Numerical evaluation of the energetic performances of structured and random packed beds in regenerative thermal oxidizers

Applied Thermal Engineering 27 (2007) 762–770 www.elsevier.com/locate/apthermeng

Numerical evaluation of the energetic performances of structured and random packed beds in regenerative thermal oxidizers Mario Amelio *, Pietropaolo Morrone Department of Mechanical Engineering, University of Calabria, 87030 Arcavacata di Rende, Italy

Abstract Regenerative thermal oxidizers (RTO) can be conveniently used to control volatile organic components (VOC) emissions, because of their thermal efficiency and cost effectiveness. In the RTO technology, beds of inert material are used in order to heat the polluted air by cooling burnt gases, through a sequence of cyclic operations which cut the fuel requirements. A computational 1D unsteady model, able to account for both structured and random packed bed regenerators, is developed and applied to realistic plant conditions. Process thermal efficiency and gas pressure drop are calculated as functions of the system geometry and operating parameters. The code can be usefully employed in the analysis and design of RTO systems and in order to choose the more suitable type of regenerator, structured or random packed bed (even considering various particle shapes). Energetic performances of both random and structured regenerators were compared, showing that the first ones exhibit a little higher thermal efficiency but also an elevated pressure drop, at a same value of exchange surface per unit volume of the bed. Random packed bed regenerators resulted less attractive from the energetic point of view and their usage is advisable if their lower cost satisfy economical requirements.  2006 Elsevier Ltd. All rights reserved. Keywords: Regenerative thermal oxidizers; Thermal efficiency; Structured bed; Random bed

1. Introduction Volatile organic compounds (VOC) are pollutants generated by transportation, chemical or petrochemical industries, as well as by processes where they are employed as solvents (e.g. painting). Their abatement can be effectively achieved by a thermal oxidization, with temperature greater than 800 C. In order to save fuel in reaching such a temperature, it is necessary to recover heat from burnt gases and transfer it to the polluted air, before its combustion. This is accomplished by regenerators so the plant operates as a regenerative thermal oxidizer (RTO).

*

Corresponding author. E-mail address: [email protected] (M. Amelio).

1359-4311/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.10.016

RTOs are particularly attractive due to the fact that no post-treatment is necessary, as compared to other alternatives such as activated charcoal oxidizers [1,2]. In the RTO technology, thermal regenerators of inert material (usually ceramic materials) pre-heat the air to be processed and recover heat from burnt gases, through a sequence of cyclic operations which maximizes the operation yield, from the energy saving point of view. In each cycle, the VOC polluted air increases its temperature by flowing through the hot bed, P, (Fig. 1a) which acts as a pre-heater, then completes the oxidization in the combustion chamber and, eventually, releases most of its sensible heat by flowing through a cold bed, A, which acts as an accumulator of thermal energy. The bed A (Fig. 1a) then becomes hot and ready to act as a pre-heater P (Fig. 1b) of the inlet effluent in the next thermal exchange cycle. The switch is accomplished by

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Nomenclature A Ac a Bi cs cp ds Deq h ks k G f Nu p P Pr

cross-sectional area of the bed (m2) cross-sectional area of one channel (m2) exchange surface per unit volume of the bed (m2 m3) Biot number (–) specific heat of the solid phase (J kg1 K1) specific heat of air (J kg1 K1) diameter of a sphere having the same volume of the real particle (m) hydraulic diameter convective heat transfer coefficient (W m1) thermal conductivity of the solid phase (W m1 K1) air thermal conductivity (W m1 K1) specific air mass flow rate (kg m2 s1) fanning friction factor Nusselt number (–) gas pressure (Pa) channel perimeter Prandtl number (–)

Re R* S t T Tc Ti Ts T0,acc u z

Reynolds number (–) Constant gas (J kg1 K1) cross-sectional area of the channel wall (m2) time (s) air temperature (C) combustion chamber temperature (C) inlet air temperature (C) solid temperature (C) temperature of the gas leaving the accumulator (C) air superficial velocity (m s1) axial co-ordinate (m)

Greek symbols e bed voidage (–) us sphericity (–) gacc accumulator efficiency (–) l air viscosity (kg m1 s1) q air density (kg m3) qs solid density (kg m3)

Fig. 1. RTO scheme.

