CFD studies on efficacy of flow modulation in a hydrotreating

Subscriber access provided by Karolinska Institutet, University Library

Kinetics, Catalysis, and Reaction Engineering

CFD studies on efficacy of flow modulation in a hydrotreating trickle bed reactor Soumendu Dasgupta, and Arnab Atta Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b02632 • Publication Date (Web): 06 Sep 2019 Downloaded from pubs.acs.org on September 6, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

CFD studies on efficacy of flow modulation in a hydrotreating trickle bed reactor Soumendu Dasgupta and Arnab Atta∗ Multiscale Computational Fluid Dynamics (mCFD) Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India E-mail: [email protected] Phone: +91 (3222) 283910

1

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Hydrodesulfurization (HDS), a pivotal process for sulfur removal that is essential in deep processing of crude oil, is typically carried out in steady state trickle bed reactors (TBRs). Familiarized with such operation, researchers are now investigating the benefits of flow modulation strategies in TBRs for improved conversion efficiency. In this work, a computational fluid dynamics model of a hydrotreating TBR is developed to delineate the efficacy of flow modulation in a HDS reaction system. Fast and slow modes of on–off and min–max flow modulations with different split ratios are compared with time averaged continuous operation for reaction conversion. On-off and min–max flows resulted in relative improvement in conversion by 36% and 19%, respectively. Combined analysis of reaction conversion improvement along with oscillating pressure drop revealed the efficacy of fast mode on–off strategy in maximum conversion of the considered system at the expense of lower pressure drop undulations.

2


Page 2 of 32

Page 3 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction Trickle bed reactors (TBRs) refer to a classical configuration of the multiphase packed bed reactors (PBRs), where gas and liquid flow cocurrently downward through a fixed bed of packing particles. 1 Industrial affinity of TBRs arise from its major applicability toward hydroprocessing of petroleum fractions, especially hydrodesulfurization (HDS), hydrocracking, hydrodenitrogenation, and hydrodearomatization of diesel oil. 2–4 Sulfur and aromatic content are of primary concern to comply with environmental standards of SOx , N Ox and other volatile organic matter emissions during combustion of diesel oil. 5,6 Contextually, catalytic hydrotreating is well established owing to its efficacy to remove sulfur, nitrogen, heavy metals, and aromatics in petroleum fractions at high temperatures and hydrogen pressures. 7 From the modeling perspective, Gunjal and Ranade 8 formulated an isothermal 2D model of a TBR for hydroprocessing reactions at the pilot and industrial scale reactors to understand the influences of hydrodynamic parameters namely particle characteristics, porosity distribution, and reactor scale. Isothermal and non–isothermal CFD models were also developed for HDS process to analyze the influences of particle characteristics, porosity distribution, operating pressure, gas and liquid flow rates, feed temperature, and gas phase sulfur concentration on reactor conversion. That study demonstrated an improvement of 9% desulfurization efficiency in non-isothermal operation under adiabatic conditions. Recently, Silva et al. 4 developed a 3D CFD model to investigate HDS and hydrodearomatization (HDA) in a small scale TBR assuming fully wetted bed and isothermal condition. Two different operation strategies, co–current and counter–current TBRs were compared to quantify the effects of liquid hourly space velocities (LHSV), gas–liquid ratio and partial pressure of H2 S on reactor performance in terms of liquid holdup, pressure drop, and conversion efficiency. TBR hydrodynamics is essentially governed by two or more fluids coursing through convoluted routes formed in between packing particles. 9–11 Non–linear fluid interactions at varying length scales coupled with multiscale transport processes not only prescribe diverse flow regimes but also render modeling of TBRs an intriguing task. 12,13 Moreover, challenges alle3



viate for modeling unsteady state (cyclic or periodic) TBRs, which proved to be beneficial for process intensification. 14,15 Several researches demonstrated the efficacy of periodic flow modulation in sustainable operation and in achieving improved efficiency of TBR, its service life and higher throughputs, particularly in terms of increased reaction conversion rates. 16,17 Flow modulation is characterized by the periodic/cyclic toggling of one fluid phase at the inlet, between a low (base) and a high (peak) flow rate in presence of another continuously flowing phase, which is typically termed as min–max operation. When the base flow rate is set to zero, it is referred as on–off operation. 18 Flow modulation can be also classified as slow and fast modes, based on the duration of peak and base flow periods. 19–22 Generally, commercial processes in chemical industries are characterized by either liquid or gas phase limiting reactions. Therefore, it is important to choose an appropriate mode of cyclic operation in such processes. 23,24 A detailed insight on the merits and applicability of cyclic flow operation in PBRs has been summarized by Atta et al. 25 . Khadilkar et al. 26 and Wongkia et al. 27 examined the influence of various cyclic parameters e.g., period, split, and peak liquid mass velocity on hydrogenation rate of αMethylstyrene. It was found that fast mode of liquid flow modulated on–off cyclic operation resulted in enhanced conversion rate up to 18%. Ayude et al. 28 also examined the effect of flow rates, splits and cyclic periods of on–off operation on oxidation of methanol. They claimed a significant improvement in catalyst activity of 30% for larger split (shorter off duration) at constant modulation periods. Liu and Mi 29 developed a transient model to analyze the influence of cyclic parameters on catalyst wetting and conversion rates for hydrogenation of 2–ethylanthraquinone. Conversion rates and catalyst wetting fraction were found to significantly improve by 21% and 12%, respectively for cyclic flow operation. Tukač et al. 30 explored hydrogenation of olefins in pyrolysis gasoline, for both steady state and min–max flow operations. They reported a considerable improvement in reaction rate of about 30% for periodic flow conditions. Liu et al. 16 conducted a comparative study between five different modes of flow operation for on–off and min–max variations, of both liquid flow

