- Email: [email protected]
Cold modeling of a direct coupling autothermal methane reforming reactor
Chemical Engineering Journal 168 (2011) 303–311
Contents lists available at ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Cold modeling of a direct coupling autothermal methane reforming reactor Yu-qin Wang, Zheng-hua Dai ∗ , Hong Cheng, Jian-liang Xu, Fu-chen Wang Key Laboratory of Coal Gasification of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
a r t i c l e
i n f o
Article history: Received 29 May 2010 Received in revised form 27 December 2010 Accepted 4 January 2011 Keywords: Autothermal reactor Flow field Numerical simulation Maldistribution Penetration depth
a b s t r a c t The aim of this work was to investigate the flow characteristics in a direct coupling autothermal reactor established in laboratory for methane reforming. A 2-D turbulence model (realizable k-ε) was applied for simulating the flow fields in the combustion chamber and a porous media model was adopted for simulating those in the catalyst bed, and both models were validated according to the experimentally measured velocities and pressures drop. The flow characteristics were assessed by examining velocity profile, turbulence intensity and reflux ratio in the combustion chamber as well as maldistribution factor and penetration depth in the catalyst bed. The focus was on the influences of inlet flow rate, catalyst bed height and stack porosity on the flow characteristics. Numerical results demonstrated that an increase in the height or the stack porosity of catalyst bed increased the velocity in the combustion chamber zone in front of the catalyst layer, and an increase in the higher inlet flow rate amplified the turbulence in the jet flow zone of the combustion chamber and in the combustion chamber zone near to the catalyst layer. The reflux ratio profiles in the combustion chamber were reasonably varied with the height and stack porosity of catalyst bed. Results of the maldistribution factor revealed that a non-uniform or fluctuating flow occurred within the upper layer of catalyst bed, and a reduction in the stack porosity mitigated the flow non-uniformity and shortened the penetration depth. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Methane reforming has been an important industrial process for the production of hydrogen and syngas in the manufacturing of ammonia, methanol, and other chemicals. It will gain increased attentions as diverse methane resources such as coal oven gas, coal bed methane and refinery gas are available for utilization [1]. Technologies of methane reforming are currently well established, mainly including steam reforming (SR), partial catalytic reforming (POX) and autothermal reforming (ATR). ATR is a combined process of the partial combustion with the catalytic steam reforming [2,3]. The ATR reactor used for methane reforming is usually a direct coupling type, which is configured by a combustion chamber coupled with a fixed catalyst bed. The exothermic oxidation reactions occurring in the combustion chamber supply energy or heat for the endothermic methane steam reforming in a so-called direct heat coupling way [4–6]. The ATR reactor has major advantages over other reforming alternatives for high energy efficiency, moderate process temperature, and easily regulated gas composition [7]. However, it practically often meets an operational problem of the hot spot in the catalyst bed. It is envisaged that the dynamic characteristics of fluid can be a critical factor for triggering the hot
∗ Corresponding author. Tel.: +86 021 6425 0784; fax: +86 021 6425 1312. E-mail address: [email protected] (Z.-h. Dai). 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.01.013
spot, which may be controlled by adjusting the reactor design and the operating conditions. Therefore, it is eagerly needed to know how the reactor configuration and the operating conditions influence the flow field. To investigate the methane reforming processes from an engineering viewpoint, we have constructed a laboratory ATR reactor, which will be shown in the experimental section. The purpose of this paper is to simulate the flow field under a cold state of this reactor using the realizable k-ε turbulence model and the porous media model. The former model and the latter one are validated by comparing the numerical velocity and pressure drop data, respectively, with the corresponding experimental data. Similar investigations were performed by some researchers in simulation of the flow field in a confined jet using the realizable k-ε turbulence model [8], a finite element model [9], and the k-ω (SKW) turbulence model [10]. Singh et al. [9] pointed out that the aspect ratio was the main factor affecting the entrainment and mixing. Kandakure et al. [10] reported that the enclosure size and the draft tube diameter greatly impacted turbulence characteristics. On the other hand, Jafari et al. [11] applied the porous media model for studying the flow behavior and dispersivity in a packed bed. Atta et al. [12] used the same model to forecast the liquid maldistribution in a trickle-bed reactor under cold-flow conditions. Based on the simulated results, we further evaluate the flow uniformity in the catalyst bed in the light of the maldistribution factor and the penetration depth proposed by Darakchiev et al. [13] and Petrova et al. [14] To our knowledge, no
304
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Nomenclature C2 Dij ,Cij d0 d dP F0 g H h L Mf P Qr Qr,0 r y ri R Rreactor Si ur,i v
vj vmag v∞ v0 wi wo
inertial resistance coefficient (1/m) matrixes nozzle diameter (mm) reactor diameter (mm) particle diameter (mm) total column cross-section (m2 ) acceleration of gravity (m2 /s) reactor height (mm) capped section height (mm) height of catalyst bed (mm) maldistribution factor pressure drop (Pa) reflux (m3 /h) inlet flow rate (m3 /h) grid coordinates (radial direction) grid coordinates (axial direction) axial distance of i point (m) reflux ratio radius of reactor (m) momentum source term (kg/(m s2 )) axial velocity of i point (m/s) fluid velocity (m/s) velocity on direction j (m/s) velocity magnitude (m/s) mean velocity in porous media (m/s) nozzle velocity (m/s) local gas velocity (m/s) mean gas velocity (m/s)
Greek symbols 1/˛ viscous resistance coefficient (1/m2 ) ε stack porosity viscosity (Pa s) density (kg/m3 ) stress tensor (Pa)
section (h). A mimic catalyst bed was filled with spherical glass globule of 3–5 mm in diameter (dp ), with a stack porosity of 0.20 or 0.44. To examine the influence of the catalyst bed height on the flow characteristics, three heights (L = 100, 200, 300 mm) were used. The nozzle (d0 = 16.28 mm) was installed at the top of the reactor. The two dimensional coordinate with the axial direction (y) and the radial direction (r) was defined as depicted in figure, and the outlet centre of the nozzle was orientated as an origin of the coordinate. Air was flowed into the reactor through the nozzle along the y direction. To examine the influence of flow rate on the flow characteristics, three flow rates (45, 60 and 75 m3 /h) were used, which corresponded to the inlet velocities of 60, 80 and 100 m/s, respectively. The velocity profile in the combustion chamber was probed by the Streamline4 type Hot-Wire Anemoneter (HWA, Dantec Ltd.). This detector gave a maximal non-vector velocity. The value was averaged with the sampling time of 5 s. The detection range was between 0.02 and 300 m/s, with the error smaller than 2%. The pressure drop was measured by the pitot tube. 3. Model descriptions The realizable k-ε turbulent model is used for simulating the flow field in the combustion chamber and the bottom compartment beneath the catalyst bed (see Fig. 1). This model has been classically used for simulating both confined flows and free flows. The descriptions regarding this model may be referred to the literature [15,16]. The isotropic porous media model is applied for simulating the flow field in the catalyst layer. In this model, a momentum source term, Si , is added to the standard fluid flow equation, giving ∂ (v) + ∇ × (v v) = −∇ p + ∇ × () + g + Si ∂t
Si embraces a viscous loss term and an inertial loss term due to the collision between the fluid and catalyst beads:
⎛
Si = − ⎝
3
Dij vj +
j=1
publication has been found regarding cold modeling of a methane reforming autothermal reactor.
