Effect of Process Conditions on Fluidization

Abstract

The influence of process conditions such as temperature and the presence of fines on the fluidization behaviour of gas-fluidized beds is of major importance in industrial fluid bed processes, which are often operated at temperatures well above ambient and where it is common practice to add fine particles to improve the reactor performance. Several works have demonstrated that process conditions can influence the role of the interparticle forces in the fluidization behaviour of powders. In particular, the beneficial effect on fluidization of adding fines to the bulk of the material is well known.

The objective of this paper is to review experimental and theoretical studies of gas-solids fluidized beds operated at high temperature and the effect of fines and fines distribution within the bed. The survey begins with a review of the effect of temperature on fundamental fluidization parameters such as minimum fluidization, bed expansion and deaeration, and the role of hydrodynamic and interparticle forces at ambient conditions and high temperature is discussed. The effect of temperature and fines and fines size distribution on the dynamics of gas-fluidized beds is considered next, highlighting areas of current gaps in knowledge. Given the complexity of the phenomena involved, a direct quantification of the particle-particle interactions in fluidized beds and of their changes under process conditions is very difficult. The review concludes by touching upon powder rheology as a methodology to evaluate indirectly the effects of the IPFs on fluidization. This leads to a review of the work done at UCL on linking rheological measurements to fluidization tests in the attempt to quantify the effect of process conditions, i.e. high temperature and the effect of fines on fluidization.

1. Introduction

Fluidization is the operation by which solid particles are transformed into a fluid-like state through suspension in a gas or liquid (Kunii and Levenspiel, 1991). Fluidized beds can be considered the most powerful method to handle a variety of solid particulate materials in industry (Horio, 2013).

Fluidized beds are widely applied in industry for their ability to provide a high heat transfer rate and rapid solids mixing which lead to isothermal conditions in the particle bed, and high heat and mass transfer rates between gas and particles. Whenever a chemical reaction employing a particulate solid as a reactant or as a catalyst requires reliable temperature control, a fluidized bed reactor is often the choice for ensuring nearly isothermal conditions by suitable selection of the operating conditions.

Fluidization was created as an industrial operation in the Winkler process for the gasification of lignite and the ignifluid process for the combustion of coal, but it was only with introduction in the 1940s of the FCC process that its true potential became apparent.

It was in 1942 when a desperate need for aviation fuel during the Second World War brought together a group of oil companies which included Standard Oil Indiana (later Amoco and now BP Amoco), M.W. Kellogg, Shell and the Standard Oil Development Company (now Exxon) to design the first fluidized solids process for catalytic cracking. Fluidization started as an innovative and successful oil refining technology, revealing the potential of the technique for gas-solids reaction engineering. Since then it has been applied in many other areas, becoming a firmly established technique in the processing industries. The applications are spread throughout the chemicals, environmental, energy, nuclear, petrochemical, pharmaceuticals, and process industries. Some examples of industrial applications are presented in Table 1.

Table 1 Some industrial applications of fluidized beds

Process	Example	Process conditions
		T [°C]	P [atm]	Fines Content [%]
Cracking of hydrocarbons	FCCa	480–550	1–3	10–30
	Ethylene and propyleneb	750	∼1	10–30
Chemical synthesis	Acrylonitrileb	400–500	1.5–3	20–40
	Melaminea	400	> 1	—
	Maleic anhydride (Mitsubishi Chem. Ind.)c	410–420	1–5	25–55
	Maleic anhydride (DuPont)c	360–420	< 5	—
	Ethylene dichloridec	220–245	2.5–6	30
	Phthalic anhydridec	345–385	2.7	28
	Polyethylenec	75–105	20–25	—
Metallurgical industry	Irona	850	3.5	—
	AlF3 synthesisc	530	1	—
	Alumina calcinationc,d	800–1200	1	0–50
	Limestone calcinationd	770	1	Variable
	Gold roastingc	650	1	—
	SO2 from sulphide ore roastingb	650–700	1	—
	Pyrite roastingb	660–920	1	—
	FeS2 from sulphide ore roastingd	650–1100	1	< 3
Drying of solids	Inorganic materialsd	60–110	1	Variable
	Pharmaceuticalsd	60	1	Variable
Semiconductor industry	SiHCl3 productionb,d	300	1	100
	Silicon productionc	600–800	∼1	—
Nuclear industry	Separation of U-235 from U-238b	450	—	—

a  Winter and Schratzer (2013)

b  Kunii and Levenspiel (1991)

c  Jazayeri (2003)

d  Bruni (2005)

In addition to this, fluidized bed technology has witnessed a resurgence of interest particularly from the point of view of clean energy generation over the last two decades. Fluidized beds are employed for the combustion and gasification of solid fuels (coal, wastes and biomass), to generate steam for boilers, syngas, chemicals or fuels (Newby, 2003; Arena, 2013; Basu, 2013), including the recent development of a dual-stage fluid-bed plasma gasification process in UK for the production of electricity and biosubstitute natural gas from waste gasification (Materazzi et al., 2013, 2015); fluidized beds are also employed in the waste incineration of solids and sludge (Horio, 2013). Another development gaining prominence in this area and aimed at new processes for clean energy production is the use of fluidized beds for chemical looping combustion, Fan (2010). A review of fluid bed industrial applications can be found in Kunii and Levenspiel, 1991; Jazayeri, 2003; Winter and Schratzer, 2013.

In parallel with industrial developments, fluidization also became the focus of a great deal of academic effort aimed at providing a theoretical framework to underpin the subject.

The first examples are the pioneering study of bubble motion in fluidized beds by Davidson (1961), later developed by Davidson and Harrison (1963), Jackson (1963) and Murray (1965), and Geldart’s empirical classification (Geldart, 1973) of fluidizable powders into four groups, A, B, C and D, according to their particle size and density and gas density (see Yates, 1996).

It is important to note that both bubble motion theories and Geldart’s classification are based on observations made under ambient conditions, hence it is not immediately obvious how accurate their predictions would be under process conditions such as high temperature and pressure.

For these reasons, fluid beds are commonly used when high thermal efficiency, excellent temperature control and intimate gas-solids contact are desired. Despite this, the effects of process conditions on fluidization are still not entirely understood. Design criteria and performance predictions for fluid bed units working at high temperature have been largely based on fluid-dynamic models and correlations established from tests developed at ambient temperature. However, extrapolating the results and relationships available at ambient conditions to elevated temperatures can lead to misleading predictions of the fluid bed performance at high temperature. Drastic changes can occur in the fluidization behaviour between low and high temperatures, due to possible modifications induced by the temperature in the structure of the fluidized bed. In order to understand the factors responsible for such changes in fluidization behaviour, the role of the interparticle forces (IPFs) and hydrodynamic forces (HDFs) has been studied, but much controversy still remains to define their relative importance.

This work reviews experimental and theoretical research on the effect of process conditions such as high temperature, fines content and fines size distribution on fluidization. The review will begin by considering the influence of temperature on fundamental parameters of gas-solids fluidization such as minimum fluidization, bed expansion, bed voidage and deaeration rates.

The review will then address the effect of fines and fines size distribution on the dynamics of gas-fluidized beds. This will lead to a review of the main techniques used for the characterization and prediction of the flow properties of powders. These include the standard bed collapse test and rheological tests. The latter covering both stationary measurements (angle of repose, Hausner ratio, etc.) as well as dynamic tests (shear-cell-type tests and viscometer-type tests). The paper will conclude by reviewing the work done at the University College London on linking rheological measurements to fluidization tests, in the attempt to quantify the role of the interparticle forces on the fluidization behaviour of different industrial powders.

2. Effect of temperature on minimum fluidization conditions

Although several studies have been carried out on the influence of operating conditions on fluidization, the findings are still controversial and a satisfactory understanding of the phenomena which cause differences between ambient conditions and high temperature processes has not yet been achieved (Grewal and Gupta, 1989; Geldart, 1990; Fletcher et al., 1992; Knowlton, 1992; Yates, 1996; Lettieri et al., 2000, 2001, 2002; Coltters and Rivas, 2004).

The operating conditions influence the operation of fluid-particle systems because they affect gas density and viscosity. Increasing temperature causes the gas density to decrease and gas viscosity to increase. Most predictions of fluidization behaviour at high temperatures have been based solely on considering such changes in the gas properties. However, this approach is valid under the condition that only hydrodynamic forces control the fluidization behaviour. Temperature can have a considerable effect on particle adhesion, enhancing the role of the interparticle forces (IPFs) on the fluidization quality, if the system is operated at temperatures close to the minimum sintering temperature of the particles. In addition, the increase of temperature may enhance the Hamaker constant and therefore the van der Waals’ attractive forces.

As reported by Lettieri et al. (2000), the effect of temperature on a fluidized bed is also strongly dependent on the particle size, which in turn defines the type of particle-particle and fluid-particle interaction, thus determining the stronger or weaker role of the IPFs. Much theoretical debate is reported in the literature on the role of the inter-particle forces on the fluid-bed behaviour and a sound understanding of the phenomena which control changes in fluidization behaviour at high temperature has not yet been achieved.

In this section we report some of the most significant findings of the effect of temperature on the fluid-bed behaviour, outlining some of the most important aspects.

The minimum fluidization velocity, u_mf, is a fundamental parameter when designing fluidized-bed systems. The minimum fluidization velocity may be found by measuring the pressure drop across a bed of particles as a function of the gas velocity. At u_mf, the weight of the bed is fully supported by the flow and the pressure drop becomes constant. u_mf may also be calculated on the basis of the Ergun equation for the pressure drop through a packed bed.

