Experimental Investigation on Transport Characteristics of Fluidized

Jun 2, 2016 - Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States. Ind. Eng. Chem...
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Experimental Investigation on Transport Characteristics of Fluidized Geldart A/B Particles in a Geldart D Packed Bed Pengfei He, Alan Wang, and Liang-Shih Fan* Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States ABSTRACT: Redox reactions between fine solid fuels, such as pulverized coal powder, and coarse oxygen carrier particles can be carried out in a fixed/moving bed reactor chemical looping system. The migration pattern of the solid fuel powder and its contact time with coarse particles can significantly affect the reaction rate and the product yield. A number of challenges exist in transporting/mixing of fuel powder and in removing noncombustible waste (e.g., coal ash) from the reactor vessel in the chemical looping operation. Thus, it is important to understand the hydrodynamic behaviors of fine particles in such situations. This study describes an experimental approach that examines migration characteristics of fine particles (Geldart A/B), in both spatial and temporal aspects, in a packed bed of coarse particles (Geldart D). The experimental variables include the particle size distribution of the fine powder, the fine to coarse mass ratio, and flow conditions. At a given upward aeration flow within the range that is higher than the terminal velocity of the fine particles but lower than the minimum fluidization velocity of coarse particles (Ut < Us < Umf,c), the fine particles may travel both upward and downward depending on the gas flow rate and the physical properties of particles and gas. The spatial transport pattern in terms of the upward and static transport partition (wt %) of Geldart A particles can be characterized as an exponential function of a group of dimensionless numbers (e.g., Stk*, Rep* and Us/Ut). The time-dependent upward transport rate of fine particles is measured to determine the temporal migration characteristics. Cluster response time (τc) is introduced to describe how fast a cluster of fine particles in a packed bed respond to the ambient flow. This parameter is normalized by the response time of fine particle (τp) and further correlated with the pseudo-particle Reynolds number (Rep*) via an inverse power function with two coefficients.

1. INTRODUCTION The disparately sized solid−solid redox reactions in a multiphase reactor have important applications in many industrial processes, including the catalytic conversion of solid carbonaceous fuels (e.g., coal direct chemical looping process, blast furnace of steelmaking process, catalytic oxidation− dehydrogenation of butene to butadiene process, etc.).1−7 These processes typically involve complex mixing and transport phenomena of pulverized solid fuel particles through a packed/ moving bed consisting of coarse catalyst material.8 The coal direct chemical looping (CDCL) process developed at The Ohio State University (OSU) is one such example of a novel thermochemical process that converts coal to other valuable products via cyclic redox reactions.9 The migration and dispersion characteristic of pulverized coal in the moving bed of coarse oxygen carrier particles is imperative to the overall system stability and the carbon conversion. Because of the differences in their particle size distribution and density, the hydrodynamic properties of the pulverized coal powder and the oxygen carrier particle vary significantly, thus providing an interesting research topic with regard to the transport of fine particles species in the binary mixture. As illustrated in Figure 1, the solid fuel (coal) powders are injected into the reducer reactor packed with coarse oxygen carrier particles.10 The coal powders gradually permeate and transport over the entire bed © 2016 American Chemical Society

Figure 1. Schematic diagram of coal direct chemical looping (CDCL) system.

driven by the combination of the gravitation, drag (from enhancer gas flow), and collision (interaction with packed oxygen carrier particles) forces. Upon heating, the coal powders start to release volatile matter and react with the oxygen carrier particles. The evolution of gaseous products (volatile, CO, Received: Revised: Accepted: Published: 6866

January 26, 2016 May 3, 2016 June 2, 2016 June 2, 2016 DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874

Article

Industrial & Engineering Chemistry Research

2. EXPERIMENTS The proposed experiment aims to investigate the spatial and temporal hydrodynamic transport characteristics of the fluidized fine particles in a fixed bed of coarse particles. The schematic diagram of the experimental apparatus is shown in Figure 2. The system consists of a cylindrical fixed bed column,