Fig. 1 shows the cylindrical reactor and the experimental flow sheet used in this study. The size of the reactor was 280 mm in inner diameter (d), 670 mm in height (H), and 100 mm in capped
3
⎞
Cij
vmag vj 2
⎠
(2)
j=1
For the case of a homogeneous porous media, Si is simplified as Si = −
2. Experimental
(1)
˛
vi + C2
vmag vi 2
(3)
where 1/˛ is the viscous resistance coefficient (˛ is called permeability) and C2 is the inertial resistance coefficient. This momentum term results in the pressure drop through the porous cell. For a packed bed, the pressure drop can be calculated in terms of Ergun equation: |P| 1.75 (1 − ε) 2 150 (1 − ε)2 v∞ + v∞ = L dP ε3 ε3 dP2
(4)
In the case of laminar flow, equation (4) can be approximate to the following equation: |P| 150 (1 − ε)2 v∞ = L ε3 dP2
(5)
while in the case of turbulent flow, the loss term can be ignored, thus |P| 1.75 (1 − ε) 2 = v∞ L dP ε3 Fig. 1. Autothermal reactor and experimental test system. 1—Computer, 2—anemometer, 3—probe, 4 —reactor, 5—pressure gauge, 6—flow meter, 7—valve, 8—roots blower.
(6)
We can accordingly obtain the constant values of viscous resistance coefficient and the inertial resistance coefficient from the following
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
305
equations: 150 (1 − ε)2 1 = 2 ˛ ε3 dP (8)C2 =
(7)
3.5 (1−ε) dP ε3
In the numerical calculation, we use the velocity inlet and pressure outlet as the boundary conditions. Moreover, we check the grid influences on velocity and pressure drop with the different grid amounts, and find that the grid has little influences on the results. 4. Results and discussions 4.1. Model validation Fig. 2 shows the experimental results of the axial velocity and the simulated results in combustion chamber at an inlet flow rate of 75 m3 /h and a catalyst bed height of 100 mm. The axial velocity at the radial distances near to zero decayed dramatically along the y direction. At each cross section, the axial velocity was the maximum along the central line, and it decreased towards the radial direction. The decay pattern became flat as the flow was away from the nozzle. The experimental data were well predicted by simulation. However, some numerical data were negative on the edge of the combustion chamber due to the back flow, whereas the HWA only detected the absolute values of velocity. Fig. 3 shows the numerical pressure isolines in the reactor at an inlet flow rate of 75 m3 /h and a catalyst bed height of 100 mm.
Fig. 2. Axial velocity profiles on varied cross sections. Conditions: () y = 107.5 mm, (䊉) y = 287.5 mm, () y = 437.5 mm, () y = 612.5 mm; L = 100 mm, Qr0 = 75 m3 /h, ε = 0.44.
Numerical results showed that the pressure drop through the catalyst bed was 68.37 Pa, very close to a value of 64.26 Pa measured by experiment. The consistence between the numerical data and the experimental data in the velocity and pressure drop has allowed us to validate the models used in this study. 4.2. Overall flow maps in the ATR reactor Fig. 4 shows the stream function in the ATR reactor at different heights and stack porosities of catalyst bed as well as at
Fig. 3. Static pressure isolines (Pa) in the reactor. Conditions: L = 100 mm, Qr0 = 75 m3 /h, ε = 0.44.
Fig. 4. Stream functions (kg/s) in the reactor with varied conditions. Conditions: (a) Qr0 = 75 m3 /h, L = 0 mm, ε = 0.44; (b) Qr0 = 75 m3 /h, L = 200 mm, ε = 0.44; (c) Qr0 = 75 m3 /h, L = 300 mm, ε = 0.44; (d) Qr0 = 45 m3 /h, L = 300 mm, ε = 0.44; (e) Qr0 = 45 m3 /h, L = 300 mm, ε = 0.20.
306
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 5. Radial distributions of axial velocity with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
the different inlet flow rates. The stream function is formulated from a relation between the stream line and the mass conservation of fluid. One stream line stands for a constant stream function, and two adjacent stream lines form a constant difference in the stream function, or a constant mass flow rate. As a consequence, a larger density of stream line represents a larger mass flow rate. Along the axial direction from the nozzle to the reactor bottom, the stream lines showed different shapes. In the upper zone of the combustion chamber, a small jet flow zone with dense stream lines was in contrast to a broad back flow zone with sparse stream lines. The jet flow developed with the y direction in the shape of a cone. In the lower part of the combustion chamber, two vortexes formed in the back flow zone, with dense stream lines around their cores. In the catalyst layer, the stream lines became sparse and well-ordered, indicative of a relatively uniform and mild flow rate. Beneath the catalyst bed, the stream lines displayed some disorder. Varied flow patterns occurred in the outlet of the reactor under the different conditions. We should expand our understanding of such varied flows in the reactor under the different conditions. In the case of no catalyst bed, or in the case of an entrained-flow reactor, no plug flow was formed even under the lower part of the reactor at the conditioned aspect ratio, and the jet flow and back flow prevailed. In the case of a catalyst bed packed, a part of fluid was back flowed when the flow approached the catalyst bed, while a part of fluid entered and passed through the catalyst bed. The velocity distribution in the ATR reactor trended to be uniform shortly after the fluid entered the packed layer. An increase in the catalyst bed height reduced the size of two asymmetric vortexes and increased the zone of the uniform flow in the catalyst bed. A reduction in the inlet flow rate or in the stack porosity of catalyst bed also reduced the vortexes in the combustion chamber and increased the flow uniformity in the catalyst bed.
