Article pubs.acs.org/IECR
Experimental Evaluation of Distributor Technologies for Trickle-Bed Reactors Frédéric Bazer-Bachi,* Yacine Haroun, Frédéric Augier, and Christophe Boyer IFP Énergies Nouvelles, Rond point de l’échangeur de Solaize, BP 3, 69360 Solaize, France ABSTRACT: In this paper, different technologies of distributors for trickle bed reactors were compared, in terms of intrinsic performance of distribution and resistance to tray unlevelness. γ-ray tomography has first been used, in a large column unit, to visualize gas−liquid distribution just below several tray technologies. Results obtained show a better distribution performance under multiaperture chimney trays, in comparison with gas-lift and bubble cap systems. Then, a specific cold mock-up was designed in order to mimic tray tilt between two tray elements. Sensitivities to tray unlevelness of both gas-lift and multiaperture systems are comparable, far better than the one for the bubble cap system. Multiaperture chimneys have indeed excellent behavior at nominal conditions, while gas-lift technology is interesting for its ability to behave similarly over a large flow range. Considering those results, some guidelines are finally given for the choice of the distribution technology. have been the subject of recent reviews.8,9 Both reviews, mainly based on industrial advertising and communications such as Patel et al.,10 have highlighted promising performances of the recent gas-lift technology. The objective of this work is to complete these reviews, by experimentally comparing different distributor tray types (chimney trays, bubble cap trays, and gas assisted lift tube trays), in terms of both distribution performance and resistance to unlevelness. As a first step, distribution performances of different distributors have to be qualified and compared in a large cold flow experimental unit. To this end, several techniques can potentially be used to map spatial distribution of liquid and gas at the top of the catalyst bed: wire mesh tomography11−13 or imaging techniques such as nuclear magnetic resonance (NMR) imaging,3,14 electrical tomography,13 X-ray tomography,15 and γ-ray computed tomography.12,16 γ-ray tomography was chosen for this benchmark because of its excellent spatial resolution, its noninvasiveness, and its potential use on large reactors contrary to NMR imaging. As a second step, the impact of tray unlevelness on the global distribution has to be quantified. Tray tilt is industrially due to its own bending and to a potential angle deviation from the horizontal plane during installation. For large reactor diameters, the height difference between two points of the tray may reach 10 mm. A small scale mock-up was specifically implemented so as to compare gas and liquid flows coming out of two tray elements placed with a definite height difference. In order to posttreat in the best way the experiments results achieved, the impact of the maldistribution measured with this experimental setup has also been quantified in terms of changes in reactor performance.
1. INTRODUCTION Fixed-bed reactors operated under trickle-flow condition (TBRs) are one of the important classes of three-phase gas− liquid−solid reaction systems encountered in industrial practice. They are currently employed in hydrotreatments and in chemical and biochemical processes for the petroleum, petrochemical, and chemical industries. TBRs consist of a fixed bed of solid catalyst particles contacted by a cocurrent gas− liquid downflow. The reaction occurs between the dissolved gas and the liquid phase at the catalyst surface or inside the catalyst pellet. For its part, the trickling regime is characterized by small liquid flow rates and low to moderate gas flow rates. Liquid trickles over the catalyst bed, with the gas being a continuous phase. Recently, increasing environmental standards of fuels have led to the development of high performance units with improved catalyst activities. However, TBR efficiency relies also on a good distribution of liquid feed over the catalyst bed cross section, which means both an effective liquid inlet distributor and a perfect bed loading. Otherwise, channeling may appear, causing a significant loss in catalyst activity1 and an earlier catalyst deactivation. When coupled with highly exothermal reactions, gas and liquid maldistribution may be amplified by the fast drying of the catalyst and may possibly lead to local hot spots.2,3 Poor flow distribution generated by distributor technologies can be partially corrected by optimized layers of grading materials, with specific packing particles being able to enhance phase radial distribution.4−6 Unfortunately, this corrective approach is often not sufficient, with the catalyst bed having in any case few transverse mixing properties.7 All these facts have motivated recent developments of new distributors in order to enhance their general performance. Some specifications are indeed required: very good performance at design conditions, the flexibility to operate over a broad range of gas/liquid flow rates (numerous industrial operating conditions possible for a single reactor, difference in degree of feed vaporization from start of run to end of run, etc.), and a low sensitivity to tray unlevelness. These tray improvements © 2013 American Chemical Society
Received: Revised: Accepted: Published: 11189
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2. MATERIALS AND METHODS 2.1. Distributor Trays. Recent reviews8,9 listed types of distributor trays classically found in industrial trickle-bed reactors. Maiti and Nigam9 suggested a classification for vapor−liquid distributors, with four categories (Figure 1): perforated plate or sieve trays, chimney trays, bubble cap trays, and gas assisted lift tube trays.