inverting the gas flow towards the two beds, through a valve equipment. A burner is located in the combustion chamber in order to ensure complete VOC oxidation. It is generally used only in the start-up phase, when the exit temperature from the pre-heater is not sufficient to guarantee VOC auto-ignition. In an efficient RTO system, when VOC concentration in the incoming polluted air exceeds a minimum level, it is possible to achieve the complete oxidation of impurities in the combustion chamber, without adding auxiliary combustible. After a start-up phase, steady-state operation is achieved and the system sustains by itself thanks to VOC enthalpy of combustion. In this situation, the two regener-

ators follow a thermal cycle constituted by a pre-heating and a recovering phase, which allows a significant saving of energy. The thermal efficiency of an RTO system depends on the efficient use of combustion heat within the combustion chamber, on the heat retention capacities of the regeneration chambers, and on the proper switching of the ceramic beds between their function of heat-charge or discharge chambers [1]. Ordinary regenerators are made by inert material of two geometric types: ceramic bricks with longitudinal square holes having a 3 mm · 3 mm cross flow area (these are usually referred to as ‘‘structured beds’’), or randomly arranged pebbles, with average diameter usually larger than 1 cm

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(‘‘random packing beds’’). The main difference between the two categories lays in the ratio between fixed and variable costs of the related process. For a structured packing, the purchase expenses are far higher, but operative costs, connected to the pressure loss throughout the bed, are lower [1]. On the contrary, unstructured materials are easier to produce, so they have lower prices than structured ones, but pressure drops and the related costs are higher. The best choice derives from profitability analysis, once the flow rates and the consequent RTO plant size have been defined. The path towards a definition of a cost-effective plant hence includes: • a model of the main phenomena occurring into both types of regenerator, as the thermal exchange and the airpressure drop, from which the energy demand depends on; • a sizing of the plant; • a subsequent economic analysis that accounts for operating costs, associate mainly with energy consumption, and construction costs, associate with the size of the plant and with the material involved. The aim of the present work is the set-up of the model reported in the first item while cost analysis in the last one, is beyond it. 2. Background In the literature very few studies on packed bed RTOs are available. Boger [3] 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 for several outlet to inlet flow rate ratio (in case of addition of air or auxiliary fuel). In the same paper, the influence of the temperature profiles on the thermal stresses has been 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 Yi [4] 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 oxidization only depends on temperature level and, if it is high enough, no continuous operation of the burner is necessary. 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 towards these systems. Cheng et al. [5] 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.

The outcomes have shown that high removal efficiency can be achieved in two-bed RTOs. In another paper [6] Lewandowski et al. carried out an experimental analysis of the thermal efficiency, pressure drop and efficiency of VOC removal, by varying the cycle duration and the flow rate of the polluted gas. There are various papers on the properties of thermal regenerators, although in operating conditions different from those typically encountered in RTOs. For example, spherical particles are assumed, while in industrial plant more complex shapes (hollow cylinders, saddle-like particles [7]) are utilized to maximize the thermal exchange and minimize the pressure drop. Also, lower flow rates or small temperature changes are assumed in order to simplify the problem. In particular, in a paper from Zarrinehkafsh and Sadrameli [8] 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 Lopez [9] compared structured and woven-screen beds, in terms of thermal efficiency and flow rates far smaller than those processed in regenerative thermal oxidizers. In addition, aluminium was used as material, thus limiting the applicability to catalytic rather than thermal oxidizers. In the latter, the typical temperatures would melt the structure of the unit. The model described in the present paper handles wide temperature ranges so it has to take into account the gas velocity change. Moreover it considers the operation of the entire plant, paying attention to both regenerators (pre-heater and thermal accumulator bed). Finally, after the simulation of the start-up period, it calculates the whole plant performance, through a global steady-state thermal efficiency and the estimate of energy demand to induct the flow.

3. RTO thermal model A one-dimensional transient model was used to simulate the thermal exchange between the regenerators and the polluted incoming air. The basic model assumptions are the following: 1. the characteristics of the flowing fluid was assumed to be that of pure air; 2. mono-dimensional unsteady flow; 3. constant (in time) mass flow rate; 4. negligible thermal accumulation of the gas in the regenerator; 5. conductive and irradiative energy exchange mechanisms negligible compared to convective heat exchange; 6. adiabatic systems towards the surroundings; 7. negligible temperature gradient within the solid phase.

