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Ind. Eng. Chem. Res. 2009, 48, 10094–10103
Modeling of Multiphase Flow and Heat Transfer in Radiant Syngas Cooler of an Entrained-Flow Coal Gasification Guangsuo Yu,* Jianjun Ni, Qinfeng Liang, Qinghua Guo, and Zhijie Zhou Key Laboratory of Coal Gasification of Ministry of Education, East China UniVersity of Science and Technology, Shanghai 200237, People’s Republic of China
A comprehensive model has been developed to analyze the multiphase flow and heat transfer in the radiant syngas cooler (RSC) of an industrial-scale entrained-flow coal gasification. The three-dimensional multiphase flow field and temperature field were reconstructed. The realizable k- turbulence model is applied to calculate the gas flow field, while the discrete random walk model is applied to trace the particles, and the interaction between the gas and the particle is considered using a two-way coupling model. The radiative properties of syngas mixture are calculated by weighted-sum-of-gray-gases model (WSGGM). The Ranz-Marshall correlation for the Nusselt number is used to account for convection heat transfer between the gas phase and the particles. The discrete ordinate model is applied to model the radiative heat transfer, and the effect of ash/slag particles on radiative heat transfer is considered. The model was successfully validated by comparison with the industrial plant measurement data, which demonstrated the ability of the model to optimize the design. The results show that a torch shape inlet jet was formed in the RSC, and its length increased with the diameter of the central channel. The recirculation zones appeared around the inlet jet, top, and bottom of the RSC. The overall temperature decreased with the heat-transfer surface area of the fins. The concentration distribution, velocity distribution, residence time distribution, and temperature distribution of particles with different diameters have been discussed. Finally, the slag/ash particles size distribution and temperature profile at the bottom of the RSC have been presented. 1. Introduction The Integrated Gasification Combined Cycle (IGCC) is the most advanced technology for generating electricity from coal cleanly. Coal-based IGCC technology is very close to being economically competitive with pulverized coal-fired (PC) plants and can meet extremely stringent environmental emission standards.1,2 Gases leave the gasifier at high temperatures, varying from 1200 °C to 1600 °C for some entrained-flow slagging gasifiers. Thus, it is necessary to recover the sensible heat in the syngas to improve power generation efficiency. The radiant syngas cooler (RSC) is used to contain and cool the syngas produced by a coal gasification process used in the IGCC power plant.3 The cooling process occurs without liquid or sticky slag particles touching the heat-transfer surface and causing fouling, while the flow patterns achieve the requirement of considerable care in design.4 However, RSC designs have a practical limitation of overall outside diameter, because of the economics of pressure vessel containment and shipping size limitations to most power plant sites. Based on these limits to vessel diameter, it is necessary to optimize the performance of RSC to achieve a cost-effective and compact design. Currently, the information on multiphase flow, slag flow behavior, and heat transfer in entrained-flow gasifiers has been published elsewhere.5-8 However, very little information about the RSC operating conditions to assist future coal IGCC plant design is available. The chemical properties of deposit formation and corrosion phenomena in coal gasification in the RSC have been analyzed.9,10 That knowledge can help to explain what happens in the RSC, although it is difficult to relate this knowledge to complex multiphase flow in the RSC under high temperature and pressure. Therefore, to gain a better understanding of the multiphase flow field and temperature field in * To whom correspondence should be addressed. Tel.: +86-21-6425 2974. Fax: +86-21-6425 1312. E-mail address:
[email protected].
