Shortages In Fossil Energy Engineering Essay

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ABSTRACT

The efficiency of contacting between gas and biomass particles in the fluidized beds is dictated to a large extent by the bubble dynamics which impacts on heat (fluid-particle and/or wall-to-bed) and mass transfers and ultimately the quality of biosyngas. Several strategies toward improving the efficiency of fluidized beds have targeted renewal of the bubble surface to interchange fluid between bubbles and interstitial gas in the emulsion phase. Various researchers have realized the significance of bubbles in gas-solid fluidized beds and employed various internals, e.g., baffles, tubes, packings, and inserted bodies, and other configurations to generate evenly distributed smaller-bubbles to improve the quality of fluidization. Their main features and inherited limitations have been thoroughly discussed in the current report. Nowadays, computational fluid dynamics (CFD) simulations have become a viable tool to predict the hydrodynamic properties of multiphase flow systems and many commercial codes are available in this regard. Focusing on CFD simulations of gas-solid fluidization, Eulerian-Eulerian (E-E) and Eulerian-Lagrangian (E-L) models including the kinetic theory of granular flows are used with the aid of some closure models available in the literature. The details of models available in the literature have been mentioned in this report. A new concept to harness bubble dynamics, enhance heat transfer and mixing of biomass particles in the corrugated wall bubbling fluidized bed proposed by our research group has also been described at the end.

Keywords: corrugated-walled bubbling fluidized bed; incipient fluidization; bubbles growth and frequency; heat transfer; mixing and segregation; Euler-Euler simulations.

1-Introduction

Anticipating shortages in fossil energy supplies over the next decades is mobilizing sustained efforts in industry and academia to develop efficient renewable-energy based technologies. Residual (non-edible) biomass, owing to its carbon-neutral appeal in relieving greenhouse gas emissions, is explored as an alternative energy source to put a restraint on fossil-energy reliance. Gasification technology for biomass conversion is being brought into focus to convert residual biomass into bio-fuels or bio-products [ [1] ]. However, significant R&D efforts are still required to come up with innovative gasifier designs. Gasification technology must ideally be bestowed with the following traits: auto/allothermal process, nondiluted biosyngas abolishing downstream N2 separation or upstream O2 enrichment, thermal coupling via micro-segmentation between endothermic and exothermic steps to improve heat exchanges and enhance thermal efficiency, and high yield and heating value of biosyngas. These attributes represent the foremost challenges next-generation biomass steam gasifiers must cope with. With the endeavor of approaching such ideal configuration, Iliuta et al. proposed a reactor concept of allothermal cyclic multicompartment bubbling fluidized beds [ [2] ]. Thermochemical conversion of biomass in periodic time and space sequences of steam biomass gasification and char/biomass combustion was envisioned in which combustion compartments cyclically provide heat into an array of interspersed steam gasification compartments (Fig. 1). This concept could enhance unit heat integration and thermal efficiency while procuring N2-free syngas requiring no addition of oxygen (or air) to steam gasification compartments, nor contact between flue and synthesis gases.

Most of the studies on indirectly heated fluidized-bed gasifiers agreed on the challenging difficulties to achieve allothermicity. These arise mainly because of significant heat losses and poor heat transfer through the walls that separate the combustion and gasification enclosures [ [3] ],[ [4] ],[ [5] ]. While the former concern can be resolved via the numbering-up of micro-segmentation between the endothermic and exothermic enclosures as illustrated in Fig. 2, the latter needs further investigations as it is related to the quality of fluidization. Hence, a further step to move on with such a concept requires information-gathering about cold-prototype hydrodynamic studies to ascertain bubble structure, dynamics and distribution in noncylindrical bubbling fluidization enclosures consisting of flat or corrugated walls for heat transfer enhancement.

The efficiency of contacting between gas and particles in bubbling fluidized beds is dictated to a large extent by the bubble dynamics which impacts on heat (fluid-particle and/or wall-to-bed) and mass transfers [ [6] ],[ [7] ],[ [8] ],[ [9] ],[ [10] ],[ [11] ],[ [12] ],[ [13] ],[ [14] ]. Since bubble breakup and coalescence are directly controlling bubble growth and frequency, and rise velocity [ [15] ],[ [16] ],[ [17] ],[ [18] ],[ [19] ],[ [20] ],[ [21] ] a bubbling fluidized bed achieving evenly distributed smaller-size bubbles is expected to operate more efficiently. In the current literature survey various aspects of the strategies toward improving the efficiency of fluidized beds, hydrodynamic and heat transfer parameters, and the available computational fluid dynamics models and approaches to simulate the experimental results have been briefly addressed. At the end a new design of chemical reactor with its potential applications in the multiphase (Gas/Liquid/solid) flow systems has been proposed.

