfunction
239
fifi :_1‘:_ _1_1. _ _'__ _ I_ _ _1‘
________%1h _I ___H_’ 1___ __H _ 1A__1 /2‘ _
H I
H _v__ _ -'___11__i2_ ____ _ r ’ _"_ 2”’ _‘ __t “__1122 __'
I111A_1,1,1]
21_,2_11 1
/1‘_r____ 11113% 6_if/_ 1%] 1_ _1 12 _‘H’ 121__‘__ ‘_ H_ __1_‘ 121 _1?:
.____ 21 In $22221] 1_1_ ‘ 1_
_4 21J jg _"2 ’
______ _{T /_ _ “_]'_1-L2“ #l_~P1
_1 _1r _ __ 1_H___'_I_n __
__ Y‘ __ ___1_ _/ _ _iI -1 F____
_____‘_ ________1_ __ _1_____~I1 1__] _g &___________' 11_
U11_1_
j 3_ I 1____F __1* _-\ '_'_121___/ _____‘ 1 kn _ 1_ 1_. I _‘____ __1_1T_ _ _ .* I __21 ____"_ ___1_ _-__
_I _ \_' 1!__“__ _J __§F1tJ_1____1_" _1, _m__*_wy_m
. ___ A“ _211___1__1 __]__ 1____ _ \___ ___" 11’
72 IJ:“1*__ 22 __ §__u____j_‘__
_ 1 $1 ___ _ €_1__‘ ________"1 ?__ 7qq__ __ __I _I‘
g F 2112___J____m__ fr H__ __I1_-1___
__ I__
1- _
/J _ ______