the RSC, the online temperature measurement and modeling prediction should be performed. Manickam et al.11 proposed a computational fluid dynamics (CFD) model to predict the operating conditions of a waste heat recovery boiler utilizing plant off-gas that consisted of gaseous and combustible particulate. Richard et al.12 developed a mathematical model and computer program to predict the flow field and temperature distribution for boiler design and optimization. The flow and heat transfer in the connection of the gasifier to the RSC was studied using numerical simulation approach.13 Until now, there is no report about three-dimensional (3D) mathematic modeling of multiphase flow and heat transfer in RSC using the CFD approach, and no measurement data have appeared in the literature. The objective of this work is to (i) develop a mathematical model that is capable of quantitatively predicting the multiphase flow field and the complex heat-transfer process in an industrialscale RSC and (ii) provide an optimized design and guidelines for controlling the ash deposition on the RSC water wall. The outline of gas-particle flow and heat-transfer coupling model are described. The integrated gas-particle flow field and temperature field, mean residence time, and temperature distribution of particles, which have different sizes in RSC, are presented. The influences of the water wall arrangement on RSC are discussed. A comparison of calculation results and industrial online measurement results is also presented. 2. Mathematical Model For comprehensive modeling of the gas-particle turbulent flow and heat transfer in the RSC, the following physical processes are included in the present model: (1) turbulent flow of gas flow and radiative heat transfer of syngas; (2) entrainment of slag/ash particles and their turbulent dispersion; (3) convective and radiative of slag/ash particle cooling; and (4) slag/ash
10.1021/ie901203d CCC: $40.75 2009 American Chemical Society Published on Web 10/13/2009
Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009 Table 1. Syngas Components at the Radiant Syngas Cooler (RSC) Inlet component
amount (vol %)
H2 CO CO2 H2S + COS CH4 N2 + Ar H 2O
26.40 35.80 15.00 0.23 0.05 0.48 22.04
particle depositing on the water wall of RSC. The numerical methods and the submodels recommended for the gas-particle flow and heat-transfer process in the present model are discussed in the following sections. 2.1. Multiphase Flow Hydrodynamics. 2.1.1. Continuous-Phase Flow Model. Gas turbulence is modeled by a twoequation model (the realizable k- model)14 for closure, and it is assumed to be steady state. This model has been extensively validated for a wide range of flow, including round confined jet flow.14,15 The gas phase is a mixture of nine species, and the average compositions of typical syngas are listed in Table 1 for coal water slurry feed gasification. The local mass fraction of each species Yi can be calculated through the solution of a convection-diffusion equation for the ith species. This species transport equation takes the following general form:
[(
) ]
µt ∂Yi ∂(FgujYi) ∂ ) FD + ∂xj ∂xj g i,m Sct ∂xj
(1)
where Sct is the turbulent Schmidt number. In addition, no chemical reaction is assumed to occur among the gas species in the RSC. The volume-of-fluid (VOF) free-surface model is used for the interface modeling between the liquid and syngas in the RSC, and an explicit geometric reconstruction scheme is applied to represent the interface tracking, using a piecewise-linear approach.16 2.1.2. Discrete-Phase-Flow Model. The motion of a slag/ ash particle is described by the so-called stochastic Lagrangian multiphase flow model. The trajectories of discrete phase particles were predicted by integrating the force balance on the particles. Therefore, the governing equation is written as gx(Fp - Fg) dup ) FD(u b-b u p) + + Fx dt Fp
(2)
b-b up) is the drag force per unit particle mass, which where FD(u is given by FD )
( )
18µ Re CD 2 24 Fpdp
( )
the model described ignores the effect of particle-particle interaction. This treatment has been widely accepted for dilute flows.18,19 2.2. Heat-Transfer-Analysis Model. Because radiation dominates the heat flux toward the RSC membrane water wall, it is necessary to apply an appropriate radiation model. The compositeflux radiation model has been widely used in combustion chambers and furnaces.20,21 However, many limitations about the composite-flux radiation method have been indicated by Habibi et al.22 In the present work, the DOM23 is used to solve radiative equations. The numerical solution for radiation leads to the distribution of radiant intensity and radiant heat flux for a given temperature field. The solution is coupled to energy conservation equations and relationships between temperature and thermodynamic properties of gases and particles. 2.2.1. Heat-Transfer Modeling. In this work, the VOF model and heat transfer, using the same energy equation, is shown as follows: ∂(FqE) + ∇ · (U[FqE + p)] ) ∇ · (keff∇T) + Sh ∂t
u the velocity of the continuous where b up is the particle velocity, b phase, FD the drag force of the particle, and dp the particle diameter. Re is the relative Reynolds number, and CD is the drag coefficient. Fx is an additional acceleration term that includes thermophoresis force, Brownian force, and Saffman’s lift force. The discrete-phase particles can dampen or produce turbulent eddies.17 Therefore, the two-way coupling method is used to consider the effects between the gas phase and the discrete phase. The two-way coupling is accomplished by alternately solving the discrete-phase and continuous-phase equations until the solutions in both phases stop changing. However, note that
(4)
where the energy (E) and temperature (T) are mass-average variables. Sh represents the term of radiative source. The radiative heat-transfer equation for an absorbing, emitting, and scattering medium at position r in the direction s is
( )
dI(r, s) σT4 + (R + σs)I(r, s) ) Rn2 + ds π σs 4π I(r, s′)φ(r, s′) dΩ′ 4π 0
∫
(5)
where R and σs represent absorption and scattering coefficients, respectively. Here, R is a function of the local concentrations of syngas species, path length, and total pressure. In this work, the weighted-sum-of-gray-gases model (WSGGM) for the computation of a variable absorption coefficient is developed. The WSGGM is a reasonable compromise between the oversimplified gray-gas model and the computationally tooexpensive complete model, which takes into account particular absorption bands. It has been demonstrated that the WSGGM can be applied to the radiative transfer equation (RTE) and any solution method of transfer equation (exact, P-N approximation, DOM, etc.) when all boundaries are black and the medium is nonscattering.23 2.2.2. Gas and Particle Thermal Properties. The basic assumption of the WSGGM is that the total emissivity over the distance s can be presented as N
(3)
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R)
(
J
∑ ∑b i)0
j)0
ε,i,jT
)
j-1
[1 - exp(-Kips)]
(6)
where bε,i,j are the emissivity gas temperature polynomial coefficients, Ki is the absorption coefficient of the ith gray gas, p is the sum of the partial pressures of all absorbing gases, and s is the path length. The values of coefficients are estimated by fitting the aforementioned equation to the table of total emissivities obtained experimentally.24,25 The temperature dependence of fluid species on thermal conductivity, mixture viscosity, and specific heat capacity are calculated by the mass-weighted mixing law. For example, the specific heat capacity is calculated as C ) ∑Ni Yi(∫TTrefCp,i dT), where Cp,i is the specific heat capacity of the ith gas at standard temperature and pressure. The syngas density is computed by
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Table 2. Physical Properties of Slag/Ash Particles
a
property
value
density heat capacity conductivity scatteringa emissivitya heat of fusionb IT (initial temperature) ST (softening temperature) HT (hemisphere temperature) FT (flowing temperature)
2700 kg/m3 1450 J kg-1 K-1 1.87 W m-1 K-1 0.1 m-1 0.83 100 kJ/mol 1225 °C 1234 °C 1260 °C 1292 °C
Data taken from ref 26. b Data taken from ref 27.