Figure 2. Adding grid dispersive system under tray distributor.17
IQ =
Flow − Fhigh Faverage
(1)
where Flow and Fhigh are respectively phase flows through the low and high distributors and Faverage represents the average phase flow. The IQ criterion can be calculated for both gas and liquid phases, with the liquid (L) being preferentially used to characterize the maldistribution. A low value of IQL indicates a low sensitivity of distributor to tray tilt. By contrast, a high value of IQL points to a strong imbalance of distribution. Figure 3 shows a typical evolution of IQL for various distributors. Concerning results with multiaperture chimneys, the evolution of IQL exhibits alternatively higher and lower values corresponding respectively to liquid levels close to and far from apertures. As a consequence, careful design must be done to minimize these high value zones for IQL. Bubble cap trays are significantly different, with chimneys consisting of a cap centered concentrically over a standpipe (Figure 1). Vapor passes through slotted lateral openings, lifting liquid into the upflow channel and then downflow into an internal conduit. As a consequence, this technology operates on a gas assist principle compared to the liquid weight principle employed by multiaperture chimneys. Operation with a wider liquid flow range is believed possible. Yet sensitivity to tray unlevelness seems not reduced, in spite of this gas driving force (Figure 3). Moreover, because of their large diameters, centerto-center spacing for bubble cap trays is limited (fewer drip points). Gamborg and Jensen19 proposed a modified bubble cap system, named “vapor lift”, with only one upflow tube leg elevated above the tray. The operational principle is the same as for bubble caps: gas flows through the nozzles and then by gravity falls onto the catalyst bed. Following the authors, because liquid flow is not sensitive to the local liquid level at the nozzle, this gas-lift tray a priori exhibits an excellent sensitivity to unlevelness (Figure 3). Due to its rectangular configuration and smaller/fewer slots, center-to-center spacing is close to the one of the chimney tray, with a square pitch, allowing much better catalyst utilization than bubble cap trays. Lastly, according to the inventors, this design allows wide liquid flow ranges. The main dimensions of trays evaluated during this study, i.e., two chimney trays with/without dispersion devices, a classical bubble cap tray, and a gas-lift tray, are given in Table 1. The distribution performance of the bubble cap tray was not studied. Several types of gas-lift configurations, based on different geometric characteristics, were compared during maldistribution measurements.
Figure 1. Different types of distributors: (a) perforated trays, (b) multiport chimney, (c) bubble cap, and (d) gas-lift tube.8
Multiaperture chimneys are generally composed of lateral openings (holes or slots/notches spaced vertically up the axis of the chimney) for liquid and superior apertures for gas, allowing vapor−liquid contacting of both phases in the conduit. As a consequence, gravity is the main driving force for the liquid flow. Good distribution under the tray is generally achieved by minimizing the distance between two chimneys, with a triangular rather than square pitch preferred. Cost and fabrication constraints practically limit this center-to-center spacing to about 100 mm. Some enhancements are proposed by adding a dispersive system under the chimneys. The Shell HD tray may be designed with nozzles under the conduits,5 generating an overlapping of the created sprays, thus eliminating any grading material under the tray. IFPEN EquiFlow technology17 is characterized by several dispersive devices with rims, such as grids (Figure 2). Both solutions allow, theoretically, having an excellent liquid and gas distribution, avoiding any disk-type discharge pattern under the chimneys. As detailed by Maiti and Nigam,9 the surface area of lateral openings is determined to ensure a certain liquid level on the tray. The pressure balance establishes that the liquid velocity in the holes is directly correlated to the liquid height above the hole, with a 0.5 power dependence. As a result, when the liquid level is close to holes, this class of tray is also sensitive to unlevelness. Nevertheless, by keeping a minimum liquid head over the holes, this sensitivity is drastically reduced. To describe this sensitivity, an indicator IQ is defined18 between two chimneys submitted to an elevation difference (10 mm being generally considered): 11190
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Figure 3. Sensitivity to tray tilt for different technologies, with a 10 mm elevation difference.18
Table 1. Main Dimension Characteristics of Distributor Trays Used during This Study A, chimney tray with grid center-tocenter spacing (mm) pitch chimney diameter (mm) chimney height (mm) dispersive element
B, chimney tray with deflector
C, bubble cap tray
D, gas-lift tray
200
100
100
100
triangular 50
triangular 50
triangular 105
square 50
250
250
190
280 → 500
grid
deflector
−
−