Various correlations can be found in the literature to predict u_mf at high temperature (see Table 2), as for example the correlation given by Wu and Baeyens (1991). However, this approach is uncertain and not necessarily reliable, because it is often necessary to extrapolate results for the conditions of interest and, in addition, it overlooks possible changes induced by temperature on the structure of the fluidized bed that can in turn cause drastic alterations in the flow behaviour and powder stability (Yang et al., 1985; Lettieri et al., 2000).

Table 2 Selected equations for the calculation of minimum fluidization velocity

Authors	Equation
Ergun (1952)	$$150\frac{{\mu }_{\text{g}}{u}_{\text{mf}}}{{\left(\phi d_{\text{p}}\right)}^2}\frac{(1-{\epsilon }_{\text{mf}})}{{\epsilon }_{\text{mf}}^3}+1.75\frac{{\rho }_{\text{g}}{u}_{\text{mf}}^2}{\phi d_{\text{p}}}\frac{1}{{\epsilon }_{\text{mf}}^3}=g({\rho }_{\text{p}}-{\rho }_{\text{g}})$$(1)
Carman (1937)	$$u_{\text{mf}}=\frac{{\left(\phi d_{\text{p}}\right)}^2}{180}\frac{({\rho }_{\text{p}}-{\rho }_{\text{g}})}{{\mu }_{\text{g}}}g\left(\frac{{\epsilon }_{\text{mf}}^3}{1-{\epsilon }_{\text{mf}}}\right)$$(2)
Miller and Logwinuk (1951)	$$u_{\text{mf}}=\frac{1.25\times {10}^{-3}{d}_{\text{p}}^2{\left({\rho }_{\text{p}}-{\rho }_{\text{g}}\right)}^{0.9}{\rho }_{\text{g}}^{0.1}g}{{\mu }_{\text{g}}}$$(3)
Leva et al. (1956)	$$u_{\text{mf}}=\frac{7.39d_{\text{p}}^{1.82}{\left({\rho }_{\text{p}}-{\rho }_{\text{g}}\right)}^{0.94}}{{\rho }_{\text{g}}^{0.06}}$$(4)
Goroshko et al. (1958)	$$u_{\text{mf}}=\frac{{\mu }_{\text{g}}}{{\rho }_{\text{g}}{d}_{\text{p}}}\left(\frac{\mathit{Ar}}{1400+5.2\sqrt{\mathit{Ar}}}\right)$$(5)
Leva (1959)	$$u_{\text{mf}}=\frac{8.1\times {10}^{-3}{d}_{\text{p}}^2\left({\rho }_{\text{p}}-{\rho }_{\text{g}}\right)g}{{\mu }_{\text{g}}}$$(6)
Broadhurst and Becker (1975)	$$u_{\text{mf}}=\frac{{\mu }_{\text{g}}}{{\rho }_{\text{g}}{d}_{\text{p}}}{\left(\frac{\mathit{Ar}}{2.42\times {10}^5{\mathit{Ar}}^{0.85}{\left(\frac{{\rho }_{\text{p}}}{{\rho }_{\text{g}}}\right)}^{0.13}+37.7}\right)}^{0.5}$$(7)
Riba et al. (1978)	$$u_{\text{mf}}=\frac{{\mu }_{\text{g}}}{{\rho }_{\text{g}}{d}_{\text{p}}}\left(1.54\times {10}^{-2}{\left(\frac{d_{\text{p}}^3{\rho }_{\text{g}}^{2}g}{{\mu }_{\text{g}}^2}\right)}^{0.66}{\left(\frac{{\rho }_{\text{p}}-{\rho }_{\text{g}}}{{\rho }_{\text{g}}}\right)}^{0.7}\right)$$(8)
Doichev and Akhmakov (1979)	$$u_{\text{mf}}=\frac{{\mu }_{\text{g}}}{{\rho }_{\text{g}}{d}_{\text{p}}}\left(1.08\times {10}^{-3}{\mathit{Ar}}^{0.947}\right)$$(9)
Wu and Baeyens (1991)	$$u_{\text{mf}}=\frac{u_{\text{g}}}{{\rho }_{\text{g}}{d}_{\text{p}}}\left(7.33\times {10}^{-5}\times {10}^{\sqrt{8.24{\text{log}}_{10}\mathit{Ar}-8.81}}\right)$$(10)

Despite this, the Ergun equation (Eqn. 1) is one of the most frequently equations used in order to evaluate the effect of temperature on minimum fluidization conditions. Although the unknown voidage at minimum conditions may be a problem in applying this equation, numerous predictive correlations for u_mf are based on a modified Ergun equation, as developed by Wen and Yu (1966). Eqn. 1 can be rewritten using Archimedes dimensionless number (Ar) and Reynolds number at minimum fluidization conditions as follows:   

$$\mathit{Ar}=150\frac{(1-{\epsilon }_{\text{mf}})}{{\phi }^2{\epsilon }_{\text{mf}}^3}{\mathit{Re}}_{\text{mf}}+\frac{1.75}{\phi {\epsilon }_{\text{mf}}^3}{\mathit{Re}}_{\text{mf}}^2$$(11)

Wen and Yu (1966) showed that the voidage and shape factor functions in both the viscous and inertial term of Eqn. 11 can be approximated as:   

$$\frac{1-{\epsilon }_{\text{mf}}}{{\phi }^2{\epsilon }_{\text{mf}}^3}\approx 11$$(12)

  

$$\frac{1}{\phi {\epsilon }_{\text{mf}}^3}\approx 14$$(13)

Leading to a modified form of Eqn. 11:   

$$\mathit{Ar}=1650\hspace{0.17em}\hspace{0.17em}{\mathit{Re}}_{\text{mf}}+24.5\hspace{0.17em}\hspace{0.17em}{\mathit{Re}}_{\text{mf}}^2$$(14)

That can be rearranged to the general formulas:   

$$\mathit{Ar}=A\hspace{0.17em}\hspace{0.17em}{\mathit{Re}}_{\text{mf}}+B\hspace{0.17em}\hspace{0.17em}{\mathit{Re}}_{\text{mf}}^2$$(15)

or   

$${\mathit{Re}}_{\text{mf}}=\sqrt{a^2+b(\mathit{Ar})}-a$$(16)

where $a=\frac{A}{2B}$ and $b=\frac{1}{B}$

Values reported in the literature for the constants a and b are listed in Table 3. However, predictions using Eqn. 14 do not take into account possible changes in the voidage which may occur with increasing temperature, as discussed later.

Table 3 Values for the constants a and b in Eqn. 16.

Authors	${\mathit{Re}}_{\text{mf}}=\sqrt{a^2+b\hspace{0.17em}\mathit{Ar}}-a$
	a	b
Wen and Yu (1966)	33.7	0.0408
Bourgeois and Grenier (1968)	25.46	0.03824
Saxena and Vogel (1977)	25.28	0.0571
Babu et al. (1978)	25.25	0.0651
Richardson and Jerónimo (1979)	25.7	0.0365
Grace and Hetsroni (1982)	27.2	0.0408
Chitester and Kornosky (1984)	28.7	0.0494
Thonglimp et al. (1984)	31.6	0.0425
Lucas and Arnaldos (1986)	25.2	0.0672
Bin (1993)	27.31	0.0386
Reina et al. (2000)	48	0.045

Pattipati and Wen (1981) reported that the Wen and Yu correlation is capable of predicting changes in u_mf when temperature increases for sand material. They did not observe important changes with temperature in the voidage at minimum fluidization and they found good matching between experimental and predicted u_mf values.

The effect of temperature on the minimum fluidization velocity has been reported by several other authors. At first, we review work that is specific to large particles falling within Geldart’s Group B and D particles. Generally, the experimental findings confirmed the trend predicted by the Wen and Yu equation. Nevertheless, absolute values did not always match the experiments. Knowlton (1992) stated that one of the reasons lies in the evaluation of the correct mean particle size and shape factor. He suggested that this could be back-calculated from the Ergun equation using previously measured values of u_mf. Doing so, an effective value for the particle size and shape factor would be found.

Botterill et al. (1982) reported experimental verification of the temperature effect on u_mf for some Group B and D powders. They observed a decrease of u_mf with increasing temperature for Group B materials due to the consequent increase in gas viscosity. They compared their results with predictions from the Wen and Yu equation and noted that the decrease was less than that predicted since a change in ε_mf had occurred. This is not in agreement with the results of Pattipati and Wen (1981). For Group D powders, Botterill et al. (1982) observed an increase in u_mf, because of the decrease of gas density. They also found that ε_mf for the Group D materials did not change with temperature. Their experimental data matched predictions obtained from the Ergun equation, using the values of ε_mf measured at the corresponding operating temperatures, and using also an appropriate value of the shape factor, back-calculated from the Ergun equation for a given experiment (Lettieri, 1999).

Fletcher et al. (1992) reported that applying Eqn. 16 can introduce a significant error into the prediction of u_mf, mainly because the a and b constants are a function of the shape factor (ϕ) and voidage at minimum fluidization conditions, which are difficult to measure experimentally. They proposed different correlations for the prediction of Re_mf at ambient temperature on the basis of the shape of the particles, see Table 4.

Table 4 Correlations for the prediction of Re_mf at ambient temperature (Fletcher et al., 1992).

