Chemical Engineering Science 135 (2015) 441–451
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Modeling transport phenomena and reactions in a pilot slurry airlift loop reactor for direct coal liquefaction Qingshan Huang a, Weipeng Zhang b, Chao Yang b,n a
Key Laboratory of Biofuels, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao, Shandong 266101, China Key Laboratory of Green Process and Engineering, National Key Laboratory of Biochemical Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
b
H I G H L I G H T S
An integrated model for direct coal liquefaction is validated. Hot test of a pilot internal airlift loop reactor is well predicted. Distributions of key components are revealed for direct coal liquefaction. A modified SIMPLE algorithm for multiphase flow is put forward. Special boundary conditions for steady continuous bubbly flow are developed.
art ic l e i nf o
a b s t r a c t
Article history: Received 26 July 2014 Received in revised form 29 December 2014 Accepted 6 January 2015 Available online 12 January 2015
Modeling of hydrodynamics, mass/heat transfer and chemical reactions with bubbly flow in a pilot slurry internal airlift loop reactor (IALR) for the process of direct coal liquefaction (DCL) under the conditions of elevated pressure and high temperature is performed with a steady two-fluid model. A modified numerical method for multiphase flow and the developed boundary conditions to promote the convergence of steady solutions are also proposed. The results show that the predicted average gas voidage, average liquid velocity and temperature at two locations in the riser agree reasonably well with experimental data. The snapshots of temperature and concentrations of the reactants in respective phases and the product in slurry are all well captured. The models and numerical procedure developed in this work can be used as an effective tool for design and scale-up of IALRs for the DCL process. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Airlift loop reactor Hydrodynamics Mass transfer Heat transfer Direct coal liquefaction Slurry
1. Introduction As a viable option of production of transportation fuels, direct liquefaction of coal is a promising approach for clean and effective utilization of coal in China (Wang et al., 2009; Wei et al., 2000). Moreover, it will play an important role in maintaining the worldwide energy safety (Ren et al., 2009b). A million-ton/year direct coal liquefaction (DCL) plant using Shenhua’s subbituminous coal, which was built by Shenhua Group Co. since late 2008, has recently become operational and profitable in Inner Mongolia Autonomous Region of China, notably marking the beginning of a new stage of industrial DCL (Shui et al., 2010). However, it is important to note that the industrial-scale coal liquefaction technology is still in a demonstration stage, and significant
n
Corresponding author. Tel.: þ 86 10 62554558; fax: þ 86 10 82544928. E-mail address:
[email protected] (C. Yang).
http://dx.doi.org/10.1016/j.ces.2015.01.003 0009-2509/& 2015 Elsevier Ltd. All rights reserved.
technological and engineering challenges still exist (Zhao and Gallagher, 2007). Thus, selection and application of liquefaction reactors remain to be a key issue in DCL commercialization (Ren et al., 2009a). Although slurry reactors, for instance, bubble column, ebullated reactor and airlift loop reactor (ALR), have been tested for DCL on the pilot plant scale, intensive R&D works are urgently desired to meet the industrial scale production. For DCL, it was known that the installation of a draft tube in the first-stage bubble column reactor could increase the mixing efficiency, but significant coking deposits were also found for long draft tubes, resulting in frequent shutdown or even complete plugging of the internal tube (Bakopoulos, 2001). Compared to ebullated reactors, the big advantage related to ALRs is the very low installation cost and the increased safety for high pressure applications (Bakopoulos, 2001). In view of the advantages of internal airlift loop reactors (IALR) (Freitas et al., 2000; Huang et al., 2007), it was tested for cutting the operating cost and eliminating the mechanical breakdown of expensive recirculating
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pumps in the Chinese Process of DCL by replacing an ebullated reactor with an IALR. However, the problems of reaction heat, coking and solid sediment must be solved in IALRs before they can be used for DCL (Ren et al., 2009a). Fortunately, these problems can be solved with an elaborate design of the IALR conceptually. The temperature rise can be easily controlled due to the good mixing in IALRs, and the coking and coke deposition on catalysts can also be suppressed by maintaining sufficient concentration of dissolved hydrogen (Artok and Schobert, 2000). The problem of solid particle deposition in the reactor can be totally avoided by optimizing the reactor structure and operating conditions to keep an appropriate axial liquid velocity above the terminal slip velocities of particles. Since the dependence of chemical reactions with the reaction heat and the local hydrodynamics, simple models such as the continuous stirred tank reactor model and the plug flow reactor model cannot get satisfactory results for these reactors. Sundaresan (2000) pointed out that reliable multiphase reactor models that can be used with confidence for improving existing processes and scale-up of new processes were not yet available. Therefore, it was desired to explore the feasibility of using an IALR for DCL by modeling of its operation under the conditions of elevated pressure and high temperature. The detailed information on circulation of oil–coal slurry, contact efficiency between hydrogen and coal, and concentration and temperature distributions throughout the reactor can be obtained from the numerical simulation, and it will shed light on the productivity, coking on internal wall and possible particle deposition. Although there have been significant research efforts concerning the fundamental characteristics of IALRs under ambient conditions (Heijnen et al., 1997; Huang et al., 2007, 2008; Lin et al., 1997a, 1997b; Mudde and Van den Akker, 2001; Talvy et al., 2007a, 2007b), the scale effect on the flow structure is still not fully understood. Sound understanding of the hydrodynamic behavior in IALRs (e.g., flow regime, phase holdup, bubble characteristics, interfacial phenomenon, backmixing, and interphase transport) is therefore essential in designing and scaling up these slurry reactors, especially under