2.2. Experimental Setup for Intrinsic Distribution Measurements. Experiments were conducted in a 0.6 m inner diameter column in order to evaluate the influence of tray type on distribution uniformity (Figure 4). All distributor trays were put at the top of the cylindrical column, after a feed diffuser: the behaviors of the gas and liquid on and just under the tray were visualized thanks to a local part of the column made of Plexiglas. Several successive solid layers followed: two grading layers (3/4 and 1/4 in. spherical particles), one catalyst layer (Axens HMC841), and one last grading layer (1/4 in. spherical particles). The number and height of these layers were chosen to mimic an industrial configuration. The mock-up was operated with hydrocarbon (heptane) and nitrogen, at low pressure (100−400 mbar gauge) and room temperature (about 25 °C). The liquid velocity vsl and gas velocity vsg were varied respectively between 0.2 and 0.8 cm·s−1 and between 2 and 20 cm·s−1, so as to test a maximum of industrial conditions for the trickling regime. γ-ray tomography was implemented at the top of the catalyst layer to provide a two-dimensional map of the liquid retention across the catalyst bed section. This choice of tomography position is deliberate in order to take into account the possible effect of grading on the gas/liquid distribution at the top of the catalyst layer. This tomographic system is composed of a 137Cs γ source (300 mCi in activity) and 32 detectors with BgO crystals). The whole system, γ-ray source and detectors, rotates around the fixed bed column. Attenuation of γ radiation between the
Figure 4. Experimental setup for distribution performance study.
source and detectors depends directly on the material crossed densities. These attenuation data are analyzed to reconstruct 64 × 64 pixel images and thus a resolution of 6.25 × 6.25 mm2. The uncertainty of liquid retention measurements is less than ±3%.16 A special algorithm based on algebraic reconstruction had to be used for image reconstruction, in order to characterize sharp liquid retention gradients.5,20 2.3. Experimental Setup for Maldistribution Measurements. A schematic diagram of the setup used for the maldistribution experiments is shown in Figure 5. The experiment setup is a transparent Plexiglas column of 400 mm internal diameter, composed of two partitioned sections. The upper domain contains two half-trays, each supporting a distributing element. The general level distance between two half-trays is 10 mm. Thus, one of the distribution elements is slightly higher than the other. The lower domain is placed below both of the half-trays. It is divided into two collector chambers by a tight vertical separation passing by the median. The outlet liquid and gas flow rates are independently measured at the exit of each collector chamber to exactly 11191
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et al.21 Whatever distributor tray is implemented, the liquid retention points are close to each other, falling into the anticipated uncertainty margin (±3%). Moreover, experimental data follow the same trend as the model curve. The relatively good agreement between experimental results and the model of Boyer et al. validates the technology of γ-tomography for the comparison between distributor trays. About 100 two-dimensional (2D) images of spatial distribution of liquid and gas were achieved at the top of the catalyst, depending on the tray distributor and operating conditions (liquid and gas superficial velocities). As an example, Figure 7 shows 2D maps of liquid retention distributions for two different operating conditions. Different kinds of distributions are observed depending on the distributor tray. Qualitatively, distribution is better for tray A with grids and tray B with deflectors, because of a better wall coverage and fewer microheterogeneities between two drip points. The presence of a grid (tray A) enables an excellent distribution, even for a far larger step between chimneys (200 mm). The absence of deflectors for tray B worsens distribution: a disk-type discharge pattern under chimneys is clearly emphasized, particularly at high superficial liquid velocity. The importance of spray induced by the deflector under the chimney is proved; nevertheless, this solution is limited for low and medium tray spacing (≤100 mm). The worst distribution is obtained for the gas-lift distributor (tray D): square-type discharge patterns under the drip points are visible for all operating conditions, and liquid wall coverage is poor compared to other distributors (important gas channelling near wall). This situation has not been improved even at very high superficial gas velocities (vsg = 20 cm·s−1). One may finally add that those spatial distributions with nonnegligible heterogeneities are obtained after 200 mm of grading materials, which, as discussed previously, generally improves slightly radial dispersion. Qualitative tendencies have been converted into distribution efficiencies η. This efficiencies are defined by the surface fraction of the image where the liquid retention β is within a range of 20% compared to mean liquid retention:
Figure 5. Schematic diagram of experimental setup for the maldistribution evaluation study.