Type of sands
Round	$${\mathit{Re}}_{\text{mf}}=\frac{\mathit{Ar}}{1400+5\sqrt{\mathit{Ar}}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\left(\mathit{Ar}\ge 1480\right)$$(17a)
	$${\mathit{Re}}_{\text{mf}}=\frac{\mathit{Ar}}{1400}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\left(\mathit{Ar}<1480\right)$$(17b)
Moderately sharp	$${\mathit{Re}}_{\text{mf}}=\frac{\mathit{Ar}}{1700+\sqrt{\mathit{Ar}}}$$(18)
Very angular, coked	$${\mathit{Re}}_{\text{mf}}=\frac{\mathit{Ar}}{790+7\sqrt{\mathit{Ar}}}$$(19)

A decade later, Coltters and Rivas (2004), proposed a new equation to estimate the minimum fluidization velocity without having to experimentally determine the bed voidage and shape factor:   

$$u_{\text{mf}}=K{\left[\frac{d_{\text{p}}^2({\rho }_{\text{p}}-{\rho }_{\text{g}})g}{\mu }{\left(\frac{{\rho }_{\text{p}}}{{\rho }_{\text{g}}}\right)}^{1.23}\right]}^{\alpha }$$(20)

where K and α are constants and are functions of the solids-gas system. They tested their correlation against 189 experiments reported in the literature on about 90 different materials, and their results showed good agreement with the experimental data. In parallel, Delebarre (2004), proposed the following revisited Wen and Yu equations for the prediction of u_mf without the dependency on the voidage and shape factor:   

$$\mathit{Ar}\hspace{0.17em}\hspace{0.17em}=24.5\hspace{0.17em}\hspace{0.17em}{\mathit{Re}}_{\text{mf}}^2+29400\hspace{0.17em}\hspace{0.17em}{\epsilon }_{\text{mf}}^3(1-{\epsilon }_{\text{mf}}){\mathit{Re}}_{\text{mf}}$$(21)

The relative role of the hydrodynamic and interparticle forces on the minimum fluidization conditions at elevated temperature for Group A and C powders has been analysed by various authors. Lucas et al. (1986) reported that changes with temperature in ε_mf can be explained on a hydrodynamic basis, contrary to Raso et al. (1992) and Formisani et al. (1998) who later related such changes to a variation of IPFs with temperature.

Lucas et al. (1986) explained the variation of ε_mf with temperature in terms of a change in the flow pattern inside the bed. They analysed the variation of ε_mf as a function of Re_mf and observed that under flow regimes with Re_mf, less than 0.75, ε_mf remains constant while it decreases when this value is exceeded, becoming constant again at an Re_mf higher than 2. They explained that at low Re_mf a sucking effect is produced in the particle boundary layer which increases the closeness of the particles and causes ε_mf to decrease. At higher values of Re_mf, the attractive forces between the particles decrease and ε_mf gradually increases up to an approximately constant value. From this theory, a powder classification scheme based on the nature of the boundary layer around a particle was elaborated by Mathur and Saxena (1986), and validated with data on u_mf and ε_mf obtained by Botterill et al. (1982) and Lucas et al. (1986) at high temperatures.

In agreement with Raso et al. (1992), Yamazaki et al. (1995) reported that the role of the IPFs should not be ignored when trying to explain changes in ε_mf with temperature. They showed that variations in bed voidage depend both on the physical properties of the fluidizing fluid, i.e. density and viscosity, and on changes in the physicochemical properties of the particles. In particular, they studied the effect of water adsorbed onto the surface of silica particles with increasing temperature. At low temperatures, they observed a decrease in ε_mf as humidity increased, while at higher temperatures higher values of ε_mf were found for the same humidity. They explained such changes in terms of the amount of water adsorbed onto the surface of the silica, and concluded that variation of the ε_mf with temperature is caused by a change in the adhesion forces, which at velocities as low as u_mf can cause the formation of clusters, making the bed settle with a relatively looser structure.

Formisani et al. (1998) and Lettieri et al. (2000) also reported on the effect of temperature on minimum fluidization conditions, and they stated that the Ergun equation and Wen and Yu correlation are capable of predicting changes in the minimum fluidization velocity with temperature if, in addition to changes of gas density and viscosity, the dependence of ε_mf on temperature is also accounted for.

Formisani et al. (1998) observed a linear increase of ε_mf for various Group A, B and D powders and a linear increase of the voidage of the fixed bed with temperature (Fig. 1–2). Formisani et al. (1998) performed their experiments in a transparent quartz column equipped with a stainless steel porous plate able to provide a homogeneous gas distribution; a video camera was used to record the experiments. The total pressure drop across the particle bed was measured with a pressure tap located just above the gas distributor level; a graduated scale was used to determine the bed height at each temperature, and the average bed voidage was subsequently determined from the values of the bed height. The authors reported that bed height measurements were affected by a 0.5-mm approximation, which caused uncertainty in the bed voidage evaluations of around 1 %.

Fig. 1

Effect of temperature on the fixed bed voidage for glass ballotini and silica sand particles of different size. Reprinted with permission from Ref. (Formisani et al., 1998). Copyright: (1998) Elsevier Limited.

Fig. 2

Effect of temperature on the bed voidage at minimum fluidization for glass ballotini and silica sand particles of different size. Reprinted with permission from Ref. (Formisani et al., 1998). Copyright: (1998) Elsevier Limited.

They attributed the increase of the fixed bed voidage to an increase of the interparticle forces which was thought to stabilize the structure of the fixed bed state, in the total absence of a gas flow. They found a close similarity between the slope of the fixed bed voidage and ε_mf and so they concluded that the increase of ε_mf, and in turn changes in u_mf with temperature, are not due only to changes in the properties of the fluidizing gas but also to changes in packing properties.

They attributed the capability of the bed to form a looser structure to an increase of the Van der Waals’ forces with temperature. The results of Formisani et al. (1998) confirmed findings reported by Raso et al. (1992) on a 2D fluidized-bed.

Lettieri et al. (2000, 2001) reported experimental observations on the effect of temperature on the fluidization of three fresh FCC catalysts and an equilibrium (E-cat) FCC tested at ambient pressure and at temperatures up to 650 °C. Where changes in fluidization at high temperature were observed, the factors responsible were investigated via thermo-mechanical analyses. The physical properties of a porous Group A powder were changed deliberately in order to highlight under which conditions the fluidization behaviour is dominated by the IPFs.

These results demonstrated how temperature can increase the effect of IPFs, causing a Group A material to behave in a similar manner to a Group C material. Fig. 3 shows the effect of temperature on the fluidization at minimum fluidization conditions for three silica catalysts doped with different amounts of potassium acetate (KOAc). Fig. 3 shows that the prediction and experimental values of u_mf match only for the catalyst sample doped with 1.7 %wt of KOAc. Values of u_mf obtained for the doped samples with 7 % and 10 %wt of KOAc were found to be higher than the predicted ones at ambient temperatures. Lettieri et al. (2000) explained that during the drying process, some potassium acetate might have migrated to the mouth of the pores from within, making this responsible for the higher values of u_mf, hence reflecting the influence of the IPFs on the fluidization behaviour.

Fig. 3

u_mf vs temperature for a silica catalyst doped with increasing values of potassium acetate, comparison of experiment with prediction. Reprinted with permission from Ref. (Lettieri et al., 2000). Copyright: (2000) Elsevier Limited.

Significant changes in the fluidization quality of the sample with 10 %wt of potassium acetate occurred with increasing temperature. The ratio between the measured and calculated pressure drop across the bed of material is plotted against gas velocity in Fig. 4, as temperature is increased. The fluidization behaviour of this material significantly changed when the bed temperature was about 200 °C. A rapid decrease of the pressure drop was noted and channels were seen on the X-ray images. This material exhibited a typical cohesive Group C behaviour. Good fluidization at 200 °C could be achieved only when operating the system at a higher velocity, thus causing the channels and rat holes to be broken down. When the bed was cooled down to 150 °C, good fluidization was obtained again at low velocities.

Fig. 4

ΔP_m/ΔP_c vs bed velocity as a function of temperature for a silica catalyst doped with 10 %wt of potassium acetate. Reprinted with permission from Ref. (Lettieri et al., 2000). Copyright: (2000) Elsevier Limited.

Lettieri et al. (2000) explained that at increasing temperature, the potassium acetate contained within the catalyst pores became mobile and migrated to the surface of the particles due to decreases in the surface tension and viscosity. The presence of potassium acetate on the surface of the catalyst caused the material to become sticky and therefore to channel. On the other hand, as the bed temperature decreased, re-absorption of the potassium acetate into the catalyst pores may have occurred, thus allowing good fluidization of the material to be re-established.

Several authors have also investigated the combined effects of temperature and particle size and particle size distribution (PSD) on minimum fluidization velocity, Lin et al. (2002), Bruni et al. (2006), Subramani et al. (2007), Hartman et al. (2007), Goo et al. (2010), Chen et al. (2010) and Ma et al. (2013).

Hartman et al. (2007) performed experimental measurements on beds of ceramsite over a temperature range from 293 K to 1073 K, using very narrow fractions of ceramsite particles spanning a range of 0.13–2.25 mm. They reported that u_mf decreases with increasing bed temperature for all the particles, except for the largest ones (2.25 mm), which exhibited a non-monotonic dependence of u_mf on temperature.

Goo et al. (2010) investigated the effects of temperature and particle size on minimum fluidization velocity in a dual fluidized bed, using silica sands over a range of temperature between 298 K and 1073 K. They reported that u_mf decreases with increasing operating temperatures regardless of particle diameters or particle types, and they proposed a correlation to predict such a velocity at different temperature. Chen et al. (2010) have also observed similar behaviour.

