Thermal combustion of lean methane air mixtures: Flow reversal research and demonstration reactor model and its validation

Transcription

1 Polish Academy of Sciences, Institute of Chemical Engineering From the SelectedWorks of Krzysztof Gosiewski 2012 Thermal combustion of lean methane air mixtures: Flow reversal research and demonstration reactor model and its validation Krzysztof J Gosiewski Available at:

2 Chemical Engineering Journal (2012) Contents lists available at SciVerse ScienceDirect Chemical Engineering Journal journal homepage: Thermal combustion of lean methane air mixtures: Flow reversal research and demonstration reactor model and its validation Krzysztof Gosiewski, Anna Pawlaczyk, Manfred Jaschik Institute of Chemical Engineering, Polish Academy of Sciences, Gliwice, Poland highlights " Fairly large thermal combustion of lean methane air mixtures reactor was simulated. " Mathematical models with and without heat capacity of the wall were compared. " Simulation results for the two model options (with and without the wall) are similar. " Agreement of measured and simulated temperature profiles is sufficient for practice. " Both model (with and without the wall) options may be used for design purposes. article info abstract Article history: Available online 20 July 2012 Keywords: Chemical reactors Reversed flow reactors Thermal combustion Methane VAM TFRR Problem of the coal mine shafts ventilation air methane (VAM) utilization is briefly presented. A research and demonstration plant experiments were carried out as the first step to a future industrial application. The plant contained a thermal flow reversal reactor (TFRR) as the main unit where lean methane air mixture is combusted. The study consisted of the plant experiments and mathematical model simulations as well. The paper presents the mathematical model description and its experimental validation based on comparison of the model results with measured plant data. The aim of the paper is to assess whether dynamic, one dimensional (in space) model may be useful for a fairly large scale reactor simulations. The model was developed and tested in the 2 versions: without and with heat accumulation in the reactor wall. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Corresponding author. Mobile: ; fax: address: k.gosiewski@iich.gliwice.pl (K. Gosiewski). Methane released during coal mine exploitation is not only greenhouse gas but also a valuable energy carrier. The so-called Ventilation Air Methane (VAM), is emitted with mine ventilation air at a concentration of about CH 4 vol.% [1]. Such lean mixture can be considered as an alternative fuel for energy production by applying modern combustion technologies such as Flow Reversal Reactors (FRRs). Extensive review [1] discusses both: catalytic (CFRR) and thermal (TFRR) VAM utilization methods, but practically TFRR seems to be the more attractive method [2]. Experiments in the present study were carried out on the research and demonstration TFRR plant built in the Institute of Chemical Engineering of the Polish Academy of Sciences. General view of the plant is shown in Fig. 1, while simplified flowsheet of the plant is given in Fig. 2. The main unit of the plant a thermal flow reversal reactor (TFRR) consists of two parts Section I and Section II. They are connected by a duct at the top. Part of the hot gas can be withdrawn from this duct to the heat recovery exchanger. Both sections are packed with ceramic monolith blocks with a large number of straight and parallel channels (3 3 mm), resulting in low pressure drop. The concentration of methane was varied from 0.1 to 1 vol.% by mixing natural gas with air. Electric heaters mounted at the top of TFRR were used only for preheating the monoliths to enable start of normal operation. Gas feed was varied from 200 to 400 m 3 STP/h. Experimental results for a gas feed of 400 m 3 STP/h are presented in Table 1. For methane concentrations equal or higher than 0.22 vol.% the operation was autothermal, but reasonable heat recovery is only possible above 0.4 vol.%. Since the results of the experiments were very promising as the next step build-up of an industrial pilot plant is projected. Thus along with experimental research a mathematical model was developed and validated. A majority of FRRs models published in the literature (for abundant bibliography see [3] or [4]) either are most often validated on very small laboratory setups or even sometimes are not validated at all (e.g. [5]). Every FRR is subject to heat loss, difficult to be precisely included to the model. When the reactor is small the heat loss may be so significant that its validation becomes practically worthless. To cope with this problem usually a /$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.