4


Page 4 of 32

Page 5 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


rate and concentrations. A hybrid operation involving variation of both flow rate and concentration simultaneously was also proposed. Min–max operation of a single parameter in this case was reported to improve reaction efficiency by 10–20%, which was further increased by another 15% on incorporating the hybrid operation. Despite proven advantages, implementation of unsteady or periodic flow operation in PBRs is non–trivial at the commercial scale due to its highly non–linear hydrodynamics, which might endanger process control safety. 25 Few researches have attempted to develop comprehensive numerical models to envisage the influence of operating conditions in periodically operated TBRs. 31–34 However, robust computational approaches to conjugate TBR hydrodynamics with reactor performance and HDS reaction conversion has rarely been reported. 4,8,30 Additionally, none of the earlier studies explored the influence of flow modulation in a HDS process and investigated the optimal cyclic mode and split with respect to mass transfer and reactions. In this work, an isothermal 2D axis–symmetric two-phase Eulerian model, describing the flow domain as a non-uniform porous region, is developed and utilized to simulate a HDS process in PBRs operating under trickle flow regime. The closure terms for phase interactions are accounted by relative permeability concept. 35,36 The developed model is firstly validated with the experimental data available in the literature for steady state flow operation. It is subsequently extended to study the influences of min–max and on–off flow operations in a HDS system and to assess the potential benefits of periodic operation in improving reaction conversion. Transient overall pressure drop, a crucial factor for process control safety, is also analyzed for all periodic flow strategies to identify the desirable modulation scheme and split with respect to improved reaction conversion.

Computational model In this work, multiphase flow dynamics is resolved by the two-phase Eulerian framework, where the interphase drag forces are estimated using relative permeability concept. 35,37 In

5



Page 6 of 32

such cases, the interstitial voids, created by packing particles in a fixed bed, are envisaged as a porous media having directional resistances. The details and efficacy of this approach have already been demonstrated elsewhere. 18,36,38 Following governing equations are considered for modeling the flow system.

Governing equations Volume averaged Navier–Stokes equations are solved for each flowing phase, and are given by: Continuity Equation: ∂k ρk + 5.(k ρk ~uk ) = 0 ∂t

(1)

∂(k ρk ~uk ) + 5.(k ρk ~uk ~uk ) = −k (5Pk − ρk~g ) + 5.k τ k + F~k ∂t

(2)

Momentum equation:

where ~u is the velocity vector, ρ is the density, P denotes pressure, g is the acceleration due to gravity, τ is the volume averaged viscous stress tensor, and F~k is the total drag force exerted by phase k per unit volume of the bed. Phase interaction terms in Eq. 2 is addressed by the relative permeability concept, 35 which expresses: Fα 1 Reα Re2α = A +B ρα g α kα Gaα Gaα

α = pth /k th phase

(3)

where A and B are the Ergun constants. Reynolds (Reα ) and Galileo (Gaα ) numbers are defined as: Reα =

ρα uα de µα (1 − )

(4)

Gaα =

ρ2α gd3e 3 µ2α (1 − )3

(5)

6


Page 7 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where de =

6Vp Ap

(6)

Incorporation of relative permeability (kα ) in the Ergun equation essentially takes into account the presence of a second phase as a function of saturation or holdup of the corresponding phase. After investigating several data sets over a considerable range of Reynolds and Galileo numbers, Saez and Carbonell 35 resolved relative permeability of liquid to be a function of reduced saturation, which is characterized by the effective flow volume available to liquid with respect to total bed volume. Saez and Carbonell 35 further examined various sets of pressure and holdup data, and eventually proposed empirical correlations for liquid and gas phase permeabilities as:

where sg = 1 −

0l ,

and δl =

kl = δl2.43

(7)

kg = s4.80 g

(8)

l −0l . −0l

Static liquid holdup (0l ) can be estimated from: 35

0l =

ρl gd2p 3 1 ∗ where E = 0 20 + 0.9E0∗ σl (1 − )2

(9)

More detailed derivation and discussions of these equations can be found elsewhere. 35,36

Chemical reaction model This work only focuses on modeling hydrodesulfurization reaction in TBRs, where the liquid phase is assumed to be diesel oil consisting aromatic sulfur compound (ArS), poly-aromatic compounds, napthenics, and parafins (Table S1). Here, dibenzothiophene (DBT) is chosen as the ArS, which reduces to biphenyl (BP) and produces hydrogen sulfide in the process.

7



Page 8 of 32

The considered HDS reaction can be represented in the following generalized form: ArS(l ) + 2 H2 (g) −−→ Ar(l ) + H2 S(g) According to Girgis and Gates 39 and Chowdhury et al. 2 , HDS is a set of irreversible reactions for a specific set of process condition. Sulfur compounds and H2 favor reaction, whereas H2 S in the product stream has a negative influence on the reaction rate and consequent overall conversion. The kinetic model utilized in this work is adopted from Chowdhury et al. 2 , where the reaction rate is expressed as: 1.6 0.56 −KHDS CArS CH 2 [kmol/(kg.s)] 1 + kad CH2 S

rHDS =

(10)

where CArS is the concentration of aromatic sulfide, which is essentially DBT in this study. CAr is the concentration of BP, CH2 S is the concentration of H2 S, and KHDS is the rate constant for desulfurization process, defined as:

12

KHDS = 2.5 × 10 exp

−19384 Ta

[(m3 )2.16 /(kg.(kmol)1.16 .s)]

(11)