the condition of elevated pressure and high temperature with relevance to industrial reactive processes. Owing to the complexity of two-phase flow patterns, thorough understanding of the hydrodynamics involved has not been achieved (Kumar et al., 1997). It has been reported that the hydrodynamic behavior in a coal liquefaction reactor affected the product quality and conversion (Wasaka et al., 2003). It is particularly important to understand the relationship between the reaction behavior and the hydrodynamics in an IALR for scale-up of a coal liquefaction reactor. From the overall thermal effect, coal direct liquefaction is an exothermic process (Ren et al., 2009a). Magiliotou et al. (1988) found that the heat transfer coefficient at high gas holdups was always higher than that at low gas holdups. Therefore, the effect of pressure on heat transfer could be complicated with the decrease of bubble size and the increase of gas holdup under the conditions of elevated pressure and high temperature. The effect of pressure on heat transfer behavior would be appreciable, and simple extrapolation of correlations based on the ambient conditions may be risky (Luo et al., 1997). The design and scale-up of these reactors require the knowledge of the hydrodynamics and mass/heat transfer characteristics in these reactors under real operation conditions. Although such characteristics have been extensively reported in the literature (Heijnen et al., 1997; Huang et al., 2010; Yeoh and Tu, 2005), most studies were limited to the ambient conditions and little has been reported under elevated pressure condition with relevance to industrial processes (Luo et al., 1997; Yang and Fan, 2003). Additionally, the majority of modeling and simulation for bubbly flows was commonly focused on large bubbles under ambient pressure. As we know, small bubbles in an upward
flow drift toward the pipe wall, whereas large bubbles move to the center of the pipe (Guet et al., 2003). The hydrodynamics of bubbly flows in IALRs with small bubbles is different from that with large ones and should be studied in detail for the safety and controllability of operation. Through the variation of the physical properties of fluids, especially the gas phase, the pressure affects bubble size and bubble size distribution. Higher pressure yields smaller bubbles and more uniform bubble size distributions (Luo et al., 1997). Nevertheless, the bubble coalescence is suppressed and the bubble breakup by particles (for instances, the catalyst and coal in the coal liquefaction slurry) is enhanced under the elevated pressure conditions. It was reported that the increased system pressure or gas density changed the hydrodynamics in gas–liquid bubble columns (Letzel et al., 1999). However, the extent of hydrodynamic governing by pressure in slurry reactors is still unknown and needs to be quantitatively evaluated. As pointed out by Yeoh and Tu (2005), there is an increasing need to develop a more robust mathematical model capable of handling complex phenomena associated with hydrodynamics, mass/heat transfer and chemical reactions. The present work is undertaken with an objective to validate the comprehensive mechanism models and understand the coupling of flow, mass/heat and multiple chemical species in a pilot IALR for the Chinese DCL Process by using the CFD technique. To the best of our knowledge, there is no report of integrated simulations on the DCL under the industrial conditions. In this contribution, a Reynolds averaging two-fluid model combined with the RNG k–ε model for turbulent stresses is applied; special boundary conditions for steady bubbly flows with a continuous mode of operation and a modified SIMPLE algorithm for multiphase flow to promote the convergence are proposed. The complex transport phenomena in an IALR, for a 6 t (coal)/d pilot DCL process development unit (PDU) constructed by Shenhua Group Co., China (Liu et al., 2010), are numerically predicted. The hydrodynamics and the multicomponent transports in or between the gas and the slurry are modeled, and the hydrodynamic parameters and the distributions of concentrations in the IALR for coal, oil products, gas hydrogen and dissolved hydrogen are obtained. Moreover, a heat transport equation developed for the bubbly flow is also put forward to account for the heat transfer in the IALR.
2. Mathematical models For simulation of the bubbly flow, a validated Reynolds averaging two-fluid model is used here (Huang et al., 2007, 2008). In this approach, mass and momentum balance equations are solved for each phase, and the coupling between gas and liquid is achieved through interphase momentum exchange terms. For the sake of brevity, the Euler–Euler two-fluid model is not reviewed here and can be referred elsewhere (Huang et al., 2007). The interfacial momentum exchange accounts for the interaction between the continuous and dispersed phases. The important interphase forces including drag, lift force and wall force are considered here. The lift force, wall lubrication force and its corresponding coefficients can be found in our previous work (Huang et al., 2010), so only the closures for drag are addressed here: FD ¼
3 CD ρ αg ug ul ul ug 4 db l
ð1Þ
where CD is the drag coefficient of a swarm and can be written as (Huang et al., 2007; Yang et al., 2011) ( 24 ð1 þ 0:15Re0:687 Þ; if Re o 1000 C d ¼ Re ð2Þ 0:44; if Re Z 1000 C D ¼ C d αl 3
ð3Þ
Q. Huang et al. / Chemical Engineering Science 135 (2015) 441–451
Re ¼
db ug ul ρl
The RNG k–ε mixture model combined with the bubbleinduced turbulence model recommended by Sato et al. (1981) is employed here to obtain the shear-induced turbulent viscosity. Detailed descriptions of the turbulence model can be found elsewhere (Chow and Li, 2007; Huang et al., 2010; Yang and Mao, 2014). Due to low solubility of gas in the liquid, low rates of chemical reactions and excessive gas in the system of DCL, the effects of mass transfer on the mass and momentum balances in the simulation of fluid dynamics are neglected in this work. The influence of temperature rise due to reaction heat on the physical properties, i.e., viscosity, density, surface tension and so on, is negligible for the strong mixing performance of the IALR, which limited the temperature difference within a few degrees. The solid content in the reactor is assumed to be uniform due to the same reason, and the solid holdup is supposed to be approximately equal to the volume fraction of coal and related to the carbon conversion (xfc E90%). Since the superficial gas velocity is less than 0.03 m/s in all the operations of