CO2, etc.) shrinks the coal particles as they continue to migrate through the packed bed reactor. The system should be designed in a way that there is sufficient contact time between pulverized coal and oxygen carrier particles in the reducer reactor (i.e., fuel solids residence time) for complete coal conversion in the presence of enhancer gas flow. To achieve a balance between stable hydrodynamics and sufficient reaction conversion in the reducer reactor, it is essential to understand the transport pattern of the fuel solids (fine particles) in the packed bed of coarse particles. The transport pattern may relate to the fine particle and gas properties, the flow rate, and solid packing conditions, yet there lacks such knowledge that can quantitatively describe the spatial and temporal distribution of fuel solids migration based on those information. The transport characteristics of gas−solid (fine particles) flow through a bed of coarse particles have been investigated by a number of researchers both experimentally and numerically.6,11−19 Most of these studies focus on the relationship between hydrodynamics (i.e., pressure drop over the bed, gas− solid mass flux) and the physical properties of the fine particles as well as the steady state permeability of the bed under either concurrent or countercurrent granular flow.11,12,20,21 In higher flow regime (coarse particles fluidized), Fan et al. experimentally investigated the hydrodynamic characteristics (Umf, Ut, fine particle hold-up) of the multisolid turbulent bed (MSTB) system.22−25 Applications of computational fluid dynamic (CFD) methods have advanced the understanding of the mixing behavior of such fully fluidized binary mixture particulates systems.26−28 In the lower flow regime (coarse particles packed), Nemec et al. reported that the migration of fine particles is subjected to diffusional resistance from the relative permeability in the packed bed (or “solid-phase friction factor”,14 i.e., packing density or void fraction of packed bed of coarse particles).11,12 The diffusion rate may depend on the gas phase flow conditions described by the Reynolds number as well as the relative particle properties, such as the particle shape, density, and size.11,12 Other studies13,16,17,29−31 suggested that the relative particle size, the extent of cluster formation, and the local void fraction of the packed bed are closely related to the migration and transport of fine particles through the packed bed of staggered particles. The mass ratio of coarse to fine particles shall be considered according to Nastui et al., because stagnate fine cluster formation can be observed at the bottom of the packed bed when this ratio is sufficiently low.15 Although many efforts have been exerted on the fine particle migration characteristics at steady state conditions, few have developed a quantitative correlation to relate the spatial and temporal (especially in transient condition) migration pattern to the flow condition and properties of gas and particles in the lower flow regime. In summary, the proposed experimental approach examines the spatial and temporal migration characteristics of fine particles in a packed bed of coarse particles with upward aeration flow. The flow regime relevant for the current work falls between the minimum fluidization velocity of coarse particle and the terminal velocity of fine particles. Three different types of fine particles (categorized as Geldart group A/B) are tested in a packed bed consisting of millimeter sized glass beads (Geldart D) in over 50 trials covering various flow rates and fine-to-coarse (FTC) mass ratios. The analysis of experimental data results in empirical correlations that describe the spatial and temporal transport pattern of fine particles.

Figure 2. Schematic diagram of experiment setup.

a cyclone separator to capture the entrained fine particles, and two reservoirs to collect the settled particles. The entire apparatus is made of transparent plexi-glass for better visual observation. The solid charge in the main column, consisting a mixture of fine and coarse particles, rests on a mesh plate distributor above the windbox that allows passage of only the fluidization gas and settled fine particles. The solid charge contains three discrete layers prior to each run. A mixture of fine and coarse particles constitutes the middle layer, whereas coarse particles make up the top and bottom layers. The top and bottom layers serve as transition sections to minimize the boundary effect during the migration of fine particles. The thickness of the transition layers is at least the same order of magnitude as the mixture layer. Larger thickness of the transition sections shows barely different results based on our attempts on several cases. The fluidization gas enters the windbox between the distributor and the lower solid reservoir, then transports the fine particles upward and/or downward. Fine particles migrating downward are collected in the lower reservoir, whereas those moving upward are captured in the upper reservoir. A copper wire is twined around the column and attached to a grounding source to eliminate the effect of static charge build-up along the wall. A tape ruler, attached to the upper reservoir, measures the solid height with respect to time, which was recorded using a video camera. Knowing the total weight collected in the upper reservoir, the transient accumulated weight can be calculated proportionally based on the transient solid height. The pressure of the fluidization gas is regulated to maintain steady flow to the rotameter. The gas is conditioned by removing its moisture, oil, and particulate components. Note that the fluidization gas flow in the test range is higher than the terminal velocity of fine particles, but lower than the minimum fluidization velocity of coarse particles. Under this condition, the fine particles are to be fluidized and transported without displacing the coarse particles. 6867

DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874

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Industrial & Engineering Chemistry Research Table 1. Physical and Chemical Properties of Solid Material iron I chemical composition (wt %)

>97.7% Fe

iron II

silica sand

glass beads

>99.5% Fe 99.5% SiO2 0.157% Al2O3

particle size distribution (μm)

bulk density (g/cm3) particle density (g/cm3) terminal velocity (m/s) a

dp < 44 (97.5%) 44 < dp < 74 (2.4%) 75 < dp < 150 (0.1%) 1.98 7.8 0.29

dp < 45 (30.5%) 45 < dp < 75 (37%) 75 < dp < 106 (22%) 106 < dp < 212 (10.5%) 2.52 7.8 1.16

dp < 74 (21.1%) 74 < dp < 105 (32.8%) 105 < dp < 149 (31.8%) 149 < dp (14.3%) 1.37 2.65 0.88

65−75% SiO2 0−5% Al2O3 6−15% CaO 10−20% Na2O 1500 < dp < 2000

1.3 2.5 2.36a

The minimum fluidization velocity of glass beads, accounted by bed voidage (Umf,c/ε).

Specific sized coarse and fine particles are selected according to the proposed experimental methodology. The packed bed coarse solid charge consists of spherical glass beads (Mo-Sci Corp GL0191SB, 1.5−2.0 mm), classified as Geldart Group D particles.32,33 Three types of fine particles are selected: (1) iron I powder (Geldart Group A); (2) iron II powder (Geldart Group B); (3) silica sand (Geldart Group A). The minimum fluidization velocity of selected glass beads is orders of magnitude higher than that of the fine particles, which will ensure the coarse particles stay packed during the fluidization of fine particles. Detailed physical properties of the particles and the dimensions of the packed bed column are listed in Tables 1 and 2, respectively. The collection efficiency of cyclone is over 99% for the fine particles used in this experiment.

3. RESULTS AND DISCUSSION The proposed one-dimensional experimental approach aims to study the transport characteristics, specifically the spatial and temporal transport pattern, of fluidized fine particles through a packed bed of coarse particles under aeration. The typical fine particle migration pattern given upward aeration is illustrated in Figure 3. The fine particles are distributed in the interstitial

Table 2. Other Geometric and Operational Parameters in Current Apparatus column inner diameter total bed height fine-coarse mixture layer height distributor mesh size

4 in. 12 in. 2 in. 16 × 16 (1.2 mm × 1.2 mm)

Figure 3. Typical fine particles migration pattern with upward aeration.

With each type of fine particle, the test matrix covers three fine-to-coarse (FTC) mass ratios and various gas flow rates. The FTC ratios in this study are set as 0.01, 0.02, and 0.04, respectively, with same weight of glass beads (4 kg) for each case. There are in total more than 50 cases are tested in this work. For each case, the solids collected in both upper and lower reservoirs are weighed, respectively. The upward migration rate, indicated by the particle entrained rate, is measured in a manner of the transient height of settled particles in the upper reservoir. The test is terminated when the solids level in the upper reservoir becomes constant for at least 2−3 min. At last, the amount of fine particles remaining in the column is quantified by elutriation. All obtained data information are further analyzed and discussed in next section. It is noted that replicated tests are attempted to quantify random error of the experimental method. The results indicate a quite acceptable error for static transport (overall less than 6%). The error for upward transport at higher gas flow (≥8 SCFM) is less than 2%, and it can reach up to 10% at a lower gas flow (6 SCFM, close to the terminal velocity of fine particles), which is still acceptable. This error can be narrowed down by limiting the upward transport distance above the bed surface and the pipe size in the future design.