Concept

Figure Concept of allothermal cyclic multi-compartment fluidized bed for biomass steam gasification.

HeatLosses_multicompart

Figure Reduction of heat losses through micro-segmentation of alternating endo/exothermal fluidization compartments: Dual versus multi-compartment configuration.

2-Background

Several strategies toward improving the efficiency of fluidized beds have targeted renewal of the bubble surface to interchange fluid between bubbles and interstitial gas in the emulsion phase. Various researchers have realized the significance of bubbles in gas-solid fluidized beds and employed various internals, e.g., baffles, tubes, packings, and inserted bodies, and other configurations to generate evenly-distributed smaller-bubbles to improve the quality of fluidization. Their main features and inherited limitations have been thoroughly discussed by Jin et al. [ [22] ], the core issues of which are briefly summarized here, along with more recent findings [ [23] ][ [24] ][ [25] ][ [26] ][ [27] ][ [28] ].

Most transverse baffles in fluidized beds effectively increase gas residence time and reduce solids entrainment. However, this is achieved at the expense of formation at high gas velocities of unwanted gas cushions underneath baffles [22],[27]. These dilute gas-solid environments hinder solids motion and favor axial particles segregation and large pressure drops. Hydrodynamic structure of internals free bed is significantly affected by the introduction of baffles and bed diameter which makes it to difficult to scale up with baffles (Jin et al., 2003 and Zhang et al., 2009).

Horizontal or vertical tube banks have been used for bubble breakup and heat exchange purposes. While vertical arrangements promote better heat transfer, horizontal ones favor bubbles breakup. For an effective use, these have to be placed closer to each other (Yates and Ruiz-Martinez, 1987) [ [29] ]; though closer spacing can promote channeling and gushing both lowering gas-solid exchange and heat transfer performances (Jin et al., 2003) [22].

Fluidized beds have also been filled with stationary (regular or irregular) (Grace and Jarrison, 1970) and floating packings to break large bubbles for accomplishing even gas distribution (Goikhman et al., 1968). However, as compared to internals-free fluidized beds, their utilization is limited by excessive pressure drop, dead spots, channeling-prompting environment, segregation of particles and lower effective thermal conductivity (Ziegler, 1963) [22].

Inserted bodies like pagoda shaped (Jin et al., 1982), ridge shaped (Jin et al., 1986), inverse cone (Zheng et al., 1990), bluff bodies (Gan et al., 1990), and spiral flow pates (Li, 1997) have been used in turbulent/fast fluidizations to control bubble size, improve fluidization quality and enhance gas-solid contact efficiency.

Other configurations like swages (Davies and Graham, 1988) and centre circulating tubes (Fusey et al., 1986 and Milne et al., 1992) have also been used in pneumatic conveying or circulating fluidized beds to achieve high solids circulation rates and uniform solids residence time distribution.

Other innovative designs have recently emerged to reduce bubble sizes and to enhance gas-solid contacting, such as the rotating fluidized bed (RFB) and its static variant with tangential gas injection [24][25], and electrically-stimulated fluidized beds applying electrical fields on uncharged polarizable particles [ [30] ].

C:\Documents and Settings\rehman\Bureau\Internals.bmpFigure Various types of internals for gas-solid fluidized beds encompass baffles (a-e), tubes (f,g), packings (h-j), inserted bodies (k-o), and other configurations (p-q).

3-Hydrodynamic Parameters

3.1-Geldart Classification

Based on their size and density, solid particles are divided into four categories as Geldart A, B, C, and D (Geldart Classification) [ [31] ]. Geldart C belongs to the cohesive or very fine particles which are difficult to fluidize while Geldart A (small size, ρs<~ 1400 kg/ m3) & B (40 µm < dp < 500 µm, 1400 < ρs < 4000 kg/ m3) are known as aeratable particles and relatively easy to fluidize. Large and/ or dense particles fall in the category of Geldart D. These are the spoutable particles and difficult to fluidize especially in the deep beds because of their erratic behavior which results in the large bubbles, severe channeling and uneven gas distribution. Figure 3 sketches the Geldart classification as a function of particles sizes and density.

Figure Geldart classification of fluidized beds based on particles properties.