DCL, the flow pattern in the reactor can be reasonably deduced to be in the homogeneous regime (Vial et al., 2001; Zhang et al., 2014). In addition, small bubbles resulted from the elevated pressure and high temperature delay the regime transition velocity and make it more doubtless (Krishna et al., 1994). Therefore, a homogeneous bubby flow is assumed, and a constant bubble diameter is reasonably adopted considering the immaturity of the population balance model (Wang et al., 2007) under the condition of industrial DCL. Since the particles are small and the concentrations are low, the coal particles follow the mean turbulent flow of the slurry practically with no slip (Bakopoulos, 2001), and the slurry can be regarded as pseudo-homogeneous without significant deviation (Huang et al., 2014). Thus, hypothesis of an IALR for coal liquefaction under the conditions of high pressure (19 MPa) and high temperature (673– 723 K), containing hydrogen-rich gas bubbles as the gas phase and the slurry consisting of oil and particles of catalyst and coal (less than 150 μm, whose settling velocity is lower than 0.0036 m/s) as the liquid phase, is assumed in this contribution. The solid holdup in the slurry is considered to have an impact on the viscosity of the continuous phase, and that can be determined by the Einstein equation as (Muroyama et al., 2007; Viamajala et al., 2009)
μslurry ¼ μl ð1 þ 2:5αs Þ
αs ¼ αs0 ð1 xf c Þ
ð5Þ
where μslurry, αs and αs0 are the slurry viscosity developed for suspension of monodisperse spheres, the average solid holdup in the slurry and at the inlet of the preheating process (in this work αs0 ¼30%), respectively. It is widely accepted that coal liquefaction is a complex freeradical reaction process. Due to the complexity of the intrinsic kinetics of DCL, a lumped kinetics model, which was regressed from the experimental data, is used to approximate the kinetics in the first stage reactor of DCL in this work. A typical model of kinetics for Shenhua subbituminous coal is shown in Fig. 1 and adopted (Shi, 2009). In order to simplify the modeling, the combination of a pseudo first-order reaction and a second-order reverse reaction with respect to the mass fraction of the coal is assumed in this work. The kinetics for Shenhua coal can be approximated as follows:
dyc ¼ ay2c þ byc dt
k1
ð4Þ
μl
yc ¼
C C0 C I C I0
ð6Þ
where yc is defined as the carbon mass fraction of the active part left to the total active part in the coal. The parameters in the kinetics equation are regressed from experimental data with the
443
M1 k2
Oil
Mc Fig. 1. The typical kinetic scheme for Shenhua coal in DCL (M1 and Mc refer to the parts of coal with activity and the inert part, respectively).
following relations: a ¼ 5:588 0:01251 T; b ¼ 8:916 þ 0:03877 T 4:194 10 5 T 2
ð7Þ
The fraction of inert coal C0 is temperature dependent and it can be designated from a regression of experimental data as C 0 ¼ maxð0; 9:088 10 4 T þ 0:4738Þ
ð8Þ
where T is in unit of 1C. The concentrations of hydrogen in the slurry and gas phase and the concentrations of coal and products in the slurry are the essential parameters in the process of DCL. The general transport equations of the concentrations in gas and liquid for the process of DCL can be expressed as follows (Talvy et al., 2007b): ∇ ðαg ug C g Þ ¼ ∇ ðDtg αg ∇C g Þ F R
ð9Þ
∇ ðαl ul C L Þ ¼ ∇ ðDtl αl ∇C L Þ þF R αl r R
ð10Þ
∇ ðαl ul C Rl Þ ¼ ∇ ðαl Dtl ∇C Rl Þ αl r c
ð11Þ
∇ ðαl ul C Pl Þ ¼ ∇ ðαl Dtl ∇C Pl Þ þ αl r P
ð12Þ
rR ¼
dyc 1 ðC I C I0 Þ ¼ r P 2 dt
ð13Þ
where FR, rR, rP and rc represent the interfacial transport of the species between the two phases, the reaction rates of the dissolved hydrogen, product and coal in the bulk slurry, respectively. The interfacial mass transfer is given by F R ¼ kL aðC nL C L Þ
ð14Þ
C nL ¼ HRTC g
ð15Þ
The diffusivities of liquid and gas can be expressed as Dtl ¼
2 νt k 1 þ Dl ¼ C μ þD σt ε σt l
ð16Þ
2 νt k 1 þD ¼ C μ þ Dg ð17Þ σt g ε σt where σt is the turbulent Schmidt number and a value of 0.75 is
Dtg ¼
taken here. A validated model of the volumetric mass transfer coefficient (Huang et al., 2010), which is based on the penetration theory (Higbie, 1935), is adopted here as follows to estimate the local mass transfer in the reactor: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12αg Dl uslip kL a ¼ ð18Þ db π db Heat transfer is important as the DCL reaction is exothermal and depends strongly on temperature. In the multiphase model, there are separate enthalpy and temperature fields for each phase. In the process of DCL, the reaction happens in the liquid bulk and heat is transferred from liquid to gas due to the difference of
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temperature between these two phases. The general steady transport equation for static enthalpy for multiphase flow can be written as vt λk ∇ α k uk T k þ ∇T k σ t ρk C p;k ¼
n X
β¼1
Γ kþβ hβs Γ βþk hks =ρk C p;k þ Q k =ρk C p;k þ Sk þ αk r R ΔH=ρk C p;k ð19Þ
where Tk, λk, Sk and Qk denote the temperature and the thermal conductivity of phase k, and the external heat source and the interphase heat transfer to phase from other k across interface þ þ phase, respectively. The term Γ kβ hβs Γ βk hks represents the heat transfer induced by interphase mass transfer, and the term αk rR ΔH is the heat due to chemical reactions. The rate of heat transfer per unit time across the interface per unit volume Aαβ from phase β to phase α, Qαβ, is Q kβ ¼ cðkhβÞ ðT β T k Þ
ð20Þ
where the volumetric heat transfer coefficient is modeled using the particle model corrections described below: cðkhβÞ ¼ hkβ Akβ hkβ ¼
λk Nukβ dβ
ð21Þ ð22Þ
It is often convenient to express the heat transfer coefficient in terms of a dimensionless Nusselt number. The following correlation, which relates the Nusselt number with the particle Reynolds number and the Prandtl number of the surrounding fluid, is used (ANSYS, 2006): ( 2 þ 0:6Re0:5 Pr 0:33 0 rRe o 776:06; 0 r Pr o250 Nu ¼ ð23Þ 2 þ 0:27Re0:62 Pr 0:33 776:06 r Re; 0 r Pr o250