space among coarse particles in the mixture layer prior to aeration. The flow of fluidization gas breaks the static equilibrium by introducing drag force to the fine particles as well as the collision force from the fine−fine particles and fine− coarse particles interactions. The irregular gas phase flow in the interstitial spaces creates additional complexity and unpredictability to the collision forces. With the combined drag, collision, and gravitation forces, the fine particles spread and migrate toward the adjacent interspaces. From the experimental results, the spatial migration pattern can be upward (direction of gas flow), downward (direction of gravity), or bidirectional at the same time, depending on the flow conditions and the properties of the gas and fine particle. For instance, in the drag force dominant flow range, fine particles are more likely to migrate upward; whereas in the flow range with balanced drag and collision forces, the gravitation effect may lead to downward migration. On the temporal aspect, the pattern of migration may refer to the timedependent transport of the fine particles or the time required for clusters of fine particles to respond to the gas flow. The quantitative analysis on the spatial and temporal pattern of fine particle migration are discussed separately in the following subsections. 6868

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Figure 4. Sample weight partition distributions (FTC = 0.01): (a) iron I; (b) iron II; (c) silica sand.

3.1. Spatial Transport Pattern Analysis. Physically, there exists three possible migration patterns for fine particles: (1) upward transport (Yu, collected by a cyclone in the upper reservoir), (2) downward transport (Yd, collected in the lower reservoir), and (3) static transport (Ys, remain in the packed bed). The summation of the three weight partitions is constrained by Yu + Yd + Ys = 1

at about 2−3Ut to initiate upward transport and at 8Ut to complete. This trapping phenomenon (in a bed of smaller particles than larger particles) can be described by the deep bed filtration theory, which reports that smaller-sized fine particles (with size of 10 μm) may have higher collection efficiency due to significant Brownian diffusion effect.34,35 Overall speaking, with the increase of gas flow (within the range of Ut < Us < Umf,c), upward transport partition will increase and static transport partition will decrease accordingly. From Figure 5a, the upward transport partitions of both iron I or silica sand particles reach over 97% as the gas flow approaches the minimum fluidization velocity of coarse particles (i.e., Umf,c), whereas about 80% for iron II particles. The static transport partitions of all particles accordingly descend relative to the superficial gas velocity, as illustrated in Figure 5b. Less than 5% of all particles stay in the column when the gas flow reaches the upper limit of the flow range (Umf,c). As shown in Figure 5c, both iron I and silica sand exhibit minimal downward transport, whereas the downward transport partition of iron II particles peaks at 50% (for FTC ratio equals 0.02 and 0.04) then descends to around 20% at the upper limit of gas flow. The unique behaviors of the downward transport pattern for iron II particles (Geldart B) at various experimental superficial gas velocities are attributed to the distinct hydrodynamic properties of particles (e.g., size and density). Because of the relatively wide size distribution of iron II in this study, the given gas flow rate that just beyond its terminal velocity, which calculated from the mean particle size, may not exceed the terminal velocity of the portion with larger size. Thus, a considerable amount of locally fluidized larger fine particles might remain trapped and even transport downward at such flow range (Ut, mean < Us < Ut, large). To prove this, size distribution of collected particles is obtained once the experiment is completed. In the sample case of iron II at 8 cfm, more than 54% of upward transport particles are below the size of 53 μm, while 97% of downward transport particles are over 53 μm. Interestingly, despite the wide size distribution of silica sand, it barely transports downward. The higher density of iron II particles relative to silica sand can translate to a longer

(1)

Figure 4 shows the sample weight partition distribution against the superficial velocity of iron I, iron II, and silica sand at the FTC of 0.01. All three particles show a similar increasing trend with respect to the superficial velocity for upward transport partition, and a decreasing trend for static transport partition. Specifically, at higher gas flow rates, a greater portion of fine particles migrate upward due to the increased momentum of drag force. There is an unneglectable portion of iron II (Geldart B) moving downward, whereas very limited portion of iron I and silica sand (Geldart A) migrating against the gas flow. The similar pattern of partition distribution exists at other tested FTC mass ratios (0.02 and 0.04). Note that here the definition of the superficial velocity of fine particles accounts for the bed voidage: Us =

4Q πD 2 · ε

(2)

Here the voidage of the packed bed of coarse particles, ε, is assumed to be a constant (0.63) considering the relatively small FTC ratio. The weight partition distribution, illustrated in Figure 5, parts a, b, and c, are plotted along the ratio of the superficial gas velocity and the terminal velocity of the fine particles (Us/Ut). The terminal velocity is calculated and listed in Table 1. Figure 5a compares the upward transport weight partition distribution of the three tested particles (at various FTCs). Similarly, Figure 5 parts b and c compares the static transport partition and downward transport partition, respectively. In the case of iron II and silica sand particles, transport upward can be completed at two times the terminal velocities of fine particles. In comparison, iron I (smaller size) particles require gas velocities 6869

