Modeling Process Characteristics and Performance of Fixed and

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Ind. Eng. Chem. Res. 2006, 45, 4782-4790

Modeling Process Characteristics and Performance of Fixed and Fluidized Bed Regenerative Thermal Oxidizer Pietropaolo Morrone,*,† Francesco P. Di Maio,‡ Alberto Di Renzo,‡ and Mario Amelio† Dipartimento di Meccanica, UniVersita` della Calabria, Via P. Bucci, Cubo 44c, 87036 Rende (CS), Italy, and Dipartimento di Ingegneria Chimica e dei Materiali, UniVersita` della Calabria, Via P. Bucci, Cubo 44a, 87036 Rende (CS), Italy

The abatement of volatile organic components (VOC) in emissions is an extremely stringent environmental problem. One of the most frequently used technologies is the regenerative thermal oxidation (RTO), because of its thermal efficiency and cost-effectiveness. In the present paper, a computational one-dimensional unsteady model, able to account for fixed as well as fluidized beds of particles, is developed, validated, and applied to realistic plant conditions. Process thermal efficiency and gas pressure drop are calculated as functions of the system geometry and operating parameters. Results of a validation against experimental data are presented first, showing very good agreement. The overall thermal efficiency is obtained as the performance index for packed beds of spheres and Rashig rings and fluidized beds of spheres, allowing a direct comparison of the two systems. The simulation results clearly show that, despite the high efficiency of gas-solid contact in fluidized beds, their thermal performances are unacceptably poor, because of the cyclic nature of the process. 1. Introduction The regenerative thermal oxidizer (RTO)1,2 is utilized in abatement, through thermal oxidation, of the volatile organic compounds (VOC), released in the atmosphere as emissions from transportation and the chemical and petrochemical industry, as well as in processes where solvents are utilized (e.g., painting). RTOs are particularly attractive as a result of the fact that no post-treatment is necessary, as compared to other alternatives such as activated charcoal oxidizers. In the RTO technology, beds of inert material (usually ceramic materials) are preheated to provide heat to the air to be processed, through a sequence of cyclic operations which maximizes the operation yield, in terms of thermal exchange. In each cycle, the VOC polluted air flows through the hot bed B1 (Figure 1a) which acts as a preheater, raising the gas temperature, then completes the oxidation in the combustion chamber CC, and eventually, flows through a cold bed B2 which acts as an accumulator, releasing its enthalpy of combustion. The regenerated bed B2 is then ready to act as a preheater of the inlet effluent in the next treatment cycle (Figure 1b). The change is accomplished by inverting the feed flow to the two beds through a valve system (Figure 2). After a start-up phase, steady-state operation is achieved, where the system is thermally auto-sufficient. In these conditions, the two regenerators follow a thermal cycle constituted by a preheating and a regeneration phase, which allows the exhaust gas energy to be recovered with a maximum efficacy. A burner is located in the combustion chamber to ensure complete VOC combustion. It is used in the start-up phase, when the exit temperature from the preheater is not sufficient to guarantee VOC auto-ignition. For the same reason, when the inlet VOC concentration is low, auxiliary fuel is injected to bring the mixture within the boundaries of the ignition zone. The exchange zones traditionally utilized are constituted by inert material of two geometric types: ceramic bricks with * To whom correspondence should be addressed. Tel.: +39 0984 494162. Fax: +39 0984 494673. E-mail: [email protected]. † Dipartimento di Meccanica. ‡ Dipartimento di Ingegneria Chimica e dei Materiali.

Figure 1. Scheme of RTO plant operation and gas temperature before (a) and after (b) the switch.

square longitudinal holes of about 3 mm of size (these are usually referred to as “structured beds” or “structured packing”) or randomly arranged pebbles with average diameter usually larger than 1 cm (“random packing” or “porous media”). The main difference between the two categories lays in the ratio between fixed and variable costs of the corresponding process. For a structured packing, the purchase expenses are far higher, because of the cost to produce complex structures, but operative costs, related to the pressure loss throughout the bed, are lower, as a result of the guided paths the fluid follows in its flow through the system. On the contrary, unstructured materials are easier to produce and so have lower prices than structured ones, but the tortuosity of the flow through the bed interstices generates pressure drops up to five times higher. The best choice derives from profitability analysis once flow rates and the corresponding RTO plant size have been defined. In the traditional industrial applications the variable costs related to the blower significantly affect the total costs.1 Therefore, the alternative of utilizing fluidized rather than fixed beds appears to be interesting, as they offer a considerably lower pressure drop, and this is independent of the air flow rate. The characteristics of fluidized beds in operation generally allow better conditions for thermal exchange to be established