(b) The pressure correction equation of mixture is solved with the method of IDA-SIMPLE and the velocities of both phases are corrected; (c) The fraction of each phase is computed with traditional methods and normalized; (d) The pressure correction equation of each phase is separately solved, and the velocity of each phase is corrected but no correction to the shared pressure filed; (e) All other transport equations are solved; (f) Return to step (a) and iterate until the residuals of all equations converge to a small specified tolerance. From the approach addressed above, it can be seen that the modified SIMPLE algorithm for multiphase flow has an additional step (d) in the iteration loop compared to the traditional SIMPLE algorithm, and it costs more computation in the inner iteration loop. However, less computational cost is resulted in a long run because of less iterative steps needed in the outer loop. It has been found that the modified SIMPLE algorithm can promote the convergence in our preliminary tests, and thus it is employed here at the intermediate iteration stage. In the DCL process, there exists close coupling between mass/heat transfer and reactions, and the reaction kinetics and mass transfer are all temperature dependent. On the basis of solutions of hydrodynamics in the reactor, the concentration fields of key components and the distributions of temperature in respective phases are solved iteratively in sequence in this contribution. The CFD simulations are performed using an in-house developed message passing interface (MPI) parallel code, in which the simulations can be performed with any number of processors, and a multi-block method is used to discretize the flow domain. The discretization of the governing equations is accomplished by volume integration over each cell with a staggered arrangement of variables using the finite volume method. A second-order upwind (SOU) scheme with a deferred-correction method for all the transport equations is adopted to reduce the error of discretization with nonuniform grids (Li and Baldacchino, 1995; Li and Rudman, 1995).
3. Numerical methods
4. Boundary conditions
Since the two-fluid model is deduced via a time averaging procedure, steady mathematical models are taken here to reduce the expensive computation cost and get an efficient and reliable solution. It is very difficult to get a steady solution for bubbly flow simulations because of the strong coupling between velocities, pressure and gas holdups. The SIMPLE and related modified algorithms for bubbly flows are commonly chosen to decouple the pressure from the velocities of gas and liquid phases. Although great achievements have been done to promote the convergence of iterative computation, for instances, the partial elimination algorithm (Darwish and Moukalled, 2001; Bove, 2005) and the implicit decoupling algorithm SIMPLE (IDA-SIMPLE) proposed by Huang et al. (2010), the convergence speed for bubbly flow is still a severe problem. This is probably due to the immaturity of algorithm for multiphase flows and the residuals of the governing equations bounce up and down with little corrections on the pressure field in some cases. The phenomena that the overall volume balance for the mixture in each cell is satisfied but the balance of each phase is not guaranteed still exist after a long time of iterations. To avoid this difficulty, a modified SIMPLE algorithm is presented in this work and the details of the method are as follows:
A steady two-dimensional (2D) scenario in a cylindrical reference frame is chosen to reduce the enormous amount of computational time. The reactor axis is considered to be axisymmetric in the 2D cylindrical coordinate system. A no-slip boundary is applied at solid walls and the standard wall functions are adopted for all phases (Versteeg and Malalasekera, 1995). The inlet boundary conditions are assigned by prescribing fixed inlet velocities related to the superficial velocities of gas and liquid phases. The fraction of each phase at the inlet is set to equal to the ratio of its corresponding volume to the total mixture volume. The inlet conditions for the turbulent kinetic energy and the dissipation rate are approximated by
(a) The momentum equations of liquid and gas are solved in sequence without special treatment;
kl;in ¼ 0:004u2g;in 3
3
εl;in ¼ C 4μ k2in =ð0:07DÞ
ð24Þ ð25Þ
where D is the hydraulic diameter of the inlet. Bubbles are assumed of uniform size in the DCL reactor and the average diameter is 1 mm, which has been confirmed experimentally by Shi et al. (2008). Although there are lots of reported data of terminal slip velocities for bubbles in air–water systems in ambient conditions (Sokolichin et al., 2004), the experimental data of the terminal slip velocities for the bubbles less than or equal to 1 mm is very scattered, and especially rare under harsh reactive conditions. However, the terminal slip velocities of the bubbles can be calculated
Q. Huang et al. / Chemical Engineering Science 135 (2015) 441–451
by assuming the balance of pressure force and the drag for the bubbles in a stationary liquid: FD ¼ FP
ð26Þ
3 C F D ¼ ρl αg d u2slip C ρl ρg αg g 4 db
ð27Þ
So the slip velocity of bubbles can be written as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u4 ρ ρ gdb l g t uslip 3 ρl C d
ð28Þ
The above formula can be computed by combining the drag coefficient of Eq. (2) and the following definition of bubble Reynolds number: Re
db uslip ρl
μl
ð29Þ
The terminal slip velocity of a 1 mm bubble calculated is thus about 0.1024 m/s in the DCL slurry, and quite close to the experimental data of 0.09–0.10 m/s by others (Onozaki et al., 2000; Shi et al., 2008), hence it is adopted in this work. The outflow boundary of the reactor is simplified and assumed to be a Neumann type, and special treatments are required to accelerate the rate of convergence for the steady simulations (Huang et al., 2008). As far as we know, there is no open publication on a steady model with the continuous mode of operation, and it is very complicated to approximate it because of the coupling between the velocity and the fraction for each phase in bubbly flows. A developed boundary condition, which is extended from the work of Huang et al. (2008) for the semicontinuous operation at ambient condition, is taken here, and the outflow boundary is thought to be flat and the vertical gas velocity component relative to the liquid is simply defined as the terminal slip velocity of bubbles in quiescent slurry. The revised boundary condition is proposed regarding to both fluids operated with a continuous mode as follows:
αg ¼ αg;c0
ð30Þ
ul ¼ maxð0; ul;c0 Þ
ð31Þ
ug ¼ ul þ uslip
ð32Þ
445