4.3. Velocity profile, turbulence intensity and reflux ratio in the combustion chamber In this section, we will shed light on the influences of the catalyst bed height, catalyst bed stack porosity and inlet flow rate on velocity profile, turbulence intensity, and reflux distribution in more details. Turbulence intensity is defined as the ratio of the root-mean-square of the velocity fluctuation, u , to the mean flow velocity, uavg . The reflux ratio is defined as R=
Qr Qr0
(9)
where Qr0 is the inlet flow rate and Qr is the reflux, calculated by the following equation: Qr =
(ur,i+1 + ur,i )(r 2 − r 2 ) i+1 i 2
ur < 0
(10)
i
in which ri is the radial distance of i point, and ur,i is its axial velocity. Figs. 5 and 6 show the dependence of velocity profile in the combustion chamber on the catalyst bed height and catalyst bed stack porosity, respectively. Along the axial direction, we select three cross sections y1 , y2 , and y3 , to examine the change trend of the velocity profile with the different conditions. y1 and y2 are two positions representative of the upper space of the combustion chamber far away from the catalyst bed. y3 is the representative position near to the catalyst bed and it holds the fixed distance of 10 mm to the top layer of the catalyst bed. The velocity profiles at the cross sections y1 and y2 with different heights (Fig. 5(a) and (b)) and stack porosities (Fig. 6(a) and (b)) of the catalyst bed are almost the same, indicating that the catalyst bed height and porosity caused little variations of the velocity profiles within the upper space of the combustion chamber. The velocity profiles had a turning point (A and B) at which the jet flow changes to the
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
307
Fig. 6. Radial distributions of axial velocity with varied packing porosity of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
back flow from the inner side to the outside, as shown in figure. As the extended axial distance, the turning point moved towards the outside. At the cross sections close to the catalyst bed (for example, y3 ), both the catalyst bed height and the stack porosity appreciably affected the velocity profiles (Figs. 5(c) and 6(c)). At smaller radial distances (smaller than the radial distance of C and D) where the jet flow was dominant, an increase in the catalyst bed height or porosity led to the increased axial velocity, because a higher catalyst bed meant a lower momentum attenuation at a shorter axial distance and a larger porosity makes the back flow near catalyst bed smaller. At larger radial distances (larger than the radial distance of C and D) where the back flow was dominant, the result was opposite because a higher catalyst bed led to a stronger back flow. Similar results were observed on the impacts of the stack porosity. A larger stack porosity led to a lower pressure drop through the catalyst bed and thus to a weaker back flow at larger radial distances. Yu et al. [17] reported the velocity distribution in an entrained-flow gasifier. They experimentally observed that the catalyst bed height and stack porosity had a negligible effect on the flow field of combustion zone. Their results were essentially consistent with the numerical results obtained in this study. Fig. 7 shows the variations of the velocity profiles with different inlet flow rates at a cross section far away from the top layer of the catalyst bed (y1 ) and another cross section near to that (y3 ). On the cross section y1, a higher inlet flow rate gives rise to a higher axial velocity in the jet flow zone, while in the back flow zone, the influence is insignificant because of the dominant back flow. On the cross section y3 , the axial velocity is nearly not affected by the inlet flow rate.Figs. 8 and 9 show the influences of the height and stack porosity of the catalyst bed on the turbulence intensity distribution on the three cross sections y1 , y2 , and y3 , which are the same as those selected for analysis of the axial velocity profiles as illustrated in Figs. 5 and 6. Unlike the result of the axial velocity, the turbulence intensity on the
cross section y1 showed a peak in the jet flow zone (point E in Fig. 8(a) and (b)). This was because the turbulence was caused by the velocity gradient shear. A high velocity magnitude did not mean a high turbulence. However, a smaller velocity in the back flow zone certainly led to a weaker turbulence, so the turbulence intensities became small as the radial distance increased towards the back flow zone. Similar to the results of the axial velocity, the turbulence intensity distributions on the cross sections y1 and y2 were little influenced by the height (Fig. 8) and the stack porosity of catalyst bed (Fig. 9). Nevertheless, a higher catalyst bed led to a stronger turbulence on the cross sections near to the catalyst bed in the combustion chamber (e.g., y3 ). A change in the stack porosity varied the axial velocity profiles on the cross sections y3 (Fig. 6(c)), but it did not disturb the turbulence on these cross sections (Fig. 9(a–c). It could be seen from Fig. 10 that a high inlet flow rate amplified the turbulence on the cross sections near to the catalyst bed
Fig. 7. Radial distribution of axial velocity with varied inlet flow rates. Conditions: L = 300 mm, y1 = 100 mm, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
308
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 8. Turbulence intensity distribution with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
(e.g., y3 ) along the whole radial direction, while on the cross section near to the nozzle (e.g., y1 ), a high inlet flow rate intensified the turbulence only in the jet flow zone, with no effect of the inlet flow rate on the turbulence in the back flow zone. Turbulence is an
important parameter characteristic of the mixing state of the fluids in the reactor. Intense turbulence improves mixing at the macroand micro-scales, and it generally accelerates the mass transfercontrolled reactions. Among three factors including the height and
Fig. 9. Turbulence intensity distribution with varied packing porosity of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 10. Turbulence intensity distribution with varied inlet flow rates. Conditions: L = 300 mm, y1 = 100 mm, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
stack porosity of catalyst bed as well as the inlet flow rate examined, the inlet flow rate behaved as a main factor affecting the turbulence of the fluids in the reactor. Fig. 11 shows the changes of reflux ratio (R) with the dimensionless axial distance (y/d0 ) at three heights and two stack porosities of the catalyst bed. The reflux ratio exhibits a peak with y/d0 , regardless to the variations of three factors. The axial distance of the peak corresponded to that of the vortex center from the nozzle (see Fig. 4). At a y/d0 value smaller than 20, the change profiles of the reflux ratio with y/d0 are irrespective of the height and stack porosity of the catalyst bed. More fluid was circulated as a backflow with increasing the axial distance. At a y/d0 value larger than 20, the change trend of the reflux ratio with the height of catalyst bed became diverged. As the fluid approached the catalyst bed, the reflux ratio decreased. It was reasonable that a maximal reflux ratio occurred at a smaller y/d0 for the case of a higher catalyst bed. At a lower catalyst bed, the reflux ratio over the surface of the catalyst bed was lower because of a lower pressure drop through the catalyst bed, which enabled more fluid to enter the catalyst bed. The stack porosity slightly influenced the reflux ratio in the space near to the catalyst bed. A higher stack porosity allowed more fluid to pass through the catalyst bed and this consequence was a lower reflux ratio. Fig. 12 shows the influence of the inlet flow rate on the reflux ratio. A higher inlet flow rate meant a higher magnitude of flow momentum. Although the amount of back flow (Qr ) was increased with the inlet flow rate increasing, the reflux ratio was only slightly affected by the inlet flow rate.
309
Fig. 12. Reflux ratios with varied inlet flow rates. Conditions: L = 300 mm, ε = 0.44.
Fig. 13. Two arrangement methods for local velocity.
4.4. Flow uniformity in the catalyst bed In the direct coupling autothermal reactor, the flow in the combustion chamber, when impinging on the catalyst bed surface, are partitioned to two streams: a flow back to the combustion chamber and another flow entering the catalyst bed. The uniformity of the flow in the packed layer is generally of particular concern because it is possibly a direct cause for the hot spot. The uniformity of the flow in the stacked layer can be denoted by the maldistribution factor and the penetration depth. The maldistribution factor (Mf ) is defined as the ratio of the mean standard deviation of local velocities (wi ) to the mean of local velocities (w0 ):
1 F0
Mf = where w0 =
1 F0
F0
w − w 0 i w0
0
dF
(11)
F0
wi dF
(12)
0
Rumen Darakchiev [18] reported that two classical arrangements are used for local velocity measurement. One is to divide the apparatus cross-section into cells with equal surface, and local velocity is obtained in the cell center (Fig. 13(a)). The other is to divide the cross-section in coaxial ring sectors. The local velocity is obtained from different points on the middle line of ring sectors (Fig. 13(b)). In this work, the local velocities are obtained with the second method. In 2-D asymmetry numerical calculation, the local velocity should be calculated from: w0 =
Fig. 11. Reflux ratios with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h; open symbol, ε = 0.44; solid symbol, ε = 0.20.