3.2-Incipient Fluidization Condition and Flow Regimes

The force acting on the particles in a flowing fluid is mainly due to the flow of fluid around the particles. This force known as "drag force" is proportional to the fluid dynamic pressure induced by the fluid and the projected area of particles.

Equation

where, = drag force, = fluid dynamic pressure, = Projected area of particle and = drag coefficient. In case of gas-solid fluidization, the bed is said to be at minimum fluidization condition when the weight of the particles is balanced by this drag force due to the upward moving gas (Kunii and Levenspiel, 1991 and Yang, 2003).

Equation

where, = pressure drop across the bed, = cross sectional area, and are the volume of bed and solids volume fraction respectively at minimum fluidization condition, =specific weight of solids

Rewrite the equation 2 as:

Equation

Since the bed at incipient fluidization condition and can be considered in the loosest sate of packed bed so the voidage at this stage (εmf) can be estimated either from the random packing data or experimentation. Therefore, the gas superficial velocity at the minimum fluidization condition can be estimated reasonably by combining the equation 3 with the packed bed frictional pressure drop equation (equation 4) , known as Ergun equation [ [32] ] yielding equations 5 and 6 as:

Equation

Equation

Or

Equation

whereas, Rep,mf and Ar are the dimensionless particle Reynold number and Archimedes (or Galileo) number respectively.

3.2.1-Umf of Very Fine Particles

In order to estimate the minimum fluidization velocity of very fine particles (Rep,mf < 20) the equation 5 can be simplified to:

Equation

3.2.2-Umf of Fine Particles

Following correlation [ [33] ] [Abrahamsen and Geldart, 1980] can be employed to estimate the minimum bubbling velocity of particles (Umb) but not valid if estimated Umb < Umf [ [34] ] [LS FAN]

whereas, F45 is the mass fraction of the fine particles having diameter less than 45 µm. This correlation has developed for the following gas-solid systems:

Gas: viscosity (0.9Ã-10-5 - 2.1Ã-10-5 Pa.s) and density (0.18 - 5.1 kg/m3)

Solid: diameter (20 - 72 µm) and density (1100 - 4600 kg/m3)

3.2.3-Umf of Large Particles

In case of very large particles with Rep,mf > 1000, the equation 5 can be simplified to:

Equation

These are the useful equations to estimate the minimum fluidization velocity of particles with known voidage at minimum fluidization condition (εmf) and sphericity (), Table 1 reports the experimental value of εmf [Leva, 1959]. If this information is not available for a particular particulate system then Umf can be roughly estimated after simplifying the equation 6 as:

Equation

whereas C1 and C2 are the constants and have been determined by various researchers for different particulate systems and conditions, as mentioned in Table 2.

3.2.4-Generalized Correlation by Coltters and Rivas [ [35] ]

Coltters and Rivas (2004) have carried out an extensive literature review to develop a new correlation to estimate the Umf of 90 different materials, mentioned below:

Use of this correlation does need any extra information of bed voidage at minimum fluidization condition and sphericity of the particles, which are difficult to determine.

3.2.5-Recommended Method to Estimate the Particle Diameter

Practically, a particular gas-solid system covers a wide range of particles size distribution, which needs to determine a representative diameter of system in the estimation of minimum fluidization velocity. In this regard surface-volume mean diameter () is the most recommended way to estimate the particle diameter as [Wen-Ching Yang. Cahpter 3]:

whereas, xi is the weight fraction of particle size dpi.

Table Voidage at minimum fluidization conditions (εmf) [ [36] ]

Size, dp (mm)

Particles

0.02

0.05

0.07

0.10

0.20

0.30

0.40

Sharp sand, = 0.67

-

0.6

0.59

0.58

0.54

0.5

0.49

Round Sand, = 0.86

-

0.56

0.52

0.48

0.44

0.42

-

Mixed round sand

-

-

0.42

0.42

0.41

-

-

Coal and glass powder

0.72

0.67

0.64

0.62

0.57

0.56

-

Anthracite coal, = 0.63

-

0.62

0.61

0.60

0.56

0.53

0.51

Absorption carbon

0.74

0.72

0.71

0.69

-

-

-

Fischer-Tropsch catalyst, = 0.58

-

-

-

0.58

0.56

0.55

-

Carborundum

-

0.61

0.59

0.56

0.48

-

-

Table Constants C1 and C2 in Equation 9 for Various Particulate Systems

Researchers

Description

C1

C2

Wen and Yu (1966)