perforated plate. The system was studied with a fixed superficial liquid velocity (based on the cross-sectional area of the reactor) uR, l of 0.00225 m/s and the variable superficial gas velocities (also based on the cross-sectional area of the reactor) uR,g in the range of 0.0212–0.0264 m/s. All the properties of gas and slurry used in the simulation of multiphase flow are listed in Table 2. All other parameters related to the Shenhua subbituminous coal, mass transfer and heat transfer are summarized in Tables 3 and 4. It is noteworthy that the apparent specific heat is applied here to the gas and slurry phases for the sake of simplification, and the varieties of physical properties (e.g., density, viscosity and surface tension etc.) due to temperature rise and mass transfer are neglected in this work because of limited temperature difference across the reactor. Additionally, the apparent density of gas in the reactor is higher than the density of the inlet gas mixture due to the evaporation of liquid. Therefore, different densities are used in the simulations of hydrodynamics and heat transfer, respectively. It has been proved that the reactions in DCL are very complicated and the cracking reactions of coal are almost complete in the stage of preheating in only several minutes under the condition of 350– 380 1C. The conversion of coal at the inlet of the IALR can be expressed as follows: ( maxð0; 13:96 0:08074 T þ 1:167 10 4 T 2 Þ T Z 354 1C xc ¼ 0 T o 354 1C ð33Þ In the process of DCL, the hydrogen atoms come from the hydrogen-donor solvent first and when the hydrogen atoms in the hydrogen-donor solvent are used up, part of the dissolved hydrogen in liquid reacts with coal. Then, the coal left and the intermediate products, including preasphaltene and asphaltene, Table 1 Temperature at the inlet in the process of DCL (Shi, 2009). Superficial gas velocity (m/s)
Temperature at the inlet (oC)
0.0264 0.0250 0.0240 0.0230 0.0212
346.3 356.1 358.7 371.7 354.3
Additionally, the gas and liquid velocities are slightly adjusted according to the rules of mass balance. All the walls in the reactor are treated as adiabatic in this work. In the experiments of DCL, the inlet temperature is adjusted by adding some cold hydrogen into the reactor to prevent the phenomenon of runaway from taking place. The inlet temperature corresponding to five test cases is outlined in Table 1 (Shi, 2009).
5. Results and discussion The experimental data of an IALR for the pilot plant of DCL in Shenhua Group Co. are chosen to validate the CFD results. The reactor has a diameter of 320 mm and a height of 6860 mm. A draft tube of 200 inner and 206 mm outer diameters with a height of 6436 mm was mounted into the column 150 mm above the gas distributor. The reactor bottom was shaped to be an inverted cone to avoid possible “dead zones”, with the height of 154 mm and the base radius of 103 mm. A conical section (base outer radius of 87 mm, top outer radius of 103 mm and a height of 56 mm) with 3 mm thickness was attached to the bottom of the draft tube. The schematic representation of the investigated IALR is illustrated in Fig. 2. Below the bottom of the riser, the gas and the slurry mixture were introduced from the mixer through a stainless steel
Fig. 2. Schematic representation of the DCL reactor and details of the grid distribution in radial and axial directions.
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Q. Huang et al. / Chemical Engineering Science 135 (2015) 441–451
Table 2 Properties of gas and liquid used in simulation of fluid dynamics. Physical parameter
Value
Operating density of gas Operating density of slurry Coal density Viscosity of gas Viscosity of liquid Surface tension Average solid fraction in the reactor (vol/vol%) Bubble diameter Operating temperature Operating pressure Ratio of gas to liquid (v/v) Relative molecular weight of oil
40 kg/m3 876 kg/m3 1440 kg/m3 5.0 10 5 Pa s 1.76 10 3 Pa s 2.7 10 2 N/m 3% 1.0 10 3 m 450 1C 19.0 MPa 700–1000 120
Table 3 Parameter values used in mass transfer simulation. Physical parameter
Value
Coal concentration (mass fraction) Diffusion coefficient of gas Diffusion coefficient of liquid Diffusion coefficient of coal Henry constant (H) Purity of coal Volume fraction of H2 at the inlet
45% 1.55 10 5 m2/s 1.8 10 9 m2/s 0 m2/s 1.05 10 5 mol/m3/Pa 95% 0.818
Table 4 Parameters used in heat transfer simulation. Physical parameter
Value
Density of inlet gas Apparent specific heat of gas Apparent specific heat of slurry Thermal conductivity of gas Thermal conductivity of slurry Thermal conductivity of steel Heat of reaction
11.77 kg/m3 13,000 J/kg/K 3630 J/kg/K 0.1672 W/m/K 0.163 W/m/K 16.27 W/m/K 50 kJ/(mol H2)
continue to react with the hydrogen dissolved in liquid phase in the reactor. As determined by the preliminary experiments, some of the liquid is vaporized by the reaction heat. It is shown that 0.28% of the liquid is vaporized when the temperature rises by 1 1C according to the distillation curve of the solvent, and the effect of evaporation capacity has been incorporated into the apparent specific heat of liquid for simplification. The hydrogen consumed in the reaction is related to the conversion of coal, and a phenomenological model is ( Y¼
0:1257 xc 0:064312
xc Z60%
0:0116 xc þ 0:002671
xc o60%
and 6.2 m above the bottom of the draft tube, respectively. However, the liquid average velocity was determined by measuring the time lag of temperature in the riser between these two measuring points when an operation disturbance occurred. Because it is very complicated to arrange the grids in the zones of the conical frustum by using the body-fitted grids, simple staircase approximation is used in this work. Before carrying out the simulations, the mesh resolution required to get a gridindependent solution has been surveyed. It is found that the grid with 79 1738 (radial axial) nodes as shown in Fig. 2 is sufficient and the numerical error of discretization can be neglected, so this grid is finally used in all subsequent simulations. 5.1. Validation against experimental data Typical operating conditions for five test cases of DCL (seen Table 1) are chosen to test the applicability of the integrated model. The comparisons of CFD results under a fixed superficial liquid velocity and different superficial gas velocities are illustrated in Figs. 3 and 4. The average gas holdup and the average liquid velocity in the riser are also presented in these figures. It can be observed that the averaged gas holdup and the cross-sectional area averaged liquid velocity at the middle height of the draft tube riser are all reasonably predicted. However, the predicted gas holdups in the riser are a little lower than the experimental data, especially for high superficial gas velocities. On the contrary, the predicted liquid velocities in the riser are higher than the experimental values. The deviations between the experimental data and the predicted results are all acceptable. The maximum deviation of the averaged gas voidage in the riser is less than 10%; however, the maximum discrepancy of the liquid velocity