The adsorption coefficient (kad = 50,000 m3 /kmol) is assumed to be independent of temperature. Species transport model in ANSYS Fluent 18.0 was used for simulating the chemical reaction, and the rate of reaction was specified by a user defined function. Values of velocity and volume fraction estimated from the hydrodynamic model were used to solve the species transport equation. Mass balance of ith species in the k th phase is defined as: ∂k ρk Ci,k + 5.(k ρk uk Ci,k ) = 5.(k ρk Di,m 5 Ci,k ) + k ρk Si,k ∂t

(12)

where Ci,k is the concentration of ith species in the k th phase, Di,m denotes mass diffusivity of ith species. ρk and k are the density and volume fraction of phase k, respectively, and Si,k represents the source term of species i in k th phase (gas or liquid). Source term for species, i, in the gas phase is defined as: 8


Page 9 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Si = −(kgl agl )i

Ci,g − Ci,l Hi

(13)

Similarly species i in the liquid phase can be calculated from: Si = (kgl agl )i

j=n X Ci,g − Ci,l + ρb η rij Hi j=1

(14)

where, kgl and agl are the gas–liquid mass transfer coefficient and interfacial area, respectively; Ci,l and Ci,g are the concentrations of species i in liquid and gas phase, respectively, Hi is Henry’s constant, r is the rate of reaction, n is the number of reactions, ρb is catalyst bulk density, and η is wetting efficiency. In this two-phase Eulerian framework, the solid catalyst particles are not modeled as a separate phase, and the catalyst particles are assumed to be completely wet 8 all the time. Particularly, on–off flow modulation in TBRs leads to considerable drainage, which at a certain point in time may result in a dry bed void of any liquid. In such cases, not only the liquid distribution, but also the catalyst wetting efficiency will play a significant role in the reaction kinetics. However, in our work, based on the peak velocities for the on–off flow modulation, the split and cycle times were chosen such that liquid dry-out phenomenon is avoided inside the TBR for all operating conditions. The characteristic drainage time in such cases are always lesser than the pulse periodicity of liquid induced at the inlet. This results in presence of residual liquid, necessary for particle wetting, even during the off period of all cycles, which is evident in the liquid holdup analysis, as discussed in a later section. Additionally, DBT is considered to be nonvolatile, i.e., kgl agl =0, and Eq. 14 consequently reduces to:

Si =

j=n X

rij

(15)

j=1

Density and viscosity of oil at the considered temperature and pressure 2 were calculated using Standing-Katz correlation: 8

9



Page 10 of 32

ρl = ρlo + ∆ρlP − ∆ρlT

∆ρlP

(16)

P × − 0.01 = 0.167 + 16.181 × 10 1000 2 P −0.0603×ρl0 × × 0.299 + 263 × 10 1000 0.0425×ρlo

∆ρlT = 0.0133 + 152.4 × (ρl0 + ∆ρlP )2.45 × [T − 520] − 8.1 × 10−6 − 0.0622 × 10 − 0.764 × (ρl0 + ∆ρlP ) × [T − 520]2

(17)

(18)

where ρl0 is the density at standard conditions (15.6 ◦ C; 101.3 kPa). Accordingly, oil viscosity is determined in terms of API gravity from Eq. 19:

µ = 3.141 × 1010 × (T − 460)−3.444 × [log10 (AP I)]a

(19)

a = 10.313 × [log10 (T − 460)] − 36.447

(20)

where

Gas–liquid mass transfer co-efficient was calculated using the following correlation by Goto and Smith 40 :

4

(kgl agl )i = 1.11 × 10 × Di,m

Gl µl

0.4

µl ρl Gl

0.5 (21)

where (kgl agl )i is the specific mass transfer coefficient of ith species over gas–liquid interface, and Gl is the liquid mass flux. Henry’s constant was calculated from the following equation: 41

10


Page 11 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Hi =

Vn λi ρ l

(22)

where, Vn is the molar gas volume, λi is the solubility and ρl is the density of oil. Solubility of H2 (λH2 ) and H2 S (λH2 S ) were calculated by the following equations: 41

λH2 = a0 + a1 T + a2

T T + a3 T 2 + a4 2 ρl ρl

λH2 S = exp (3.3670 − 0.008470T )

(23)

(24)

where, a0 = −0.559729, a1 = −0.42947 × 10−3 , a2 = 3.07539 × 10−3 , a3 = 3.1.94593 × 10−6 , a4 = 0.835783.

Model implementation and boundary conditions The aforementioned model equations are solved in a 2D axis–symmetric domain (Fig. 1a) of 0.5 m length, 0.019 m diameter, and an average porosity of 0.5 formed by packing particles having an effective diameter of 0.0016 m. The flow domain is defined as a porous media for cocurrent down–flow of gas and liquid phases inside the TBR. Uniform flow rates of gas and liquid at inlet of the domain was defined by a inlet boundary condition. Gas and liquid were incorporated as primary and secondary phases, respectively. No–slip boundary condition was set for impermeable solid wall. Atmospheric pressure was maintained at the bottom of the column using pressure outlet boundary condition, and gravity was defined along the flow direction. Overall liquid volume fraction was calculated using Eq. 25 and was assigned for all the numerical simulations. Re2g ρg 1 Rel Re2l 1 Reg A +B − A +B =1 kl Gal Gal kg Gag Gag ρl

11


(25)


Page 12 of 32

Fine structured quadrilateral mesh elements (Fig. 1b) were used for unsteady state simulations with a time step size of 0.001 s to obtain the numerical solutions.

Figure 1: Schematic representation of (a) flow domain, and (b) grid elements of computational domain. The radial porosity variation inside the bed was considered as per the correlation proposed by Mueller 42 (Eq. 26), and was implemented by a user defined function.