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Industrial & Engineering Chemistry Research

opposite with respect to the static partition. In conclusion, the variation in the FTC ratios from 0.01 to 0.04 resulted in minimal changes in their transport weight partitions for all types of particles as shown in Figure 5 panels a, b, and c. On the basis of the experimental results of both iron I and silica sand particles (Geldart Group A), we can simplify eq 1 as

∑ Yi = 1,

i = u, s

(3)

Here, i represents the upward or static partition, respectively. Theoretically, the distribution of transport weight partitions (Yi) is determined by the physical properties of the fine particles and the gas, for example, particle size, particle density, gas density, and viscosity; the flow condition which facilitates the migration; as well as the voidage of the packed bed. The aforementioned effects cumulate to a complicated relationship for the transport weight partitions, which can be expressed in general as Yi = f (d p , ρp , ρg , μg , Q , D , ε),

i = u, s

(4)

From the dimensional analysis, these variables can be grouped into several important characteristic parameters, for example, the particle Reynolds number, Stokes number, and the ratio of superficial velocity to the terminal velocity. A more concise variation of eq 4 with simplified variables is proposed as ⎛ U⎞ Yi = f ⎜Stk*, Rep*, s ⎟ , Ut ⎠ ⎝

i = u, s (5)

where Stk* and Rep* are pseudo-particle Stokes number and pseudo-Reynolds number, which are defined as Stk* ≡ and Re*p ≡

ρg d pUs μg

ρp d pUs 18μg

, respectively. Note that instead of the local

relative velocity between the gas and solid phase (|up − ug|) normally being used as the character velocity for particle Reynolds number and Stokes number, here the superficial velocity (Us) is adopted. Equation 5 provides a generic description of the spatial migration pattern of fine particles in a packed bed, yet the formulation is still undetermined. In this study, an exponential function is proposed to correlate the transport partition, I = 1 − exp[−C·(Ts − Ts,c)], Ts ≥ Ts,c

(6)

where C is an undetermined coefficient. The term I on the lefthand side is the fine particle transport index in a packed bed, defined as

Figure 5. (a) Upward transport partition of various types of particles and FTCs. (b) Static transport partition of various types of particles and FTCs. (c) Downward transport partition of various types of particles and FTCs.

I≡

response time, which may also contribute to its downward transport tendency when the fine particles are fluidized. On the other aspect, the effect of the FTC mass ratio on the fine particle transport partition distribution seems inconclusive at the given experimental conditions. For instance, a relative higher FTC of silica sand may lead to a slightly higher static partition but lower upward partition in low gas flow range; however, this effect is reversed when the gas flow approaches Umf,c. On the contrary, a higher FTC for iron I shows a slightly lower static partition but higher upward partition in the low gas flow range, and this effect is gradually extinct when gas flow approaches Umf,c. The effect of the FTC ratio for iron II is similar to silica sand with respect to the upward partition, yet

Yi − Yi ,0 Yi ,e − Yi ,0

, i = u, s (7)

where Yi,0 is the weight partition collected in the upper reservoir (Yu,0) or stay in column (Ys,0) without introducing any gas flow. Obviously, for iron I and silica sand particles, the quantity Yu,0 equals to zero and Ys,0 equals to 1. The term Yi,e is the corresponding weight partition when particles elutriated at the flow rate right at (or slightly smaller than) the minimum fluidization velocity of coarse particle. This quantity is related to the physical properties of both the coarse and fine particles (e.g., size and density) and can be determined experimentally. In this study, the quantity Yu,e is 98%−100% and Ys,e is less than 2% for silica sand and iron I. The transport index, ranging from 0 to 1, represents the transport pattern relative to its limiting 6870

DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874

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Industrial & Engineering Chemistry Research case at elutriative condition. The term Ts on the right-hand side of eq 6 is spatial transport number and defined by a group of dimensionless numbers, Ts ≡

Re*p Us Stk* Ut

FTC ratios and superficial velocities are illustrated in Figure 7 panels a, b, and c, respectively.