Lin et al. (2002) and Ma et al. (2013) demonstrated that operating temperature and PSD can influence the minimum fluidization velocity simultaneously, making variations of u_mf non-monotonic with temperature. In particular, Ma et al. (2013) investigated quartz sand and bottom ash in a bench-scale bubbling fluidized bed reactor at atmospheric pressure, with four PSDs between 30 and 600 °C. The PSDs evaluated included a narrow cut (as reference powder), a Gaussian-type powder, a binary mixture and a uniformly distributed powder. They concluded that the minimum fluidization velocity of the powders with wide PSD decreases with the increase in bed temperature and varies with the mass fraction of rough particles. In addition, they observed that the binary and uniform PSD behaved similarly to each other but generally they had higher values of u_mf than the Gaussian and narrow cut distributions. To predict the correct values of u_mf for wide-range-sized particles, Ma et al. (2013) proposed new correlations based on their experimental data.

Several correlations have been derived for the prediction on the minimum fluidization conditions at high temperature, these are, however, case-specific. The debate of the phenomena causing changes in behaviour with increasing temperature remains controversial with still much disagreement on the role of the hydrodynamic and interparticle forces.

3. Effect of temperature on bed expansion and minimum bubbling conditions

Many attempts have been made to describe the fluid dynamic properties of fluidized beds, with special attention paid to the transition between the particulate and bubbling regime of Geldart’s (1973) Group A powders. These materials are those which exhibit a stable region of non-bubbling expansion between minimum fluidization velocity, u_mf, and minimum bubbling velocity, u_mb, with u_mb/u_mf > 1. The phenomenon of uniform expansion, or delayed bubbling, has been the subject of much research since it is significant to show differences between gas-and liquid-fluidized beds for the formation of gas bubbles in the former but not generally in the latter. The mechanism of bubble-free expansion in gas-fluidized beds has been assumed by some workers to be the same as the homogeneous expansion in a liquid-fluidized bed to which the Richardson and Zaki (1954) equation applies:   

$$u=u_{\text{t}}{\epsilon }^n$$(22)

where u is the liquid velocity of the suspension, u_t is the terminal fall velocity and n is a parameter that depends on the free-fall particle Reynolds number and normally has values between 4.65 (viscous regime) and 2.4 (turbulent regime). However, the validity of this comparison has not always been accepted. Massimilla et al. (1972) and Donsi’ and Massimilla (1973) made some experimental observations on the bubble-free expansion of gas-fluidized beds of fine particles and described the expansion mechanism as being due to the nucleation and growth of cavities which they assumed had occurred because of a broad distribution of interparticle forces. The phenomenon of delayed bubbling is not only limited to fine Geldart’s Group A powders, it has also been observed with large particles fluidized under high pressure conditions, see Yates (1996), and also with magnetised large particles, as reported by Agbim et al. (1971) and later by Siegell (1989).

This phenomenon of delayed bubbling has been the subject of much research since it has a strong bearing on the difference between gas- and liquid-fluidized beds and on the reasons for the formation of bubbles in the one but not in the other.

The limiting condition for the stability of gas-fluidized beds is defined by the voidage at minimum bubbling, ε_mb, whose determination has been at the centre of much theoretical controversy due to the ill-defined role of the HDFs and IPFs. Mathematical models have been developed by various authors to predict the transition between particulate and bubbling regime. Two different approaches have been considered. On the one hand, criteria have been developed based on the assumption that hydrodynamic forces (HDFs) are the controlling factor. On the other hand, interparticle forces (IPFs) were considered to play the dominant role over the hydrodynamic forces. The first stability criterion based solely on hydrodynamic forces was proposed by Jackson (1963). His model failed to predict a stable region for the expansion of fluidized beds of fine materials. He found that the fluidized state was intrinsically unstable towards small concentration disturbances, regardless of the fluid-particle system considered. This conclusion is contrary to the experimental evidence obtained for Geldart’s Group A powders.

Verloop and Heertjes (1970) re-formulated the hydrodynamic model applying the Wallis (1969) stability criterion, which compares the propagation of kinematic and dynamic wave velocities through the fluidized bed. According to this criterion, bubbles form when the propagation velocity of a voidage disturbance reaches the velocity of an elastic wave in the bed. Foscolo and Gibilaro (1984) adopted the approach of Verloop and Heertjes and developed a model (the “particle-bed model”) to predict the onset of bubbling, ε_mb, in a fluidized bed. The key to application of their criterion lies in the formulation of the fluid-particle interaction model. This is discussed in Foscolo et al. (1983). A detailed formulation of the particle-bed model is reported in Foscolo and Gibilaro (1987) where reasonable agreement between predictions and experimental data available at ambient and high pressure conditions was found. Furthermore, Brandani and Foscolo (1994) mapped the various fluidization behaviours by analysing the discontinuities arising from the one-dimensional equations of change in the particle-bed model.

On the other hand, interparticle forces were considered to play the dominant role over the hydrodynamic forces (Mutsers and Rietema, 1977; Piepers et al., 1984; Cottaar and Rietema, 1986; Rietema et al., 1993).

Rietema and co-workers formulated a stability model which accounted for additional forces to the fluid-dynamic forces and gravitational weight. They assumed that the interparticle forces between cohering particles give rise to a powder structure with a certain mechanical strength even in the expanded state of homogeneous fluidization. This mechanical structure can be broken only with gas velocities sufficiently high so that the drag force exerted by the fluid becomes greater than the cohesive forces. Rietema and co-workers assumed that the mechanical strength of the powder structure controls the stability of a fluidized system. Similarly to Foscolo and Gibilaro (1984), Mutsers and Rietema (1977) followed the approach of Wallis to predict the stability of a fluidized system, and gave expressions for the kinematic and dynamic wave velocities. Their formulation for the bed elasticity and the theoretical concept behind it represents, however, the crucial difference between their model and the criteria developed solely on the basis of the hydrodynamic forces.

According to Mutsers and Rietema, the bed elasticity is the essential property which determines the dynamic behaviour of the bed, and whose origin is to be found in the Van der Waals’ forces which the solid particles exert upon each other.

However, whereas models based on HDFs such as Foscolo and Gibilaro (1984) provide explicit formulations for the minimum bubbling condition, the formulation proposed by Rietema and co-workers cannot be used to make a-priori predictions.

The effect of temperature on the transition between particulate to bubbling fluidization was investigated by Rapagna’ et al. (1994), who demonstrated the capability of the Foscolo and Gibilaro criterion to predict ε_mb for FCC powders of mean particle sizes of 65 and 103 μm in a 50-mm i.d. column from ambient conditions up to 900 °C. They used a fast responding pressure transducer connected to an oscilloscope to detect the passage of bubbles in the bed. They observed a decrease in the average bubble size and a delay of the onset of bubbling with increasing temperature for both FCC powders. This corresponded to an increase in the voidage at minimum bubbling with temperature. Also, a larger increase in ε_mb was observed for the finer materials, a comparison of their experimental values for ε_mb with those predicted by the Foscolo and Gibilaro fluid-bed model showed good agreement for both powders at ambient and high temperatures (Fig. 5). Xie and Geldart (1995) investigated the role of the IPFs on the bubbling conditions with increasing temperature by measurements of the voidage. They observed virtually no change in ε_mb as the temperature increased for any of the FCC catalysts investigated, in contrast to the results of Rapagna’ et al. (1994). They also reported that predictions of ε_mb given by the Foscolo and Gibilaro (1984) and the modified particle-bed model by Jean and Fan (1992) matched experiments at ambient temperature for FCC powders larger than 60 μm. However, both models over-predicted ε_mb values at ambient temperatures for the finer powders, and they also predicted significant changes in ε_mb with temperature, in contrast to the experimental results reported.

Fig. 5

Experimental and calculated values of bed voidage at minimum bubbling conditions as a function of temperature for sample I (on the left) and sample II (on the right), Reprinted with permission from Ref. (Rapagna et al., 1994). Copyright: (1994) Elsevier Limited.

The failure of the hydrodynamic models to correctly predict the transition between the particulate and bubbling regime was assumed to be the result of ignoring the interparticle forces.

The onset of bubbling was also studied by Formisani et al. (1998). They measured changes in the minimum bubbling velocity of FCC catalysts and silica sand with increasing temperature from ambient up to 800 °C in a 55-mm i.d. quartz column. They relied on visual observation to determine the commencement of bubbling. For all materials tested, they observed an increase of u_mb with increasing temperature with a trend very similar to the increase observed for u_mf. Unlike Rapagna’ et al. (1994), they observed a very small bed expansion increase with increasing temperature.

Lettieri et al. (2001) investigated the fluid-bed stability of three fresh FCC catalysts both experimentally and theoretically as a function of increasing temperature. Values of the voidage at minimum bubbling conditions were obtained from 20 °C up to 650 °C, and compared with predictions given by the Foscolo and Gibilaro particle-bed model.

For all FCC catalysts, the experimental ε_mb values increased little with increasing temperature. At first, the values were compared with predictions obtained using the Foscolo and Gibilaro particle-bed model. This predicted changes in ε_mb much greater than found experimentally, see Fig. 6. The disagreement between predicted and experimental ε_mb values was related to the large discrepancy between the values of n and ut in the Richardson and Zaki equation, obtained from the experimental bed expansion profiles and the calculated ones.

Fig. 6

Comparison between measured ε_mb values and predictions using the original and generalized Foscolo- Gibilaro particle-bed model for an FCC catalyst. Reprinted with permission from Ref. (Lettieri et al., 2001). Copyright: (2001) Elsevier Limited.

For all FCC catalysts, the highest values of the experimental n and u_t were found at ambient conditions.

