A CFD study on the start-up hydrodynamics of fluid catalytic cracking regenerator integrated with chemical looping combustion

Figures & data

Figure 1. An illustration showing the configuration of a regenerator used in CFD simulations (Chang et al. 2013, 2016; Gao et al. 2009a).

Table 1. Numerical parameters determined in the study.

Variable	Unit	Value/Condition	References
Solid-gas model	-	Euler-Euler	(Alzate Hernández 2016; Chang et al. 2013; Gao et al. 2009a)
Coefficient of specularity	-	0.6	(Chang et al. 2013)
Coefficient of restitution	-	0.95	(Alzate Hernández 2016; Chang et al. 2013)
Boundary condition (wall)	-	Partial slip (solids), No slip (gas)	(Chang et al. 2013; Gao et al. 2009a)
Time step size	s	0.0005	(Chang et al. 2016)
Max iterations per time step	-	20	(Azarnivand, Behjat, and Safekordi 2018; Chang et al. 2016)
Convergence criteria	-	0.001	(Alzate Hernández 2016; Azarnivand, Behjat, and Safekordi 2018; Chang et al. 2016)
Superficial gas velocity	m/s	0.6, 0.7, 0.8, 0.9, 1.0	-
Velocity-pressure coupling	-	Simple	(Alzate Hernández 2016; Azarnivand, Behjat, and Safekordi 2018; Chang et al. 2016)
Discretisation Scheme	-	First-order upwind scheme	(Alzate Hernández 2016)
Max volume fraction of solid packing	-	0.63	(Alzate Hernández 2016; Gao et al. 2009a)
The diameter of particle catalysts^+	mm	0.00065	(Chang et al. 2016)
The density of particle density^+	kg/m^3	1560	(Wang et al. 2011)

⁺Solid particles in the regenerator were presumed to have the same density and diameter (Güleç et al. 2021).

Table 2. Governing equations and constitutive relations.