1 2 Rreactor
Rreactor
2rwi dr
(13)
0
where Rreactor is the radius of reactor. A smaller Mf means a better uniformity of the flow in the catalyst bed [19]. As the flow passes through such a distance in the packed
310
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 14. Maldistrbution factor distributions with varied heights and porosities of catalyst bed. Conditions: Qr0 = 75 m3 /h; open symbol, ε = 0.44; solid symbol, ε = 0.20.
layer that the Mf tends to be invariable, this distance is termed the penetration depth (PD). In this article, the PD is defined as the distance from the top of packing layer to 20% of the top Mf . The penetration depth is an index which measures the ability of a certain packing to equalize the gas flow velocity profile. Fig. 14 shows the maldistribution factors with different heights and stack porosities of the catalyst bed, respectively. At a stack porosity of 0.44, a non-uniform zone of the flow appeared in the upper catalyst layer, and the Mf decreased as the flow penetrated into the catalyst bed. Fig. 15 illustrates the penetration depths with the different heights of the catalyst bed at the stack porosity of 0.44. It could be seen that a higher catalyst bed not only resulted in a larger Mf at the initial point of the catalyst layer but also a larger PD, indicating that an increase in the catalyst bed height worsened
Fig. 16. Maldistribution factors with varied inlet flow rates. Conditions: L = 300 mm, ε = 0.44.
the uniformity of the flow in the upper catalyst layer. However, it was reported that the relation between the Mf and PD was not monotonous, despite a dependence of the PD on the initial value of Mf [20]. Results also showed that the stack porosity was an important factor affecting the uniformity of the flow at the upper catalyst bed. At a lower stack porosity (ε = 0.20), the values of Mf were not varied with the heights of the catalyst bed, and the Mf remained small through the whole catalyst bed. It was implied that the uniformity of flow in the catalyst bed might be effectively improved by changing the stack porosity. It should be noticed that a slightly turbulent flow was likely to happen in a bottom space of the catalyst bed. Darakchiev [13] reported a similar result. This was because the flow was disturbed on the border from the catalyst bed to the bottom void compartment. The non-uniformity of the flow in the bottom space was more salient at the catalyst bed height of 200 mm than for the other two cases. This indicated that the non-uniformity in the upper catalyst space did not have a monotonous relationship with that in the bottom catalyst space. Fig. 16 shows the influence of the inlet flow rate on Mf . Under three flow rates, the change of Mf with the axial distance and the PD were almost identical, indicating that the influence of the inlet flow rate on the velocity gradient in the catalyst bed was insignificant. 5. Conclusions
Fig. 15. Penetration depths with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h, ε = 0.44.
The experimentally validated 2-D turbulence model (realizable k-ε) and porous media model were used to simulate the flow fields in a laboratory direct coupling authothermal reactor. The flow characteristics in the combustion chamber were assessed in terms of velocity profile, turbulence intensity and reflux ratio, and those in the catalyst layer were assessed in terms of maldistribution factor and penetration depth. The influences of three main cold operating factors including the inlet flow rate, catalyst bed heights and stack porosity on the flow behaviors or characteristics were examined. Numerical results showed that the height and stack porosity of the catalyst bed had little influence on the velocity profile in the upper space of the combustion chamber but did in the combustion chamber zone near to the catalyst bed. The turbulence intensity in the combustion chamber zone near to the catalyst bed was increased with increasing the height of catalyst bed, but that in upper space was irrespective of the porosities and catalyst bed heights. An increase in the inlet flow rate amplified the turbulence in the jet flow zone in the upper space of combustion chamber as well as in the combustion chamber zone near to the catalyst bed. The reflux ratios in the combustion chamber were not varied with the inlet flow rate, but did in the space near to the catalyst bed, with the height and stack porosity of catalyst bed.
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
The maldistribution factors and penetration depths were not susceptible to the inlet flow rate, but influenced greatly by the heights and stack porosity of catalyst bed. It is a little surprising for us to observe that the flow maldistribution in the bottom catalyst layer was not monotonously correlating to that in the upper catalyst layer. Overall, it could be concluded that the height and porosity of catalyst bed had small influences on the flow characteristics in the combustion chamber than the inlet flow rate, but they could appreciably vary the uniformity of the flow in the catalyst bed. Acknowledgements This work was supported by National Key Technologies R&D Program in China (no. 2006BAE02B02). The first author would also like to thank student Huahui Zhou in the experiment conduct. Special thank is due to Professor Jie Wang for his revision of this paper. References [1] J. Zhu, D. Zhang, K.D. King, Reforming of CH4 by partial oxidation: thermodynamic and kinetic analyses, Fuel 80 (2001) 899–905. [2] S. Freni, G. Calogero, S. Cavallaro, Hydrogen production from methane through catalytic partial oxidation reactions, Journal of Power Source 87 (2000) 28–38. [3] S.S. Bharadwaj, L.D. Schmidtatalyst, Catalytic partial oxidation of natural gas to syngas, Fuel Processing Technology 42 (1995) 109–127. [4] B. Glockler, A. Gritsch, A. Morillo, G. Kolios, G. Eigenberger, Autothermal reactor concepts for endothermic fixed-bed reactions, Chemical Engineering Research and Design 82 (2004) 148–159. [5] B. Glockler, H. Dieter, G. Eigenberger, U. Nieken, Efficient reheating of a reverseflowreformer-an experimental study, Chemical Engineering Science 62 (2007) 5638–5643. [6] G. Kolios, J. Frauhammer, G. Eigenberger, Autothermal fixed-bed reactor concepts, Chemical Engineering Science 55 (2000) 5945–5967.
311
[7] M.H. Halabi, M.H.J.M. de Croon, J. van der Schaaf, P.D. Cobden, J.C. Schouten, Modeling and analysis of autothermal reforming of methane to hydrogen in a fixed bed reformer, Chemical Engineering Journal 137 (2008) 568–578. [8] L.P. Chua, A.C. Lua, Measurements of a confined jet, Physics of Fluids 10 (1998) 3137–3145. [9] Ghanshyam Singh, T. Sundararajan, U.S.P. Shet, Entrainment and mixing studies for a variable density confined jet, Numerical Heat Transfer 35 (1999) 205–223. [10] M.T. Kandakure, V.C. Patkar, A.W. Patwardhan, Characteristics of turbulent confined jets, Chemical Engineering and Processing 5339 (2007) 1–12. [11] A. Jafari, P. Zamankhan, S.M. Mousavi, K. Pietarinen, Modeling and CFD simulation of flow behavior and dispersivity through randomly packed bed reactors, Chemical Engineering Journal 144 (2008) 476–482. [12] Arnab Atta, Shantanu Roy, Nigam Krishna D.P., Investigation of liquid maldistribution in trickle-bed reactors using porous media concept in CFD, Chemical Engineering Science 62 (2007) 7033–7044. [13] Rumen Darakchiev, Tatyana Petrova, Simeon Darakchiev, Gas distribution in columns with packing Raschig Super-Ring, Chemical Engineering and Processing 44 (2005) 827–833. [14] Tatiana Petrova, Krum Semkov, Chavdar Dodev, Mathematical modeling of gas distribution in packed columns, Chemical Engineering and Processing 42 (2003) 931–937. [15] Masoud Rahimi, Arsalan Parvareh, Experimental and CFD investigation on mixing by a jet in a semi-industrial stirred tank, Chemical Engineering Journal 115 (2005) 85–92. [16] Tsan Hsing Shih, W. William Liou, Aamir Shabbir, Zhigang Yang, Jiang Zhu, A new k-ε eddy viscosity model for high Reynolds number turbulent flow, Computers Fluids 24 (1995) 227–238. [17] Yu Zunhong, Shen Caida, Wang Fuchen, Yu Jiangguo, Xiao Kejan, Gong Xin, Three-region model for gasification process in coal-slurry-gasifier, Journal of Fuel Chemical and Technology (Chinese) 21 (1993) 90–96. [18] Rumen Darakchiev, Chavdar Dodev, Gas flow distribution in packed columns, Chemical Engineering and Processing 41 (2002) 385–393. [19] R.J. Kouri, J. Sohlo, Liquid and gas flow patterns in random packings, The Chemical Engineering Journal 61 (1996) 95–105. [20] D.P. Edwards, K.R. Krishnamurthy, R.W. Potthoff, Development of an improved method to quantify maldistribution and its effect on structured packing column performance, Institution of Chemical Engineers 77 (1999) 656–663.