(8)

The term Ts,c denotes the critical spatial transport number, served as a criteria for upward transport. The fine particles are only able to transport upward when the spatial transport number reaches beyond its critical value (Ts ≥ Ts,c). In this study, for iron I and silica sand particles, the critical spatial transport number is experimentally determined as 0.24. The transport index is calculated from each case and plotted against the spatial transport number. As shown in Figure 6, the

Figure 6. Normalized transport index as a function of spatial transport number.

profiles of different particles are able to be normalized uniformly, with the coefficient C determined to be 5.14 by fitting the data point by the least-square method. The correlation of upward and static transport partition for iron I and silica sand (Geldart A particles) can be thus determined from the transport index via eqs 6 and 7. In summary, the proposed empirical correlations with determined coefficients are obtained based on experimental results within the flow range between the minimum fluidization velocities of coarse particle and the terminal velocity of fine particle (or Ts,c ≤ Ts ≤ 1 in this work). Note that the effect of the surface properties (e.g., surface roughness, elasticity) of coarse particles is beyond the scope of this study, thus additional caution may be necessary to apply this correlation when the coarse particles are completely different from the ones used in this work. 3.2. Temporal Transport Pattern Analysis. As described in the experimental section, the temporal transport pattern corresponds to the transient accumulation weight of fine particles in the upper reservoir (mu(t)), which may be affected by different particles, gas flow rate, and FTC ratios. For the purpose of cross comparison with different cases, the dimensionless weight is defined as m u − m u, ∞ m u*(t ) = m u,0 − m u, ∞ (9)

Figure 7. (a) Dimensionless weight collection transient in upper reservoir (iron I). (b) Dimensionless weight collection transient in upper reservoir (iron II). (c) Dimensionless weight collection transient in upper reservoir (silica sand).

Figure 7 panels a, b, and c suggest that fine particles migrate faster at a higher gas flow rate, whereas the effect of FTC mass ratios can be quite subtle. For instance, the results of both iron II and silica sand tests suggest that higher FTC ratio attributes to slower migration rate while the effect of FTC ratio for iron I is inconclusive. In general, the effect of the FTC ratio (from 0.01 to 0.04) is limited comparing to the gas flow rate.

where mu,0 is the initial collection amount (mu,0 = 0), and mu,∞ represents the ultimate collection weight (i.e., the asymptotic value given infinite time). Sample results which show the transient migration of iron I, iron II, and silica sand with various 6871

DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874

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Industrial & Engineering Chemistry Research The quantitative description of the temporal migration pattern of the fine particles requires the determination of a parameter that physically evaluates the transport time. Here, an exponential function describing the transient profiles of the dimensionless accumulation weight is proposed, ⎛ t⎞ m u* = exp⎜ − ⎟ ⎝ τc ⎠

τp ≡

ρp d p2 18μg

Equation 12 provides a generic description on the temporal respects of fine particles migration in a packed bed, yet the exact correlation is undetermined. In this study, an inverse power function with two undetermined coefficients is proposed to correlate the cluster response time, τc = ATt−B τp (13)

(10)

where τc, named cluster response time, is defined as the characteristic time of the cluster response to the ambient flow in a packed bed at the given flow condition. This quantity can be determined by curve fitting each data points set in Figure 7a,b,c via the linear least-square method. In turn, the exponential assumption is supported by the linearity of each data set. Figure 8 illustrates the cluster response time of three different particles with the respect to the ratio of the superficial

where the term Tt is temporal transport number and defined by a group of dimensionless numbers ⎛ Re * U ⎞−0.5 p s⎟ *2 Tt ≡ ⎜⎜ ⎟ (Rep ) * Stk U t⎠ ⎝

(14)

The cluster response time of various particles can be normalized by plotting the ratio of cluster response time to particle response time (τc /τp) with respect to temporal transport number, as shown in Figure 9. The coefficients, A and B, are found to be e15.05 and 1.35 respectively by fitting the data point via the least-square method.