Fine particles (0.001 ≤ Re ≤ 4000)

33.7

0.0408

Richardson (1971)

-

25.7

0.0365

Saxena and Vogel (1977)

Dolomite at high temperature and pressure

25.3

0.0571

Babu et al., (1978)

Based on all the data published upto 1977

25.3

0.0651

Grace (1982)

Fine particles

27.2

0.0408

Chitester et al., (1984)

Coarse particles (coal, char, ballotini; upto 64 bar)

28.7

0.0494

3.2.6-Flow Regimes

Figure 4 explains the different stages of flow regimes in the gas-solid fluidized beds with the aid of ∆P - Ug curve for a typical gas-solid system (figure 5). For a particular case, these regimes depend on the gas superficial velocity and mainly classified into 5 stages. Figure 5 shows that pressure drop increases with the gas velocity in the packed bed upto the minimum fluidization condition. An increase in Ug, after onset of fluidization of particles prompts the formation of rising bubbles from excess gas (Ug-Umf) [ [37] ] and then the pressure drop remains constant in the range of 1 Umf to 6 Umf (bubbling fluidization). Figure 6 depicts the behavior of ratio Umb/Umf for different Geldart classes. It shows that the bubble formation occurs immediately after the onset of fluidization condition in case of larger particles (especially Geldart D) whereas in case of fine particles (Geldart A) the height of bed increases monotonically after the onset of incipient fluidization condition (from hmf to hf) once it reaches the minimum bubbling point (Umb). This regime (Umf < Ug < Umb) is known as particulate fluidization [ [38] ] [LS Fan principles of gas solid flows]. After further increase in gas velocity, pressure drop slightly increases in the slugging regime and then it drops sharply once the pneumatic transport of particles is started [ [39] ].

Figure Flow regimes in gas-solid fluidized bed [32].

Figure ΔP-Ug plot demonstrating the different stages of flow regimes [32].

Figure Minimum bubbling velocity ratio decreases sharply with increase in particle size [Knii and Levenspiel, 1991]

3.3-Two Phase Theory of Fluidization

Toomey and Johstone (1952) proposed the two-phase theory of fluidization which assumed that the aggregative fluidization consists of two phases, i.e., the particulate (or emulsion) phase and the bubble phase. The gas flow rate through the emulsion phase is equal to the flow rate for minimum fluidization, while the excess gas than Umf causes the formation of bubbles. Mathematically, the two-phase theory can be expressed as:

Equation

where GB is the average visible volumetric bubble flow across a given cross section of the bed. The two phase theory has been found a good and simple approximation for various systems but experimental endeavors have shown that it needs to be corrected at high pressure as:

Equation

This deviation from the theoretical two phase theory would be because of an increase in interstitial gas velocity in the emulsion phase above that required for minimum fluidization and the through flow inside the bubbles. Therefore a modified or n-type two-phase theory was proposed by Grace and Clift (1974), mathematically:

Equation

where, is the average volume fraction of visible bubble phase in the bed. The flow through particulate phase is and the through flow relative to bubbles is . The value of n depends upon the gas solid system, height of the bed and the gas superficial velocity. It is difficult to measure the accurate value of n due to lack of information of invisible component of total flow. n = 0 for classical two phase theory by Toomey and Johstone (1952).

3.4-Bubble and Solids Dynamics

Theory of two phase flow has explained that the excess gas (Ug - Umf) leads to the origination and propagation of rising bubbles in the gas-solid fluidized beds. Various invasive and non-invasive techniques have been reported in the literature to investigate the behavior of bubbles in the gas-solid fluidized beds. A brief description of them is illustrated below:

3.4.1-Invasive Techniques:

Pressure Measurements

Pressure measurement technique is being widely used by various researchers because of its simplicity in use and cheap availability. Pressure drop across the bed at various gas superficial velocities from rest to the fully fluidization stage is used to est the bed is

Pressure fluctuations in the fluidized bed have been

used successfully as a measure of bubbling intensity,

and the method is found particularly useful for the

study of behavior of beds with internals (Kang et al.,

1967; Newby and Keairns, 1978; Staub and Canada,

1978). Jiang et al. (1991) measured an increase in

pressure drop when four ring baffles with an opening

area of 56% were installed in their riser 0.1 m in I.D.

Gan et al. (1990) experienced a localized high-pressure

reduction across their bluff body, accompanied by

significant solids acceleration.