the ideal gas law of mixtures. The species mass diffusion coefficient of the syngas is calculated using the multicomponent Fick’s law. The relationship between radiative properties of slag/ash particle and the chemical composition has been discussed using synthetic coal slag.28,29 On the other hand, radiative properties of slag/ash particle are also influenced by the particle size, particle shape, and surface roughness.30 Fortunately, the thermal properties of coal slag/ash formed in a slagging gasifier has been measured by Mills and Rhine,26 and the thermal expansion of slag/ash samples from gasifier has been studied.31 For this work, the physical properties of slag/ash used in the present model are listed in Table 2. The thermophoretic coefficient of particle diffusion uses the form suggested by Talbot.32 In the RSC, the size of slag/ash particles entrained by syngas is small, and the particle density is larger than that of syngas, so the hypothesis that the particles cannot go back to flow space once deposited on water wall is reasonable while the particle temperature is higher than IT. A simple heat balance is applied to calculate the particle temperature (Tp). The convective heat transfer and the absorption/emission of radiation at the particle surface are represented: mpCp
dTp ) hAp(Tg - Tp) + εpApσ(θR4 - Tp4) dt
(7)
where the heat transfer coefficient (h) is evaluated using the Ranz-Marshall correlation:33 Nu )
hd ) 2.0 + 0.6(Red1/2Pr1/3) k∞
(8)
where k∞ is the thermal conductivity of continuous phase and Pr is the Prandtl number of the continuous phase. Red is the Reynolds number that is based on the particle diameter and the relative velocity. The heat lost or gained by the particle as it traverses each computational cell, and the energy balance, also be calculated using the continuous-phase energy equation.
Figure 1. Computational domain and measurement points of the radiant syngas cooler (RSC). Table 3. Operating Conditions variable
value
syngas and particle inlet temperature inlet water temperature of water wall tube temperature of slag pool operating pressure inlet syngas volume flow rate inlet particle mass flow rate
1300 °C 315 °C 45 °C 3.5 MPa 59448 Nm3/h 3154 kg/h
syngas species, velocities, pressure, k, and ) were achieved when the iteration residuals were reduced to 4 orders of magnitude. The numerical simulations were performed for an industrialscale RSC; the schematic structure is shown in Figure 1, and the operating conditions are given in Table 3. Division walls 1 and 2 represents the octagonal cage wall and the radial platens (fins), respectively. The inner syngas flow channel, with diameter D, was the central unfinned core of the RSC. The effects of the diameter D for three cases (case 1, D ) 2.524 m; case 2, D ) 1.480 m; and case 3, D ) 1.220 m) on heat transfer and flow field were discussed. The thickness of slag deposits is difficult to measure or establish. Therefore, according to industrial operating conditions and the photographs from the RSC chamber shown in Figure 2, a constant was assumed for deposit thicknesses as follows. When D ) 1.220 m and D ) 1.480 m, the slag thickness of division wall 2, the ash thickness of the annular water wall, and the inner surface of division wall 1 were estimated to be 2 mm, 0.5 mm, and 0.5 mm, respectively. When D ) 2.254 m, division wall 2 was removed. The slag/ash thickness of division wall 1 and the ash thickness of the annular water wall and division wall 1 were estimated according to the literature.9 Therefore, the slag thickness of the inner surface of
3. Numerical Solution Procedure The governing equations for the conservation of momentum, energy, turbulence, and radiation were solved sequentially using the finite-volume method (FVM). The velocity correction was realized to satisfy continuity through the SIMPLE algorithm,34 which couples velocity and pressure. To evaluate the convective terms and turbulent kinetic energy, the second-order QUICK scheme was used. The PRESTO! scheme was used for pressure discretization, and the first-order upwind was used for other terms (turbulent dissipation rate, energy, and DOM). The convergence criteria for flow and heat transfer (energy, DOM,
Figure 2. Photograph of the deposition on upper division wall 2.