10.1021/ie051300y CCC: $33.50 © 2006 American Chemical Society Published on Web 05/26/2006

Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4783

Figure 2. Scheme of the physical location of the two beds and the combustion chamber with valves to redistribute gas flow to the beds.

and to carry out a more efficient temperature control.3,4 In fact, as energy is accumulated or released from the solid phase, the continuous agitation of the particles distributes the heat evenly throughout the system, thus avoiding dead-zones or preferential paths in the fluid phase which would compromise the efficacy of thermal exchange. In addition, compared to fixed beds containing comparable sized particles, fluid beds require a lower pressure or, for comparable pressure loss, they have significantly smaller size. On the other hand, fluid beds are more difficult to operate due to the formation of dust, plant vibration, and other issues arising mainly from the particle motion. Despite the highlighted advantages, no papers dealing with fluid bed RTOs, to the authors’ knowledge, can be found in the literature, and the present work constitutes the first modeling attempt in this direction. On the contrary, some experimental and modeling studies were conducted on packed bed RTOs. Boger5 analyzed computationally the performance of structured systems. This author, through a simple combustion model, obtained simulations of the temperature profiles in a two-bed RTO at various pollutant concentrations and outlet to inlet flow rate ratio. In the same paper, the influence of the temperature profiles on the thermal stresses is investigated. However, the work lacks an analysis of the performance, in terms of the overall thermal efficiency and pressure drop, at various operating and design conditions. Regarding random packed bed RTOs, Choi and Yi6 presented a simulation study of the process through the commercial software Fluent 4.0. The focus was on assessing the efficiency of VOC removal as a function of parameters such as bed height and gas inlet velocity. Choi and Yi demonstrated how the oxidation is of thermal nature and that no continuous operation of the additional burner is necessary during the cycle. In addition, NOx formation is negligible as a result of the relatively low combustion temperatures (usually around 800 °C), which justifies the attention of several industrial designers toward these systems. Cheng et al.7 carried out an experimental campaign on three RTOs with random packing of irregular SiO2 pebbles (mean diameter 12.5 mm). VOC removal was analyzed by measuring their instantaneous concentration. Their results show that high removal efficiency can be achieved in two-bed RTOs. In another paper8 the group of Lewandowski carried out an analysis of the thermal efficiency, pressure drop, and efficiency

of VOC removal by varying the cycle duration and the flow rate of the gas to be treated. There are various papers on the properties of thermal regenerators in general, although in operating conditions different from the ones typically encountered in RTOs. For example, spherical particles are assumed, while in the industrial plant more complex shapes (hollow cylinders, saddle-like particles9) are utilized to maximize the thermal exchange and minimize the pressure drop. Also, lower flow rates or small temperature changes are assumed to simplify the problem. In particular, in a paper from Zarrinehkafsh and Sadrameli10 a model is proposed to investigate the thermal recovery efficiency in regenerators involving spherical particles, assuming constant gas velocity throughout the regenerator. This last point restricts the model validity to systems with limited temperature variations, far from those observed in RTOs (typically from 25 to 800 °C). In their work, Duprat and Lopez11 compared structured and woVen-screen beds, in terms of thermal efficiency and flow rates far smaller than those processed in RTOs. Also, aluminum was used as the material, thus limiting the applicability to catalytic rather than thermal oxidizers. In the latter, the typical temperatures would melt the structure of the unit. Chou et al.12 performed experiments intended to measure the gas and solid temperatures in time in a catalytic thermal oxidizer operated with two random packing beds and a catalytic combustion chamber. In the same paper, a simulation model was developed for the thermal exchange in the regenerator accounting for thermal diffusion. In the present work, a mono-dimensional computational model of a RTO plant with preheater and regenerator is proposed to simulate the dynamics of energy exchange systems with random packing. The model is applicable to traditional fixed beds of particles as well as to fluidized beds, making it possible to explore the potential of such a technology, efficiently utilized in other fields of the process engineering. The model validation will be carried out with experimental results available in the literature. Then, the computational code in which the model is implemented will be utilized to analyze and compare the process characteristics and performance of RTOs under various operating conditions. Both single units (preheater and regenerator) and the whole plant will be examined through a global steady-state thermal efficiency. 2. Model of a Fixed and Fluidized Bed Regenerator A mono-dimensional transient model including mass, momentum, and energy conservation equations was developed. The basic model assumptions are as follows: (1) pure air as the process fluid; (2) mono-dimensional unsteady flow; (3) constant (in time) mass flow rate; (4) uniformity of voidage within the bed of particles; (5) negligible thermal accumulation of the gas in the regenerator;13 (6) conductive and irradiative energy exchange mechanisms negligible compared to convective heat exchange; (7) adiabatic systems toward the surroundings; (8) negligible temperature gradient within a solid particle; and (9) uniformity of the temperature in a fluidized bed. The absence of a temperature gradient within each particle can be considered valid when the Biot number (Bi ) h(ds/6φs)/ ks) is smaller than 0.1.13 This is always accomplished in the flow conditions of the present analysis. The hypothesis of constant gas velocity in the regenerator present in some papers in the literature10,14 was not adopted in the present work, to allow the thermal behavior of beds of particles with large temperature changes during the cycle to be considered.