Contents lists available at ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Cold modeling of a direct coupling autothermal methane reforming reactor Yu-qin Wang, Zheng-hua Dai ∗ , Hong Cheng, Jian-liang Xu, Fu-chen Wang Key Laboratory of Coal Gasification of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
a r t i c l e
i n f o
Article history: Received 29 May 2010 Received in revised form 27 December 2010 Accepted 4 January 2011 Keywords: Autothermal reactor Flow field Numerical simulation Maldistribution Penetration depth
a b s t r a c t The aim of this work was to investigate the flow characteristics in a direct coupling autothermal reactor established in laboratory for methane reforming. A 2-D turbulence model (realizable k-ε) was applied for simulating the flow fields in the combustion chamber and a porous media model was adopted for simulating those in the catalyst bed, and both models were validated according to the experimentally measured velocities and pressures drop. The flow characteristics were assessed by examining velocity profile, turbulence intensity and reflux ratio in the combustion chamber as well as maldistribution factor and penetration depth in the catalyst bed. The focus was on the influences of inlet flow rate, catalyst bed height and stack porosity on the flow characteristics. Numerical results demonstrated that an increase in the height or the stack porosity of catalyst bed increased the velocity in the combustion chamber zone in front of the catalyst layer, and an increase in the higher inlet flow rate amplified the turbulence in the jet flow zone of the combustion chamber and in the combustion chamber zone near to the catalyst layer. The reflux ratio profiles in the combustion chamber were reasonably varied with the height and stack porosity of catalyst bed. Results of the maldistribution factor revealed that a non-uniform or fluctuating flow occurred within the upper layer of catalyst bed, and a reduction in the stack porosity mitigated the flow non-uniformity and shortened the penetration depth. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Methane reforming has been an important industrial process for the production of hydrogen and syngas in the manufacturing of ammonia, methanol, and other chemicals. It will gain increased attentions as diverse methane resources such as coal oven gas, coal bed methane and refinery gas are available for utilization [1]. Technologies of methane reforming are currently well established, mainly including steam reforming (SR), partial catalytic reforming (POX) and autothermal reforming (ATR). ATR is a combined process of the partial combustion with the catalytic steam reforming [2,3]. The ATR reactor used for methane reforming is usually a direct coupling type, which is configured by a combustion chamber coupled with a fixed catalyst bed. The exothermic oxidation reactions occurring in the combustion chamber supply energy or heat for the endothermic methane steam reforming in a so-called direct heat coupling way [4–6]. The ATR reactor has major advantages over other reforming alternatives for high energy efficiency, moderate process temperature, and easily regulated gas composition [7]. However, it practically often meets an operational problem of the hot spot in the catalyst bed. It is envisaged that the dynamic characteristics of fluid can be a critical factor for triggering the hot
∗ Corresponding author. Tel.: +86 021 6425 0784; fax: +86 021 6425 1312. E-mail address: [email protected] (Z.-h. Dai). 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.01.013
spot, which may be controlled by adjusting the reactor design and the operating conditions. Therefore, it is eagerly needed to know how the reactor configuration and the operating conditions influence the flow field. To investigate the methane reforming processes from an engineering viewpoint, we have constructed a laboratory ATR reactor, which will be shown in the experimental section. The purpose of this paper is to simulate the flow field under a cold state of this reactor using the realizable k-ε turbulence model and the porous media model. The former model and the latter one are validated by comparing the numerical velocity and pressure drop data, respectively, with the corresponding experimental data. Similar investigations were performed by some researchers in simulation of the flow field in a confined jet using the realizable k-ε turbulence model [8], a finite element model [9], and the k-ω (SKW) turbulence model [10]. Singh et al. [9] pointed out that the aspect ratio was the main factor affecting the entrainment and mixing. Kandakure et al. [10] reported that the enclosure size and the draft tube diameter greatly impacted turbulence characteristics. On the other hand, Jafari et al. [11] applied the porous media model for studying the flow behavior and dispersivity in a packed bed. Atta et al. [12] used the same model to forecast the liquid maldistribution in a trickle-bed reactor under cold-flow conditions. Based on the simulated results, we further evaluate the flow uniformity in the catalyst bed in the light of the maldistribution factor and the penetration depth proposed by Darakchiev et al. [13] and Petrova et al. [14] To our knowledge, no
304
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Nomenclature C2 Dij ,Cij d0 d dP F0 g H h L Mf P Qr Qr,0 r y ri R Rreactor Si ur,i v
vj vmag v∞ v0 wi wo
inertial resistance coefficient (1/m) matrixes nozzle diameter (mm) reactor diameter (mm) particle diameter (mm) total column cross-section (m2 ) acceleration of gravity (m2 /s) reactor height (mm) capped section height (mm) height of catalyst bed (mm) maldistribution factor pressure drop (Pa) reflux (m3 /h) inlet flow rate (m3 /h) grid coordinates (radial direction) grid coordinates (axial direction) axial distance of i point (m) reflux ratio radius of reactor (m) momentum source term (kg/(m s2 )) axial velocity of i point (m/s) fluid velocity (m/s) velocity on direction j (m/s) velocity magnitude (m/s) mean velocity in porous media (m/s) nozzle velocity (m/s) local gas velocity (m/s) mean gas velocity (m/s)
Greek symbols 1/˛ viscous resistance coefficient (1/m2 ) ε stack porosity viscosity (Pa s) density (kg/m3 ) stress tensor (Pa)
section (h). A mimic catalyst bed was filled with spherical glass globule of 3–5 mm in diameter (dp ), with a stack porosity of 0.20 or 0.44. To examine the influence of the catalyst bed height on the flow characteristics, three heights (L = 100, 200, 300 mm) were used. The nozzle (d0 = 16.28 mm) was installed at the top of the reactor. The two dimensional coordinate with the axial direction (y) and the radial direction (r) was defined as depicted in figure, and the outlet centre of the nozzle was orientated as an origin of the coordinate. Air was flowed into the reactor through the nozzle along the y direction. To examine the influence of flow rate on the flow characteristics, three flow rates (45, 60 and 75 m3 /h) were used, which corresponded to the inlet velocities of 60, 80 and 100 m/s, respectively. The velocity profile in the combustion chamber was probed by the Streamline4 type Hot-Wire Anemoneter (HWA, Dantec Ltd.). This detector gave a maximal non-vector velocity. The value was averaged with the sampling time of 5 s. The detection range was between 0.02 and 300 m/s, with the error smaller than 2%. The pressure drop was measured by the pitot tube. 3. Model descriptions The realizable k-ε turbulent model is used for simulating the flow field in the combustion chamber and the bottom compartment beneath the catalyst bed (see Fig. 1). This model has been classically used for simulating both confined flows and free flows. The descriptions regarding this model may be referred to the literature [15,16]. The isotropic porous media model is applied for simulating the flow field in the catalyst layer. In this model, a momentum source term, Si , is added to the standard fluid flow equation, giving ∂ (v) + ∇ × (v v) = −∇ p + ∇ × () + g + Si ∂t
Si embraces a viscous loss term and an inertial loss term due to the collision between the fluid and catalyst beads:
⎛
Si = − ⎝
3
Dij vj +
j=1
publication has been found regarding cold modeling of a methane reforming autothermal reactor.