3.4.2-Non-invasive Techniques:

Table 3 Correlations available in literature to estimate bubble size in beds using Geldart D particles

Reference

Correlation

D0

Hilligardt and Werther, 1986

0.0123 (3-D bed)

0.01955 (2-D bed)

Lim et al., 1993

(2-D bed)

All terms are in SI units

c = proportionality constant for the distance travelled by a bubble in a stream before coalescing with the adjacent stream to form a single new stream of larger bubbles ( 2), dimensionless.

4-Heat Transfer

Heat transfer has always been one of the objective issues of gas-solid fluidized bed reactor which can be categorized as: between the solid and gas phases (within two phase system) and between the two phase system and a solid surface. These mechanisms can be well understood with an example of coal combustion by air in a fluidized bed reactor, in which coal particles are fluidized by air. Surface of a coal particle is at high temperature due to the strong exothermic oxidation of carbon which creates a temperature gradient and consequently heat transfer between the hot particle surface and fluidizing air (within two phase system). Since, the heat is generated purposely so it is carried from the hot two phase system to the cold solid surface of submerged heat exchanger (e.g., steam generation, gasification process etc.). Currently, in the industry tube banks have been extensively used to execute this job. Heat transfer within the two phase system is a rapid phenomenon which reduces the particles surface temperature quickly and affects the matters such as ash agglomeration in the bed. While, the heat transfer from the two phase system to the solid surface provides the basis to calculate the effective surface area of heat exchanger tubes. In the design calculations of gas-solid fluidized bed reactor the later has achieved much attention but the presence of former cannot be totally ruled out from the efficiency point of view.

The mechanisms to carry out the aforementioned heat transfer are determined by the operational flow regime of the bed. Normally the beds are classified into two regimes namely; dense bubbling fluidized bed and fast circulating fluidized bed. Several correlations are available in the literature to predict the heat transfer coefficients for a particular set of operating conditions (flow regime). Since our work is focused on bubbling fluidized beds so the following discussion will deal with this regime.

4.1-Particle Surface-to-Gas Heat Transfer

Heat transfer between the surface of a single particle at fixed position and the surrounding flowing gas may be regarded as convective mode. Mathematically heat transfer coefficient (hp) in this case will be:

Since the gas-solid fluidization involves the complex hydrodynamic features which affect the heat transfer coefficient greatly so its estimation is not so straightforward and needs valid correlations. Complications originate mainly from the estimation of particles (Tp) and gas (Tg) temperatures in the fluidized bed. Based on higher particles diffusivity in the bubbling beds an isothermal condition is assumed which considers the particles as well mixed. As far as the gas is considered, plug flow model has achieved much attention as compared to the well mixed model because it shows less scattering of data and allows the use of analogies in mass transfer study between particles and fluidizing gas (Kunii and Levenspiel, 1969). It is pertinent to mention here that all the models do not provide the correct results due to the significant deviation of assumptions from the practical gas solid bubbling fluidized beds.

Kunii and Levenspiel (1969) have developed the correlations (Equations 13 & 14) to estimate hp for different flow regimes which are based on experimental results obtained from 22 research works.

Equation

Equation

Equation

where,

(Nusselt Number)

(Reynolds Number)

(Prandtl Number)

Equations 13 & 14 have been compared against the single sphere convection correlation (Equation 15) as proposed by the Ranz (1952) at Pr = 0.7 in Fig. 8. Equation 15 assumes that all the particles are well mixed. Figure shows that the Nup of bubbling fluidized beds at low Reynolds number (< 20) is lower than that estimated from the single particle model and slightly increases at Re > 60. Equation 15 shows the minimum limit of heat conduction i-e. 2 as the Reynolds number approaches to zero value. All the experimental values summarized in equations 13 and 14 fall well below this limit which is attributed to the bubbling behavior of the bed. Lower Rep means that the bed is operating with fine particles at low gas superficial velocity and lower values of Nup in this case validates the inefficient gas-solid contact due to the clouded bubbles with entrained particles. On the other hand, the gas-particle contact is more efficient at higher Re where the bed is experiencing coarser particles fluidizing at higher gas superficial velocities. Relatively cloudless bubbles in the later case improve the contact and cause to increase the Nup.

Figure Nusselt numbers for particle-gas heat transfer in dense bubbling beds for Prg = 0.7.

Heat transfer coefficient increases with the increase in density, thermal conductivity, the relative velocity of gas and the decrease in viscosity of gas.