3 K. Gosiewski et al. / Chemical Engineering Journal (2012) Nomenclature a j exponent for concentration term in general kinetic Eq. (11) a v specific surface area, m 1 c s solid phase specific heat, J kg 1 K 1 c g gas phase specific heat, J mol 1 K 1 C CH4 ; C CO CH 4 or CO concentration, respectively, in Eq. (11), mol m 3 d h hydraulic diameter of the monolith channel, m D r reactor diameter or square size, m D eff effective mass dispersion coefficient, m 2 s 1 E j activation energy for jth reaction, J mol 1 h heat transfer coefficient, W m 2 K 1 I single,i twin a measure of distance from CSS acc. to Eq. (16) or (17), K k 0,j pre-exponential factor in general kinetic Eq. (11), mol (1 a) m 3(1 a) s 1 l subsequent number of consecutive half-cycle L w wall thickness, m n g molar flux of gas, mol m 2 s 1 n r number of reactions n indicator of repeatability in Eq. (11) of the half-cycles (n = 1 for symmetric and n = 2 for asymmetric half-cycles) Pe g Peclet number for mass dispersion Q gen,q rec heat generated and heat recovered (respectively), W r hom, j jth homogeneous reaction rate (defined per monolith volume by Eq. (11), mol m 3 s 1 R universal gas constant, J mol 1 K 1 t time, s T temperature, K or C u linear gas velocity, m s 1 X total CH 4 conversion at the outlet y i mole fraction of ith component z axial coordinate, m z L,z R left (inlet) and right (outlet) axial coordinate of each TFRR section, m Z total length of the reactor packing (i.e. for Section I + Section II), m Greek letters a gas solid heat transfer coefficient, W m 2 K 1 dt difference between initial (starting) temperatures in consecutive half-cycles, K dt twin difference between initial (starting) temperatures in consecutive full cycles, K DH j heat of reaction j, J mol 1 DT ad adiabatic temperature rise ¼ð DHÞC inlet CH 4 =ðc g q g Þ,K DT exp experimentally measured temperature rise, K DT s temperature effect caused by any heat withdrawal from the reactor, K e void fraction coefficient e rad emissivity of radiation r Stefan Boltzmann constant, W m 2 K 4 k eff effective thermal conductivity of gas phase, W m 1 K 1 k s thermal conductivity of solid phase, W m 1 K 1 q density, kg m 3 or mol m 3 s, s/2 flow reversal cycle and half-cycle, respectively, s m i,j stoichiometric coefficient of component i in reaction j Subscripts and superscripts average averaged in time over n half-cycles av averaged in space over TFRR packing length exp experimentally measured g gas i, j component i or reaction j number (respectively) k number of arbitrarily chosen control points along the reactor length in Eqs. (16) and (17) l number of consecutive reversion half-cycle in Eqs. (14) and (15) inlet at the reactor inlet outlet at the reactor outlet s solid single concerns single consecutive half-cycle twin concerns consecutive full cycle (i.e. 2 consecutive half-cycles) start beginning of a subsequent half-cycle surr surroundings w wall Acronyms CFRR Catalytic Flow Reversal Reactor CSS Cyclic Steady State DDS Direct Dynamic Substitutions (Pickard s iteration) FRR Flow Reversal Reactor TFRR Thermal Flow Reversal Reactor VAM Ventilation Air Methane compensatory heating is applied (e.g. [6] and other authors as well). The point is that for practical purposes it is not important to compensate the heat losses, which in industrial plants are inevitable but reliably include them into the model. These questions arise in reactors with non-catalytic, i.e. thermal combustion due to much higher temperatures of operations resulting in higher share of the heat loss in the reactor heat balance. Another question concerns the heat accumulation in the reactor walls, especially in the TFRR wall and construction elements. Weight of the concrete lining in such unit can be comparable with the weight of TFRR packing; therefore it might have significant impact on the thermal dynamics of the plant. The first version of the model, described shortly in [7] revealed satisfactory agreement of the simulated plant temperature profiles with the results of experiments, but simulated transition time of attainment of consecutive Cyclic Steady States CSS (for definition of CSS see [8]) after simulated process disturbances was far from the reality. One could expect that including heat accumulation in the reactor wall and body could improve