In order to correctly apply the particle-bed model to these particle systems, Lettieri et al. (2001) generalized the expression of the drag force given by Foscolo and Gibilaro for the viscous flow regime. Consequently, they re-examined the procedure followed to obtain the Foscolo and Gibilaro stability criterion and proposed a generalized expression of their criterion. Predicted ε_mb values obtained with the generalized expression of the Foscolo-Gibilaro criterion were within 5 % for all FCC catalysts. Although the particle-bed model was originally developed on the assumption that the hydrodynamic forces govern the fluid- bed stability, the results presented by Lettieri et al. (2001) suggested that the contribution of the interparticle forces to the bed stability of the materials studied cannot be ruled out.

As a follow-up study, Lettieri and Mazzei (2008) analysed the effect of temperature on the fluid-bed stability of the same three FCC catalysts used in Lettieri’s previous work, but this time through considerations on the fluid-bed elasticity.

They reported experimental findings on the effect of temperature on the elasticity modulus at minimum bubbling conditions, calculated according to the theory of Foscolo & Gibilaro (1984) and also adopting the criterion of Mutsers & Rietema (1977). In accordance with the theoretical postulation of Mutsers & Rietema, the results from bed expansion presented by Lettieri and Mazzei (2008) and previously by Lettieri at al. (2002) showed that the role played by the IPFs can affect the stability of Group A powders. However, the sensitive analysis carried out by Lettieri and Mazzei (2008) on the parameters which dominate the elasticity modulus revealed that the gas viscosity was the dominant factor which defined its variations with temperature, as shown in Figs. 7 and 8. This highlighted the importance of both HDFs and IPFs on the stability of Group A powders and the need for a correct and complete description of both contributions.

Fig. 7

Effect of temperature on the elasticity modulus at ε_mb according to the Mutsers & Rietema criterion, for all fresh FCCs. Reprinted with permission from Ref. (Lettieri and Mazzei, 2008). Copyright: (2008) Elsevier Limited.

Fig. 8

Influence of gas viscosity on the elasticity modulus at ε_mb according to the Mutsers & Rietema criterion, for all fresh FCCs. Reprinted with permission from Ref. (Lettieri and Mazzei, 2008). Copyright: (2008) Elsevier Limited.

In line with Lettieri et al (2001), Valverde and co-workers (2001) emphasized the importance of the interparticle forces on the settling and particulate fluidization of fine powders. They proposed an extension of the Richardson and Zaki empirical correlation and the theoretical Mills-Snabre (1994) model, originally developed for the settling of non-cohesive spheres, to predict the settling of aggregates which may form when the interparticle forces exceed the particle weight by several orders of magnitude. Valverde et al. (2003) extended the previous study, investigating—from both macroscopic and local measurements—the transition between the solid-like, fluid-like and bubbling fluidization of gas-fluidized fine powders. They showed that the transition between the solid-like and the fluid-like regimes takes place along an interval of gas velocities in which transient active regions alternate with transient solid networks. Using optical probe local measurements, they showed the existence of meso-scale pseudo-turbulent structures and short-lived voids in the fluid-like state, which make the prediction of the transition between the different regimes a complex task.

Castellanos (2005) observed that the onset of fluidization of fine and ultrafine powders was characterized by the presence of agglomerates which give place to a highly expanded state of uniform fluid-like fluidization. In an attempt to unify the above observations, Valverde and Castellanos (2008) proposed an extension of Geldart’s classification of powders to predict the gas-fluidization behaviour of cohesive particles, which reconciles the role of the interparticle and hydrodynamic forces on the existence of a non-bubbling regime. In the new phase diagram proposed by Valverde and Castellanos, the boundaries between the different types of fluidization are defined as a function of fluid viscosity, particle density, the fractal dimension of the agglomerates and the powder’s compaction history, as previously reported by Valverde and Castellanos (2006).

Girimonte and Formisani (2009) reported on the influence of operating temperature on the transition to the bubbling regime for samples of FCC, silica and corundum sands, at temperatures ranging from 30 to 500 °C. They determined the minimum bubbling velocity using four different methods and obtained different results for u_mb with increasing temperature. The first method was based on the direct observation of the velocity at which the first bubble erupted on the free surface of the bed. The second method was based on measurement of the pressure drop across the whole bed, and u_mb was taken as the point where a shallow minimum of the Δp versus u curve occurs. The last two methods were derived from analysis of the “fluidization map”, namely examination of the expansion behaviour of the bed over a range of fluidization velocities from the fixed-bed state to the bubbling regime.

They demonstrated that the optical method and the method based on detection of the pressure drop minimum were unreliable for correctly determining the starting point of bubbling. They stated that only the analysis of bed expansion as a function of the fluidization velocity allows the succession of phenomena through which a stable flow of bubbles across the solid mass ensues to be reconstructed.

More recently, Girimonte and Formisani (2014) reported on new experiments carried out on the effect of temperature on the fluidization of FCC particles. They used a non-invasive optical technique for acquiring images of the bubbles’ eruption at the free surface and results from bed collapse tests. Their experiments showed that high temperature influences the quality of bubbles and produces a smoother regime of bubbling, which they attributed to the thermal enhancement of IPFs that in turn leads to a higher porosity and lower interstitial flow in the emulsion phase.

In summary, high temperature clearly affects the stability of fluidized beds of Group A powders; well-established theories and models fail to predict correctly the voidage at minimum bubbling with increasing temperature. Models corrected on the basis of experimental data are capable of reproducing correct trends; however, a-priori predictions of the fluid-bed stability with increasing temperature are yet to be achieved. The challenge here is still in the ability to describe the forces that determine the transition from particulate to bubbling fluidization. Hence, some kind of quantification of the effects of the IPFs on fluidization is needed in order to advance the understanding of fluidization at high temperature.

4. Effect of fines content and fines size distribution on fluidization

The presence of fine particles is known to improve the fluidization quality of fluidized beds (Rowe et al., 1978; Abrahamsen and Geldart, 1980; Newton, 1984). For this reason many industrial fluidized bed reactors operate with a high fines fraction (d_p < 45 μm) of between 10 and 50 wt% in order to improve the fluid bed performance and to achieve high product yields (Pell and Jordan, 1987; Lorences et al., 2003; Bruni et al., 2006). Furthermore, the fines increase the mass transfer rate between the dense and bubble phase, the minimum bubbling velocity, the interstitial gas velocity, the bed expansion and reduce bubble size (Werther, 1983; Rowe, 1984; Sun and Grace, 1992; Lorences et al., 2003). Fresh catalysts generally contain a higher proportion of fines and show less of a tendency to segregate or cluster (Avidan and Yerushalmi, 1982).

However, as pointed out by Lorences et al. (2003), there is an associated cost in maintaining a high level of fines. Plant investment may be higher because more cyclones and a larger reactor volume are required due to the lower solids suspension density. Catalyst make-up costs are also higher because of the increased attrition rate.

Many researchers have investigated the effect of fines on the fluidization quality in order to determine the optimal amount of fine particles to be added (Rowe et al., 1978; Barreto et al., 1983; Newton, 1984; Avidan and Edwards, 1986; Yates and Newton, 1986; Pell and Jordan, 1987; Sun and Grace, 1990; Lorences et al., 2003; Bruni et al., 2006).

Rowe et al. (1978) examined the dense phase voidage ε_d of freely bubbling fluidized beds containing different amounts of fines using the X-ray absorption technique. Voidage measurements were made by comparing the X-ray absorption of the dense phase of the freely bubbling bed with that of a calibration wedge containing the same material. They carried out experiments on a commercial silica-based catalyst of mean particle diameter 52 μm, but with three different percentages of fines: 2.7, 20 and 27.6 %. They found that both the dense phase voidage and the overall expansion of the bed increased with increasing fines content. Furthermore, they observed that the measured voidage of the dense phase was an order of magnitude greater than the voidage corresponding to the minimum fluidization condition. Accordingly, they deduced that the interstitial gas flow in a bubbling bed is greater than the minimum fluidization flow, hence questioning the validity of the “two-phase” theory of Toomey and Johnstone (1952) on beds of fine particles. This states that all gas in excess of that required to just fluidize the particles passes through the bed in the form of bubbles. Rowe et al. (1978) concluded that since the dense phase is much more effective in bringing about a chemical reaction than the bubble phase, the overall performance of a catalytic fluidized bed reactor can be enhanced by the addition of fines.

Later, Barreto et al. (1983) compared the Rowe et al. (1978) measurements with those obtained with a bed collapse test technique. They found good agreement between the dense phases properties obtained using the two techniques over the range of velocities studied.

In order to test the conclusions from the earlier study of Rowe et al. (1978), Newton (1984) and Yates and Newton (1986) also examined the influence of fines fractions on fluidization by monitoring the conversion in catalytic fluidized bed reactors containing different amounts of fines. They highlighted that an increase in the conversion measured for a given throughput of reactant can be obtained by increasing the fines content and that this is due to changes caused by fine particles in the gas distribution between the dense phase and the bubble phase. Newton (1984) carried out experiments on a commercial oxidation catalyst, and he used three batches containing 0, 16 and 27 % of fines with a mean particle diameter of 81, 58 and 52 μm, respectively. Results at each temperature showed an increase in conversion with increasing fines content and for the same fines content an increase in conversion with temperature, therefore confirming the hypothesis that increasing fines content causes more gas to flow through the emulsion phase and less through the bubble phase.

Abrahamsen and Geldart (1980) had also extensively investigated the effect of fines on the fluidization of Geldert’s Group A powders and found that the dense phase voidage increases as the fraction of fines increases; they stressed, however, the need for studying the effects of fines fractions, mean diameter and size distribution independently.