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Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006

-

2 1.75(1 - ) 2 ∂p 150(1 - ) µ ) u+ Fu 2 2 3 ∂z φ d φ d 3 s

s

(4)

s s

whereas, for a fluid bed, a force balance for suspended particles easily provides the required relation

Figure 3. Schematic diagram of the control volume and corresponding variables.

The control volume is schematically illustrated in Figure 3. The variables F, u, p, and T are the density, velocity, pressure, and temperature of the air, while Ts is the solid temperature inside the regenerator. All variables are functions of the axial coordinate z and time t. The index i denotes the ith spatial step. With reference to the control volume in Figure 3, the mass and energy balance equations, using the above-mentioned assumptions, are

{

∂Fu )0 ∂z (1)

∂cpT + ha(Ts - T) ) 0 -Fu ∂z

hds ) 2 + 1.8Pr1/3Re1/2 k

valid for Re > 100 (fixed bed) (2a)

Nu ) 0.03Re1.3

valid for Re < 50

(fluid bed) (2b)

where ds is the diameter of a sphere having the same volume of the real particle considered and Re ) Fuds/µ. The correlations for fixed beds proposed by Yoshida et al.15 were also tested in the model. It provides similar results as eq 2a but without limitations on the Reynolds number. The exchange surface per unit volume of the bed a (m2/m3), in terms of the particle properties, is

a)

6(1 - ) φsds

(3)

where φs is the sphericity, defined as the ratio between the surface of the sphere of diameter ds and the surface of the real particle. This value is equal to 1 only for perfectly spherical particles, whereas in all other cases it is less than 1. The variable A denotes the cross-sectional area of the bed. The momentum balance equation for a fixed bed is taken into account through the semiempirical Ergun’s equation,16,17 relating the pressure drop per unit length to the fluid velocity through the porous medium

(5)

The system of equations (eq 1) was numerically solved through a McCormack predictor-corrector scheme18 (see the appendix for details), starting from a pre-assigned temperature profile along the bed Ts ) Ts(z). Within a time interval ∆t this profile is assumed not to vary while, once the spatial distribution of u, p, T, and F have been determined, the temperature of the solid is updated according to the following unsteady balance:

∂Ts(z) ) Gcp dT(z) ∂t

-FscsA dz(1 - )

(6)

In terms of finite differences, the solid-phase temperature at the time t + ∆t and point i is

Tsi(t + ∆t) ) Tsi(t) +

where h is the gas-solid heat transfer coefficient. Its value is significantly affected by the status of the bed, that is, fixed or fluidized. As far as the determination of the heat transfer coefficient in fluidized beds is concerned, no general theory is available today capable of accounting for the bubbles, due to the extreme complexity of the phenomenon. Indeed, various correlations present in the literature yield very different values. Unfortunately, the choice of the relation to be used is crucial. Thus, in the present work, the well-established and rather conservative relations proposed by Kunii and Levenspiel3 are used:

Nu )

∂p ) g(F + (1 - )Fs) ∂z

Gcp∆t

(Ti(t) - Ti+1(t)) (7)

FscsA(1 - )∆z

According to the hypothesis of temperature spatial homogeneity for the solid phase, the energy balance in a fluidized bed is as follows:

dTs ) dt

-FscsAL(1 - )

∫0LGcp dT(z)

(8)