the model. In lit. [9] such inclusion of the wall was done into the spatially two-dimensional model. In the present paper a similar, but simpler approach for one-dimensional model is proposed. One dimensional model can be justified when radial heat and mass transports are negligible with respect to the convective axial ones. In monolith packing with a number of wall-separated parallel channels there is no radial mass transport. Experiments with TFRR in the present study, with a large square cross section, did not reveal significant differences of temperatures measured at different points at the same horizontal level. Therefore one could expect that 1D model might be accepted. 2. A brief description of the mathematical model Due to a very large heat capacity of a concrete refractory lining of the reactor wall, the dynamic mathematical model was developed in the two options: with and without heat accumulation in

4 78 K. Gosiewski et al. / Chemical Engineering Journal (2012) consist of parabolic partial heat and molar dynamic balance equations. For brevity the model equations are coupled together while extensions are marked in bold fonts. Heat balance for the gas phase: e q g c ¼ n g c þ e k T þ a a 2 m ðt s T g Þ where þ e rad r a m ðt 4 s T4 g ðdh Þ Xnr j r hom;j Þ j¼1 ð1þ k eff ¼ n g c g d h Pe g ; Pe g ¼ ud h D eff ð2þ Heat balance for the solid phase (packing): Fig. 1. General view of the research & demonstration TFRR plant. the reactor walls. Due to fairly large TFRR and rather uniform cross section temperature profiles it could have been expected that even if the wall heat capacity is large the wall effect on the simulation results may not be very significant. To check this, the both options of the model were investigated. The models used for simulations ð1 eþq s c t ¼ð1 eþk T a a 2 m ðt s T g Þ e rad r a m ðt 4 s T4 s Þ radial heat outflow through the wall zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ 4 h w ðt s T out Þ D r Optional variable T out in Eq. (3) which appears in the term radial heat outflow through the wall depends on the model option, as follows: ð3þ Fig. 2. Simplified flowsheet of the research & demonstration TFRR plant.

5 K. Gosiewski et al. / Chemical Engineering Journal (2012) Table 1 Parameters of the TFRR averaged for experiments carried out in the present study. Summary of results for ca. 400 m 3 STP =h VAM Half-cycle period CH 4 conversion Hot gas withdrawal flowrate Hot gas temp. Heat recovery efficiency [Eq. (20)] Expected heat recovery a vol.% s % m 3 STP =h C % MW t reactor extinguishes a Recalculated for an average ventilation shaft flowrate of 720; 000 m 3 STP =h. T out = T w for model with wall. T out = T surr for model without wall. Heat balance for the wall (valid only for model with wall): L w D r L w q w c w ðd r L w þ L 2 w Þ T w t ¼ k w ðd r L w þ L 2 T w w Þ 2 z 2 þ D r ½h w ðt s T w Þ h surr ðt w T surr ÞŠ Molar balances for the ith component: e q ¼ e q g D y 2 n þ Xnr j¼1 ðr hom;j m i;j Þ Eq. (4) (given in bold type) is solved only for the model option with heat accumulation in the wall. Boundary conditions: For z = z L: e k ¼ n g c p;g ½T g ðz L ; tþ T g;in ¼ 0; ¼ 0 ð7þ z¼zl e D eff 1 ¼ n g;iðz L ; tþ n inlet g;i where z L = 0 for Section I and z L = Z/2 for Section II For z = z ¼ 0 w ¼ 0 ; ¼ ¼ 0 ð9þ z¼zr z¼zr where: z R = Z/2 for Section I and z R = Z for Section II Initial conditions: For the 1st (i.e. start for simulations) half-cycle: t ¼ 0 T g ðz; 0Þ ¼T s ðz; 0Þ ¼f 1 ðzþ y g;i ðz; 0Þ ¼f 2 ðzþ T w ðz; 0Þ ¼T w;0 ðzþ ¼f 3 ðzþ ð4þ ð5þ ð6þ ð8þ ð10þ where f 1 (z) if 2 (z) are taken arbitrarily. In every next half-cycle the final temperatures and concentrations profiles are reversed and taken as initial profiles for the consecutive half-cycle. To illustrate notation used for the radial heat outflow to surrounding through the wall a simple sketch is given in Fig. 3. The wall included in the model as a lumped so-called side heat capacity is obviously a very coarse simplification but it enables to simulate TFRR still as one-dimensional in space object. A simplified kinetic model, regarding the three following reactions was studied in [10]: Complete combustion to CO 2 : CH 4 þ 2O 2! CO 2 þ 2H 2 O Combustion to CO: CH 4 þ 3=2O 2! CO þ 2H 2 O Combustion CO to CO 2 : CO þ 1=2O 2! CO 2 ðiþ ðiiþ ðiiiþ to the TFRR a model of consecutive combustion to CO, reaction (II) and next combustion CO, reaction (III) were assumed for simulations, i.e. according to the following mechanism: reactionðiiþ reactionðiiiþ CH 4 ƒƒƒƒƒƒ! CO ƒƒƒƒƒƒ! CO2 Monolith with general kinetic equation where parameter k 0,j is defined with respect to the monolith (not gas phase) volume: r hom;j ¼ e dc i ¼ k dt 0;j exp E j C a j RT i ð11þ where i ¼ CH 4 for j ¼ II; or i ¼ CO for j ¼ III Taking given above consecutive reaction mechanism, direct reaction (I) used in, e.g. [10] for the consecutive parallel scheme was neglected in the present study [11]. 