∗

= b + (1 − b )J0 (ar∗ )e−br , f or 2.61 ≤ D/dp

(26)

where,

a = 8.243 −

12.98 , f or 2.61 ≤ D/dp ≤ 13.0 (D/dp + 3.156)

(27)

2.932 , f or 13.0 < D/dp (D/dp − 9.864)

(28)

0.724 D/dp

(29)

a = 7.383 −

b = 0.304 −

r∗ = r/dp , 0 ≤ r/dp

12


(30)

Page 13 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


b = 0.379 +

0.078 D/dp − 1.80

(31)

where D is diameter of bed, J0 is Bessel function of the first kind or zero order. The radial variation of porosity thus created inside the domain is shown in Fig. 2. Commercial CFD solver Ansys 18.0 was used to solve the aforementioned governing equations. The computational domain was initially simulated for steady state flow conditions coupled with species transport model to incorporate the HDS reaction system. After validating the developed model with experimental data available in literature, various flow modulation strategies with different splits were incorporated by user defined functions.

Figure 2: Radial variation of porosity along the bed length by a user defined function obtained from Eq. 26.

Results and discussion The developed CFD model was initially validated with the experimental results of Chowdhury et al. 2 for steady state flow. The influence of liquid hourly space velocity (LHSV) on conversion was compared. The operating conditions chosen for validation are listed in Table S2.

13



With increasing LHSV, the conversion was found to decrease, as shown in (Fig. 3), which conforms well with the experimental results of Chowdhury et al. 2 , and establishes the model accuracy.

Figure 3: Comparison of model predictions with experimental data 2 for sulfur conversion.

Flow modulation strategies The validated model was subsequently subjected to periodic flow for fast and slow modes of on–off and min–max operations, which were implemented by user defined functions. Five different split ratios (R = tp /(tp + tb ): 0.1, 0.33, 0.5, 0.67, and 0.9) with varying cycle periods ((tp + tb ): 10 s, 15 s, 20 s, 1 min, 2 min) were investigated that resulted from toggling of inlet flow velocity between peak and base duration (1–9 s, 5–5 s, 9–1 s, 5–10 s, 10–5 s, 10–10 s, 30–30 s, and 60–60 s). It is evident from Fig. 3 that reaction conversion was lowest at the highest liquid flow rate (LHSV = 4 h−1 ) under steady state operation. Therefore, this condition is selected as the time averaged continuous liquid flow rate to realize the efficacy of liquid flow modulation at a fixed gas flow rate. Accordingly, peak (up ) and base (ub ) velocities for each cycle corresponding to this time averaged steady state velocity (uc ) were

14


Page 14 of 32

Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


calculated by the following equation:

uc = R × up + (1 − R) × ub

(32)

Table S3 summaries the considered flow modulation strategies and its characteristics. Fig. 4 shows an example of both on–off and min–max operations for symmetric and asymmetric splits along with the time averaged continuous flow velocity. Base flow velocity

Figure 4: Schematic of peak and base velocities for on–off and min–max operations with splits (a) 10–10 s, and (b) 10–5 s. for min–max was assigned as half of the peak value, and for on–off operation, it was set to zero. Analyses were carried out after simulations attain pseudo steady state for all periodic operation cases. Thereafter, influences of different split ratios of on–off and min–max operations are compared with the steady state time averaged continuous flow with respect to reaction conversion and pressure drop.

Hydrodesulfurization (HDS) of dibenzothiophene (DBT) To understand the influence of both cycle time and split ratio on the HDS process of DBT, periodic flow with varying split ratios (0.1, 0.33, 0.5, 0.67, and 0.9) and cycle periods (10 s, 15 s, 20 s, 1 min, and 2 min) were studied for transient behavior of reaction conversion 15



inside the TBR. Fig. 5 shows transient analysis of DBT conversion for on–off and min–max

Figure 5: Variation of DBT conversion for cycle time of 10 s with split ratio of 0.1, 0.5, and 0.9 for (a) on–off, and (b) min–max flow operations. flows having a cycle period of 10 s and splits ratios of 0.1, 0.5, and 0.9. These fast mode modulations resulted in improved reaction conversion compared to the time averaged continuous flow operation, which is more prominent in case of on–off than min–max mode. It was evident from Fig. 3 that a lower liquid feed rate led to higher reaction conversion, which also implied that a lower liquid holdup would result in a higher reaction conversion. For a cycle period of 10 s in on–off mode, Fig. 5a demonstrates that 1–9 s split provides the × 100% with respect to time best conversion with an improvement of 32.75% = 0.77−0.58 0.58 averaged continuous flow. Intermediate and high split ratios (5–5 s and 9–1 s) show similar trend in conversion but relatively lesser (enhanced by 29.61% compared to the time averaged continuous flow) than the 1–9 s split. This is because peak flow rates of liquid were maintained for longer period in the bed, which eventually resulted in reduced gas–liquid contact time and faster drainage of unreacted liquid. Fig. 6a reveals that 1–9 s on–off to have the lowest liquid holdup, which endorses the reason for relatively better conversion. Min–max mode produced oscillating conversion profiles (Fig. 5b), which is ascribed to two different inlet flow rates during peak and base periods. This leads to higher and lower conversions at base and peak 16


Page 16 of 32

Page 17 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6: Variation of liquid holdup for cycle time of 10 s with split ratio of 0.1, 0.5, and 0.9 for (a) on–off, and (b) min–max flow operations. flow rates, respectively. Due to longer peak period, maximum conversion during 9–1 s split (improvement of 11.34% from the time averaged continuous flow) is observed to be relatively lower than 1–9 s and 5–5 s, where the conversions were enhanced by 13.79% and 13.34%, respectively from its time averaged continuous flow (Fig. 5b). Moreover, all variations of on–off flow resulted in marginally lower values of liquid holdup than their corresponding min–max counterparts (Fig. 6b), which explains the reason behind better reaction conversion in all flow splits of on–off modulation.