Fig. 1 shows the cylindrical reactor and the experimental flow sheet used in this study. The size of the reactor was 280 mm in inner diameter (d), 670 mm in height (H), and 100 mm in capped
3
⎞
Cij
vmag vj 2
⎠
(2)
j=1
For the case of a homogeneous porous media, Si is simplified as Si = −
2. Experimental
(1)
˛
vi + C2
vmag vi 2
(3)
where 1/˛ is the viscous resistance coefficient (˛ is called permeability) and C2 is the inertial resistance coefficient. This momentum term results in the pressure drop through the porous cell. For a packed bed, the pressure drop can be calculated in terms of Ergun equation: |P| 1.75 (1 − ε) 2 150 (1 − ε)2 v∞ + v∞ = L dP ε3 ε3 dP2
(4)
In the case of laminar flow, equation (4) can be approximate to the following equation: |P| 150 (1 − ε)2 v∞ = L ε3 dP2
(5)
while in the case of turbulent flow, the loss term can be ignored, thus |P| 1.75 (1 − ε) 2 = v∞ L dP ε3 Fig. 1. Autothermal reactor and experimental test system. 1—Computer, 2—anemometer, 3—probe, 4 —reactor, 5—pressure gauge, 6—flow meter, 7—valve, 8—roots blower.
(6)
We can accordingly obtain the constant values of viscous resistance coefficient and the inertial resistance coefficient from the following
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
305
equations: 150 (1 − ε)2 1 = 2 ˛ ε3 dP (8)C2 =
(7)
3.5 (1−ε) dP ε3
In the numerical calculation, we use the velocity inlet and pressure outlet as the boundary conditions. Moreover, we check the grid influences on velocity and pressure drop with the different grid amounts, and find that the grid has little influences on the results. 4. Results and discussions 4.1. Model validation Fig. 2 shows the experimental results of the axial velocity and the simulated results in combustion chamber at an inlet flow rate of 75 m3 /h and a catalyst bed height of 100 mm. The axial velocity at the radial distances near to zero decayed dramatically along the y direction. At each cross section, the axial velocity was the maximum along the central line, and it decreased towards the radial direction. The decay pattern became flat as the flow was away from the nozzle. The experimental data were well predicted by simulation. However, some numerical data were negative on the edge of the combustion chamber due to the back flow, whereas the HWA only detected the absolute values of velocity. Fig. 3 shows the numerical pressure isolines in the reactor at an inlet flow rate of 75 m3 /h and a catalyst bed height of 100 mm.
Fig. 2. Axial velocity profiles on varied cross sections. Conditions: () y = 107.5 mm, (䊉) y = 287.5 mm, () y = 437.5 mm, () y = 612.5 mm; L = 100 mm, Qr0 = 75 m3 /h, ε = 0.44.
Numerical results showed that the pressure drop through the catalyst bed was 68.37 Pa, very close to a value of 64.26 Pa measured by experiment. The consistence between the numerical data and the experimental data in the velocity and pressure drop has allowed us to validate the models used in this study. 4.2. Overall flow maps in the ATR reactor Fig. 4 shows the stream function in the ATR reactor at different heights and stack porosities of catalyst bed as well as at
Fig. 3. Static pressure isolines (Pa) in the reactor. Conditions: L = 100 mm, Qr0 = 75 m3 /h, ε = 0.44.
Fig. 4. Stream functions (kg/s) in the reactor with varied conditions. Conditions: (a) Qr0 = 75 m3 /h, L = 0 mm, ε = 0.44; (b) Qr0 = 75 m3 /h, L = 200 mm, ε = 0.44; (c) Qr0 = 75 m3 /h, L = 300 mm, ε = 0.44; (d) Qr0 = 45 m3 /h, L = 300 mm, ε = 0.44; (e) Qr0 = 45 m3 /h, L = 300 mm, ε = 0.20.
306
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 5. Radial distributions of axial velocity with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
the different inlet flow rates. The stream function is formulated from a relation between the stream line and the mass conservation of fluid. One stream line stands for a constant stream function, and two adjacent stream lines form a constant difference in the stream function, or a constant mass flow rate. As a consequence, a larger density of stream line represents a larger mass flow rate. Along the axial direction from the nozzle to the reactor bottom, the stream lines showed different shapes. In the upper zone of the combustion chamber, a small jet flow zone with dense stream lines was in contrast to a broad back flow zone with sparse stream lines. The jet flow developed with the y direction in the shape of a cone. In the lower part of the combustion chamber, two vortexes formed in the back flow zone, with dense stream lines around their cores. In the catalyst layer, the stream lines became sparse and well-ordered, indicative of a relatively uniform and mild flow rate. Beneath the catalyst bed, the stream lines displayed some disorder. Varied flow patterns occurred in the outlet of the reactor under the different conditions. We should expand our understanding of such varied flows in the reactor under the different conditions. In the case of no catalyst bed, or in the case of an entrained-flow reactor, no plug flow was formed even under the lower part of the reactor at the conditioned aspect ratio, and the jet flow and back flow prevailed. In the case of a catalyst bed packed, a part of fluid was back flowed when the flow approached the catalyst bed, while a part of fluid entered and passed through the catalyst bed. The velocity distribution in the ATR reactor trended to be uniform shortly after the fluid entered the packed layer. An increase in the catalyst bed height reduced the size of two asymmetric vortexes and increased the zone of the uniform flow in the catalyst bed. A reduction in the inlet flow rate or in the stack porosity of catalyst bed also reduced the vortexes in the combustion chamber and increased the flow uniformity in the catalyst bed.