3. An outline of the simulation process TFRR operates in continuous unsteady state caused by cyclic flow reversal, but for such reactor a cyclic steady state (CSS) can be defined, however [12]. Simulations were carried out applying Pickard s, i.e. so-called direct dynamic substitutions (DDS) iteration method (for details of the method see [8]). The steady state of any process occurs when the variations of mass and energy accumulation in this process vanish. In the case of processes occurring in a forced unsteady state, the fulfillment of this principle is valid for average values over some time intervals. T s h w T w Wall h surr T surr Fig. 3. Sketch showing notation used in description of the heat transfer through the wall to surroundings.

6 80 K. Gosiewski et al. / Chemical Engineering Journal (2012) When any reactor operates in a steady state then even momentary value of difference between outlet and inlet temperature can be regarded as a result of the energy conservation principle: T outlet T inlet ¼ DT ad X DT s ð12þ where DT s presents correction for possible heat loss to surroundings or other heat withdrawal from the reactor. When the reactor operates in constant unsteady state, as it appears in any FRR, a rule similar to (12) is still valid, it should, however, concern not momentary, but appropriately time averaged values if only the process becomes to be repeatable. In FRRs the matter concerns the CSS and for such case Burghardt in [13] derives formally, for the one-dimensional continuous two-phase model criterion of autothermicity, based on this principle including both one- and multireaction system. The condition in question, resulting from the first law of thermodynamics was reduced in [8] to the following form: T average outlet zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ Z! 1 tþn s 2 DT ad X average ¼ n s T outlet ðtþdt T inlet þ DT s 2 t ð13þ Condition (13) is not necessarily fulfilled in each reversal halfcycle (n is not necessarily unity, i.e. n P 1). In particular, it indicates that the successive half-cycle may not necessarily constitute a mirror copy of the preceding half-cycle when temperature profiles along the reactor are spatially asymmetric. Since numerical estimation of DT s is not easy straightforward in [8] another CSS indicator was proposed. The two following measures of the accuracy of attainment of CSS in a reverse-flow reactor were defined: dtðzþ ¼T start ðzþ T start ð14þ s;l and dt twin ðzþ ¼T start s;l s;l 1 ðzþ ðzþ T start s;l 2 ðzþ ð15þ The measure (14) corresponds to assumption of the value n = 1 in Eq. (13), i.e. the assumption that successive half-cycles constitute the mirror copy of the preceding cycle, the average heat balance of the reactor being fulfilled already for a single half-cycle. On the other hand, the measure (15) assumes that n = 2, which means that the repeatability occurs only for the full cycles (i.e. for consecutive 2 half-cycles) and only for the full cycle is the average heat balance of reactor fulfilled. Both measures (14) and (15) are function of axial coordinate, thus in [8] some averaged measures of convergence to CSS were proposed: I single ¼ DT am ¼ 1 k and I twin ¼ DT twin am ¼ 1 k X k i¼1 X k i¼1 dtðz i Þ dt twin ðz i Þ ð16þ ð17þ where k is an arbitrarily selected number of control points along reactor bed length. One of the measures, either Eq. (16) or (17) should converge to 0 (practically to some small value) when CSS is attained. Simulations in the present study revealed that majority of CSSs are asymmetric, what means that usually I twin < I single, when asymmetry is very large then I twin I single. Simulations of consecutive half-cycles were carried out until