Continuity equations	$\frac{\mathrm{\partial }}{\mathrm{\partial }\mathit{t}}\left({\alpha }_g{\rho }_g\right)+\mathrm{\nabla }.\left({\alpha }_g{\rho }_g{\vec{\upsilon }}_{\mathit{g}}\right)=0$	(1)
	$\frac{\mathrm{\partial }}{\mathrm{\partial t}}\left({\alpha }_s{\rho }_s\right)+\mathrm{\nabla }.\left({\alpha }_s{\rho }_s{\vec{\upsilon }}_{\mathit{s}}\right)=0$	(2)
	${\alpha }_g+{\alpha }_s=1$	(3)
Momentum equations	$\frac{\mathrm{\partial }}{\mathrm{\partial t}}\left({\alpha }_g{\rho }_g{\vec{\upsilon }}_{\mathit{g}}\right)+\mathrm{\nabla }.\left({\alpha }_g{\rho }_g{\vec{\upsilon }}_{\mathit{g}}{\vec{\upsilon }}_{\mathit{g}}\right)=-{\alpha }_g\mathrm{\nabla }{p}_g+{\alpha }_g{\rho }_g\vec{g}-\mathit{\beta }\left({\vec{\upsilon }}_{\mathit{g}}-{\vec{\upsilon }}_{\mathit{s}}\right)+\mathrm{\nabla }.{\alpha }_g\overline{\stackrel{‾}{\tau }}{ }_g$	(4)
	$\frac{\mathrm{\partial }}{\mathrm{\partial }\mathit{t}}\left({\alpha }_s{\rho }_s{\vec{\upsilon }}_{\mathit{s}}\right)+\mathrm{\nabla }.\left({\alpha }_s{\rho }_s{\vec{\upsilon }}_{\mathit{s}}{\vec{\upsilon }}_{\mathit{s}}\right)=-{\alpha }_s\mathrm{\nabla }{p}_g-\mathrm{\nabla }{p}_s+{\alpha }_s{\rho }_s\vec{g}-\mathit{\beta }\left({\vec{\upsilon }}_{\mathit{s}}-{\vec{\upsilon }}_{\mathit{g}}\right)+\mathrm{\nabla }.{\alpha }_s\overline{\stackrel{‾}{\tau }}{ }_s$	(5)
Turbulence kinetic energy (k)	$\frac{\mathrm{\partial }}{\mathrm{\partial }\mathit{t}}\left({\alpha }_q{\rho }_q{k}_q\right)+\mathrm{\nabla }.\left({\alpha }_q{\rho }_q{\vec{\upsilon }}_{\mathit{q}}{k}_q\right)=\mathrm{\nabla }.\left({\alpha }_q\left({\mu }_q+\frac{{\mathit{\mu }}_{\mathit{t},\mathit{q}}}{{\sigma }_k}\right)\mathrm{\nabla }{k}_q\right)+\left({\alpha }_q{G}_{\mathit{k},\mathit{q}}-{\alpha }_q{\rho }_q{\epsilon }_q\right)+{\alpha }_q{\rho }_q{\mathrm{\Pi }}_{k_q}$	(6)
Turbulence dissipation rate (ε)	$\frac{\mathrm{\partial }}{\mathrm{\partial t}}\left({\alpha }_q{\rho }_q{\epsilon }_q\right)+\mathrm{\nabla }.\left({\alpha }_q{\rho }_q{\vec{\upsilon }}_{\mathit{q}}{\epsilon }_q\right)=\mathrm{\nabla }.\left({\alpha }_q\left({\mu }_q+\frac{{\mathit{\mu }}_{\mathit{t},\mathit{q}}}{{\sigma }_{\epsilon }}\right)\mathrm{\nabla }{\epsilon }_q\right)+{\alpha }_q\frac{{\epsilon }_q}{k_q}\left(C_{1\mathit{\epsilon }}{G}_{\mathit{k},\mathit{q}}-C_{2\mathit{\epsilon }}{\rho }_q{\epsilon }_q\right)+{\alpha }_q{\rho }_q{\mathrm{\Pi }}_{{\epsilon }_q}$	(7)
Turbulence viscosity	${\mu }_{\mathit{t},\mathit{q}}=\frac{{\rho }_q{C}_{\mu }{k}_q^2}{{\epsilon }_q}$	(8)
Constants of the turbulence model	$C_{1\mathit{\epsilon }}=1.44,C_{2\mathit{\epsilon }}=1.92,{\sigma }_k=1.0,{\sigma }_{\epsilon }=1.3$	(9)
Transport equation for Granular Temperature	$\frac{\partial }{\partial \mathit{t}}\left({\alpha }_s{\rho }_s\mathit{\Theta }\right)+\nabla .\left({\alpha }_s{\rho }_s\mathit{\Theta }{\overrightarrow{\upsilon }}_{\mathit{s}}\right)=\frac{2}{3}-p_s\overline{\overline{I}}+\overline{\overline{\tau }}\mathit{s}:\nabla .{\overrightarrow{\upsilon }}_{\mathit{s}}+\nabla .\left({\Gamma }_{\Theta }\nabla \mathit{\Theta }\right)-{\gamma }_s+{\varphi }_{\mathit{gs}}$	(10)
Syamlal–O’Brien drag model	$\mathit{\beta }=\frac{3{\rho }_g{\alpha }_g{\alpha }_s\left|{\vec{\upsilon }}_{\mathit{g}}-{\vec{\upsilon }}_{\mathit{s}}\right|}{4{\upsilon }_{r,s}^2{d}_s}{C}_D\left(\frac{R{e}_s}{{\upsilon }_{\mathit{r},\mathit{s}}}\right)$ $C_D={\left(0.63+\frac{4.8}{{\left({Re}_s/{\upsilon }_{\mathit{r},\mathit{s}}\right)}^{1/2}}\right)}^2$ ${Re}_s=\frac{{\rho }_g{\alpha }_g\left|{\vec{\upsilon }}_{\mathit{g}}-{\vec{\upsilon }}_{\mathit{s}}\right|d_s}{{\mu }_g}$ ${\upsilon }_{\mathit{r},\mathit{s}}=0.5\left(\mathit{A}-0.06{Re}_s+{\left({\left(0.06R{e}_s\right)}^2+0.12{Re}_s\left(2\mathit{B}-\mathit{A}\right)+A^2\right)}^{1/2}\right)$ $\mathit{A}={\alpha }_g^{4.14},\mathit{B}=\left(\begin{array}{cc}0.8{\alpha }_g^{1.28}& {\alpha }_g\le 0.85\\ {\alpha }_g^{2.65}& {\alpha }_g>0.85\end{array}\right)$	(11)
The gas-phase stress tensor	${\bar{\tau }}_{\mathit{g}}={\mu }_{\mathit{t},\mathit{g}}\left[\mathrm{\nabla }{\vec{\upsilon }}_{\mathit{g}}+{\left(\mathrm{\nabla }{\vec{\upsilon }}_{\mathit{g}}\right)}^{\mathit{T}}\right]+\left({\lambda }_g-\frac{2}{3}\ast {\mu }_{\mathit{eff},\mathit{g}}\right)\mathrm{\nabla }{\vec{\upsilon }}_{\mathit{g}}\overline{\stackrel{‾}{I}}$	(12)
The solid-phase pressure	$p_s={\alpha }_s{\rho }_s\mathrm{\Theta }\left[1+2g_0{\alpha }_s\left(1+\mathit{e}\right)\right]$	(13)
The radial distribution functions	$g_0=\left[1-{\left(\frac{{\alpha }_s}{{\alpha }_{\mathit{s},\mathit{max}}}\right)}^{\text{1}/\text{3}}\right]$	(14)
Granular Temperature	$\mathrm{\Theta }=\frac{1}{3}\ast \left(\overline{{\upsilon }^{\prime }{\upsilon }^{\prime }}\right)$	(15)
The solid-phase stress tensor	$\overline{\stackrel{‾}{\tau }}{ }_s={\lambda }_s\mathrm{\nabla }.{\vec{\upsilon }}_{\mathit{s}}\overline{\stackrel{‾}{I}}+{\mu }_s\left[\mathrm{\nabla }.{\vec{\upsilon }}_{\mathit{s}}+{\left(\mathrm{\nabla }.{\vec{\upsilon }}_{\mathit{s}}\right)}^{\mathit{T}}\right]-\frac{2}{3}\ast \left(\mathrm{\nabla }.{\vec{\upsilon }}_{\mathit{s}}\right)\overline{\stackrel{‾}{I}}$	(16)
The solid-phase bulk viscosity	${\lambda }_s=\frac{4}{3}\ast {\alpha }_s^2{\rho }_s{d}_s{g}_0\left(1+\mathit{e}\right){\left(\frac{\mathrm{\Theta }}{\pi }\right)}^{1/2}$	(17)
The shear viscosity of solid particles	${\mu }_s=\frac{4}{5}{\alpha }_s{\rho }_s{d}_s{g}_0\left(1+\mathit{e}\right){\left(\frac{\mathrm{\Theta }}{\pi }\right)}^{1/2}+\frac{{\alpha }_s{\rho }_s{d}_s{\left(\mathit{\pi \Theta }\right)}^{1/2}}{6\left(3-\mathit{e}\right)}\left[1+\frac{2}{5}{\alpha }_s{g}_0\left(1+\mathit{e}\right)\left(3\mathit{e}-1\right)\right]$	(18)
The collisions dissipation energy	${\gamma }_s=3\left(1-e^2\right){\alpha }_s^2{\rho }_s{g}_0\mathrm{\Theta }\left(\frac{4}{d_s}{\left(\frac{\mathrm{\Theta }}{\pi }\right)}^{1/2}-\mathrm{\nabla }.{\vec{\upsilon }}_{\mathit{s}}\right)$	(19)
The coefficient of granular diffusion	${\mathrm{\Gamma }}_{\mathrm{\Theta }}=\frac{150{\rho }_s{d}_s{\left(\mathit{\pi \Theta }\right)}^{1/2}}{384\left(1+\mathit{e}\right)g_0}{\left[1+\frac{5}{6}\left(1+\mathit{e}\right)g_0{\alpha }_s\right]}^2+2{\alpha }_s^2{\rho }_s{d}_s{g}_0\left(1+\mathit{e}\right){\left(\frac{\mathrm{\Theta }}{\pi }\right)}^{1/2}$	(20)
The transfer of fluctuating kinetic energy	${\varphi }_{\mathit{gs}}=-3\mathit{\beta }\mathrm{\Theta }$	(21)