3. Model Validation The predictive capabilities of the model were tested on experimental data reported by Chou et al.12 regarding a thermal oxidation plant consisting of two randomly packed beds (see Table 1). The air enters the regenerator at a temperature of 400 °C, the bed is at 30 °C, and the flow is maintained for 120 min. A set of thermocouples were located on the two beds to measure the solid phase and gas temperatures. In Figures 4 and 5 the comparison of the experimental and model results is illustrated. In particular, Figure 4 shows the particle temperature, in time, corresponding to the thermocouple locations. The agreement between measured and calculated values is very good, especially for the 0.05, 0.5, and 1.5 m curves. The maximum error on the 0.05 m curve is 4%. It is worthwhile to mention that a similar calculation carried out with the model developed by the same authors12 is affected by an error of about 15%. Figure 5 shows the comparison between experiments and model results for the gas temperature along the bed after 60 and 120 min. The model predictions are in excellent agreement with the experiments at 60 min and in good agreement at 120 min. 4. Simulation Results The model was developed with the aim to predict the heat transfer efficiency and the pressure drop across the units present in a RTO plant, with special emphasis on the possibility to conduct comparisons on various configurations and on the opportunity to substitute traditional fixed bed regenerators with fluidized bed units. The thermal cycle under investigation consists of a succession of preheating and the accumulation (regeneration) phase, of

Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4785 Table 1. System Properties regenerator size particle diameter particle sphericity bed voidage specific mass flow rate bed temperature measure locations (m) gas temperature measure locations (m) inlet gas temperature initial particle temperature

Table 2. System Properties for Fixed Bed RTOs 20 × 200 cm (diameter × height) 12.5 mm 0.7 0.41 0.25 kg/(s m2) 0.05, 0.50, 1.05, 1.50, 1.95

regenerator height (m) spherical particles properties

Raschig rings properties 0.35, 0.65, 1.05, 1.35, 1.65, 2.00 400°C 30°C

specific mass flow rate inlet air temperature temperature of the gas leaving the CC

0.25, 0.50, 0.75, 1.00, 1.25, 1.50 bed voidage sphericity ds (mm) a (m2/m3) bed voidage sphericity size (mm) a (m2/m3) 1 kg/(m2 s) 25 °C 800 °C

44% 1 6, 10, 12.5, 15 560-224 72-77% 0.3 6, 10, 12.5, 19 964-239

Figure 4. Comparison between experimental results12 and model calculation of the particle temperature in the regenerator. Figure 6. Thermal efficiency along a spherical particle fixed bed regenerator for various particle sizes.

accumulator at the same temperature Ti at which the cold gas enters the preheater:

∫TT (t)cp(T) dT ηreg(t) ) ∫TT cp(T) dT o,reg

c

i

(9)

c

Figure 5. Comparison between experimental results12 and model calculation of the gas temperature in the regenerator.

duration equal to the sum of each phase duration (semi-cycle). Steady-state conditions were reached by setting an initial temperature profile in the regenerator and then periodically switching the gas flow. In this way, preheating and the regeneration phase were alternatively simulated. Steady state is attained when bed temperatures in two subsequent cycles are numerically equal, with a difference of less than 0.1 °C. Regarding the particle types, various shapes can be considered such as spheres, solid or hollow cylinders (usually referred to as Rashig rings), or complex shapes such as Pall rings, Berl saddles, and so on, each with its own exchange surface per unit volume a and typical packing voidage .19 In the following sections, spheres and hollow cylinders in fixed beds and fluidized spherical particles will be analyzed. Before we examine the simulation results let us define the thermal efficiency, a key variable from the point of view of process characteristics. It represents the ratio between the energy transferred to the solid phase from the gas and the maximum energy the regenerator is able to accumulate, that is, the energy the gas would release to the solid if it were to leave the

where To,reg(t) is the instantaneous temperature of the gas exiting from the regenerator. More often, as will be seen below, temporally averaged values are conveniently used for limited periods of time. 4.1. Process Characteristics of Fixed Bed RTOs. The first set of results is concerned with a detailed analysis of the process characteristics of fixed bed RTOs as the parameters involved in the plant operation are varied. The robustness and flexibility of the computational code developed, as well as the versatility typical of numerical simulations, allow several different configurations to be tested in their performance. In the present study, alumina (Al2O3) spherical and hollow cylindrical (with height equal to the diameter) particles are considered. Significantly different properties between the former and the latter are present: sphericity φs (1 versus 0.3, respectively), packing voidage (44% versus values generally around 70%, respectively), and specific area a (560 m2/m3 for spherical particles of 6 mm of diameter and 793 m2/m3 for 6 × 6 mmsdiameter × heightshollow cylinders). It is noteworthy that hollow cylinders (Rashig rings), compared to other nonspherical particles, are easy to produce and cheap. Geometrical data related to them are collected from Coulson and Richardson.19 The thermophysical properties of alumina are taken from Perry’s Handbook.20 The properties of the modeled system are listed in Table 2. Figures 6 and 7 show the thermal efficiency as a function of the regenerator height and type of particle, for a RTO plant

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Figure 7. Thermal efficiency along a Rashig ring fixed bed regenerator for various particle sizes. Note: bed voidage varies for different values of the particle size.