one of the indicators Eq. (16) or (17) (usually indicator (17)) revealed a relatively small value (e.g. <1 K). On the other hand attainment of CSS can be also controlled using a value of experimentally measured reactor temperature increase in the reactor. DT exp ¼ T average outlet T inlet ð18þ When T inlet const the value of T average outlet, taking into account possible asymmetry, should be averaged for at least 2 consecutive half-cycles (i.e. for the full reversal cycle). The value of (18) is stabilized when CSS is attained. Moreover value of (18) may be used to estimate a thermal efficiency of the reactor. Tavazzi et al. in [14] as a measure of this efficiency proposed very simple term which using DT ad notation of the present paper will be: DT exp Thermal efficiency ¼ DT ad X average ð19þ Efficiency calculated according to Eq. (19) is useful when there is no heat recovery (i.e. a heat withdrawal) in the reactor and this value enables to estimate influence of the heat losses on the reactor performance. When the heat recovery is applied more useful seems to be the heat recovery efficiency defined as the ratio of the heat recovered (Q rec ) to the total heat generated by methane combustion (Q gen ): Heat recoveryefficiency ¼ Q rec Q gen ð20þ Therefore the values given in Table 1 were calculated using the definition (20). If the heat recovery is very effective then thermal efficiency value defined by formula (19) is very small. Obviously it should be positive but, moreover, large enough to keep only necessary safety margin against extinction. To numerically find CSS the DDS (i.e. Pickard s) iteration was used, and initial profiles of state variables correspond to the actual initial state of reactor, then it seems that this approach to CSS resembles the actual transient process in the reactor. Intuitively one could expect that simulated transition time from an initial reactor state to CSS should imitate a real transition time. Simulations carried out with a model neglecting heat accumulation in the reactor wall and thermal insulation revealed that the model concordance in this respect was poor. Thus, it was expected that including the wall heat accumulation to the model would improve its accordance with the actual plant transition time between the consecutive initial disturbancies (e.g. variations of the inlet methane concentration). To this end the model was extended and simulations results (without and with the wall) are analyzed in the present study. 4. Models validation and simulation results A brief discussion given in Section 1 suggest that due to the heat loss more valuable for future industrial purposes is a model validation using for comparison experiments carried out at the plant larger than laboratory scale. The literature comparing simulation results with larger scale unit experiments, especially for TFRRs, is not abundant. Some references to industrial process experiments could be found e.g. in [3], mainly they concern CFRRs, not TFRRs however. Computed and measured temperature profiles for noncatalytic large scale TFRR are presented in [15]. Variables selected for comparison should comprise a set of the most important process state variables. In the case discussed here they would be temperatures in the reactor and outlet CH 4 concentration. Temperature profiles along the monolith packing were measured using very thin 1.5 mm movable sheathed thermocouple probes inserted into the selected channels of the demonstration plant monoliths. In spite of that in the lower part of the monolith

7 K. Gosiewski et al. / Chemical Engineering Journal (2012) packing temperature measurement was impossible; the most interesting part of the profiles could have been effectively registered, however. Other state variables, i.e. the CH 4, as well as other components (CO, CO 2 ) concentrations at the outlet were measured using IR analyser. However, in FRR appears a phenomenon of short lasting, uncontrolled blow out of uncombusted gas (called as puff in [15]) after each flow reversal. This well known phenomenon, which will not be discussed here in details, disturbs estimation of the real CH 4 conversion in TFRR itself. Chart in Fig. 4 illustrates this phenomenon. The model in the present study does not include calculations of the amount of methane blown out this