Figure 7: Variation of DBT conversion for cycle time of 15 s with split ratio of 0.33 and 0.67 for (a) on–off, and (b) min–max flow operations.

17



Analysis of 15 s cycle time with on–off splits of 5–10 s and 10–5 s (Fig. 7a) did not show any improvement than the aforementioned conversion results of 5–5 s and 9–1 s for the cycle period of 10 s. It is ascribed to the fact that 10–5 s split operates at almost the same peak flow rate to that of 5–5 s, which also results in similar holdup values as shown in Fig. 8a. Moreover, there is no change in reaction conversion between 5–10 s and 10–5 s,

Figure 8: Variation of liquid holdup for cycle time of 15 s with split ratio of 0.33 and 0.67 for (a) on–off, and (b) min–max flow operations. as shown in Fig. 7a. This is because 5–10 s split has a double flow rate value sustained for half the peak duration of 10–5 s. Moreover, the marginal difference during base period was not sufficient to produce any appreciable change with respect to reaction conversion. As evident from Fig. 7b, min–max flow modulation of 5–10 s and 10–5 s showed similar trends in conversion profiles as compared to 1–and 9 s 5–5 s splits, respectively (Fig. 5b). Moreover, min–max modulation showed no change in holdup values for 5–10 s and 10–5 s (Fig. 8b), thereby resulting in similar reaction conversions, thus eliminating any distinction between split ratios. As evident from Fig. 7b, min–max flow modulation of 5–10 s and 10–5 s showed similar trends in conversion profiles as compared to 5–5 s split (Fig. 5b). Moreover, min–max modulation showed no change in holdup values for 5–10 s and 10–5 s (Fig. 8b), thereby resulting in similar reaction conversions, thus eliminating any distinction between split ratios. 18


Page 18 of 32

Page 19 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Slow and fast modes of periodic operation were also investigated for different cycle periods (20 s, 1 min and 2 min) for symmetric splits as shown in Fig. 9. On–off flow leads to a

Figure 9: Variation of DBT conversion for slow and fast modes with symmetric splits of on–off and min–max operations with cycle times of (a) 20 s, (b) 1 min, and (c) 2 min. better reaction conversion than min–max flow operation, corroborated by lower liquid holdup as shown in Fig. 10. However, results for the 10–10 s on–off and min–max (Fig. 9a) are similar to 1–9 s on–off (Fig. 5a) and 5–5 s min–max (Fig. 5b) splits, with no significant improvement. Distinction between periodic flow modes is more pronounced for slow mode

Figure 10: Variation of liquid holdup for slow and fast modes with symmetric splits of on–off and min–max operations with cycle times of (a) 20 s, (b) 1 min, and (c) 2 min. operation with respect to better reaction conversion (Figs. 9b and 9c) and lower liquid holdup (Figs. 10b and 10c). In addition to a slight improvement (3.78%) than the fast mode periodic operation, Fig. 9b displays an oscillatory behavior for both on–off and min–max flows of 30–30 s. Although this effect is slightly more pronounced for cycle period of 2 min, but reaction conversion for base flow duration deteriorates to steady state operation thereby compromising on overall reactor performance (Fig. 9c). Therefore, this study was restricted 19



to 2 min of cycle period, as further increase would yield to lower conversion values than continuous flow operation. Liquid holdup profiles in Fig. 10 portray that on–off always has a lower value than min–max flow. This difference gets more detectable with increase in cycle time. As evident in Fig. 10c, peak holdup values for both on–off and min–max flows are considerably high, thus leading to very low conversion profiles, as shown in Fig. 9c. Contextually, all splits for slow mode modulation strategy display significantly lower values of liquid holdup than fast mode operation. Furthermore min–max flow results in attainment of pseudo steady states indicated by saturation plateaus during both peak and base flow periods of slow mode operation (Figs. 10b and 10c).

Figure 11: DBT conversion resulting from all split ratios for slow and fast modes of on–off and min–max modulations. Fig. 11 summarizes DBT conversion for all considered cases of periodic flow with varied splits in order to explicitly delineate the influence of time period and split ratios. The improvement in conversion for all splits with respect to time averaged continuous flow is summarized in Table 1. It is evident there is no significant influence of split ratio for a particular cycle with respect to reaction conversion. However, with increase in cycle time a clear distinction was observed between slow and fast modes of operation in addition to selection of modulation strategy. Apparently 60–60 s on–off split produced the maximum

20


Page 20 of 32

Page 21 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


DBT conversion during base period. However, this reduces to substantially low values during peak flow period (Table 1), resulting in poor overall performance of the reactor. Table 1: Improvement in peak conversions during periodic flow modulation with respect to Xp −Xc × 100 . conversion obtained in time averaged continuous flow Xc Cycle/Split (R) 1-9 s 5-5 s 9-1 s 5-10 s 10-5 s 10-10 s 30-30 s 60-60 s

Improvement in conversion (%) On-off Min-max 32.75 13.79 29.61 13.34 29.45 11.34 31.94 13.86 31.76 13.10 31.88 14.29 32.77 16.66 36.38 18.51

Pressure drop Transient overall pressure drop across the bed is analyzed for six consecutive cycles of both min–max and on–off flows, under fast and slow mode operations. Figs. 12, 13, and 14 show that for any split, all cycles display the trend in a repeating manner, thereby corroborating periodic operation. Figs. 12a and 12b illustrate overall pressure drop values for 10 s fast

Figure 12: Transient pressure drop per unit length of reactor for cycle time of 10 s with split ratio of 0.1, 0.5, and 0.9 for (a) on–off, and (b) min–max flow operations.