quantify the maldistribution generated by the height difference, for the liquid and gas phases. Inlets of the liquid and gas phases are made at the upper level. Experiments were operated with a water/air system at atmospheric pressure conditions. During the tests, the liquid and gas flow rates were varied in a range corresponding to the operating conditions of hydrotreatment and hydrodesulfurization operations: vsl [0.3, 1.5] cm·s−1; vsg [2, 20] cm·s−1 (large liquid and gas flow ranges were knowingly chosen). The holes/slots of each distributor were designed for a liquid superficial velocity close to 1 cm·s−1 (chosen design condition). The liquid and gas flow rates measured at the exits of both collector chambers were used to calculate the maldistribution sensitivity of each distributor type (indicator IQ). The following distribution elements were tested: multiaperture chimney, conventional bubble cap chimney, and different configurations of gas-lift chimneys. The geometric parameters of all distributors are listed in Tables 1 and 2.
|β − β ̅ | < 0.2β ̅
3. RESULTS AND DISCUSSION 3.1. Distribution Performance of Several Tray Distributor Technologies. Figure 6 presents, on the same graph, all liquid retentions measured at the top of the catalyst bed, for each distributor tray studied, with regard to the model of Boyer
Parts a and b of Figure 8 show distribution efficiencies calculated for all distributor trays, at superficial gas velocities of 2 and 10 cm·s−1, respectively. They confirm quantitatively that the distribution performance of a multiaperture chimney tray with a grid (tray A) and a tray with a deflector (tray B) are of the same magnitude, contrary to that of the gas-lift system (tray D). Thus, these experimental results have demonstrated a clear advantage for the multiaperture chimney trays tested in terms of the intrinsic performance of the distribution. Two facts may mitigate this conclusion: the effect of pressure can slightly modify the gas/liquid distribution under the tray, and the relative importance of gas channeling near the wall is reduced for large reactor diameters. By the way, the commonly accepted conclusion about the excellent performance of a recent gas-lift tray compared to a chimney tray, exposed by recent reviews,8,9 seems highly exaggerated. 3.2. Effect of Tray Unlevelness on Distribution Performance, For Several Distributor Technologies. In this section, we discuss the effect of tray unlevelness on the deterioration in the maldistribution indicator IQL, for all the distributors studied (Table 2). As a checking procedure, preliminary studies with two identical chimneys at the same
Table 2. Hole/Slot Characteristics of Distributor Used for the Maldistribution Study gas-lift trays
chimney height (mm) hole rows hole number per row hole diameter (mm) slot number slot height (mm) slot thickness (mm)
A, chimney tray with grid
C, bubble cap tray
D1
D2
D3
250
190
300
500
280
3 3
− −
− −
− −
− −
7
−
−
−
−
− −
3 65
1 150
1 150
2 85
−
22
2
2
4
(2)
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Figure 6. Liquid retentions at the top of the catalyst bed for different distributors trays, for a superficial gas velocity of 2 cm·s−1, in comparison with the model of Boyer et al.21
caution, but it gives a first order of magnitude for the impact of a possible maldistribution. This ideal IQ value of 20% will be reported on Figure 9a−c. First, Figure 9a shows the effect of the liquid flow rate on the percentage difference of liquid flow (IQL) between two multiaperture chimneys A, at low superficial gas velocity (vsg = 2 cm·s−1). The experimental points obtained confirm the general behavior admitted for this type of distributor: low sensitivity to unlevelness, particularly at design conditions (IQL < 5%), except when the liquid level on the tray is close to hole rows (IQL,max → 40%) or when very low liquid velocities are used. An excellent agreement was obtained comparing mock-up results with those of a model established considering the pressure balance between gas and liquid phases, still highlighting the reliability of the tests. Finally, this model was adapted to another configuration of this chimney type, with a height of 500 mm and only two hole