way, since this discharge is caused by various reasons difficult to be estimated precisely: Discharge from the bed void fraction in the reactor packing (e.g. monolith channels). Discharge from empty spaces of the reactor vessel below packing, duct to reverse valves and valve chambers. Desorption of CH 4 adsorbed on the monolith surface during the preceding half-cycle. A rough estimation of influence of the two first reasons (void fraction and empty spaces discharges) may cause decrease of conversion ratio from simulated 99.9% to 99.3% for inlet concentration 0.97 vol. CH 4 % and half-cycle 240 s while for inlet concentration 0.3 vol. CH 4 % and half cycle 20 s estimated conversion drop would be from 99.7% to 91.2%. Shown in Table 1 time-averaged measured conversions were still lower than estimated taking into account only void fraction and empty space discharges. It is not easy resolve whether could it be affected by the physical desorption. Share of desorption is obviously much higher in CFRRs packed with highly porous catalyst than in TFRR packed with cordierite monolith without washcoat. Uneven flow distribution, lower temperature of monolith close to the wall, valves leakages, that everything could induce that measured conversion is lower than simulated. IR analyser lag time and time constant can have also a share in precise measurement of conversion, especially for short flow reversal cycle. There is no room in the present study to clarify and try to estimate share of all these many reasons in details, but fact is that conversion ratio at the present state could not have been used to assess the model correctness. Comparison of simulated with measured conversion values in this respect would be irrelevant and not practically justified. Thus, the model was validated using the agreement of the temperature profiles only. On the other hand, if only the temperature is well above ignition (i.e. >700 C) then even short residence time assures nearly complete combustion in the hot zone. Model reliability test is not the only purpose of its validation. Usually model involves some uncertainties, i.e. parameters difficult to be measured or estimated for a particular case of study. Model validation enables to quantify these uncertainties by comparing model predictions with the observed process data. In the present study heat transfer to surrounding appeared to be such uncertainty, difficult to valuate á priori for a relatively simple, onedimensional in space model, due to the fact that the heat escapes from the combustion zone through many ways and by various heat transfer mechanisms. Although spatially one-dimensional model as described in Section 2 is convenient and numerically relatively stable, the form of the model is not really relevant to actual geometry of a fairly large reactor simulated in the present study. Thus, the heat losses should have been described also in very simplified manner. Therefore some apparent (i.e. substitute) coefficients were applied. The problem is important since the process is sensitive to the heat outflow to surroundings, what is illustrated in Fig. 5, where simulated temperature profiles for various heat transfer coefficient h surr are shown. Increasing heat transfer coefficient to the surroundings results in forming a visible concavity (saddle) in the central part of the profiles, the higher h surr, the deeper concavity is. The same phenomenon for the model with wall was observed, when both h surr and h w coefficients were increased. On the real, measured profiles similar concavity is also clearly visible. In the present study to get satisfactory reliability of the TFRR heat balance the heat outflow to the surroundings should have been adequately estimated. So the heat transfer coefficients h w, and h surr estimated as the decision variables were adjusted by a trial and error method to get agreement of the simulated and measured temperature profiles in the reactor. Especially mainly deepness of the concavity in the middle part of the profile was taken into account. Coefficient h surr in model version without the wall and h w and h surr for version with wall were adjusted that way to get the deepness similar to that measured in the real TFRR. Moreover, amount of heat accumulated in TFRR has significant influence on the dynamic