21



mode on–off and min–max flow of various split ratios. It is clear that in all cases, overall pressure drop during cyclic operation exceeds the continuous flow pressure drop by some margin, as evident from their overshoot values due to shock wave generation in between two consecutive flow cycles. It is also apparent that cyclic splits of on–off yield marginally higher overshoot value than its min–max counterpart. However, the fall in pressure drop values during base flow period is considerably higher for on–off operation (Fig. 12a). Difference in peak pressure drop values between splits for a particular mode of periodic operation is insignificant and unrealizable from Figs. 12a and 12b. However, undesirable fluctuation of overall pressure drop dampens with increasing split ratio.

Figure 13: Transient pressure drop per unit length of reactor for cycle time of 15 s with split ratio of 0.33 and 0.67 for (a) on–off, and (b) min–max flow operations. For longer cycle time of 15 s and varying split ratio (R=0.33 and 0.67), inappreciable change in overall pressure drop compared to that of 10 s cycle was observed. However, prolonged peak and base duration in this case led to a clear demarcation of undulation between these two split ratios, as shown in Figs. 13a and 13b. Fig. 14 demonstrates similar trends in transient overall pressure drop for symmetric split ratios in fast and slow mode operation. For a particular split ratio (R) of 0.5, the overall pressure drop was found to increase with cycle time irrespective of modulation strategy due to enhanced peak flow period. As a result, symmetric split with cycle time of 2 min (60–60 s) exhibited the maximum and minimum

22


Page 22 of 32

Page 23 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


values of pressure drop for peak and base flow periods, respectively, as shown in Fig. 14c. Interestingly, min–max operation for 2 min cycle shows two discernible plateaus of constant pressure drop during peak and base periods. This can be ascribed to the attainment of pseudo-steady state of the bed during prolonged peak and base flow periods. However, such behavior is not observed for other periodic flow cases due to the lack of sufficient peak or base periods that can dampen the shock waves generated in between two consecutive cycles. Table 2 summarizes overall pressure drop fluctuation in between peak and base values for all cases of periodic flow with varied splits.

Figure 14: Transient pressure drop per unit length of reactor for slow and fast modes with symmetric splits of on–off and min–max operations with cycle times of (a) 20 s, (b) 1 min, and (c) 2 min. In the previous section, it was identified that slow mode operation of 60–60 s cycle resulted in maximum improvement of reaction efficiency with respect to peak conversion. However, from Fig. 14c, it is evident that slow mode on–off operation leads to highest undulation in overall pressure drop compared to continuous flow, which is detrimental for operational safety. Analyses of conversion profiles with respect to pressure drop fluctuations reveal that fast mode of 10 s cycle time is favorable for higher conversion of the considered reaction system. Any further increase in cycle time evidently incurred significantly higher undulation of overall pressure drop (Table 2) without appreciable improvement in reaction conversion.

23



Table 2: 4Pp −4Pb 4Pb

Overall pressure drop undulations during periodic flow modulation × 100 .

Cycle/Split (R) 1-9 s 5-5 s 9-1 s 5-10 s 10-5 s 10-10 s 30-30 s 60-60 s

Pressure On-off 3.79 1.70 0.51 4.14 1.89 5.69 21.26 35.49

drop undulation (%) Min-max 0.69 0.38 0.16 1.01 0.65 2.20 8.53 9.08

Conclusion In this work, a first principle based two-phase Eulerian model using porous media concept was used to numerically investigate a HDS reaction system in a trickle bed reactor. A 2D axis–symmetric geometry was considered as the flow domain, and relative permeability model was used to address interphase exchange terms between gas and liquid phases. After model validation with the experimental data for steady state operation, various modes of cyclic flow operations with different split ratios were incorporated to examine its efficacy in improving reaction conversion as compared to its time averaged steady state flow operation. Transient analysis of conversion revealed considerable improvement by both on–off and min–max flow modulation strategies compared to their time averaged continuous flow operation. This enhancement was significantly pronounced for the on–off slow mode operation. However, it was associated with considerable fluctuations in overall pressure drop, which is detrimental to process control safety. Moreover, reaction conversion values during base flow period dropped significantly compared to that of continuous flow operation. Interestingly, fast mode of on–off operation with lowest slit ratio (1–9 s) demonstrated the optimum improvement of 32.75% in conversion accompanied by minimum pressure drop fluctuations, which is considered as the best modulation scheme for the selected cyclic TBR study. It may further be concluded from this work that the fast mode of flow modulation with lower split ratio may prove beneficial 24


Page 24 of 32

Page 25 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


for a pseudo–first order reaction system following a Langmuir-Hinshelwood rate kinetics in TBR operation. This work advocates the efficacy of cyclic flow modulation strategies for better conversion in a hydrotreating TBR. Petroleum refining, one of the largest and crucial sectors in oil industries, are subjected to stringent environmental laws. Therefore, any intensification in HDS process with controllable overall pressure fluctuation will be beneficial to comply with environmental standards in addition to maintaining process safety. This work is expected to not only provide a comprehensive modeling approach for reactions in TBR, but also to explore the viability of cyclic flow operation as a process intensification technique.