rows. It demonstrates the very important impact of this geometric parameter (IQL,max now always under 20%), showing that chimney height is the main lever to reduce multiaperture chimney sensitivity to unlevelness. Parts b and c of Figure 9 compared the effect of liquid flow rate on IQL values for all various technologies of distribution tested, respectively, at low (vsg = 2 cm·s−1) and high (vsg = 15 cm·s−1) gas flow rates. Bubble cap distributor C is found to be by far the more sensitive technology to the tray tilt, for both conditions of the gas flow rate. The measured maldistribution exceeds 100% at high gas load. At low gas velocity, the rate of maldistribution is about 80% at the design condition. For all its arrangements, the recent gas-lift system exhibits an intermediate maldistribution. At high gas velocity (vsg = 15 cm s−1), maldistribution is of the same order of magnitude as for the multiaperture chimney A: IQL values are generally higher, particularly at design conditions, but without the local peaks encountered at low liquid flow rates for the multiaperture system. At low gas velocity (vsg = 2 cm s−1), IQL values are in general bigger. Exception was found for the D2 gas-lift configuration for which interesting IQL values were obtained, but only at high gas velocity: the impact of the distributor height is suspected (in this case, 50 cm). In conclusion, gas-lift systems D have a sensitivity to tray tilt comparable to or more
Figure 7. Two-dimensional maps of liquid retention distribution at the top of the catalyst bed for different distributor trays, depending on gas/liquid superficial velocities.
height have given IQL values close to 0% for both phases, with an absolute uncertainty of 4%, proving the equilibrium of the mock-up configuration. Before going on with the analysis of experimental data, an attempt has been made to link liquid maldistribution and drop in performance of trickle bed reactors, using a simple numerical model of a diesel fuel hydrodesulfurization (see the Appendix). The main result obtained is that, below an ideal equilibrium index IQL of 15−20%, the effect of maldistribution remains under control. These figures of course have to be taken with 11193
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Figure 8. (a) Distribution efficiencies at the top of the catalyst bed for different distributor trays, for superficial gas velocities of (a) 2 and (b) 10 cm·s−1.
A and B have good distribution capabilities and a correct resistance to nonhorizontality, except at some points of the liquid flow range (turndown regime, the case when the liquid level approaches hole rows). Distribution obtained under gaslift trays D is less interesting (more heterogeneities). Their resistance to tray tilt is comparable with those of trays A and B, lower at nominal conditions but with the advantage of being relatively constant over the liquid flow range. It is clear that few current distributor technologies respect this ideal IQL criterion of 15−20%, particularly when the design is done for a large liquid flow range. Considering all the facts, the authors propose the choice of multiaperture chimney trays for the classical liquid flow range, with the gas assisted system being interesting only for the high liquid flow range. Motivations for this choice of multiaperture chimney trays are a better distribution under this tray, an excellent resistance to unlevelness at nominal conditions (i.e., presumable unit operating conditions), and a correct resistance for all liquid velocities encountered. To support these guidelines, Table 3 presents several examples of design of multiaperture chimney trays, submitted to different liquid flow ranges. This gives some indications for the selection between classical chimney and gaslift technologies (here for a classical chimney height of 300