Figure 9. Pressure drop along bed height for the two types of particles at constant efficiency (ηacc ) 95%).

Figure 10. Influence of the cycle duration on regeneration efficiency for 10 × 10 mm Rashig rings in a 0.48 m bed. Figure 8. Pressure drop along bed height for spheres and Rashig rings of two sizes.

processing a specific air flow rate of 1 kg/(s m2), with a cycle duration of 90 s. The reported values of the efficiency differ from the definition in eq 9 in that they are temporally averaged during a semi-cycle life. An asymptotic increase of the thermal efficiency is evident along the bed height. Thus, further increases in it produce less pronounced advantages, and the corresponding costs are less and less justified. The thermal efficiency increases as the particle size decreases. Instead, for equally sized particles, ηreg is larger for Rashig rings than for spherical particles, because higher specific surface areas are available. In Figure 8 the pressure drop is reported as a function of the bed height and for two sizes of the two types of particles. The pressure drop increases rather linearly along the height and decreasing particle size. Considering again equally sized particles, Rashig rings yield a lower pressure drop. Figure 9 shows the pressure drop produced by the two types of particles at different bed heights but maintaining a similar value of the thermal efficiency (ηacc ) 95%). Spherical particles tend to give considerably higher pressure drops than Rashig rings, especially for large particles. Indeed, whereas spherical particles determine an increasing pressure drop with particle diameter, Rashig rings offer a nearly constant resistance to the fluid flow. For spheres, the positive effect given by larger particles (Figure 8) is counteracted by the increased bed length, imposed by the constant efficiency. Both unit size and pressure drop can be minimized only by decreasing particle size. In the case of Rashig rings, no clear trend can be observed. The minimum pressure drop (1.8 kPa) is observed with 10 × 10 mm Rashig rings and a regenerator length of 0.48 m. The 6 × 6 mm hollow cylinders, instead, offer a larger pressure drop

(2.1 kPa). This is mainly due the variability of the voidage with particle size (e.g., it changes from 0.77 to 0.72 by varying the dimension from 19 × 19 mm to 6 × 6 mm, respectively). For the minimum pressure drop configuration (10 × 10 mm Rashig rings and bed height 0.48 m) Figure 10 shows the influence of the cycle duration on the thermal efficiency. It is evident that longer durations produce less efficient processes. This effect is stronger for larger air flow rates. For relatively small flow rates the little decrease of efficiency could be compensated by saving on the costs related to periodic switches. Flow rate and bed height effects on the pressure drop and thermal efficiency are reported in Figure 11 for a fixed bed regenerator with 10 × 10 mm Rashig rings. The effect of a flow rate change on the efficiency tends to disappear as the bed height increases, while the pressure drop, depending as a quadratic function on the superficial velocity, is rather sensitive to the flow rate. 4.2. Comparison with Fluid Bed RTOs. Generally speaking, the thermal exchange in a fluidized bed is higher than that observed in an equivalent fixed bed. The limited pressure drop allows much smaller particles to be used. Therefore, it is specifically the exchange surface that in fluid beds is far superior and enhances the overall interphase heat transfer capabilities. By utilizing the computational model, the process characteristics and maximum performance achievable of the fixed and fluid bed systems described in Table 3 are investigated. Despite the advantageous heat transfer conditions, when a fluid bed is considered in a preheating and regeneration cycle, the system behaves extremely poorly in terms of overall thermal efficiency. To clarify this concept it is necessary to consider the process through which steady-state conditions are attained. Figure 12 shows the temperature of the gas leaving each plant


Figure 11. Effect of the flow rate on the thermal efficiency (a) and pressure drop (b) for 10 × 10 mm in a Rashig ring fixed bed. Table 3. Physical and Geometrical Properties of the Systems Considered

particle diameter system height voidage specific air flow rate cycle duration inlet air temperature initial solid temperature

fixed bed

fluid bed

10 mm 1m 0.44

1 mm 0.1 m 0.42 0.7 kg/(m2 s) 180 s 800°C 25°C

Figure 12. Temperature of the gas leaving the units as a function of the number of semi-cycles.