Nomenclature agl

Gas–liquid interfacial area (m−1 )

A

Constant in the viscous term of the Ergun equation

Ap

Particle surface area (m2 )

B

Constant in the inertial term of the Ergun equation

C

Concentration (kmol/m3 )

de

Equivalent particle diameter (6Vp /Ap )

dP

Particle diameter (m)

D

Mass diffusivity of the components (m2 /s)

Eo∗

Modified Eötvos number, ρl gd2p 3 /σl (1 − )2

Fk

Drag force on the k th phase per unit volume (kg/m2 s2 )

g

Gravitational acceleration (m/s2 )

Ga − α

Galileo number of the α phase, ρ2α uα d3e 3 /µ2α (1 − )3

Hi

Henry’s constant for ith species (M P a · m3 /kmol)

k

Relative permeability

K

Equilibrium constant (m3 /kg · s)

25



l

Length of the reactor (m)

4Pb

Base overall pressure drop during continuous flow operation (Pa/m)

4Pp

Peak overall pressure drop during flow modulation (Pa/m)

r

Reaction rate (kg · m3 /s)

Reα

Reynolds number of the α phase, ρα uα de /µα (1 − )

sα

Saturation of α phase, α /

S

Source term for species transport equation

uc

time averaged velocity for continuous operation (m/s)

Vp

particle volume (m3 )

Xc

Reaction conversion during continuous flow operation

Xp

Peak reaction conversion during flow modulation

Acronyms Di − Ar

Diaromatics

HDS

Hydrodesulfurization

LHSV

Liquid Hourly Space Velocity

M ono − Ar

Monoaromatics

P oly − Ar

Polyaromatics

Greek Symbols

Bed voidage

µ

Viscosity (kg/m · s)

ρ

Density (kg/m3 )

σ

Surface tension (N/m)

Supporting Information Available Details of diesel oil characteristics, operating conditions used for model validation, and peak and base velocities for on–off and min–max flow modulation strategies considered in this

26


Page 26 of 32

Page 27 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


study are supplied as Supporting Information.

References (1) Satterfield, C. N. Trickle-bed reactors. AIChE J. 1975, 21, 209. (2) Chowdhury, R.; Pedernera, E.; Reimert, R. Trickle-bed reactor model for desulfurization and dearomatization of diesel. AIChE J. 2002, 48, 126. (3) Tailleur, R. G. Diesel upgrading into a low emissions fuel. Fuel Process. Technol. 2006, 87, 759. (4) Silva, A.; Monteiro, C.; De Souza, V.; Ferreira, A.; Jaimes, R.; Fontoura, D.; Nunhez, J. Fluid dynamics and reaction assessment of diesel oil hydrotreating reactors via CFD. Fuel Process. Technol. 2017, 166, 17. (5) Minaev, P.; Nikulshina, M.; Mozhaev, A.; Maslakov, K.; Boldushevskii, R.; Nikulshin, P. Influence of mesostructured alumina on the morphology of the active phase in NiWS/Al2O3 catalysts and their activity in hydrotreating of SRGO and VGO. Fuel Process. Technol. 2018, 181, 44. (6) Stanislaus, A.; Marafi, A.; Rana, M. S. Recent advances in the science and technology of ultra low sulfur diesel (ULSD) production. Catal. Today 2010, 153, 1. (7) Mederos, F. S.; Ancheyta, J.; Elizalde, I. Dynamic modeling and simulation of hydrotreating of gas oil obtained from heavy crude oil. Appl. Catal. A Gen. 2012, 425, 13. (8) Gunjal, P. R.; Ranade, V. V. Modeling of laboratory and commercial scale hydroprocessing reactors using CFD. Chem. Eng. Sci. 2007, 62, 5512.

27



(9) Larachi, F.; Laurent, A.; Midoux, N.; Wild, G. Experimental study of a trickle-bed reactor operating at high pressure: two-phase pressure drop and liquid saturation. Chem. Eng. Sci. 1991, 46, 1233. (10) Jiang, Y.; Khadilkar, M.; Al-Dahhan, M.; Dudukovic, M. CFD of multiphase flow in packed-bed reactors: I. k-Fluid modeling issues. AIChE J. 2002, 48, 701. (11) Nemec, D.; Levec, J. Flow through packed bed reactors: 2. Two-phase concurrent downflow. Chem. Eng. Sci. 2005, 60, 6958. (12) Morsi, B.; Midoux, N.; Charpentier, J. Flow patterns and some holdup experimental data in trickle-bed reactors for foaming, nonfoaming, and viscous organic liquids. AIChE J. 1978, 24, 357. (13) Maiti, R.; Sen, P.; Nigam, K. Trickle-bed reactors: Liquid distribution and flow texture. Rev. Chem. Eng. 2004, 20, 57. (14) Stankiewicz, A. I.; Moulijn, J. A. Process intensification: Transforming chemical engineering. Chem. Eng. Prog. 2000, 96, 22. (15) Nigam, K.; Larachi, F. Process intensification in trickle-bed reactors. Chem. Eng. Sci. 2005, 60, 5880. (16) Liu, G.; Zhang, X.; Wang, L.; Zhang, S.; Mi, Z. Unsteady-state operation of trickle-bed reactor for dicyclopentadiene hydrogenation. Chem. Eng. Sci. 2008, 63, 4991. (17) Ayude, A.; Cassanello, M.; Martinez, O.; Haure, P. Yield Optimization in a Cycled Trickle-Bed Reactor: Ethanol Catalytic Oxidation as a Case Study. Chem. Eng. Technol. 2012, 35, 899. (18) Atta, A.; Hamidipour, M.; Roy, S.; Nigam, K.; Larachi, F. Propagation of slow/fastmode solitary liquid waves in trickle beds via electrical capacitance tomography and computational fluid dynamics. Chem. Eng. Sci. 2010, 65, 1144. 28