in the riser is as high as 39% at the lowest superficial gas velocity. These deviations can be ascribed to the experimental inaccuracy, simplified treatments for the problem being resolved, and the immaturity of two-fluid model, especially for the turbulence model and interphase forces including drag and lift force at high gas voidages. More experimental data at elevated pressure are needed to further verify the two-fluid model for simulating the case of high gas holdups. Figs. 3 and 4 suggest that both the gas voidage and the liquid velocity in the riser increase slowly with the increase of superficial gas velocity. The difference of gas holdups between the riser and the downcomer is too small to be distinguished from each other clearly, which is resulted from the presence of small bubbles and low difference of densities between the slurry and the gas in the process of DCL under the elevated pressure and high temperature. Even with a large aspect ratio (L/DE21.4), the liquid circulation velocity in Fig. 3 is very low in all the test cases due to the small difference of average gas voidages between the riser and the downcomer. Compared to the predicted liquid velocities in the riser, bigger liquid velocities in the downcomer are observed 0.32
ð34Þ
0.30
Gas holdup
0.28
where xc is the conversion of coal and Y is the mass consumption ratio of hydrogen to the coal, which is based on the concentration at the inlet, in unit of (kg H2)/(kg coal). It should be noted that the units for the concentrations of coal and hydrogen can be linked up with this model, and hence the relation of the reaction rates between the coal (rc) and hydrogen (rR) is set up. The experimental data were acquired by Shenhua Coal Liquefaction Co. and Beijing Research Institute of Coal Chemistry on the pilot test unit in Shanghai. The gas holdup was determined by the method of dynamic gas disengagement when the system was shut down, and the temperature was measured by two thermocouples located at 1 m
Experimental data in riser CFD in riser CFD in downcoer
0.26 0.24 0.22 0.20 0.18 0.16 0.020
0.022
0.024
0.026
0.028
Gas superficial velocity (m/s) Fig. 3. Comparison of gas holdups predicted by CFD simulations with experimental data.
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because of its smaller cross-sectional area. It is also indicated that the liquid velocities both in the riser and in the downcomer are much greater than the terminal slip velocities of coal and catalyst particles. Thus, it confirms that the assumption of a homogeneous slurry phase is reasonable in this work. The comparison of the predicted temperatures at two different measurement points in the riser wall with the experimental data is plotted as a function of superficial gas velocity in Fig. 5, showing the good agreement with the experiments. Although the temperature rise due to exothermic reactions in the reactor is about 100 1C, the predicted maximum error does not exceed 10 1C except two abnormal cases. Because the process of DCL is dynamic in practice and the inlet temperature varies within a narrow range for the sake of temperature control, the predicted temperature also changes with the superficial gas velocity and inlet temperature. In Fig. 5, it can be concluded that the predicted temperatures are a little lower than the experimental data, and the deviations can be attributed to the inaccuracy of models of kinetics, predicted hydrodynamics, and the estimated properties of fluids. Two abnormal cases, i.e., one case is predicted a little high and the other is predicted too low in Fig. 5, can be attributed to the peculiar inlet temperature. It is still in a heating or a cooling process for the sake of temperature control, and the temperature does not stabilize without a long enough time of operation. This scenario of delayed response is a notable feature resulted from the finite slurry flow velocity of orderly circulation in the IALR. That is to say, when the temperature in the inlet is changed, a time delay is needed for the reactor to reach a new equilibration. Unfortunately, this factor is too difficult to be cleared up in the pilot experiments of DCL in practice. It should be noted that compared to the abnormal case with high inlet temperature, the predicted temperature of another abnormal case with low inlet temperature
Liquid velocity (m/s)
0.20
447
collapsed to a very low value due to high sensitivity of kinetics on temperature and the interaction between the kinetics and the reaction heat. When the inlet temperature used in the simulation is below 354 1C, the initial conversion is zero and the chemical reaction rate decreases so significant that the heat of reactions cannot be kept around in the operating range. As mentioned above, this situation cannot happen in practice after a long time operation due to the control of operating temperature.
5.2. Distribution of gas holdup and velocity vector The trends of predicted gas holdup distributions in the reactor are similar under all operating conditions, and the typical distribution at the superficial gas velocity of 0.0212 m/s is shown in Fig. 6. It can be seen that the gas holdup in the reactor is very uniform. Additionally, the gas recirculates in a regular cycle between the riser and the downcomer. That is to say, the operation of regime III, in which the complete gas recirculation is formed, i.e., many bubbles entrained into the downcomer are carried all the way down along the downcomer and enter the riser again (Heijnen et al., 1997), actually takes place in the IALR even at a very small superficial gas velocity under elevated pressure. There is scarcely any region without gas in the whole reactor, which is very beneficial to the hydrocracking reaction, and thus the phenomenon of coking is inhibited because of the presence of dissolved hydrogen. Two small “wall-peaks” of the radial void distribution near the wall in the riser are well captured because the presence of small bubbles under the elevated pressure condition and a positive lift coefficient is resulted in the simulations. However, a zigzag distribution of voidage is observed in the reactor top because of the balance between the swirl flow and the lift force exerted on the small bubbles. The maps for gas and liquid velocity vectors in the top, middle and bottom parts with the superficial gas velocity of 0.0212 m/s are
Experimental data in riser CFD in riser CFD in downcomer
0.15
0.10
0.05
0.00 0.020
0.022
0.024
0.026
0.028
Superficial gas velocity (m/s) Fig. 4. Comparison of liquid velocities predicted by CFD simulations with experimental data.