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Figure 3. Slag/ash particle size distribution.
Figure 5. Velocity vector profile of different cases.
Figure 4. Computational grid used for simulation.
division wall 1, the ash thickness of the annular water wall, and the inner surface of division wall 1 were estimated to be 20 mm, 2 mm, and 2 mm, respectively. The slag/ash deposit thickness was estimated using measurements and the reported information.9,35 The initial surface temperature of deposits (Td) was estimated using a heat flux balance equation: l)
λ(Td - Tw) h(Tg - Td) + σε(Td - Tg ) 4
4
× 103
(9)
where the deposit surface emisivity was assumed to be 0.83,26 and the convective heat transfer coefficient was calculated based on the temperature gradient under the wall and flow conditions. The thermal conductivity of the deposit layer is a crucial model parameter, and the reference values from the experiments are 0.25 and 1.87 W/m2 for ash and slag,26,36 respectively. Slag/ash particles were considered as slag droplets and tracked from the top inlet. The particle size distribution was discretized into 150 groups, using the Rosin-Rammlar distribution method to fit the measurement data (as shown in Figure 3). The model tracked 8400 particle trajectories to obtain a steady convergence in the calculations. In the calculation domain, the mesh sensitivity analysis has been proved that 815000 mesh cells is sufficient to guarantee a solution that is practically independent from the number of cells. The external surface of computational grid is shown in Figure 4. The simulations were performed using the Fluent program (Version 6.1). 4. Results and Discussion 4.1. Model Validation. Online measurement was performed in the aforementioned RSC. The thermocouples were placed at
Figure 6. Comparison of the Y-velocity distribution along the axial line.
three different measuring points, as shown in Figure 1. Table 4 shows a comparison of the prediction and measured results. In Table 4, the first and second measurement points that are shown in Figure 1 were defined as the inflection point and the turning point, respectively. The calculated values are in good agreement with the measured data. The maximum calculation error on the prediction of the turning point temperature is 11.6%, probably because the water that evaporated from the slag pool was ignored. The multiphase flow characteristics are very similar to those described in the literature,12 which are discussed as follows. Hence, it can be claimed that the present CFD model can be extended to predict the performance of the entrainedflow coal gasification RSC. 4.2. Continuous-Phase Flow Field. Figures 5 and 6 show the calculated results for gas flow with different cases. From the calculations, the parameter D does have influence on the integrated flow field. When the value of D decreased from 2.524 m to 1.220 m, the length of inlet jet decreased from 7 m to 4.5 m, and the expanding angle of inlet jet decreased from 10° to 3°. When D ) 1.480 m, the recirculation or upward flow with a velocity of 1-4 m/s in the center is formed while the recirculation with a velocity of 1-2 m/s has also been found in
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Figure 7. Gas-temperature field of different cases (temperatures expressed in Celsius).
Figure 8. Gas-temperature distribution along the axis.
RSC by Wessel et al.12 The buoyancy and natural circulation have great influence on the flow patterns. The cooler gas near the division wall is denser and has a tendency to sink under the gravity. The hotter gases, near the center of the top chamber, are lighter and have a tendency to rise or stagnate. The axial velocity (Y-velocity) is always a maximum near the walls and a minimum (or upward) near the center. Therefore, most of the syngas flows between the division walls and proximity to the cage wall before it escapes from the RSC. Closer inspection of the flow field also shows that circulations are formed around the inlet jet, top of the inner cylinder, and above the surface of the slag pool. 4.3. Continuous-Phase Temperature Distribution. The predictions of gas temperature distributions for three cases are compared in Figures 7 and 8. Figure 7 demonstrates the influence of the heat-exchange area of the division wall. The heat-exchange area decreased as D increased. Thus, it can be determined that the average gas temperature increased as D increased. Generally, the gas temperatures of the three cases are relatively uniform through the chamber. However, the gas temperature distribution is affected by the gas flow field. A torch shape inlet jet was formed in the RSC, and its length increased with the diameter of the central channel, because the gas
Figure 9. Incident radiation (expressed in units of W/m2) of the different cases.
temperature field is dependent on the gas flow field discussed in the previous section. The gas temperature at the center of the chamber is relatively higher, relative to that of the division wall. Closer inspection of the temperature field also shows that the gas temperatures for the three cases are all