unit in the series of semi-cycles of heating and cooling. On the abscissa, the number of semi-cycles (number of switches) is reported. Ambient temperature is assumed as initial conditions for the two beds of particles. Periodic conditions are clearly identified at steady state, after an evolution involving several cycles. The most important difference between the fixed and the fluid bed systems regards

the temperatures at which the gas leaves the units at each switch. For a fixed bed in the accumulation phase, the gas exits at about 40 °C, while in the preheating phase it raises the gas temperature up to about 790 °C. On the other side, in a fluid bed system the gas temperature oscillates between about 340 °C and 510 °C, that is, at values considerably far from the theoretical extremes. This difference produces a double effect: on one hand, the low preheating temperature causes auxiliary fuel to be necessary to achieve the desired VOC conversion in the combustion chamber; on the other hand, the high exhaust temperature indicates an insufficient heat recovery and waste of the released energy. These poor performances can be more clearly interpreted by analyzing both gas and solid temperatures developed in the two units. In Figure 13 the temperature profiles of the two phases along the bed height are reported during a steady-state cycle (in particular, at the beginning, one instant before the switch, one instant past the switch, and at the end of the cycle). In practice, they have been obtained after a simulation of 100 cycles from the initial condition. As a result, the temperatures of the gas leaving the units correspond to the final temperatures in Figure 12. It can be observed that the homogeneous solid temperature within a fluid bed causes a sudden flattening of the gas temperature on that of the solid phase. During a semicycle of the preheating operation (on the left), the solid phase is slowly cooled by the gas phase flowing through it and absorbing its energy. After the switch, the solid phase temperature is taken back to the starting (of the cycle) conditions by the hot gas flowing through it. The solid phase temperature variation range, which corresponds to the temperature variation range of the gas leaving the units, is relatively narrow. On the contrary, in a fixed bed, the temperature profiles of the two phases are steep and parallel (nearly superposed) for the whole bed height, and the overall temperature variation ranges present remarkable amplitude. This is the result of the favorable conditions of the inverted flow depending on the bed behavior, as it clearly appears in the second row of charts in Figure 13. The characteristic steady-state temperature profile of the solid phase offers a nearly constant temperature approach between the phases. This yields a very high thermal efficiency along the entire bed height. Air temperatures at the end of the units are near the extremes in the interval considered, characterizing the solid phase as an excellent preheating and regeneration medium. The air leaving the beds is sufficiently hot in the preheating phase to reach the desired VOC combustion temperature and is sufficiently cooled in the regeneration phase so that the maximum enthalpy is released to the solid which, in the subsequent cycle, will act as a preheater. It is noteworthy that the above considerations result from the condition of cyclic operation of the plant. It is the continuous switch of the beds that, in the change from preheater to regenerator operation and vice versa, causes them to behave in a significantly different manner depending whether the solid is agitated or not, with a neat advantage of the latter case. Thus, it becomes interesting to investigate the influence of the cycle duration on the overall plant performance, because a sudden inversion or a prolonged operation in one mode can result in a greater or smaller impact on the final profiles developed one instant before the switch. Figure 14 shows that the instantaneous efficiency for the fixed bed system analyzed is high for the whole range of interest, while for a fluid bed this value is considerably lower and further decreases with time. A careful analysis of the phenomena occurring during the interphase heat transfer allows an understanding of how the poor

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Figure 13. Steady-state (after 100 cycles) temperature profile obtained for a fluid (upper row of charts) and fixed bed (lower row of charts). Solid line, gas temperature; dashed line, solid temperature. Note: abscissas in the two charts on the top right are reverted because for fluid beds the gas is always fed from the bottom.

Figure 14. Instantaneous efficiency for fixed and fluid bed systems.

performance of the fluid bed systems results mainly from the combination of two factors. If we reconsider the temperature profiles developed in a fluid bed regenerator (Figure 13), we can observe that a large part of the system is practically unutilized for the heat exchange purpose, because the two phases are essentially in thermal equilibrium. This would indicate that, to maximize the driving force along the system, the bed height should be significantly smaller (this same criterion was used to choose the fluid bed system size, see Table 3). Unfortunately, the effect of shortening the system with the aim to keep a significant temperature difference between the two phases is counterbalanced by the need to have a sufficient solid mass acting as the accumulator. In fact, the regenerator absorbing capacity is proportional to its total mass. To increase the capability to remove energy from the gas phase and to slow the bed temperature growth in Figure 13, a longer system would be required. The combined result of the above-discussed effects yields a significant decrease in the fluid bed regenerator overall efficiency, despite the fact that heat transfer properties in a fluid bed are better than in fixed beds. If we analyze the total energy exchanged in the two systems, we can observe that the value corresponding to a fluid bed is always smaller than that in a fixed bed (Figure 15). In particular, although trends are similar (maximum initial slope and tendency toward a plateau), while the initial slope is the same, basically