440
o
Temperature ( c)
480
400 360 320 280
Experimental data at bottom point Experimental data at top point Inlet temperature Predicted data at bottom point Predicted data at top point
0.021
0.022
0.023
0.024
0.025
0.026
0.027
Superficial gas velocity (m/s) Fig. 5. Comparison of temperatures at two points of the riser predicted by CFD simulations with experimental data.
Fig. 6. Predicted distributions of gas holdups in different parts of the DCL reactor at the superficial gas velocity of 0.0212 m/s: (a) top; (b) middle; (c) bottom.
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Fig. 7. Predicted distributions of gas velocity vectors in the DCL reactor in different parts at the superficial gas velocity of 0.0212 m/s: (a) top; (b) middle; (c) bottom.
displayed in Figs. 7 and 8, respectively. It is shown that both liquid and gas flows are in the same manner, except the bulk of the liquid reaches the outlet and then turns down to the downcomer in the disengagement zone of the reactor. There are two large eddies in the top and bottom parts of the reactor for both gas and liquid, respectively. Fig. 7 indicates that the gas rises in the riser; most of gas bubbles exit from the outlet and only a few bubbles are dragged deep into the downcomer by the circulating liquid to generate a permanent recirculation. On the contrary, it shows clearly in Fig. 8 that the overwhelming majority of liquid goes to the top of the separator and then circulates into the downcomer, and only a small fraction of it escapes from the free surface. Additionally, there is still a little liquid circulating into the downcomer directly just over the draft tube due to the large disengagement zone of the reactor. The scenarios of “dead zones” which are commonly accompanied with deposition of solid particles and depletion of key components are totally prevented by the presence of convective circulation of both phases in the whole reactor owing to the elaborate design of internals in the reactor bottom. From the aforementioned discussion, it comes to a conclusion that the IALR designed in this work has better performance and can be used for the innovative DCL process of China. It is noteworthy that the annulus-airlifted loop reactor can be replaced with a central-airlifted loop reactor and a spherical bottom can be used in DCL to reduce the fouling on the center internals at the bottom of the downcomer. Nevertheless, in that case, the slurry can be discharged at the bottom of the downcomer with a high conversion of coal. However, if a top outlet is designed, a large top clearance should be designed to prevent the slurry taking a short circuit to the outlet of the reactor.
Fig. 8. Predicted distributions of liquid velocity vectors in the DCL reactor in different parts at the superficial gas velocity of 0.0212 m/s: (a) top; (b) middle; (c) bottom.
Although the performance of mixing in the IALR is very good due to the existence of orderly circulation of fluid flow in comparison with that in bubble columns, there are still distributions of reactants and product in the reactor due to finite circulation time or mixing time. Generally speaking, the concentrations of reactants (i.e., hydrogen and coal) are higher at the riser bottom and lower at the downcomer bottom, and the situation is just the reverse for the product. For the hydrogen in gas, with the dissolution and mass transfer, the concentration decreases gradually along the circulation. However, the dissolved hydrogen reaches a maximum in a short time after the gas enters the reactor by the joint actions of mass transfer, reaction and mixing of fluid, and then it drops gradually along the flow direction due to the faster reaction consumption than that of the hydrogen transferred into slurry, which is resulted from the decrease of the driving force for mass transfer. However, the mass transfercontrolled regime does not take place in the reactor since the mass transfer coefficient is big enough. A balance between the consumption of chemical reactions and the rate of mass transfer is reached in the bottom of the downcomer, and a uniform distribution of the dissolved hydrogen is obtained in this zone. The concentration of coal decreases monotonically during the course of circulation due to chemical reactions, meanwhile the concentration of the product increases monotonically. However, if the draft tube is too long, especially in a tall industrial IALR for the DCL, the dissolved hydrogen may be depleted at the downcomer bottom as regime III is not shaped. Under this circumstance, a multistage riser should be designed. 5.4. Distribution of temperature
5.3. Distributions of species concentration Since 1 mol of H2 can produce 2 mol of products in the reactions of DCL, the product generated by the hydrogen transferred from the gas to the liquid can be also predicted. The predicted concentrations of gas and dissolved hydrogen, coal and products in the slurry with the superficial gas velocity of 0.0212 m/s and the inlet temperature of 354.3 1C are displayed in Fig. 9.
When the superficial gas velocity is 0.0212 m/s and the inlet temperature is 354.3 1C, the snapshots of the liquid and gas phase temperatures in the reactor are illustrated in Fig. 10. It can be seen that the distributions of temperature for both phases are very similar with indistinguishable difference due to the perfect heat exchange between the gas and slurry phases in the IALR. Since a decrease of bubble size and an increase of gas holdup are resulted
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due to the elevated pressure, a high heat transfer coefficient is obtained. Hot spots (zone with overreaction) or cold spots (zone with little or no reaction), which are resulted due to inadequate mixing (Sutkar et al., 2013), do not occur in the DCL process. Although the temperature rise during the process of DCL is as high as about to 100 1C, the distribution of temperature is quite uniform in the reactor and the predicted temperature difference is less than 15 1C due to the excellent performance of macro-mixing in the IALR with ordered circulating flow. It is noteworthy that the uniform distribution of temperature is very beneficial to modeling of DCL, in which physical properties are all temperature dependent. Additionally, the uniform distribution of temperature contributes to controlling the quality of hydrogenation products. It is also indicated that the constancy of physical properties for both phases (for instance, density, viscosity and surface tension) presumed in this work gives rise to little error to the final results of the simulation. The temperature increases in the direction of slurry flow due to heat accumulation, and the maximum is achieved at the bottom of the downcomer. 6. Conclusions
Fig. 9. Predicted distributions of reactants and product in the DCL reactor at the superficial gas velocity of 0.0212 m/s and the inlet temperature of 354.3 1C: (a) gas hydrogen; (b) dissolved hydrogen; (c) coal in slurry; (d) product in slurry.