Page 28 of 32

Page 29 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(19) Giakoumakis, D.; Kostoglou, M.; Karabelas, A. Induced pulsing in trickle bedscharacteristics and attenuation of pulses. Chem. Eng. Sci. 2005, 60, 5183. (20) Aydin, B.; Fries, D.; Lange, R.; Larachi, F. Slow-mode induced pulsing in trickle-bed reactors at elevated temperature. AIChE J. 2006, 52, 3891. (21) Hamidipour, M.; Larachi, F.; Ring, Z. Cyclic operation strategy for extending cycle life of trickle beds under gas–liquid filtration. Chem. Eng. Sci. 2007, 62, 7426. (22) Schubert, M.; Kryk, H.; Hampel, U. Slow-mode gas/liquid-induced periodic hydrodynamics in trickling packed beds derived from direct measurement of cross-sectional distributed local capacitances. Chem. Eng. Process. Process Intensif. 2010, 49, 1107. (23) Boelhouwer, J. G.; Piepers, H. W.; Drinkenburg, B. A. Advantages of Forced Nonsteady Operated Trickle-Bed Reactors. Chem. Eng. Technol. 2002, 25, 647. (24) Gabarain, L.; Castellari, A.; Cechini, J.; Tobolski, A.; Haure, P. Analysis of rate enhancement in a periodically operated trickle-bed reactor. AIChE J. 1997, 43, 166. (25) Atta, A.; Roy, S.; Larachi, F.; Nigam, K. D. P. Cyclic operation of trickle bed reactors: A review. Chem. Eng. Sci. 2014, 115, 205. (26) Khadilkar, M.; Al-Dahhan, M.; Duduković, M. Multicomponent flow-transport-reaction modeling of trickle bed reactors: application to unsteady state liquid flow modulation. Ind. Eng. Chem. Res. 2005, 44, 6354. (27) Wongkia, A.; Suriye, K.; Nonkhamwong, A.; Praserthdam, P.; Assabumrungrat, S. Catalytic performance improvement of styrene hydrogenation in trickle bed reactor by using periodic operation. Korean J. Chem. Eng. 2013, 30, 593. (28) Ayude, A.; Cechini, J.; Cassanello, M.; Martínez, O.; Haure, P. Trickle bed reactors: Effect of liquid flow modulation on catalytic activity. Chem. Eng. Sci. 2008, 63, 4969.

29



(29) Liu, G.; Mi, Z. Hydrogenation of 2-Ethylanthraquinones in a Periodically Operated Trickle-Bed Reactor. Chem. Eng. Technol. 2005, 28, 857. (30) Tukač, V.; Šimíčková, M.; Chyba, V.; Lederer, J.; Kolena, J.; Hanika, J.; Jiřičn` y, V.; Staněk, V.; Stavarek, P. The behavior of pilot trickle-bed reactor under periodic operation. Chem. Eng. Sci. 2007, 62, 4891. (31) Lopes, R.; Quinta-Ferreira, R.; Larachi, F. ECT imaging and CFD simulation of different cyclic modulation strategies for the catalytic abatement of hazardous liquid pollutants in trickle-bed reactors. Chem. Eng. J. 2012, 211-212, 270. (32) Dietrich, W.; Anadon, L.; Sederman, A.; Gladden, L.; Agar, D. Simulation studies on the performance enhancement in periodically operated trickle-bed reactors based on experimental local liquid distribution measurements. Ind. Eng. Chem. Res. 2012, 51, 1672. (33) Wang, Y.; Chen, J.; Larachi, F. Modelling and simulation of trickle-bed reactors using computational fluid dynamics: A state-of-the-art review. Can. J. Chem. Eng. 2013, 91, 136. (34) Hamidipour, M.; Chen, J.; Larachi, F. CFD study and experimental validation of trickle bed hydrodynamics under gas, liquid and gas/liquid alternating cyclic operations. Chem. Eng. Sci. 2013, 89, 158. (35) Saez, A.; Carbonell, R. hydrodynamic parameters for gas-liquid cocurrent flow in packed beds. AIChE J. 1985, 31, 52. (36) Atta, A.; Roy, S.; Nigam, K. Prediction of pressure drop and liquid holdup in trickle bed reactor using relative permeability concept in CFD. Chem. Eng. Sci. 2007, 62, 5870.

30


Page 30 of 32

Page 31 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(37) Carbonell, R. Multiphase flow models in packed beds. Oil Gas Sci.Technol. 2000, 55, 417. (38) Atta, A.; Roy, S.; Nigam, K. D. Investigation of liquid maldistribution in trickle-bed reactors using porous media concept in CFD. Chem. Eng. Sci. 2007, 62, 7033. (39) Girgis, M. J.; Gates, B. C. Reactivities, reaction networks, and kinetics in high-pressure catalytic hydroprocessing. Ind. Eng. Chem. Res. 1991, 30, 2021. (40) Goto, S.; Smith, J. Trickle-bed reactor performance. Part I. Holdup and mass transfer effects. AIChE J. 1975, 21, 706. (41) Korsten, H.; Hoffmann, U. Three-phase reactor model for hydrotreating in pilot tricklebed reactors. AIChE J. 1996, 42, 1350. (42) Mueller, G. E. Prediction of radial porosity distributions in randomly packed fixed beds of uniformly sized spheres in cylindrical containers. Chem. Eng. Sci. 1991, 46, 706.

31



For Table of Contents Only

32


Page 32 of 32

CFD studies on efficacy of flow modulation in a hydrotreating

Recommend Documents