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3.1. Random packed bed thermal regenerators modelling The hypothesis of constant gas velocity in the regenerator adopted in [8,10] was removed in the present work, due to the large temperature excursion typical of RTOs, which seriously affects volumetric flow rate. The control volume is schematically illustrated in Fig. 2. The variables q, 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 co-ordinate z. Referring to the control volume, the thermal exchange in a packed bed with forced fluid flow can be described as oT haðT s  T Þ ¼ oz Gcp oT s ¼ Gcp dT  qs cs dzð1  eÞ ot

ð1Þ ð2Þ

G is the mass flow rate [kg/s], e is the porosity, or void fraction, defined as volume fraction of pore space in the regenerator. Porosity was assumed to be uniform within the bed. The choice of the heat transfer coefficient is a crucial factor. Indeed, various correlations present in literature yield very different values [11–14]. Thus, in the present work, the well-established and rather conservative relations proposed by Kunii and Levenspiel [13] was adopted and we validated the model [15,16] with experimental results found in [17]. We found that the agreement of the variables calculated with respect the experimental data is very good. The average error for the gas temperature data is 2%, while for the bed temperature is 6% [15,16].

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where us is the sphericity of particles, which is the ratio of surface of the sphere of diameter ds and the real surface of the particle. Therefore, sphericity is equal to 1 only for spherical particles, while it is lower for packing units of different shapes. Pressure losses were determined using the Ergun equation [18] which relates pressure to the superficial velocity1 within a porous medium: 

op 150ð1  eÞ2 l 1:75ð1  eÞ 2 ¼ uþ qu 2 3 2 oz /s d s e3 us d s e

ð5Þ

An assumption of negligible temperature gradients within particles can be adopted if the Biot number Bi = h(ds/ 6us)/ks is lower than 0.1 [19], as in the flow condition assumed in this work. Eq. (1) was solved for by assuming that the bed temperature profile, in the interval of integration Dt, was dependent only on the z co-ordinate, and the solution is T iþ1  T s;i  ha Dz ¼ e Gcp T i  T s;i

ð6Þ

Values of T, p, u and q were calculated by applying the following procedure, over all the domain: ! 2 150ð1  eÞ l 1:75ð1  eÞ ðaÞ: piþ1 ¼ pi  þ G ui Dz / s d s e3 u2s d 2s e3 ðG ¼ qu ¼ costÞ ðbÞ: T iþ1 ¼ T s;i þ ðT i  T s;i Þe ðcÞ: qiþ1 ¼ piþ1 =ðR T iþ1 Þ ðdÞ:

ha Dz Gc p

uiþ1 ¼ G=qiþ1 ð7Þ

hd s Nu ¼ ¼ 2 þ 1:8Pr1=3 Re1=2 k qud s with Re ¼ l

for Re > 100

In the following time step, the bed temperature profile was updated using Eq. (2) with the result: ð3Þ

The wetted surface of the packed bed per unit volume was expressed by a¼

6ð1  eÞ us d s

ð4Þ

T is ðt þ DtÞ ¼ T is ðtÞ þ

Gcp Dt ðT i ðtÞ  T iþ1 ðtÞÞ qs cs ð1  eÞDz

ð8Þ

The procedure 7 was applied with the new solid temperature profile obtained by Eq. (8), and so on, with a new time step, until the end of the entire cycle time. Finally, the solution of the equations is first-order accurate. 3.2. Structured bed thermal regenerators modelling A cross section of a structured monolith bed is shown in Fig. 3. Energy equations applied to both the gas and solid phases within a single channel, give: oT hðP =Ac ÞðT s  T Þ ¼ oz Gcp oT s ¼ GAc cp dT  qs cs Sdz ot

Fig. 2. Control volume for a random packed bed regenerator.

ð9Þ ð10Þ

1 Superficial velocity is equal to G/(qA), where A is the total cross section of the regenerator.

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Fig. 3. Cross-sectional area of a structured bed.

where P is the channel perimeter and Ac is the cross-sectional area of the channel. The rate (P/Ac) has the same role as ‘‘a’’ in the case of random packed beds and Sdz is the volume of solid that exchanges thermal energy with the gas (S = 0.5(sylx + sxly)). The heat transfer coefficient h used in the model was calculated on the basis of the following correlation reported by [20] Nu ¼ hDeq =k ¼ 3:61