properties (transition times) of the apparatus. Consequently, actual specific heat of the reactor appears to be very important for the dynamic transients. Measurements of the specific heat made on cordierite samples crushed from the monolith used for the TFRR packing revealed that within the range of temperature appearing in the TFRR (from ambient to about 1000 C) the value of c s varies nearly two fold what could have significant impact on simulation results. Therefore a function of c s = f(t s ) was measured up to 1000 C and evaluated using the regression formula in the model: vol. % CH Exhausts ` 0 06:00:00 06:07:12 06:14:24 Time Inlet Outlet TEMPERATURE [ o C] SECTION I hs = 0 hs = 1.0 hs = 1.5 SECTION II BED LENGTH [ m ] Fig. 4. Chart of the inlet and outlet CH 4 concentration during several reversal of flow direction. Fig. 5. Simulated temperature profiles along the TFRR length for the model without wall and various heat transfer coefficients to surroundings.

8 82 K. Gosiewski et al. / Chemical Engineering Journal (2012) c s ¼ 1: T 3 s 2: T 2 s þ 1:5785 T s þ 62:243 ð21þ Fig. 6 presents simulated temperature profiles together with appropriate measured values compared for the two options of the TFRR model: without and with wall heat accumulation included into the model. All plots shown in Fig. 6 regard operation in CSS without any hot gas withdrawal from TFRR. Only heat Fig. 6. Measured and simulated temperature profiles along the TFRR length applying the model without and with heat accumulation in the reactor wall, for various inlet CH 4 concentration: (A) vol.% (B) vol.% (C). 0.3 vol.%.

9 K. Gosiewski et al. / Chemical Engineering Journal (2012) Table 2 Basic TFRR parameters taken for model validation. Parameter Value Units Inlet concentration CH 4 vol.% Gas flowrate m 3 STP =h Inlet temperature C Reversal half-cycle sec Reactor data Square side cross section length 90 cm Concrete lining thickness 30 cm Height of Raschig rings layer a 31 cm Length of single monolith section 120 cm Widths of monolith channels 3.0 mm Monolith OFA Monolith specific heat Acc. to Eq. (18) Jkg 1 K 1 Conductivity of monolith material 2.0 W m 1 K 1 Density of monolith material 2542 kg m 3 Concrete lining specific heat 840 J kg 1 K 1 Concrete lining density 600 kg m 3 a Parameters of Raschig rings are not given here in details. capacity of the concrete lining of 30 cm covering steel vessel from inside was regarded as the reactor wall heat capacity, while steel wall and thermal wool layer from outside capacity were neglected. Since mean value of the wall temperature is generally lower than that in the combustion zone packed with the monolith, for the concrete lining a constant value of specific heat was assumed. Basic parameters of TFRR taken for validation are given in Table 2. In simulations as a CSS indicator was recognized the state when either value of measure Eq. (16) or (17) were less than 1 K. In all cases the simulations revealed small asymmetry of profiles (i.e. I single > I twin ), therefore value of I twin (Eq. (17)), was taken into account (calculated for a number of control points along the reactor bed k = 51) as the indicator of CSS. For all simulated cases: I twin [K] at the end of simulations, thus it is justified to assume that CSS was reached in every case. On the other hand: I single what means that in every case profiles were more or less asymmetric. Sufficient accordance of measured and simulated temperature profiles shown in Fig. 6 were obtained for: h surr ¼ 1 ½Wm 2 K 1 Š or : h w ¼ 1 and h surr ¼ 3 ½Wm 2 K 1 Š for the model without wall for the model with wall Unfortunately, these heat transfer coefficients are valid only for the reactor investigated in the present study. There is no visible advantage of the model with over without wall when the temperature profiles are compared. Moreover, there is also no clear difference between the transition times of approach from one CSS to another one in both models. 