4.2- Wall (surface)-to-Bed (two phase mixture) Heat Transfer

Overall heat balance demands the transfer of the heat to/from the bed which can be accomplished either by immersing the tubes inside the bed or recirculating the solid particles through another heat exchanger. Heat transfer between the walls of immersed tubes and the bed is normally referred as wall-to-bed heat transfer and assessed by the wall-to-bed heat transfer coefficient.

Mathematically:

where, q/ aw is the heat flux, Tw is the wall temperature and Tb is the temperature of two phase medium by neglecting any small temperature difference between particles and gas. In order to design an efficient gas-solid fluidized bed, the correct estimation of wall-to-bed heat transfer coefficient (hw) and its enhancement have been the burning issues for the researchers. Figure 9 shows the experimental results of hw as a function of dimensional less gas superficial velocity. It explains that hw increases by increasing the gas flowrate and after reaching its maximum value slightly decreases by further increasing the flowrate. It reduces with the increase in particle size, which reveals its importance to investigate especially in the operations involving Geldart D particles, for example gasification-combustion units.

The effective wall-to-bed heat transfer (hw) coefficient mainly consists of two components i-e., convection (hc) and radiation (hr) heat transfer coefficients. As far as hr is concerned, it is involved in only high temperature processes while hc is further composed of two factors including wall-to-contacted gas bubble (hg) and wall-to-contacted particle/dense phase (hd) heat transfer coefficients, which can be mathematically written as:

where, fg and fd (=1-fg) are the contact time fractions of gas and dense phases respectively. Since the current project is focused on cold mock up study so the following discussion will be based on only convection heat transfer coefficient.

Figure Heat transfer coefficients for horizontal tube in bubbling beds of glass spheres, fluidized by air at atmospheric pressure (Data of Chandran et al., 1980 taken from __________).

4.2.1-Convection Heat Transfer Coefficient (hc)

Many researchers have concluded that the heat transfer coefficient in gas-solid bubbling fluidized bed is enhanced as compared to the single particle gas convection. There are four approaches available in the literature to estimate the convective heat transfer coefficient and applies to gas solid fluidized beds having internal horizontal/ vertical tubes as heat exchangers.

First approach assumes a definite thickness of boundary layer of gas phase around the walls of tubes which acts a thermal resistance and decreases with the attrition of solid particles during fluidization process. Correlations based on this approach are summarized below:

For Vertical Tubes:

Leva (1952)

Wender and Cooper (1958) valid for

where, CR is the correction factor for the radial position of tubes located away from the bed axis.

Expression for CR based on the data of Vreedenberg (1952)

where,

r = radial position of tube

Rb = radius of the bed

For Horizontal Tubes:

Vreedenberg (1958)

Average values have been recommended by the researcher for intermediate ranges of .

Andeen and Glicksman (1976) for large particles

In the second approach, some researchers have estimated the convective heat transfer coefficient contributed by both gaseous and particle convections.

Molerus et al. (1995)

Borodulya et al. (1991) for horizontal and vertical tubes

valid for 0.1 < dp < 4 mm, 0.1 < P < 10 MPa, 140 < Ar < 1.1Ã-107

Third approach is based on the packet theory and initially proposed by the Mickley and Fairbanks (1955) in which the gas bubbles and packets of particles replace each other at the same position of heat exchanger surface. This periodic replacement is mainly responsible for the transient heat conduction between the solid surface and packets during a certain period of their contact time. The gas fraction of particles packet for a period of contact with the solid surface is assumed to be nearly at the incipient fluidization condition.

Mickley and Fairbanks (1955)

where, the residence time of packets at the surface is the estimated as:

Chandran and Chen (1985) have proposed another correlation based on packet theory for the processes having higher gas fraction near the heat exchanger surface by including the bulk properties of the bed away from the heat exchanger surface.

where,

Subscript "pab" denotes the bulk packet properties of the bed away from the surface and Fo is said as Fourier Modulus. If the gas fraction in the bulk of a typical process is not known then one can assume the same at minimum fluidization condition (). Kunii and Smith (1960) have proposed the following correlation for to estimate the thermal conductivity of te bulk packet.

Kunii and Levenspiel (1991) have recommended the following expression to estimate the residence time of packet near the wall.

where, and are the volume fraction and frequency of bubbles near the walls.

The above reveals and important point that the residence time of packets increases with the decrease in bubbles frequency which results in the decrease in wall-to-bed heat transfer coefficient. Bubble frequency experienced by the horizontal tubes at a particular position as compared to the internals free bed is reduced to half because of the possibility of one of two different propagation directions for bubbles after striking the tubes.