Figure 8. Cluster response time of three different particles.

gas velocity to the terminal velocity of fine particle (Us/Ut). Figure 8 differentiates the flow range for fine particles with exhibited pattern similar to the spatial transport pattern given in Figures 5. The cluster response time ranges from a few seconds at high gas flow rates to a few minutes at low gas flow rates. The inverse relationship between the cluster response time and the superficial velocity within the testing flow range can be observed, whereas FTC mass ratios from 0.01 to 0.04 have marginal and ambiguous effects on their cluster response time for all types of particles. The temporal pattern of fine particle transport profiles shown in Figure 8 varies with respect to the type of particle. A general correlation for the cluster response time is desired for empirical application to various types of particles. Similar to the spatial transport pattern analysis, the response time of the cluster of fine particles in the packed bed condition can be a function of particle and gas properties, flow condition as well as the voidage of the packed bed, τc = f ′(d p , ρp , ρg , μg , ε , Q , D)

Figure 9. Normalized cluster response time with curve fitting correlation.

In summary, the proposed empirical correlation is modeled based on the experiment results within the flow range between the minimum fluidization velocities of coarse particle and the terminal velocity of fine particle (or 50 < Tt < 1500 in this work). It is expected to be generalizable to the transport of various fine particles (Geldart A/B) in a packed bed of coarse particles (Geldart D) within such a flow range. Note that the effect of the surface properties (e.g., surface roughness, elasticity) of coarse particles is beyond the scope of this study, thus additional caution may be necessary when the coarse particles are completely different from the ones used in this work.

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4. CONCLUDING REMARKS This study experimentally examines the spatial and temporal transport characteristics of Geldart A/B particles in a packed bed of Geldart D particles. Several important conclusions can be drawn based on the experimental results and dimensionless analysis: (1) The upward transport partition is proportional to the gas flow rate for all three tested particles. Particles with its size

The dimensional analysis of the variables in eq 11 generates a more concise variation expressed as ⎛ U⎞ τc = f ′⎜τp , Stk*, Rep*, s ⎟ Ut ⎠ ⎝

(12)

where Rep* is pseudo-particle Reynolds number, and τp is the particle response time with the definition of 6872

DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874

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Industrial & Engineering Chemistry Research ρg ρp τc τp

around ∼10 μm (iron I) needs several more times of their terminal velocity than larger fine particles (iron II and silica sand) to be transported upward. Downward transport was only significantly observed for large iron II particles (Geldart B). Empirical correlations describing the transport pattern of iron I and silica sand particles (Geldart A) with respect to the flow and particle characteristics are presented. The spatial transport index is expressed by exponential function of the spatial transport number within the test flow range of Ts,c ≤ Ts ≤ 1. The upward transport criteria is found as Ts ≥ Ts,c, where the critical spatial transport number, Ts,c, is found to be 0.24 for Geldart A particles studied in this work. (2) The cluster response time is introduced to describe the migration of a cluster of fine particles in a packed bed from an initially concentrated static state to the fluidized state at asymptotic concentrations. An inverse power function is empirically expressed for both Geldart A and B to correlate cluster response time with respect to the gas flow in term of temporal transport number within the test flow range of 50 < Tt < 1500.

■

■

density of the gas density of the particle cluster response time particle response time

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would also like to acknowledge the helpful assistance of Dawei Wang, Yaswanth Pottimurthy, and Sam Bayham during the experiments conducted in this study.

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NOMENCLATURE dp diameter of fine particles D diameter of packed bed g acceleration of gravity I index of spatial transport pattern mu weight of fine particles in the upper reservoir m*u dimensionless weight of fine particles in the upper reservoir mu,0 initial weight of fine particles in the upper reservoir mu,∞ final weight of fine particles accumulated in the upper reservoir Q gas volume flow rate Rep* pseudo-particle Reynolds Number Stk* pseudo-particle Stokes Number t time ug local gas velocity up local particle velocity Umf,c minimum fluidization velocity of coarse particle Us superficial velocity Ut terminal velocity of fine particles Yd downward transport weight partition of fine particles Yi upward or static transport weight partition of fine particles Yi,0 upward or static transport weight partition of fine particles without introducing any gas flow Yi,e upward or static transport weight partition of fine particles when elutriated at the minimum fluidization velocity of coarse particle ε voidage of the packed bed μg viscosity of the gas 6873

DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874

Article

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DOI: 10.1021/acs.iecr.6b00377 Ind. Eng. Chem. Res. 2016, 55, 6866−6874