important than the one of the multiaperture system A, contrary to what was exposed by several authors.8,9,18,19 An explanation for these results below expectations for gaslift distributors can be found in Figure 9d (effect of liquid flow rate on gas maldistribution IQG values). While there is no gas maldistribution for the multiaperture chimney A, it is catastrophic for the bubble cap distributor C, and significant for all the gas-lift configurations D (IQG ∼ 15−30%). It is believed that bubble caps and gas-lift distributors are less dependent on the liquid flow rate in comparison with classical chimneys. However, there exists a dependence on the gas flow rate due to the gas assisted principle. It is then likely that the gas maldistribution observed in Figure 9d caused the liquid imbalance established in Figure 9b,c. Besides, this gas maldistribution can have a dramatic impact for processes with hydrodynamic operating conditions close to the bubble flow regime (higher gas flow rates). 3.3. Discussion. Results previously exposed, for both distribution performance and resistance to tray unlevelness, have shown that no clear direction exists for the choice of the distribution technology. The sole certain fact established is that the bubble cap distributor C must be avoided because of its catastrophic resistance to tray tilt. Multiaperture chimney trays 11194
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Figure 9. (a) Effect of liquid load on the liquid distribution for A multiaperture chimneys, with a tray tilt of 10 mm, at low superficial gas velocity (vsg = 2 cm·s−1). Experimental results (□). Theoretical prediction: 250 mm height chimney (); 500 mm height chimney (---). (b) Effect of liquid load on the liquid distribution for different trays, with a tray tilt of 10 mm, at low superficial gas velocity (vsg = 2 cm·s−1). Experimental results: A, multiaperture chimney (□); C, bubble cap chimney (×); D1, gas-lift chimney (▲); D2, gas-lift chimney (●); D3, gas-lift chimney (◆). Theoretical predication: A, multiaperture chimney (). (c) Effect of liquid load on the liquid distribution for different trays, with a tray tilt of 10 mm, at high superficial gas velocity (vsg = 15 cm·s−1). Experimental results: A, multiaperture chimney (□); C, bubble cap chimney (×); D1, gas-lift chimney (▲); D2, gas-lift chimney (●); D3, gas-lift chimney (◆). Theoretical predication: A, multiaperture chimney (). (d) Effect of liquid load on the gas distribution for different trays, with a tray tilt of 10 mm, at high superficial gas velocity (vsg = 15 cm·s−1). Experimental results: A, multiaperture chimney (□); C, bubble cap chimney (×); D1, gas-lift chimney (▲); D2, gas-lift chimney (●); D3, gas-lift chimney (◆).
contrary to what is exposed in recent reviews mainly based on industrial communications, other tests show that gas-lift systems do not outclass multiaperture trays in terms of resistance to nonhorizontality. Thus, some guidelines were finally proposed, based on experimental conclusions and modeling, favoring the choice of multiaperture chimneys for current operating conditions of trickle-bed reactors (i.e., classical liquid flow ranges), with gaslift systems being competitive only in the case of very large liquid flow ranges (because of their constant acceptable performances vs liquid velocity). By the way, developments are still required in terms of distributor internals so as to propose an ideal technology: excellent distribution under the tray and perfect resistance to a potential unlevelness, for all operating conditions. Incontestably, more work should be done with cold flow testing. Priority will be given to two experimental axes: (1) experiments at high pressure and/or with high density gases and (2) evolution of initial liquid maldistribution over the catalytic bed. Developments of computational fluid dynamics modeling are also required, particularly for gas assisted systems.
Table 3. Effect of Liquid Flow Range on the Design of a Multiaperture Chimney and Impact on Maldistribution Criterion IQL for the Liquid Phasea liquid flow range (vsl,max/vsl,min) chimney height (mm) chimney diameter (mm) hole rows hole number hole diameter (mm) IQmean (%) IQmax (%) IQnominal (%) a
2
3
4
5
6
3 3+3+3 7+5+5 8.2 24.3 3.2
3 3+3+3 6+6+6 9.0 30.9 3.4
300 50 1 3 10 6.5 14.0 3.5
2 3+2 9+4 5.6 15.2 2.3
3 3+3+3 7+4+4 7.0 17.1 2.9
ρL = 600 kg·m−3, ρG = 30 kg·m−3, and vsl,nominal = 0.8 cm·s−1.
mm): up to a liquid flow range of 5, the performance of multiaperture chimney trays is good enough at turndown conditions (IQL,max < 20%) and excellent at design conditions.