A comprehensive model, including the hydrodynamics of gas– liquid bubbly flow, mass and heat transfer between two phases, and chemical reactions of DCL under the conditions of elevated pressure and high temperature, is presented in this work. A Reynolds averaging two-fluid model using a steady method is developed to predict the hydrodynamics of bubbly flow in a continuous operation mode in a pilot IALR for the DCL process. The solid in the slurry is taken into account by increasing the viscosity of the continuous phase using the Einstein equation. The turbulence is resolved by a RNG k–ε model and the bubble induced turbulence is calculated by the method of Sato et al. (1981). The heat and mass transfer with reactions between two phases are described with respective transport equations and the rate of interphase exchange is considered. A modified SIMPLE algorithm and the developed boundary conditions for simulation of bubbly flow with a continuous mode using a steady method are also proposed to promote the convergence of solutions. The predicted gas voidage, liquid velocity and temperature in the riser due to reactions agree well with experimental data, which indicates that the multi-fluid formulations developed in this work can be used as an effective tool for design and scale-up of the IALR for the new Chinese DCL process. Additionally, the complex transport phenomena in DCL are well captured and the details are demonstrated. Compared to the ambient condition, the difference of gas holdups between the riser and the downcomer is much smaller in the IALR of DCL under elevated pressure and high temperature, and a low liquid average velocity in the riser is resulted. The liquid and the gas form a beneficial circulation in the reactor, and the regime III of bubbly flow is formed even at a low superficial gas velocity under the conditions of DCL. The relatively uniform distributions of concentrations for individual species and temperature in the IALR reveal its strong mixing capacity. Therefore, the IALR can be used as an alternative reactor for DCL if the reactor is elaborately designed. The present investigation also suggests that the CFD models verified in this work can be used as a useful tool for modeling, design and scale-up of such type of reactor in the future.
Nomenclature
Fig. 10. Predicted distributions of temperature in the DCL reactor at the superficial gas velocity of 0.0212 m/s and the inlet temperature of 354.3 1C: (a) temperature in slurry; (b) temperature in gas.
A a, b C CD
area (m2) coefficient of kinetics dimensionless concentration (mol/m3 or kg/m3) drag coefficient of a bubble swarm dimensionless
450
Cd Cg CL CnL Cp cðkhβÞ CI CI0 C0 Cμ D Dg Dl Dt db F FR g H h k kLa L Nu Pr Qk β R Re rc rP, rR S t T x, y, z xc xfc Y yc u uslip
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drag coefficient of a single bubble dimensionless hydrogen concentration in gas phase (mol/m3) hydrogen concentration in liquid phase (mol/m3) saturation concentration of hydrogen (mol/m3) isobaric specific heat capacity (J/kg/K) volumetric heat transfer coefficient (W/K) coal concentration at the inlet (kg/m3) inert coal concentration at the inlet (kg/m3) inert coal concentration (kg/m3) constant of the turbulent model dimensionless column diameter (m) molecular diffusivity in gas phase (m2/s) molecular diffusivity in liquid phase (m2/s) turbulent diffusivity (m2/s) bubble diameter (m) body force (N/m3) interfacial transfer of concentration between two phases (mol/m3/s) acceleration due to gravity (m/s2) Henry constant (mol/m3/Pa) heat transfer coefficient (W/m2/K) turbulent kinetic energy (m2/s2) mass transfer coefficient (s 1) length of the reactor (m) Nusselt number dimensionless Prandtl number, Pr ¼ μlCPl/λl dimensionless rate of heat transfer (J/m3/s) ideal gas constant (Pa/mol/K) Reynolds number dimensionless reaction rate of coal (kg/m3/s) reaction rates of product and hydrogen (mol/m3/s) external heat source (K/s) time (s) temperature (1C) Cartesian coordinate (m) local conversion of coal dimensionless final conversion of coal dimensionless mass consumption ratio of hydrogen to coal (kg H2)/(kg coal) carbon mass fraction of the local active part left to the total active part at the inlet in the coal dimensionless velocity (m/s) slip velocity (m/s)
Greek letters
α αs0 ε λ μ μslurry νt ρ σt Γ kþβ Γ βþk
voidage of phase dimensionless solid holdup at the inlet of the preheating process dimensionless turbulent energy dissipation rate (m2/s3) thermal conductivity (W/m/K) viscosity (Pa s) suspension viscosity (Pa s) kinematic viscosity (m2/s) density (kg/m3) constant of the turbulent model dimensionless heat transfer induced by interphase mass transfer from phase k to phase β (mol/m3/s) heat transfer induced by interphase mass transfer from phase β to phase k (mol/m3/s)
Subscripts c0 D
nodes adjacent to the outlet boundary drag
g in k, β, s l p P R s t
gas inlet phase liquid pressure product reactor or reactant solid turbulent
Acknowledgements The authors acknowledge the financial support from the National Basic Research Program of China (2012CB224806, 2004CB217604), the National Natural Science Foundation of China (21106169, 21406236) and the National Science Fund for Distinguished Young Scholars (21025627). Our gratitude also goes to China Shenhua Coal Liquefaction Corporation Ltd. for permitting use of coal liquefaction data and the Supercomputing Center of USTC (University of Science and Technology of China) for the support. The helpful discussion with Prof. Shidong Shi at Beijing Research Institute of Coal Chemistry is gratefully acknowledged. We also would like to especially thank Associate Prof. Huimin Li at USTC for helping us develop the in-house code by using MPI.
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