Figure 2. Radial distribution of particle volume fraction with time-averaged for four different mesh quantities (y = 250 mm and y = 500 mm, superficial gas velocity = 1 m/s).

Figure 3. Contours of volume fraction of particles for a) mesh-3 from 0.1s to 5.0s and b) four different meshes at 8 s (steady state) at 1.0 m/s.

Figure 4. Comparison of axial bed density profiles of a) syamlal-O’Brien, b) gidaspow, and c) schiller-naumann at the early stage of fluidisation (0.1–2.0 s) and steady state (S.S.). (I.D. represent the industrial data).

Figure 5. Contours of volume fraction of particles; a) syamlal-O’Brien, b) gidaspow, and c) schiller-nauman drag models at the early stage of fluidisation.

Figure 6. The axial bed density profiles were estimated via a) laminar and b) turbulent flow regimes under geometry-3 and 1.0 m/s of superficial gas velocity at 0.1–0.5 s and steady-state.

Figure 7. Contours of volume fraction of particles for a) turbulent flow model and b) laminar flow model at the early stage of fluidisation.

Figure 8. Radial particle volume fraction distribution with time-averaged through different inlet geometries (G1, G2, G3, and G4) at different height positions within the reactor (y = 250 mm, y = 500 mm, and y = 750 mm 0 at 1.0 m/s of superficial gas velocity.

Figure 9. Bed density and contours of volume fraction of particles for a) geometry-1 (G1), b) Geometry-2 (G2), c) Geometry-3 (G3), and d) Geometry-4(G4) at mesh-3 for 10 s.

Figure 10. a) The bed density profiles at the early state (0.1s to 2.0s) of the CLC-FCC regenerator operating under 1.0 m/s of superficial velocity and b) The average bed density profiles of various superficial gas velocities (0.6–1.0 m/s) at early state (E.S., average bed density profiles from 0.05 s to 0.5 s) and steady state (S.S., average bed density profiles from 5.0 s to 10.0 s).

Figure 11. Contours of particles volume fraction at initial stages of the fluidisation; a) 0.1s, b) 0.3s, c) 0.5s, and d) 1.0s.

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