The forth approach is based on the kinetic theory of granular materials (KTGM) which addresses the transport of thermal energy across the boundary layer at the heat exchanger surface by virtue of the motion of particles.

Martin (1984)

N = Nusselt number for heat transfer during the wall-particles collision

Cc = inversely proportional to the residence time of particles at wall (dimensionless)

wp = average random particle velocity

5-Mixing and Segregation

6-Effect of Internal Tubes and Baffles in Fluidized Beds

Literature shows that the hydrodynamic parameters like bubble behavior, flow distribution, gas and solids mixing, and transition to turbulent fluidization in internals free fluidized bed have been affected by using the internal baffles and tubes. These internals possess the potential advantages and disadvantages. Advantages like narrower gas-solid residence time distribution, less chances of rushing at the surface of the bed and the reduction of solid particles entertainment favors the use of transverse baffles. Their use is limited due to high pressure drop and a diluted gas cushion beneath the each baffle at high gas flowrates, whereas, the later promotes the axial segregation of multi-sized particles in the bed. In addition to this, increasing the diameter of the fluidized bed amplifies these problems. Effect of internals on the above mentioned four basic hydrodynamic parameters is summarized in the later section.

6.1-Bubble Behavior

Bubble behavior (growth and distribution) in gas-solid fluidized beds, has been recognized as an important parameter influencing mixing of particles and both heat and mass transfer rates and therefore the overall kinetics of catalytic and non-catalytic reactions. Figure 8 compares the bubble behavior in the internals free bed with the baffles (louver), vertical tubes and pagoda shaped inserted bodies for a typical gas-solid fluidization system.

Figure 8(b) shows that small bubbles travel through the baffles and collapse at the surface of bed at low gas velocities. Bubble breakup and then regeneration occurs at slightly higher velocities with better bubble distribution as compared to the internals free bed (Figure 8a). While in the range of moderate to high gas velocities a detrimental gas cushion is observed beneath the each baffle. This leads to depress the vertical circulation of particles with lesser rain of particles from the louvers of baffles consequently promotes the segregation of particles and offers poor heat exchange.

Vertical tube banks have been employed in the gas-solid fluidized bed for heat exchange purposes and even spatial distribution of bubbles (Figure 8c) and found to have a little effect on bubbles breakup. Inserting horizontal tubes bank offers the breakup of rising bubbles (larger than tube diameter) into smaller ones which is immediately followed by the bubbles coalescence at the top of tube, thus undermining their usefulness in some cases (Yates, 1987). Large bubbles can rise over horizontal rods without experiencing breaking up (Xavier et al., 1978), and the bed expansion is not significantly affected by the rods (Newby and Keairns, 1978).

Figure Bubble growth in gas-solid fluidized bed with/ without internals

Figure Effect of internals on the expansion ratio in a two-dimensional fluidized bed.

In case of pagoda shaped bodies, small rising bubbles pass back and forth through the holes of bodies at very low gas velocities (Figure 8d). As the velocity is increased, these bodies control the size of bubbles however, some of the moving bubbles have been observed away from the wall of pipe. At high gas velocities, two regimes exist in the gas-solid fluidized bed: a bubble phase, carrying less concentrated particles upward through their wakes and an emulsion phase, where the downward moving particles are more concentrated. Intensive turbulence to promote the exchange between bubble and emulsion phases is carried out at very high gas velocities.

During the parent bubble breakup process, the total volume of off spring bubbles is always less than that of parent which means that some of the gas has been leaked to the emulsion phase of the bed. This leakage increases with the decrease in bubble size due to various types of internals. Figure 9 shows the effect of internals on the expansion ratio in the 2-D gas-solid fluidized beds. Reducing the bubble size leads to the lower rise velocities of the bubbles which increase the total concentration of the smaller bubbles in the bed and consequently found effective to enhance the chemical conversion.

6.2-Flow Distribution

The performance and efficiency of a gas-solid fluidized bed reactor depends on the gas-solid mixing which is improved by developing the more uniform flow structures in the bed. Literature survey reveals that better uniformity can be expected by inserting the internal bodies inside the bed. Figure 9 shows that the radial voidage distribution in a bed employed with ring baffles has become more uniform as compared to internals free bed (Zheng et al., 1991). The design of these internal bodies to improve the flow structures is not straight forward, so that, an ill-designed baffle can be disadvantageous and lead to even bad distribution as compared to internals free beds. Salah et al. (1996) Zheng et al. (1990).