Khoe et al. (1991) investigated the effect of changing the mean particle diameter independently of the PSD by modifying a sample of FCC catalyst and a sample of glass ballotini. They created three samples with a narrow size distribution and differing in mean particle diameter (83, 53 and 34 μm for the FCC and 113, 72 and 37 μm for the glass ballotini). Then they examined the effect of changing the PSD independently of the mean diameter by creating for each powder two more samples with the same mean particle diameter as the intermediate narrow sample (∼53 μm for the FCC and ∼72 μm for the glass), but with a wide and bimodal PSD, respectively.

They performed the bed collapse test on all samples and found that the effect of increasing the mean particle diameter for both FCC and glass powders was to increase the dense phase collapse rate and to decrease the voidage of the dense phase. These effects were enhanced when the samples with the same d_p and different PSD were compared. The most aeratable FCC sample was the one with a wide distribution, while the most aeratable glass sample was the one with a bimodal distribution.

Bruni et al. (2006) investigated the independent effect on fluidization of adding different fine sub-cuts to a virtually fines-free starting material. The fluidization behaviour of an alumina powder was monitored at temperatures ranging from ambient to 400 °C and by adding two fine sub-cuts of nominal size 0–25 and 25–45 μm to the material previously deprived of fines. Results were obtained by performing fluidization tests such as bed collapse tests, pressure drop profiles and bed expansion profiles. Fines content and fines size distribution significantly affected the fluidization behaviour of the powders tested. The fluidization tests highlighted significant differences in the characteristics of the settled and expanded bed of the materials investigated. The results showed that the addition of fines made the materials more capable of retaining the aeration gas hence expanding more and taking longer to collapse when the gas was suddenly cut off than the bed deprived of fines. The effects of the IPFs become more evident for the powders containing the smaller fines cut than for powders containing the same amount of bigger fines. Bruni et al (2007a,b) subsequently developed a parallel fluidization-rheology approach (discussed in Section 7 of this paper) to establish the relative role between the interparticle and hydrodynamic forces on the aeratability of the powders with increasing temperature.

The literature reported to this point reveals the complexity of the phenomena involved, and the difficulty of a direct quantification of the particle-particle interactions in fluidized beds and of their changes at process conditions. Within this framework, powder rheology represents an appealing tool to evaluate indirectly the effects of the IPFs on fluidization. This is tackled in the next two sections of this paper.

5. Powder flowability measurement tests

A great deal of research has been carried out over the last sixty years in order by means of simple tests to define and measure parameters apt to characterize and predict the flow properties of solid materials. To this end, various approaches have been undertaken and are presented in this section. These include both stationary measurements and dynamic tests.

On one hand, stationary measurements (angle of repose, Hausner ratio, etc.) have been proposed as simple tests to predict the flowability of bulk powders (Carr, 1965). On the other hand, dynamic tests have been used as a means for determining the flow characteristic of powders. These dynamic tests can be classified into two distinct groups: the shear-cell-type tests, first introduced by Jenike in 1953, and the viscometer-type tests, whose study was initiated by Schugerl in the late sixties. The former is a test performed on the powder in a compressed state where the shear measurements are used to obtain a yield locus that represents the limiting shear stresses under any normal stress when failure, i.e. flow, occurs. The shape of the yield locus is related to the material cohesiveness. The latter is based on the analogy between fluidized beds and liquids and in particular on the idea that in a fluidized bed, a resistance against flow exists just as in liquids, and that this resistance is a kind of internal friction between the particles in the suspension forming the dense phase and resembles the concept of viscosity used in describing the rheology of liquids.

Carr (1965) developed a classification system to predict the flow characteristics of a bulk of particulate solids. In Carr’s method, a numerical value is assigned to the results of several tests and it is summated to produce a relative flowability index for that particular bulk material. The method is further discussed in Carr (1970). Defined here are some of the main parameters used in Carr’s method: the angle of repose, the angle of fall, the angle of difference, the angle of internal friction, the angle of spatula and cohesion. In addition, the Hausner Ratio (HR, i.e. the ratio between the loose and the packed bulk density) and the compressibility are also used to define the cohesiveness and thus the flowability of a material (Geldart and Wong, 1984, 1985; Bruni, 2005).

The angle of repose is defined as the constant angle to the horizontal assumed by a cone-like pile of the material. It is a direct indication of the potential flowability of a material: materials with good flowability are characterized by low angles of repose.

The angle of fall is determined by dropping a small weight onto the platform on which an angle of repose has been formed. The fall causes a decrease of the angle of repose that is called angle of fall. The more free-flowing the material, the lower the angle of fall.

The angle of difference is the difference between the angle of repose and the angle of fall. The greater this angle, the better the flow.

The angle of internal friction is defined (Carr, 1970) as the angle at which the dynamic equilibrium between the moving particles of a material and its bulk solid is achieved. This is of particular interest for flows in hoppers and bins.

The angle of spatula is a quick measurement of the angle of internal friction. It is the angle, measured from the horizontal, that a material assumes on a flat spatula that has been stuck into the dry material and then lifted up and out of it. A free-flowing material will have formed one angle of repose on the spatula’s blade. A cohesive material will have formed several angles of repose on the blade; the average of these is taken. The higher the angle of spatula of a material, the less flowable it is.

Cohesion is defined as the apparent cohesive forces existing on the surface of fine particles or powders. The cohesion test consists of passing the material through three vibrating sieves in series. The material left on each sieve is weighed and a cohesion index is determined from the relative amounts retained.

The Hausner Ratio (HR) is the ratio between the loose and the packed bulk density and is used as an indication of the cohesiveness of the materials, see Geldart and Wong (1984). The loose bulk density (ρ_BDL) is measured by gently pouring a sample of powder into a container through a screen, whereas the packed or tapped bulk density (ρ_BDP) is determined after settling and deaeration of the powder has occurred due to tapping of the sample. In addition to the HR, the powder compressibility is also used to define cohesiveness, this is expressed as 100 (ρ_BDP−ρ_BDL)/ρ_BDP.

The main advantage of these tests is their simplicity that makes them an attractive tool to determine powder flowability and it explains their wide use in industry and academia. However, these tests are scarcely reproducible and their procedures are very difficult to standardise, as amply discussed by Santomaso et al. (2003) with special regard to the Hausner ratio. Furthermore, the link between the fluidization behaviour and the static properties is not at all straightforward, due to the uncertain relationship between the IPFs and the HDFs involved when gas is passed through a bed of particles. The use of static methods to predict the fluidization behaviour of powders, despite being widely employed, is therefore questionable, especially when the fluidization behaviour needs to be assessed under process conditions (Bruni, 2005).

5.1 Shear testers

Shear-cell-type tests, first introduced by Jenike in 1953, are performed on the powder in a compressed state where the shear measurements are used to obtain a yield locus that represents the limiting shear stresses under any normal stress when failure, or to be precise flow, occurs. The shape of the obtained yield locus is related to the material cohesiveness. Many conventional testers are available for measurement of the flowability and they can be distinguished between direct (translational and rotational) and indirect (uniaxial, biaxial and triaxial) shear testers (Schwedes, 2003). Some examples of translational direct testers are Jenike’s shear cell and Casagrande’s shear tester, while some of the most important rotational direct testers are the torsional and the ring shear testers.

Shear cell measurements are widely used to assess the flowability of powders for applications that involve powder discharge. Most of the principles of such tests have their origin in soil mechanics and in bunker designing, but they have become increasingly useful for the general characterisation of particulate materials. However, as for the static tests, a direct link between the failure properties of the material measured with a shear cell and the corresponding fluidization behaviour is not straightforward.

Shear testers are known to be very useful to predict the solids flow from a tall silo in which the relatively high loading pressure of the solids prevails. However, due to the very small or zero loads on the bulk of a fluidized powder, standard shear testers are unlikely to provide an accurate characterization of fluid bed behaviour, as values of the failure properties need to be extrapolated from data at higher loads. Barletta et al. (2005, 2007) overcame this problem in their modified Peshl shear cell by introducing a cinematic chain to counterbalance the weight of the lid of the cell and therefore allow measurements under low normal stresses. Such a modified Peschl shear cell was used by Bruni et al. (2007a, b), whose work is discussed in the next section.

Moreover, existing shear cells are not designed to operate at high temperature because applications involving powder discharge are run at ambient temperature. Therefore, shear cells are not capable of detecting possible changes in the settled bed packing with increasing temperature.

Few studies available in the literature have addressed the experimental evaluation of powder flow properties at high temperature. The first attempt was carried out by Smith et al. (1997), who preheated powder samples of MgSO₄ and CaSO₄ up to 750 °C and moved them into a Jenike shear cell and performed shear tests immediately without any control of the temperature. Experimental results for consolidation stresses in the range 40–200 kPa showed an increase of the unconfined yield strength with increasing temperature for all the analysed powders. This was explained with the aid of SEM observations and X-ray diffraction measurements which showed the formation of agglomerates during preheating of the sample.

The lack of proper measurement of the temperature during the shear tests was to some extent overcome by placing the shear cell inside a heated chamber with temperature control (Kanaoka et al., 2001; Tsukada et al., 2008).

Ripp and Ripperger (2010) designed a temperature-controlled annular shear cell for the Schulze shear tester operating from 80 °C to 220 °C. For this purpose, an electric heater was placed on the lid while the vertical walls and the bottom of the cell were provided with a double casing through which a heating or a cooling medium can flow.