4. CONCLUSION Current state-of-art trickle bed reactor distributors were tested and compared in terms of distribution performance and resistance of this performance when the tray is submitted to a nonhorizontality. Experiments quantifying the intrinsic performance of distribution have revealed an advantage for the technology of multiaperture chimneys with grids/deflectors. Moreover,
■
APPENDIX: “TWO PARALLEL PLUG REACTORS” MODEL OF MALDISTRIBUTION The impact of large scale maldistributions on the performances of fixed bed reactors is estimated by using a simple numerical model. Liquid and gas flow rates are considered as constant 11195
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considered, assuming no mass transfer limitation and a zero order kinetics on hydrogen. Following Varga et al.,22 the energy of activation Ea is taken as 80−120 kJ·mol−1. The enthalpy of reaction ΔHr is taken as 75 kJ·mol−1, a value in the range of magnitude reported by Murali et al.23 The pre-exponential factor is fitted in order to process the reaction at T = 650 K, a realistic temperature in comparison with industrial operating conditions. The liquid superficial velocity U is 0.01 m·s−1 in the reactor. The assumptions listed above simplify the model which can be easily solved by using a simple first order numerical method. Solved equations are
along the axis of the reactor. Only the case of liquid maldistribution is discussed; the gas phase is supposed to flow homogeneously in the reactor at constant superficial gas velocity. Heterogeneities of flow rates at the outlets of chimneys or distributing devices are modeled by dividing the section of the reactor into two equal areas, fed by two different liquid flow rates. The spatial scale of maldistribution between high and low flow rates is supposed to be sufficiently high to avoid attenuation of maldistribution along the vertical axis, and the reactor is assumed to behave like two parallel plug reactors, as presented in Figure 10.
Ui
∂C = −K exp( −Ea /RT ) ∂z
UiρCp
∂T = ΔHrK exp( − Ea /RT ) ∂z
(3)
(4)
where Ui is the liquid superficial velocity in the reactor i (i = 1 or 2). Ui is calculated as follows: ⎡ ⎛ 3 ⎞⎤ Ui = ⎢1 ± ⎜i − ⎟⎥U̅ IQ L ⎝ ⎣ 2 ⎠⎦
(5)
As the liquid velocity is different in each side of the reactor, the conversion is not equal between the two parallel plug reactors, and the resulting mean conversion is calculated at the outlet of the reactor. When the maldistribution indicator IQL is not null, a difference appears between temperature and concentration profiles of the two parallel reactors. The global sulfur content at the outlet of the whole reactor is also increased, as reported in Figure 11a. In Figure 11 is also reported the maximal difference of temperature in the transversal direction, between reactors, and obtained at approximately 1.3 m from the inlet. In spite of its simplicity, this example shows how maldistribution can induce radial temperature gradients and impact performances of fixed bed reactors. As a content of 10 ppm atomic sulfur is required in the diesel fuel, the loss of conversion due to maldistribution is thwarted by an increase of the temperature at the inlet of the reactor, ΔT0. The temperature adjustment depends on operating conditions of
Figure 10. Modeling maldistribution by two parallel plug reactors. The gray scale schematizes the sulfur content in the liquid phase.
Each side of the reactor is modeled as an adiabatic onedimensional reactor. Heat and mass diffusion phenomena are also neglected as convection by the liquid flow rate is predominant in the evolution of concentration and temperature in the vertical direction. The case of diesel fuel hydrodesulfurization is considered, inside a single bed reactor of 6 m height. The liquid phase properties are those of hexadecane C16H34 (ρ = 800 kg·m−3, Cp = 1800 J·kg−1·K−1). The only reactant is benzothiophene (C8H6S) present in the liquid phase only at 2% weight regarding atomic sulfur. Sulfur specification at the reactor outlet is 10 ppm. A first order apparent kinetics on benzothiophene is
Figure 11. (a, left) Loss of conversion induced by maldistribution and maximal temperature difference between both plug reactors. (b, right) Increase of inlet temperature necessary to reach the target [S]out = 10 ppm. 11196
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Industrial & Engineering Chemistry Research
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the reactors and kinetics. The energy of activation has obviously an important impact on the temperature increase linked to the maldistribution, as shown in Figure 11b. An important result obtained with the simple model “two parallel plug reactors” is that, below an equilibrium index IQL of 15−20%, the effect of maldistribution remains under control with inlet temperature adjustments below 1 °C. Higher inlet temperature adjustments are not desired as they could accelerate catalyst deactivation and finally shorten run cycle lengths.
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AUTHOR INFORMATION
Corresponding Author
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[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by IFP Énergies Nouvelles, to whom the authors wish to express their gratitude.
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REFERENCES
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dx.doi.org/10.1021/ie400504p | Ind. Eng. Chem. Res. 2013, 52, 11189−11197