5. Discussion and conclusions One-dimensional in space model elaborated in two versions of TFRR (with and without heat capacity of the wall) was tested and validated by comparison with real temperature profiles, measured at a fairly large scale research & demonstration plant. Similarity of the DDS (i.e. Pickard s) method of approaching to CSS to the real behavior of the flow reversal process suggests that simulated transition time to from one CSS to another should resemble the real one. Numerical transient process to get CSS demands simulations of several hundreds to even more than thousand flow reversals (i.e. half-cycles). It is doubtful, if any further complexity of the model, e.g. two-dimensional in space could easily improve it. The matter is that agreement of the temperature profiles shown in Fig. 6 seems to be sufficient to thermal design of objects in larger industrial scale. Kinetic study [11] reveals that in temperatures above ca. 800 C oxidation rate to CO 2 is so high that practically complete combustion should appear. Either simulations or experiments revealed that if only temperatures in TFRR are above this level CO does not appear at the exhaust from the TFRR. Small amount of uncombusted CH 4 at the outlet can appear, mainly due to mentioned in Section 4 blow-outs of uncombusted methane after each flow reversal, rather, than not complete combustion in the high temperature zone. Therefore it is the main goal of the design is to maintain autothermicity of TFRR with high enough temperature in the hot zone, being aware, that real CH 4 conversion will be lower due to some other reasons difficult to be included into the model. Simulations carried out for inlet concentrations below 0.1 vol.% revealed, that combustion extinguishes. These simulations were carried out using model without wall. Experimental results (see Table 1) revealed that in real plant extinction appears for inlet concentration already below 0.2%. One can presume that this difference stem from significantly lower CH 4 conversion for low concentrated gas at the inlet, caused by uncombusted methane blow-outs after each reversal. On the other hand each flow reversal causes also that at the beginning of every half-cycle a fraction of well converted gas is pushed back to the reactor high temperature zone. It could have been estimated that in the case of study for half-cycle 10 s and flowrate 400 m 3 STP =h this phenomenon acts as if inlet concentration were lower of about 20% (e.g. feed concentration of 0.2 CH 4 vol.% responds to TFRR conditions as if it were 0.16 CH 4 vol.% only). Thus, the model simulates an authermicity threshold at a little lower concentration level than that measured at the plant. For lower concentrations an empirical correction coefficient regarding incomplete conversion due to all occurrences after each reversal might be applied in the heat balances Eq. (1) or (3), since influence of this phenomenon is larger as the concentration decreases. The main conclusions of the present study are: The dynamic simulation results when using the two models including or excluding heat capacity of the TFRR wall are similar (see e.g. Fig. 6), thus the heat wave formation is dependent mainly on the heat accumulation in the reactor packing itself (ceramic monolith packing in the case). Much higher heat capacity of the wall behaves as a so-called side capacity which does not influence directly the temperature profiles in the reactor packing itself. Agreement of the simulated temperature profiles with measured experimentally, especially as it concerns maximum temperature and profile in the hot zone of TFRR seems to be sufficient for technical design of larger scale industrial plants. The autothermicity threshold evaluated from simulations is a little lower than measured due to increasing influence of blow outs of unconverted methane after each flow reversal for very low concentrated gas feed. It seems that for practical purposes it is not necessary to develop more complicated, e.g. 2 or 3 dimensional in space model. In spite of much greater complexity of such a model a number of uncertainties difficult to be evaluated á priori rises significantly, especially at an early stage of the technology development. Taking into account hundreds of half-cycles, which are to be simulated one should take into account possible problems with numerical stability during simulations. Acknowledgment The authors thank Prof. Krzysztof T. Wojciechowski from AGH University of Science and Technology for his assistance, help and advice in preparing physicochemical data for simulations.

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