ð11Þ

where Deq is the hydraulic diameter of a single channel. This correlation is valid in the case of square cross-sectional channels and when heat flux is constant, as at steadystate. Veser and Frauhammer [21] found that pressure loss could be defined by op 1 ¼ f qu2 oz 2Deq

ð12Þ

where f is the fanning friction factor which is equal to 64/Re for laminar flow (Re < 2000) as occurs in a structured RTOs. The equations were numerically solved in the same way as explained for random packed beds, in Section 3.1. This gives the profiles of T, p, q and u along the z-axis, of both gases and solids, during the entire thermal cycle. Eq. (9) has an exponential solution, analogous to Eq. (6), in the form: T iþ1  T s;i  hP Dz ¼ e GAc cp T i  T s;i

The thermal cycle under investigation consists of a succession of pre-heating and accumulation (regeneration) phase, of 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 regeneration phase were alternatively simulated. Steady-state is attained when bed temperatures in two subsequent cycles are numerically equal, with a difference smaller 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, etc., each with its own exchange surface per unit volume a and typical packing voidage e [22]. In the following sections, alumina (Al2O3) spheres, hollow cylinder, Berl Saddles and Lessing will be analyzed (Fig. 4). 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 left the accumulator at the same temperature Ti at which the cold gas enters the pre-heater: R T 0;acc ðtÞ cp ðT ÞdT ð14Þ gacc ðtÞ ¼ TRc T i c ðT ÞdT Tc p where T0,acc(t) is the instantaneous temperature of the gas exiting from the accumulator. More often, as will be seen below, temporally averaged values are conveniently used for limited periods of time. The first set of results is concerned with a detailed analysis of the process characteristics of random packed bed RTOs as the parameters involved in the plant operation are varied. The robustness and flexibility of the computational code developed allow, as well as the versatility typical of numerical simulations, several different configurations to be tested in their performance.

ð13Þ

4. Simulations results The model was developed with the aim to predict the heat transfer efficiency and the pressure drop across the heat exchange units present in a RTO plant, with special emphasis on the possibility to conduct comparisons on various configurations.

Fig. 4. Particles analyzed (www.rauschertus.com).

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Significantly different properties come out between spherical particles and the others: sphericity /s (1 versus about 0.3, respectively), packing voidage e (44% versus val-

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ues 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 mm – diameter · height – hollow

Table 1 System properties for random bed RTOs Regenerator height (m) Spherical particles Raschig rings Selle di Berl Lessing rings Specific mass flow rate Inlet air temperature Temperature of the gas leaving the CC

0.25; 0.5; 0.75; 1; 1.25; 1.5 Bed voidage Sphericity 44% 1 Bed voidage Sphericity 72–77% 0.3 Bed voidage Sphericity 65–70% 0.3 Bed voidage Sphericity 65–72% 0.3

ds (mm) 6; 10; 12.5; Size (mm) 6; 10; 12.5; Size (mm) 6; 10; 12.5; Size (mm) 6; 10; 12.5; 1 kg m2 s1 25 C 800 C

15 19 19; 25 19; 25

a (m2 m3) 560–224 a (m2 m3) 964–239 a (m2 m3) 1148–246 a (m2 m3) 964–223

Fig. 5. Pressure drops for all the packings analyzed, Lessing rings, Berl saddles, Raschig rings, and spheres. Specific mass flow rate 1 kg s1 m2. (a) gacc = 90%; (b) gacc = 95%.

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cylinders). It is noteworthy that hollow cylinders (Rashig rings), compared to other non-spherical particles, are easy to produce and cheap. Geometrical data related to them are collected from [22]. Alumina thermophysical properties are taken from [20]. The properties of the modelled system are listed in Table 1. Energetic performances, thermal efficiency and pressure drops, for all these packing were compared and the results are reported in Fig. 5, that shows the pressure drop produced by all the types of particles analyzed (Fig. 4) at different bed height but maintaining a similar value of the thermal efficiency (gacc = 90–95%). For example, a pressure drop of 1.8 kPa is observed with 10 · 10 mm Rashig rings and a regenerator length of 0.48 m. The 6 · 6 mm Raschig rings, 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). Spherical particles, instead, tend to give considerably higher pressure drops than other particles, 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 on pressure drops given by larger particles 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 particles different from spheres, no clear trend can be observed. Lessing ring packings give the bigger values of pressure drops due to their fins that increase the exchange surface but decrease the porosity. Berl saddle packings, on the other hand, give energetic performances comparable to those offered by Raschig ring packings. The worst energetic perfor-