6.3-Gas and Solids Mixing

High solid phase conversion and gas phase utilization determines the efficiency of a gas-solid fluidized bed reactor, which is contingent upon the degree of axial mixing of gas and particles. It adds another task of reduced gas phase backmixing in order to increase the gas-solid contact and consequently the efficiency of bed.

Internal bodies increase the local gas velocity which results in lowering the gas backmixing significantly (Ye, 1987). Horizontal baffle offers little gas backmixing between its either sides and is only effective in case of small particles or operations at lower gas velocities. Since, the fluidized beds containing larger particles operate at high gas velocities; therefore, the use of horizontal baffles is less effective in this case. Inserting horizontal tubes is more advantageous as compared to verticals at higher velocities to restrain the bed from gas backmixing because verticals offer non-uniform radial gas mixing.

In addition to gas backmixing, solids backmixing is also controlled by using the internal obstacles in the fluidized bed. The baffled fluidized bed acts as a multistage fluidized bed reactor and can be modeled as a series of perfectly mixed stages with solids backmixing between them. Experimental results of Zhao et al., (1992) show that, for a given bed material, solid back mixing mainly depends upon gas velocity, baffle free area and baffle spacing.

6.4-Transition to Turbulent Fluidization

Eruption of bubbles at the free surface and the bubbles coalescence and breakup generate the pressure fluctuating signals. These signals can be exploited to characterize the flow regimes of gas-solid fluidized beds. (Canada et al. (1978), Yerushalmi and Cankurt (1979), Sadasivan et al. (1980), Satija and Fan (1985), Rhodes and Geldart (1986), Noordergraaf et al. (1987), Andersson et al. (1989), Cai et al. (1989), and Olowson (1991)). Flow regime mainly depends on various parameters, most importantly, the fluidization pressure, particles properties and the geometric configuration (type of internals used) of the bed. Gas superficial velocity of bed at transition to turbulent fluidization is termed as transition velocity (Uc), and is lowered by employing the internal obstacles. They break the bubbles at lower pressure and velocity and create more turbulence in the beds as compared to internals free bed. Johnsson and Andersson (1990) Olsson et al. (1995).

In summary, transverse baffles and vertical tubes can control the bubble at low gas velocities to improve the gas-solid contact as compared to the internal free beds. However, their effect on the quality and performance of fluidization becomes detrimental at high gas velocities. Pagoda shaped bodies creates turbulence at very high gas velocities for better gas-solid mixing. The addition of baffles, tubes, and other obstacles restricts large-scale solids movement, reduces the gas and solids backmixing, improves the radial gas and solids mixing, but causes the segregation of particles of different sizes which can be detrimental in binary mixtures (for example, gasification and combustion processes). Horizontal tube banks are more effective than verticals to suppress the gas backmixing but less recommended for heat transfer purposes.

Figure Radial voidage distribution in a ring-baffled fluidized bed by using optical fiber concentration probe [].

7-Computational Fluid Dynamics Aspects

8-Proposed Design: Multi-compartment Corrugated Wall Bubbling Fluidized Bed (CWBFB)

The above survey reveals that the existing geometrical configurations are not easily adaptable to the slim, parallelepipedic and juxtaposed multi-compartments depicted in Fig. 1 to control bubble structure and dynamics under bubbling fluidization regime as in our proposed setup. Hence, we propose to explore in this study a new concept to harness bubble dynamics in bubbling fluidization by investigating different arrangements of walls with corrugated geometries. To the best of our knowledge, no study is presently available in the literature to address hydrodynamics in corrugated-wall bubbling fluidized beds (CWBFB). In this regard, the proposed research work encompassed cold-prototype experiments to study the effect of corrugations (corrugation angle, inter-wall clearance, flat versus corrugated, face-to-face opposite or parallel corrugations, horizontal or inclined channel) on minimum bubbling velocity, and bubble size, frequency and rise velocity. The various geometrical declinations of the cold-prototype corrugated-wall bubbling fluidized bed (CWBFB) were compared to the classical flat-wall bubbling fluidized bed (FWBFB) using high-speed digital image analysis. Euler-Euler transient full three-dimensional computational fluid dynamic (CFD) simulations were implemented to help understanding the hydrodynamic behavior of CWBFB and to elucidate the origins of fluidization inception as related to corrugation geometrical features.

Conclusion

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