4.3. Velocity profile, turbulence intensity and reflux ratio in the combustion chamber In this section, we will shed light on the influences of the catalyst bed height, catalyst bed stack porosity and inlet flow rate on velocity profile, turbulence intensity, and reflux distribution in more details. Turbulence intensity is defined as the ratio of the root-mean-square of the velocity fluctuation, u , to the mean flow velocity, uavg . The reflux ratio is defined as R=
Qr Qr0
(9)
where Qr0 is the inlet flow rate and Qr is the reflux, calculated by the following equation: Qr =
(ur,i+1 + ur,i )(r 2 − r 2 ) i+1 i 2
ur < 0
(10)
i
in which ri is the radial distance of i point, and ur,i is its axial velocity. Figs. 5 and 6 show the dependence of velocity profile in the combustion chamber on the catalyst bed height and catalyst bed stack porosity, respectively. Along the axial direction, we select three cross sections y1 , y2 , and y3 , to examine the change trend of the velocity profile with the different conditions. y1 and y2 are two positions representative of the upper space of the combustion chamber far away from the catalyst bed. y3 is the representative position near to the catalyst bed and it holds the fixed distance of 10 mm to the top layer of the catalyst bed. The velocity profiles at the cross sections y1 and y2 with different heights (Fig. 5(a) and (b)) and stack porosities (Fig. 6(a) and (b)) of the catalyst bed are almost the same, indicating that the catalyst bed height and porosity caused little variations of the velocity profiles within the upper space of the combustion chamber. The velocity profiles had a turning point (A and B) at which the jet flow changes to the
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
307
Fig. 6. Radial distributions of axial velocity with varied packing porosity of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
back flow from the inner side to the outside, as shown in figure. As the extended axial distance, the turning point moved towards the outside. At the cross sections close to the catalyst bed (for example, y3 ), both the catalyst bed height and the stack porosity appreciably affected the velocity profiles (Figs. 5(c) and 6(c)). At smaller radial distances (smaller than the radial distance of C and D) where the jet flow was dominant, an increase in the catalyst bed height or porosity led to the increased axial velocity, because a higher catalyst bed meant a lower momentum attenuation at a shorter axial distance and a larger porosity makes the back flow near catalyst bed smaller. At larger radial distances (larger than the radial distance of C and D) where the back flow was dominant, the result was opposite because a higher catalyst bed led to a stronger back flow. Similar results were observed on the impacts of the stack porosity. A larger stack porosity led to a lower pressure drop through the catalyst bed and thus to a weaker back flow at larger radial distances. Yu et al. [17] reported the velocity distribution in an entrained-flow gasifier. They experimentally observed that the catalyst bed height and stack porosity had a negligible effect on the flow field of combustion zone. Their results were essentially consistent with the numerical results obtained in this study. Fig. 7 shows the variations of the velocity profiles with different inlet flow rates at a cross section far away from the top layer of the catalyst bed (y1 ) and another cross section near to that (y3 ). On the cross section y1, a higher inlet flow rate gives rise to a higher axial velocity in the jet flow zone, while in the back flow zone, the influence is insignificant because of the dominant back flow. On the cross section y3 , the axial velocity is nearly not affected by the inlet flow rate.Figs. 8 and 9 show the influences of the height and stack porosity of the catalyst bed on the turbulence intensity distribution on the three cross sections y1 , y2 , and y3 , which are the same as those selected for analysis of the axial velocity profiles as illustrated in Figs. 5 and 6. Unlike the result of the axial velocity, the turbulence intensity on the
cross section y1 showed a peak in the jet flow zone (point E in Fig. 8(a) and (b)). This was because the turbulence was caused by the velocity gradient shear. A high velocity magnitude did not mean a high turbulence. However, a smaller velocity in the back flow zone certainly led to a weaker turbulence, so the turbulence intensities became small as the radial distance increased towards the back flow zone. Similar to the results of the axial velocity, the turbulence intensity distributions on the cross sections y1 and y2 were little influenced by the height (Fig. 8) and the stack porosity of catalyst bed (Fig. 9). Nevertheless, a higher catalyst bed led to a stronger turbulence on the cross sections near to the catalyst bed in the combustion chamber (e.g., y3 ). A change in the stack porosity varied the axial velocity profiles on the cross sections y3 (Fig. 6(c)), but it did not disturb the turbulence on these cross sections (Fig. 9(a–c). It could be seen from Fig. 10 that a high inlet flow rate amplified the turbulence on the cross sections near to the catalyst bed
Fig. 7. Radial distribution of axial velocity with varied inlet flow rates. Conditions: L = 300 mm, y1 = 100 mm, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
308
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 8. Turbulence intensity distribution with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
(e.g., y3 ) along the whole radial direction, while on the cross section near to the nozzle (e.g., y1 ), a high inlet flow rate intensified the turbulence only in the jet flow zone, with no effect of the inlet flow rate on the turbulence in the back flow zone. Turbulence is an
important parameter characteristic of the mixing state of the fluids in the reactor. Intense turbulence improves mixing at the macroand micro-scales, and it generally accelerates the mass transfercontrolled reactions. Among three factors including the height and
Fig. 9. Turbulence intensity distribution with varied packing porosity of catalyst bed. Conditions: Qr0 = 75 m3 /h, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 10. Turbulence intensity distribution with varied inlet flow rates. Conditions: L = 300 mm, y1 = 100 mm, y3 is the cross section that has the distance of 10 mm from the top of packing layer.
stack porosity of catalyst bed as well as the inlet flow rate examined, the inlet flow rate behaved as a main factor affecting the turbulence of the fluids in the reactor. Fig. 11 shows the changes of reflux ratio (R) with the dimensionless axial distance (y/d0 ) at three heights and two stack porosities of the catalyst bed. The reflux ratio exhibits a peak with y/d0 , regardless to the variations of three factors. The axial distance of the peak corresponded to that of the vortex center from the nozzle (see Fig. 4). At a y/d0 value smaller than 20, the change profiles of the reflux ratio with y/d0 are irrespective of the height and stack porosity of the catalyst bed. More fluid was circulated as a backflow with increasing the axial distance. At a y/d0 value larger than 20, the change trend of the reflux ratio with the height of catalyst bed became diverged. As the fluid approached the catalyst bed, the reflux ratio decreased. It was reasonable that a maximal reflux ratio occurred at a smaller y/d0 for the case of a higher catalyst bed. At a lower catalyst bed, the reflux ratio over the surface of the catalyst bed was lower because of a lower pressure drop through the catalyst bed, which enabled more fluid to enter the catalyst bed. The stack porosity slightly influenced the reflux ratio in the space near to the catalyst bed. A higher stack porosity allowed more fluid to pass through the catalyst bed and this consequence was a lower reflux ratio. Fig. 12 shows the influence of the inlet flow rate on the reflux ratio. A higher inlet flow rate meant a higher magnitude of flow momentum. Although the amount of back flow (Qr ) was increased with the inlet flow rate increasing, the reflux ratio was only slightly affected by the inlet flow rate.
309
Fig. 12. Reflux ratios with varied inlet flow rates. Conditions: L = 300 mm, ε = 0.44.
Fig. 13. Two arrangement methods for local velocity.
4.4. Flow uniformity in the catalyst bed In the direct coupling autothermal reactor, the flow in the combustion chamber, when impinging on the catalyst bed surface, are partitioned to two streams: a flow back to the combustion chamber and another flow entering the catalyst bed. The uniformity of the flow in the packed layer is generally of particular concern because it is possibly a direct cause for the hot spot. The uniformity of the flow in the stacked layer can be denoted by the maldistribution factor and the penetration depth. The maldistribution factor (Mf ) is defined as the ratio of the mean standard deviation of local velocities (wi ) to the mean of local velocities (w0 ):
1 F0
Mf = where w0 =
1 F0
F0
w − w 0 i w0
0
dF
(11)
F0
wi dF
(12)
0
Rumen Darakchiev [18] reported that two classical arrangements are used for local velocity measurement. One is to divide the apparatus cross-section into cells with equal surface, and local velocity is obtained in the cell center (Fig. 13(a)). The other is to divide the cross-section in coaxial ring sectors. The local velocity is obtained from different points on the middle line of ring sectors (Fig. 13(b)). In this work, the local velocities are obtained with the second method. In 2-D asymmetry numerical calculation, the local velocity should be calculated from: w0 =
Fig. 11. Reflux ratios with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h; open symbol, ε = 0.44; solid symbol, ε = 0.20.
1 2 Rreactor
Rreactor
2rwi dr
(13)
0
where Rreactor is the radius of reactor. A smaller Mf means a better uniformity of the flow in the catalyst bed [19]. As the flow passes through such a distance in the packed
310
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
Fig. 14. Maldistrbution factor distributions with varied heights and porosities of catalyst bed. Conditions: Qr0 = 75 m3 /h; open symbol, ε = 0.44; solid symbol, ε = 0.20.
layer that the Mf tends to be invariable, this distance is termed the penetration depth (PD). In this article, the PD is defined as the distance from the top of packing layer to 20% of the top Mf . The penetration depth is an index which measures the ability of a certain packing to equalize the gas flow velocity profile. Fig. 14 shows the maldistribution factors with different heights and stack porosities of the catalyst bed, respectively. At a stack porosity of 0.44, a non-uniform zone of the flow appeared in the upper catalyst layer, and the Mf decreased as the flow penetrated into the catalyst bed. Fig. 15 illustrates the penetration depths with the different heights of the catalyst bed at the stack porosity of 0.44. It could be seen that a higher catalyst bed not only resulted in a larger Mf at the initial point of the catalyst layer but also a larger PD, indicating that an increase in the catalyst bed height worsened
Fig. 16. Maldistribution factors with varied inlet flow rates. Conditions: L = 300 mm, ε = 0.44.