Table 2 System properties for structured bed RTOs Monolith

Cross section Height Channel size Distance between two nearby channel Porosity a (m2 m3)

1

2

3

150 · 150 mm 300 mm 2.26 mm 0.6 mm

150 · 150 mm 300 mm 3 mm 0.7 mm

150 · 150 mm 300 mm 4.9 mm 1 mm

0.60 1005

0.65 825

0.67 540

mances are given by spherical particles in all the simulations. The second set of results is concerned with an analysis of the process characteristics of structured packed bed RTOs, that are made by a series of blocks (monoliths) having square section holes. In comparison to the turbulent flow through random packings, flow through structured packing is laminar at the normal operating conditions of RTOs plants. Monoliths are usually characterized by the number of cells per square inch (csi). The greater this number, the greater the surface area per unit volume. The structured monoliths are available for RTO applications in various cell densities and, in order to make a comparison between energetic performances of both types of regenerators (random and structured regenerators), we considered three monoliths, whose geometric properties are listed in Table 2 (Koch catalogues – www.kochknight.com). Figs. 6 and 7 are compared thermal efficiency and pressure drops, at same values of wetted surface for unit volume of regenerator nearly 1000 m2/m3. In this conditions, thermal recovery efficiencies of randomly packed bed RTOs are greater than efficiencies of struc-

Fig. 6. Comparison between thermal recovery efficiency of structured and random beds (Raschig rings) at a same wetted surface per unit volume 1000 m2 m3.

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Fig. 7. Comparison between pressure drops of structured and random beds (Raschig rings) at a same wetted surface per unit volume 1000 m2 m3.

Fig. 8. Comparison between pressure drops related to random regenerators (Raschig rings) and structured regenerators at a same value of thermal recovery efficiency (gacc = 95%). Specific mass flow rate 1.0 kg s1m2. Geometric properties of structured beds are reported in Table 2.

tured packed bed RTOs, but pressure drops are significantly higher. It is interesting to compare the pressure drop produced by the two kind of regenerators, random beds (packing of Raschig rings) and monoliths at different bed heights but at a same value of thermal efficiency. In Fig. 8 it is possible observe that, in order to obtain a recovery efficiency of 95%, pressure drops given by random RTO plants with Raschig rings of various size (from 6 to 19 mm) are nearly four times greater than those obtainable with monoliths whose geometrical properties are reported in Table 2. On the other hand they can satisfy economical requirements, due to their lower cost, and are often adopted in the industrial practise. The actual best choice of regenerator therefore must derive from an economical analysis that is, however, beyond the aim of the present work.

5. Conclusions A 1D simulation model of regenerative thermal oxidizers (RTO) has been proposed. It can manage the dynamic thermal behaviour of both random and structured thermal regenerators. By means of the computational code, the influence of the key operating parameters on the energetic performance (thermal recovery efficiency and pressure drops) has been evaluated. A first set of results concerned with the evaluation of the pressure drops related to different random packing particles used in the industrial practise (spheres, Raschig rings, Berl saddles and Lessing rings), at a same value of thermal recovery (gacc = 90–95%) and as function of the length of the regenerator. The pressure drops produced by all these types of particles were compared. Results showed that

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spherical particles give the worst energetic performances, determining a pressure drop increasing with particle diameter, while other particles give a nearly constant and low resistance to the fluid flow. This analysis can be useful in establishing the regenerator size that allows a desired value of the thermal recovery efficiency. It is worthwhile to notice that the papers found in the literature involve the numerical analysis of thermal properties of randomly packed beds just for spherical particles. The numerical model here presented is, from this point of view, an original contribution. Moreover it reveals a specific advantage, since RTOs systems normally use particles characterized by more complex geometries like Raschig rings, lessing rings and Berl saddles. In a second set of results there were compared energetic performances of both random and structured regenerators, showing that the first ones exhibit an higher thermal efficiency (+1% up to +3%) but also an higher pressure drop (+100% up to +600%) at a same value of exchange surface per unit volume of the bed, in the operating conditions analyzed in the paper (Table 1). The combined effect makes the random packed bed regenerators less attractive from the energetic point of view. Nevertheless they can satisfy economical requirements, due to their lower cost, and are often adopted. The actual best choice of regenerator therefore derives from profitability analysis, once flow rates and the corresponding RTO plant size and costs have been defined. At the present, the economical analysis is beyond the aim of this work. Therefore, the application of the proposed model allows to carry out parametric studies of the several variables that affect the energetic performances of the different types of regenerators used in RTOs systems, and would be useful in the analysis and design of RTOs systems. References [1] D.A. Lewandowski, Design of Thermal Oxidation Systems for Volatile Organic Compounds, Wiley-Interscience publication, Winsconsin, USA, 2000. [2] F.I. Khan, A.Kr. Ghoshal, Removal of volatile organic compound from polluted air, Journal of Loss Prevention in the Process Industries 13 (6) (2000) 527–545. [3] T. Boger, Performance and Design of TRO/RCO with Ceramic Honeycombs – Influence of Unequal Mass Flow and Auto-Ignition, Corning GmbH, Wiesbaden, Germany, 2000. [4] B.-S. Choi, J. Yi, Simulation and optimization on the regenerative thermal oxidation of volatile organic compounds, Chemical Engineering Journal 76 (2000) 103–114.