Recently, Tomasetta et al. (2013) modified a Schulze shear cell to perform measurements of the powder flow properties of powders up to 500 °C. Electric heaters were introduced below the cell bottom and on the lid to heat the cell and the powder sample contained in it. A covering of insulating material was placed around the trough of the cell and above the lid in order to reduce the heat flux from the external surface of the cell and then to minimise the temperature gradient within the sample. They evaluated the yield loci at room temperature and at 500 °C for different samples: FCC powder, fly ashes, glass beads, natural corundum and synthetic porous α-alumina. Furthermore, in order to simulate the formation of liquid bridges derived from the melting of one of the phases and to verify the role of capillary forces on the flow properties of bulk solids at high temperature, a sample of glass beads was mixed with some (1 % of the total weight) high- density polyethylene (HDPE) which has a relatively low melting point. The results showed that there was no significant effect of the temperature in the range 20–500 °C on the shear flow of the FCC powder, fly ashes, corundum powder and alumina. On the other hand, a small but significant increase of cohesion and, therefore, of the unconfined yield strength was observed with temperature for glass beads.

More recently, Chirone et al. (2015) used the high- temperature annular shear cell developed by Tomasetta et al (2013) to characterize the flow properties of five ceramic powder samples with different particle size distributions between ambient temperature and 500 °C. Moreover, a model based on the multiscale approach proposed by Rumpf (1970) and Molerus (1975) was used to predict the effect of temperature on the tensile strength of the powder samples. They observed a significant increase of powder cohesion at 500 °C for different cuts of the same powder with a particle size larger than 20 μm. This resulted in a lower flowability of the samples. Thermal analysis on the powder samples revealed that the temperature effect on the powder flow properties was only due to van der Waals’ forces.

5.2 Fluid bed viscosity

Particles fluidized by a gas can be treated as a continuum at length scales much larger than the particle diameter. The rheology of such a continuum results from a cumulative effect of microscopic (at length scale of the particles) forces due to the interaction between particles, such as Van der Waals’, capillary or electrostatic forces and hydrodynamic drag forces. Rheological properties, in the form of flow constitutive equations, are thus an essential component of the averaged continuum equations for determining the flow of fluidized particles.

Fluid bed viscosity represents an extremely attractive parameter to characterise fluid bed behaviour, but unfortunately the results obtained in many of the works available in literature are not consistent at all with each other, as reported by Newton et al. (1999). Newton et al. reviewed the results of the available studies and reported that different orders of magnitude for the bed viscosity were obtained using the various methods.

It should be noted that the viscosity is influenced by the shape of the particles, the voidage of the bed, the fluidizing velocity and the fluidizing gas viscosity.

Moreover, according to Rietema (1991), making measurements in a freely bubbling bed is pointless because when a bubble collides with the measuring device the shear stress will locally approach zero. Therefore, only the measurement of the viscosity of the dense phase seems to be meaningful.

Various measuring devices have been employed to determine the viscosity of powders. Conventional-type viscometers are those where the material is sheared by a rotating element (Stormer, Brookfield and Couette) and the resistance to the rotation is measured. Other methods are the floating and falling ball and the torsion pendulum. In the method developed by Grace (1970), measurement of the shape of rising bubbles is used to indirectly calculate the bed viscosity. All these methods are in some ways “intrusive”, as an external object is immersed in the bed in all cases. An indirect method is the quasi-solid emulsion viscosity method developed by Kono et al. (2002), where the viscosity is measured indirectly through the measurement of fluidization parameters.

Whether a fluidized bed has to be considered a Newtonian or a non-Newtonian fluid is also a controversial question. In the early studies of gas-fluidized-bed rheology, an implicit assumption was that the fluidized beds behave as a Newtonian fluid (Matheson et al., 1949; Kramers, 1951; Diekman and Forsythe, 1953; Furukawa and Ohmae, 1958; Shuster and Haas, 1960; Daniels, 1965). Kai et al. (1991) also assumed Newtonian behaviour for the fluidized bed that they modelled. Others authors, however, described fluidized beds using a non-Newtonian visco-plastic model, in particular a Bingham fluid model (Anjaneyulu and Khakhar, 1995; Zhao and Wei, 2000).

Gibilaro et al. (2007) and Colafigli et al. (2009) also reported on the apparent viscosity of a fluidized bed and they proposed theoretical models and experimental analysis in order to evaluate such a property on the base of the analogy between fluidized beds and fluids.

In the next section, we discuss the relationship between the rheological properties of powders and the corresponding fluidization behaviour in the attempt to interpret and quantify the effect of the interparticle forces on fluidized powders.

6. Link between rheological measurements and fluidization

As shown in the previous section, a great deal of research work has been carried out towards understanding the powder rheology. Establishing a relationship between the rheological properties of powders and the corresponding fluidization behaviour is reviewed in this section.

Reiling (1992) explored the link between the apparent viscosities of fine catalyst powders and the bubble size. In particular, he studied the effects on viscosity of adding ultrafine silica cuts to the bed of catalyst, using a Brookfield paddle viscometer. Reiling (1992) questioned the validity of the instability/wave perturbation theory, according to which low-viscosity and low-density fluid beds should promote the suppression or destruction of large bubbles and thus contain smaller bubbles than beds of high viscosity or high density (Rice and Wilhelm, 1958; Romero and Johanson, 1962). The experimental data reported by the author did not support this conclusion. The addition of ultrafine silica had a large effect on the dense-phase voidage but only a small effect on the viscosity of the fluidized bed. Therefore, Reiling (1992) concluded that the link between bubble size and apparent viscosity is not supported by a viscous mechanism.

Newton et al. (1999) also tried to relate the bubble size and bubble number to the bed viscosity. They used a ball dropping technique in order to measure the viscosity of a bed of Geldart group B polymer powder with increasing temperature (17–96 °C). The authors reported that the effect of increasing temperature on the polymer cohesiveness and stickiness was demonstrated by the significant changes observed on the mean bubble size and number of bubbles. However, the viscosities measured through the ball dropping technique did not show dramatic changes with increasing temperature. Newton et al. (1999), in line with the findings of Reiling (1992), concluded that viscosity effects do not explain bubble sizes in the case of the tested powder and that they could not assign a viscosity to the dense phase.

Kai et al. (1991) related the apparent bed viscosity to the bubble diameter and to pressure fluctuation measurements. The authors, in disagreement with Reiling (1992) and Newton et al. (1999), found that the bubble diameter increased with increasing viscosity. They also carried out experiments with increasing temperature, but they did not clearly state what trend they found for the apparent viscosity with such a parameter. However, they showed that the experimental data for the bubble diameter and the viscosity at high temperatures followed the same relationship found at ambient temperature. They obtained similar results by plotting experimental data obtained at high pressure by Weimer and Quarderer (1985). The authors also proposed an empirical correlation to predict the variation of apparent bed viscosity with operating temperature.

Khoe et al. (1991) analysed the fluidization and the rheological behaviour of sets of powders differing in PSD and fines content. According to the method described by Molerus (1975, 1978), they used shear tests measurements and experimental values of ε_mf and mean particle diameter d_sv to derive an expression for the average adhesive force per contact, F. The method assumes each powder to be a semi-continuum and derives the average tensile strength, from which the average F value at the contact points between monosized particles of diameter d_sv is calculated. Khoe et al. (1991) found that the adhesive force per contact, F, correlated very well with the ratio (ε_mb-ε_mf)/ε_mf obtained from experiments. In particular, they found that F increases when the maximum dense-phase expansion increases. The authors used the F values obtained from the shear cell measurements to also question the commonly accepted assumption that at the minimum bubbling velocity, the average adhesive forces counterbalance the overall hydrodynamic forces. They developed a model to calculate a theoretical ΔF which would be needed to reach the minimum bubbling without expanding the bed, and compared it with the measured values of F. They found that ΔF << F and thus they stated that the energy needed to reach minimum bubbling without expanding the bed is much smaller than the average interparticle bond strength. Khoe et al. (1991) also concluded that vertically elongated microcavities are responsible for a premature weakening of the bed structure, allowing bubbling to start at a much lower value of the hydrodynamic force than F. This result was in agreement with findings of Donsì and Massimilla (1973), who also observed cavities and microchannels in the homogeneous expansion of Geldart group A powders.

Kono et al. (1994) performed several fluidization tests on powders differing in size, shape, density, chemical properties and surface characteristics, but all fluidizable and free from any agglomeration or segregation phenomenon. They used spent FCC, glass beads, carbon black and various starch powders with sizes ranging from 15 to 70 μm. For each powder, the fracture strength σ_f and the plastic deformation Y were evaluated at ambient temperature and, for the FCC experiments, were calculated at temperatures up to 500 °C as well. The authors proposed a correlation between Y and σ_f:   

$${\sigma }_{\text{f}}=0.11\hspace{0.17em}\hspace{0.17em}{Y}^{0.90}$$(23)

which held true for all the experimental data, regardless of the type of powder, properties or operating temperature. Kono et al. (1994) interpreted this line as a flow characteristic line, where all powders characterized by smooth fluidization should fall. This idea was supported by the fact that when powders forming agglomerates were fluidized or wall effects were significant, the rheological parameters could not be related using Eqn. 23. Furthermore, a qualitative correspondence was found between the measured rheological parameters and the observed fluidization behaviour. The smaller the values of Y and/or σ_f,mb, the larger the expansion of the dense phase at u_mb, and the smaller the values of bubble size in freely fluidized beds observed in a 2D fluidized bed. Therefore, moving along the linear relationship given by Eqn. 23, it was possible to predict different degrees of flowability among fluidizable powders. In particular, the points obtained with increasing temperature systematically shifted along the line towards the small values of the rheological parameters, which was in agreement with the widely reported positive effect of temperature on the fluidization behaviour of free-flowing materials (Lettieri, 1999).