the uniformity of the flow in the upper catalyst layer. However, it was reported that the relation between the Mf and PD was not monotonous, despite a dependence of the PD on the initial value of Mf [20]. Results also showed that the stack porosity was an important factor affecting the uniformity of the flow at the upper catalyst bed. At a lower stack porosity (ε = 0.20), the values of Mf were not varied with the heights of the catalyst bed, and the Mf remained small through the whole catalyst bed. It was implied that the uniformity of flow in the catalyst bed might be effectively improved by changing the stack porosity. It should be noticed that a slightly turbulent flow was likely to happen in a bottom space of the catalyst bed. Darakchiev [13] reported a similar result. This was because the flow was disturbed on the border from the catalyst bed to the bottom void compartment. The non-uniformity of the flow in the bottom space was more salient at the catalyst bed height of 200 mm than for the other two cases. This indicated that the non-uniformity in the upper catalyst space did not have a monotonous relationship with that in the bottom catalyst space. Fig. 16 shows the influence of the inlet flow rate on Mf . Under three flow rates, the change of Mf with the axial distance and the PD were almost identical, indicating that the influence of the inlet flow rate on the velocity gradient in the catalyst bed was insignificant. 5. Conclusions
Fig. 15. Penetration depths with varied heights of catalyst bed. Conditions: Qr0 = 75 m3 /h, ε = 0.44.
The experimentally validated 2-D turbulence model (realizable k-ε) and porous media model were used to simulate the flow fields in a laboratory direct coupling authothermal reactor. The flow characteristics in the combustion chamber were assessed in terms of velocity profile, turbulence intensity and reflux ratio, and those in the catalyst layer were assessed in terms of maldistribution factor and penetration depth. The influences of three main cold operating factors including the inlet flow rate, catalyst bed heights and stack porosity on the flow behaviors or characteristics were examined. Numerical results showed that the height and stack porosity of the catalyst bed had little influence on the velocity profile in the upper space of the combustion chamber but did in the combustion chamber zone near to the catalyst bed. The turbulence intensity in the combustion chamber zone near to the catalyst bed was increased with increasing the height of catalyst bed, but that in upper space was irrespective of the porosities and catalyst bed heights. An increase in the inlet flow rate amplified the turbulence in the jet flow zone in the upper space of combustion chamber as well as in the combustion chamber zone near to the catalyst bed. The reflux ratios in the combustion chamber were not varied with the inlet flow rate, but did in the space near to the catalyst bed, with the height and stack porosity of catalyst bed.
Y.-q. Wang et al. / Chemical Engineering Journal 168 (2011) 303–311
The maldistribution factors and penetration depths were not susceptible to the inlet flow rate, but influenced greatly by the heights and stack porosity of catalyst bed. It is a little surprising for us to observe that the flow maldistribution in the bottom catalyst layer was not monotonously correlating to that in the upper catalyst layer. Overall, it could be concluded that the height and porosity of catalyst bed had small influences on the flow characteristics in the combustion chamber than the inlet flow rate, but they could appreciably vary the uniformity of the flow in the catalyst bed. Acknowledgements This work was supported by National Key Technologies R&D Program in China (no. 2006BAE02B02). The first author would also like to thank student Huahui Zhou in the experiment conduct. Special thank is due to Professor Jie Wang for his revision of this paper. References [1] J. Zhu, D. Zhang, K.D. King, Reforming of CH4 by partial oxidation: thermodynamic and kinetic analyses, Fuel 80 (2001) 899–905. [2] S. Freni, G. Calogero, S. Cavallaro, Hydrogen production from methane through catalytic partial oxidation reactions, Journal of Power Source 87 (2000) 28–38. [3] S.S. Bharadwaj, L.D. Schmidtatalyst, Catalytic partial oxidation of natural gas to syngas, Fuel Processing Technology 42 (1995) 109–127. [4] B. Glockler, A. Gritsch, A. Morillo, G. Kolios, G. Eigenberger, Autothermal reactor concepts for endothermic fixed-bed reactions, Chemical Engineering Research and Design 82 (2004) 148–159. [5] B. Glockler, H. Dieter, G. Eigenberger, U. Nieken, Efficient reheating of a reverseflowreformer-an experimental study, Chemical Engineering Science 62 (2007) 5638–5643. [6] G. Kolios, J. Frauhammer, G. Eigenberger, Autothermal fixed-bed reactor concepts, Chemical Engineering Science 55 (2000) 5945–5967.
311
[7] M.H. Halabi, M.H.J.M. de Croon, J. van der Schaaf, P.D. Cobden, J.C. Schouten, Modeling and analysis of autothermal reforming of methane to hydrogen in a fixed bed reformer, Chemical Engineering Journal 137 (2008) 568–578. [8] L.P. Chua, A.C. Lua, Measurements of a confined jet, Physics of Fluids 10 (1998) 3137–3145. [9] Ghanshyam Singh, T. Sundararajan, U.S.P. Shet, Entrainment and mixing studies for a variable density confined jet, Numerical Heat Transfer 35 (1999) 205–223. [10] M.T. Kandakure, V.C. Patkar, A.W. Patwardhan, Characteristics of turbulent confined jets, Chemical Engineering and Processing 5339 (2007) 1–12. [11] A. Jafari, P. Zamankhan, S.M. Mousavi, K. Pietarinen, Modeling and CFD simulation of flow behavior and dispersivity through randomly packed bed reactors, Chemical Engineering Journal 144 (2008) 476–482. [12] Arnab Atta, Shantanu Roy, Nigam Krishna D.P., Investigation of liquid maldistribution in trickle-bed reactors using porous media concept in CFD, Chemical Engineering Science 62 (2007) 7033–7044. [13] Rumen Darakchiev, Tatyana Petrova, Simeon Darakchiev, Gas distribution in columns with packing Raschig Super-Ring, Chemical Engineering and Processing 44 (2005) 827–833. [14] Tatiana Petrova, Krum Semkov, Chavdar Dodev, Mathematical modeling of gas distribution in packed columns, Chemical Engineering and Processing 42 (2003) 931–937. [15] Masoud Rahimi, Arsalan Parvareh, Experimental and CFD investigation on mixing by a jet in a semi-industrial stirred tank, Chemical Engineering Journal 115 (2005) 85–92. [16] Tsan Hsing Shih, W. William Liou, Aamir Shabbir, Zhigang Yang, Jiang Zhu, A new k-ε eddy viscosity model for high Reynolds number turbulent flow, Computers Fluids 24 (1995) 227–238. [17] Yu Zunhong, Shen Caida, Wang Fuchen, Yu Jiangguo, Xiao Kejan, Gong Xin, Three-region model for gasification process in coal-slurry-gasifier, Journal of Fuel Chemical and Technology (Chinese) 21 (1993) 90–96. [18] Rumen Darakchiev, Chavdar Dodev, Gas flow distribution in packed columns, Chemical Engineering and Processing 41 (2002) 385–393. [19] R.J. Kouri, J. Sohlo, Liquid and gas flow patterns in random packings, The Chemical Engineering Journal 61 (1996) 95–105. [20] D.P. Edwards, K.R. Krishnamurthy, R.W. Potthoff, Development of an improved method to quantify maldistribution and its effect on structured packing column performance, Institution of Chemical Engineers 77 (1999) 656–663.