Figure 15. Energy exchanged between the gas and the solid phase.

because it is a function of the initial conditions, the fixed bed value of the plateau is far larger than that of a fluid bed, mainly due to the presence of a larger amount of solid present in the system. 5. Conclusions A simulation model of the dynamic behavior of a cyclic RTO based on random packing beds of particles is proposed. After a validation against experimental data available in the literature where a very good agreement was found, the model was used to analyze the influence of the key operating parameters on the process characteristics. The type and size of the particles was studied with respect to its impact on the thermal efficiency and bed pressure drop showing that a high specific surface and high voidage particles (e.g., Rashig rings) are the most suitable packing. By means of the computational code, the effect of the specific flow rate and cycle duration is highlighted in minimizing the pressure drop and plant hindrance. As compared to traditional fixed bed regenerators, fluidized beds were studied as an alternative more contact-efficient technology. However, the results clearly indicate that the cyclic inversion of the behavior of each particle bed leads to a condition where fixed beds show the most suitable preheating and regeneration temperature profile, giving overall efficiency of


the order of the 96%. On the contrary, the thermal efficiency of fluidized beds is low (around 50%) and suffers from the temperature homogeneity typical of such units.

By using this averaged value, we can calculate the corrected values of the fluxes and then the corrected values of the variables:

F.P.D.M. and A.D.R. are grateful to the Italian Ministry of Education, University and Research (MIUR), for financial support under Project No. PRIN 2003-2005 (Area 09, No. 37).

Fi+1 ) Fi +

(∂F∂z )

average

Appendix: McCormack Method McCormack’s predictor-corrector method is an explicit, predictor-corrector finite difference technique which is secondorder accurate in both space and time.18 We adopted this method to solve conservation equations in conservative form. To explain it, let us refer to the general case of the fluidized bed model (with also the kinetic energy term). The conservation equations, in the general steady case, are (for more information see the work of Anderson18):

∂F )J ∂z where

[

Fu F ) Fu2 + p Fu(cpT + u2/2)

(A1)

] [

0 J ) -g(F + (1 - )Fs) ha(Ts - T)

]

(A2)

The domain is to be discretized into a number n of nodes, where the values of the variables will be computed. Considering a general node i, where all the properties are known, the procedure will be illustrated to calculate the variables at node i + 1. Naturally, the algorithm starts at node 0 (z ) 0) where the initial conditions are given. A1. Predictor Step. At node i we can calculate the fluxes Fi and the source terms Ji. Then, from eq A1, we can estimate the values of the fluxes in the grid node i + 1 (or z + ∆z) using a forward projection:

(∂F∂z )* ) J f F i

i+1*

) Fi* + Ji∆z

Hence, solving the algebraic system

[

(A3)

]

Fi+1*ui+1* Fi+1*ui+1*2 + pi+1* ) Fi+1* Fi+1*ui+1*(cpTi+1* + ui+1*2/2)

corrected

(∂F∂z )

(A4)

) Ji+1*

where Ji+1* are the source terms calculated with the predicted variables. Now we can calculate an averaged value of the flux derivative: average

) 0.5

corrected

[(∂F∂z )* + (∂F∂z )

]

∆z f ui+1 pi+1 Ti+1

Nomenclature A ) cross-sectional area of the bed (m2) a ) exchange surface per unit volume of the bed (m2/m3) Bi ) Biot number (-) cs ) specific heat of the solid phase (J/(kg K)) cp ) specific heat of air (J/(kg K)) ds ) diameter of a sphere having the same volume of the real particle (m) g ) acceleration of gravity (m/s2) h ) convective heat transfer coefficient (W/m2) ks ) thermal conductivity of the particles (W/(m K)) G ) air mass flow rate (kg/s) Nu ) Nusselt number (-) p ) gas pressure (Pa) Pr ) Prandtl number (-) Re ) Reynolds number (-) t ) time (s) T ) air temperature (°C) Tc ) combustion chamber temperature (°C) Ti ) inlet air temperature (°C) Ts ) solid particles’ temperature (°C) To,reg ) temperature of the gas leaving the regenerator (°C) u ) air superficial velocity (m/s) z ) axial coordinate (m) Greek Symbols ) bed voidage (-) φs ) sphericity (-) ηreg ) regenerator efficiency (-) µ ) air viscosity (kg/(m s)) F ) air density (kg/m3) Fs ) particle density (kg/m3) τ ) cycle duration (s) Literature Cited

it is possible to predict the values of the variables Fi+1*, ui+1*, pi+1*, and Ti+1*. A2. Corrector Step. To obtain the corrected values of the variables, we can calculate the corrected value of the flux derivatives:

(∂F∂z )

{

Fi+1

Acknowledgment

(1) Lewandowski, D. A. Design of Thermal Oxidation Systems for Volatile Organic Compounds; Lewis Publishers: New York, 2000. (2) Khan, F. I.; Ghoshal, A. Kr. Removal of Volatile Organic Compound from Polluted Air. Journal of Loss PreVention in the Process Industries 2000, 13 (6), 527-545. (3) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd ed.; Butterworth-Heinemann: Oxford, U.K., 1991. (4) Geldart, D. Gas Fluidization Technology; J. Wiley & Sons: Bradfort, U.K., 1986. (5) Boger, T. Performance and Design of TRO/RCO with Ceramic Honeycombs - Influence of Unequal Mass Flow and Auto-Ignition; Corning GmbH: Wiesbaden, Germany, 2000. (6) Choi, B.-S.; Yi, J. Simulation and Optimization on the Regenerative Thermal Oxidation of Volatile Organic Compounds. Chem. Eng. J. 2000, 76, 103-114. (7) Cheng, W.-H.; Chou, M.-S.; Lee, W.-S.; Huang, B.-J. Applications of Low-Temperature Regenerative Thermal Oxidizers to Treat Volatile Organic Compounds. J. EnViron. Eng. 2002, 128 (4), 313-319. (8) Lewandowski, D. A.; Nutcher, P. B.; Walder, P. J. Advantages of Twin Bed Regenerative Thermal Oxidation Technology for VOC Emission Reduction. Presented at Air & Waste Management Conference “Emerging Solutions to VOC And Toxics Control”, Clearwater, FL, 1996.

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(9) Afandizadeh, S.; Foumeny, E. A. Design of Packed Bed Reactors: Guides to Catalyst Shape, Size, and Loading Selection. Appl. Therm. Eng. 2001, 21, 669-682. (10) Zarrinehkafsh, M. T.; Sadrameli, S. M. Simulation of Fixed Bed Regenerative Heat Exchangers for Flue Gas Heat Recovery. Appl. Therm. Eng. 2004, 24, 373-382. (11) Duprat, F.; Lopez, G. L. Comparison of Performance of Heat Regenerators: Relation between Heat Transfer Efficiency and Pressure Drop. Int. J. Energy Res. 2001, 25, 319-329. (12) Chou, M.-S.; Cheng, W.-H.; Huang, B.-J. Heat Transfer Model for Regenerative Beds. J. EnViron. Eng. 2000, 126, 912-918. (13) Duffie, J. A.; Beckman, W. A. Solar Engineering of Thermal Processes; John Wiley and Sons: New York, 1991. (14) Yu, J.; Zhang, M.; Fan, W.; Zhou, Y.; Zhao, G. Study on Performance of the Ball Packed-Bed Regenerator: Experiments and Simulation. Appl. Therm. Eng. 2002, 22, 641-651. (15) Yoshida, F.; Ramaswami, D.; Hougen, O. A. Temperatures and Partial Pressures at the Surfaces of Catalyst Particles. AIChE J. 1962, 8, 5-11.

(16) Ergun, S. Fluid Flow in Packed Beds. Chem. Eng. Process. 1952, 48, 9-94. (17) Niven, R. K. Physical Insight into Ergun and Wen & Yu Equations for Fluid Flow in Packed and Fluidized Beds. Chem. Eng. Sci. 2002, 57, 527-534. (18) Anderson, J. D. Computational Fluids Dynamics; McGraw-Hill: New York, 1995. (19) Coulson, J. M.; Richardson J. F. Chemical Engineering; Pergamon Press, Ltd.: Oxford, U.K., 1968; Vol. 2. (20) Perry, R. H.; Green, D. W. Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill: New York, 1997.

ReceiVed for reView November 22, 2005 ReVised manuscript receiVed April 7, 2006 Accepted April 20, 2006 IE051300Y

Modeling Process Characteristics and Performance of Fixed and

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