Quintanilla et al. (2001) investigated the correlation between bulk stresses and adhesion forces in fine powders. They presented measurements of the tensile strength as a function of the consolidation stress for a set of fine cohesive powders (i.e. xerographic toners) of 12.7 µm particle size and with a range of concentration of submicron fumed silica as a flow control additive. Castellanos et al. (2002) investigated the dynamics of fine cohesive powders inside rotating drums with the aim of studying the transition from rigid-plastic flow to gas-fluidized regime. They performed experimental measurements on the bed expansion as a function of the rotation velocity, using drums of different diameters and fine powders of different cohesiveness. They demonstrated that the onset of fluidization in the rotating drum is determined by the ratio of the powder kinetic energy per unit volume to its tensile strength, and that once the powder is completely fluidized, the average interstitial gas velocity increases proportionally to the rotation velocity. Subsequently, Castellanos et al. (2004) presented the so-called Sevilla Powder Tester (SPT), a 4.45-cm diameter, 17-cm high cylinder placed on a shaker to help fluidization of cohesive materials. The SPT showed the interdependence between the consolidation stresses, the tensile yield stress and the particle volume fraction for powders with different levels of surface additives which were used to vary the powders’ degree of flowability.

Bruni and co-workers (Bruni, 2005; Bruni et al., 2004, 2005, 2007a, 2007b) investigated the effects of adding different fines cuts on the fluidization and the rheological behaviour of an alumina powder. To this end, they followed a twofold approach to establish a link between the two aspects of the work. On the one hand, the fluidization behaviour of the alumina was studied at process temperatures ranging from ambient to 400 °C and by adding two fine sub-cuts of nominal size 0–25 and 26–45 μm, respectively (discussed in Section 5 of this paper), to the material previously deprived of fines. Fluidization experiments were carried out, changing the total fines content from 22 % to 30 % by weight. On the other hand, a new mechanically stirred fluid-bed rheometer (the msFBR, 15 cm in diameter and 30 cm tall) was designed, built and commissioned at ambient temperature to determine the rheological behaviour of the powders containing different fines sub-cuts (Bruni et al., 2005). The rheological experiments were carried out at different rates of aeration and impeller depths (Figs. 9–10).

Fig. 9

Effect of impeller depth (ID) on torque—alumina containing fines sub-cut 26–45 μm. Reprinted with permission from Ref. (Bruni, 2005). Copyright: (2005) Ph.D. Thesis, University College London.

Fig. 10

Effect of aeration rate (Δp/Δp_c) on torque—alumina containing fines sub-cut 26–45 μm. Reprinted with permission from Ref. (Bruni, 2005). Copyright: (2005) Ph.D. Thesis, University College London.

In parallel, the failure properties of the materials were also determined using a modified Peschl shear cell (Bruni et al., 2007a). A model was developed based on the failure properties of the materials to determine the stress distribution corresponding to any given rate of aeration in the msFBR (Bruni et al., 2007b). This allowed a true comparison to be made between the rheological behaviour of different powders, aiding assessment of the effect of the fines size distribution on powder rheology. Moreover, the model allowed prediction of the torque measured with the msFBR and assessment of the effect of aeration on powder rheology.

The interpretation of the failure properties of the materials provided an indication of the capability of the powders to flow and underpinned the link between the fluidization and the rheological behaviour below the minimum fluidization conditions, interpreted as the capability of the powders to fail under a certain load and their capability to attain fluidization.

In particular, for all materials tested, measurements of the torque at different impeller depths and different levels of aeration showed that the torque reaches a plateau (see Fig. 9), similar to a normal stress profile in silos (Janssen, 1895).

The effect of increasing the aeration rate was to linearly decrease the torque needed to stir the materials. These trends were explained considering that the stress distribution in the bed changes with changing aeration, as shown in Fig. 10. Thus, at a constant impeller depth and when the aeration rate is increased, the normal load on the impeller will decrease due to the additional upward drag force exerted by the gas on the powder. This reduces the apparent gravity and reduces the local state of stress that is responsible for the measured torque. On the basis of the above results, Bruni et al. (2007b) developed a model to estimate the state of stress by varying the impeller depth, following Janssen’s approach and Janssen’s analysis for silo design, which was modified to take the aeration of the bed and the possible cohesiveness of the material into account.

The model uses properties such as the dynamic and the wall yield loci of the powders used, which were estimated with a Peschl shear cell modified for small loads. The comparison between the experimental and predicted values for the torque demonstrated that the torque is defined by the plastic deformation of the powders and can be explained within a simple Mohr-Coulomb approach to powder flow.

Bruni et al. (2007a) highlighted significant differences in the rheological behaviour of the alumina sample containing the small fines sub-cut (0–25 μm) compared to the sample containing the same amount of bigger fines (26–45 μm) or to the sample that was virtually free of fines.

Under the same normal load, the torque needed to stir the alumina sample containing the small fines sub-cut was found to be higher than the torque needed to stir the sample containing the larger fines sub-cut or the sample that was free of fines. In other words, the presence of small fines increases the powder’s resistance to flow. In Fig. 11, a comparison is also shown with glass ballotini (fines-free) requiring the least torque. These results were found to be in agreement also with the results obtained for the voidage of the settled bed, the voidage of the bed at the minimum fluidization velocity, and the expansion and deaeration tests. The alumina containing the smaller fines sub-cut was arranged in a more compacted packing when settled and at the minimum fluidization compared to the alumina sample containing the same amount of bigger fines.

Fig. 11

Experimental torque vs calculated normal stress σ_z at impeller depth for all materials. Reprinted with permission from Ref. (Bruni et al., 2007b). Copyright: (2007) Elsevier Limited.

It also exhibited a more pronounced change in slope during bed expansion, which was interpreted as a weakening of the bed structure before the onset of bubbling.

More recently, Tomasetta et al. (2012) re-examined the model developed by Bruni et al. (2007b) and performed a sensitivity analysis on the wall failure properties and on some of the original model assumptions regarding the active and passive state of stress in the fluid-bed rheometer. Tomasetta et al. (2012) also proposed a novel procedure for the inverse application of the model developed by Bruni et al. (2007b), such that the powder flow properties could be estimated starting from the torque measurements. The application of this procedure provided good results in terms of effective angle of internal friction and was deemed promising for the ability of the system to explore powder flow at very low consolidation states.

7. Conclusions

This review has demonstrated the important role that process conditions, namely temperature, fines and fines distribution, play on the fluidization behaviour of gas-solids fluidized beds.

Process conditions influence fundamental parameters describing the minimum fluidization conditions, bed expansion and contraction, and the transition from particulate to bubbling fluidization.

Analysis of the influence of elevated temperatures on fluidization highlights the enhanced role that the interparticle forces can play on the fluidization quality over the hydrodynamic forces.

The review on the influence of adding fines to the fluid bed and the role played by the particle size distribution and distribution of the fines emphasized the need for a quantification of the effects of the interparticle forces.

To this end, the multidisciplinary approach based on linking rheology and fluidization is encouraging. Further work is, however, needed; the challenge lies in the difficulty to relate the different rheological measurements to fluidization, mostly due to the variety of techniques employed, which makes standardisation of rheological tests very difficult.

A more systematic assessment of the independent and the combined effects of process conditions on fluid bed rheology and fluidization still needs to be accomplished.

Nomenclature

Ar

Archimedes number (—)

d_p

Particle diameter (m)

E_MR

Elasticity modulus (N m⁻²)

g

Gravitational acceleration (m s⁻²)

HDFs

Hydrodynamic forces

IPFs

Interparticle forces

n

Richardson-Zaki exponent

PSD

Particle size distribution

Re

Reynolds number (—)

Re_mf

Reynolds number at minimum fluidization (—)

T

Temperature (°C)

u

Superficial velocity (m s⁻¹)

u_mb

Minimum bubbling velocity (m s⁻¹)

u_mf

Minimum fluidization velocity (m s⁻¹)

u_t

Terminal fall velocity (m s⁻¹)

Y

Plastic deformation coefficient (Pa)

Δp

Pressure drop (Pa)

Δp_c

Calculated pressure drop (Pa)

Δp_m

Measured pressure drop (Pa)

ε

Bed voidage (—)

ε₀

Fixed bed voidage (—)

ε_d

Dense-phase voidage (—)

ε_mb

Minimum bubbling voidage (—)

ε_mf

Minimum fluidization voidage (—)

µ

Viscosity (Pa s)

µ_g

Gas Viscosity (Pa s)

ρ_BDL

Bulk density loose (kg m⁻³)

ρ_BDP

Bulk density packed (kg m⁻³)

ρ_g

Gas density (kg m⁻³)

ρ_p

Solids density (kg m⁻³)

σ_f

Fracture strength of powder structure (Pa)

σ_z

Calculated Normal stress (Pa)

ϕ

Shape factor (—)

Author’s short biography

Paola Lettieri

Paola Lettieri FIChemE is a professor of chemical engineering at the University College London and head of the Fluidization Research Group. She has 20 years experience in particle technology and fluidization with applications spanning across the chemical, petrochemical, nuclear and energy-from-waste sectors. Her research focuses on the effect of process conditions on fluidization, encompassing experimental studies, mathematical modelling, rheology, X-ray imaging and reactor design. She has published 150 refereed articles and 6 book chapters, and has been awarded two prestigious fellowships from the Royal Academy of Engineering for her work in fluidization.

Domenico Macrí

Domenico Macrí is currently a PhD student in chemical engineering at the University College London. He received his Master’s degree in chemical engineering from the University of Calabria in 2014. His main research interests focus on the effect of temperature on the defluidization of industrial reactive powders.

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