[5] W.-H. Cheng, M.-S. Chou, W.-S. Lee, B.-J. Huang, Applications of low-temperature regenerative thermal oxidizers to treat volatile organic compounds, Journal of Environmental Engineering 128 (4) (2002) 313–319. [6] P.J. Waldern, P. Nateber, D. Lewandowski, Advantages of twin bed regenerative thermal oxidation (RTO) technology for VOC emission reduction, in: Process Combustion Corporation (PCC), Pittsburgh, Air & Waste Management Conference Emerging Solutions to VOC And Toxics Control, 1997. [7] S. Afandizadeh, E.A. Foumeny, Design of packed bed reactors: guides to catalyst shape, size, and loading selection, Applied Thermal Engineering 21 (2001) 669–682. [8] M.T. Zarrinehkafsh, S.M. Sadrameli, Simulation of fixed bed regenerative heat exchangers for flue gas heat recovery, Applied Thermal Engineering 24 (2004) 373–382. [9] F. Duprat, G.L. Lopez, Comparison of performance of heat regenerators: relation between heat transfer efficiency and pressure drop, International Journal of Energy Research 25 (2001) 319– 329. [10] J. Yu, M. Zhang, W. Fan, Y. Zhou, G. Zhao, Study on performance of the ball packed-bed regenerator: experiments and simulation, Applied Thermal Engineering 22 (2002) 641–651. [11] A.S. Gupta, G. Thodos, Direct analogy between mass and heat transfer to beds of spheres, AIChEJ 9 (1973) 751. [12] G.O.G. Lof, R.W. Hawley, Unsteady state heat transfer between air and loose solids, Industrial and Engineering Chemistry 40 (1947) 1061. [13] D. Kunii, O. Levenspiel, Fluidization Engineering, second ed., Butterworth-Heinemann, Oxford, 1991. [14] E. Achenbach, Heat and flow characteristics of packed beds, Experimental Thermal and Fluid Science 10 (1995) 17–27. [15] M. Amelio, G. Florio, P. Morrone, Simulazione dello scambio termico e delle perdite di carico all’interno di rigeneratori ad impaccamento casuale in Ossidatori Termici Rigenerativi, 60 ATI conference, Roma, 2005. [16] P. Morrone, F.P. Di Maio, A. Di Renzo, M. Amelio, Modelling process characteristics and performance of fixed and fluidized beds, Industrial & Engineering Chemistry Research 45 (2006) 4782– 4790. [17] M.-S. Chou, W.-H. Cheng, B.-J. Huang, Heat transfer model for regenerative beds, Journal of Environmental Engineering 126 (2000) 912–918. [18] R.K. Niven, Physical insight into Ergun and Wen & Yu equations for fluid flow in packed and fluidized beds, Chemical Engineering Science 57 (2002) 527–534. [19] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, Wiley-Interscience publication, Winsconsin, USA, 1991. [20] R.H. Perry, D.W. Green, Perry’s Chemical Engineers’ Handbook, seventh ed., Mc Graw Hill, New York, 1997. [21] G. Veser, J. Frauhammer, Modeling steady state and ignition of catalytic methane oxidation in a monolith reactor, Chemical Engineering Science 55 (2000) 2271–2286. [22] J.M. Coulson, J.F. RichardsonChemical Engineering, vol. 2, Pergamon Press, Oxford, 1968.