Modelling and CFD simulation of a fluidized bed

Modelling and CFD simulation of a fluidized bed reactor to capture CO2 by solid sorbents M. Molaei, K.A. Pericleous, M.K. Patel Centre for Numerical Modelling and Process Analysis University of Greenwich, Lonson SE10 9LS, UK Email:

Abstract CO2 capture from combustion exhaust gases by carbonation using a fluidised bed is a possible technological route to reduce carbon dioxide discharge to the atmosphere. Fossil fuels comprise main source of energy for power generation in existing power plants responsible, for 32% of CO2 emitted in the UK. Since most of these emissions are due to single large sources, in situ post-treatment of the combustion flue gas seems to be an efficient means of capture. In this work, CFD modelling has been used to study the efficiency of CO2 capture in a fluidized bed reactor containing a solid sorbent. A Lagrangian/Eulerian scheme has been developed for this purpose, with the particle tracking model used to describe CaO particle trajectories and mass, momentum and energy exchange with the carrier gas, entering the reactor in a typical flue gas composition. A steady-state condition is assumed, with each trajectory representing a parcel of particles of a given mass and diameter. The number of particles entering the fluidised bed is kept constant, and the fluidization velocity is chosen so that particles remain in the reactor. As the carbonation progresses, ‘heavier’ well-reacted particles are collected to the bottom of the reactor. In the case of a non-uniform size distribution, fine particles would escape from the top of the reactor; in order to keep such particles inside, the geometry was modified to reduce the fluidization velocity. CO2 reduction of the order of xx% was achieved in a single pass, with a mass loading of 116% particles to CO2 in gas phase gas and an effective reaction area of 29 m2/g of CaO

Keywords: CFD simulation, modelling, fluidized bed reactor, CO2 capture

1- Introduction Based on Intergovernmental Panel on Climate Change (IPCC) reports, the major cause of climate change and global warming is due to a high level of CO2 concentration in the atmosphere resulting from fossil fuel combustion, particularly in coal-fired power plants [IPCC, 2005]. Carbon capture and storage is the most important technique proposed to reduce CO2 from combustion flue gases. In this process, carbon dioxide is captured and may then be regenerated as pure CO2 and conducted to a permanent storage, or simply stored as a solid carbonate [Carbon8]. Capturing and storage of CO2 has an economic penalty and the main cost of this penalty is associated with the capture plant. Capturing CO2 with Lime-based solid sorbent (CaO) is the most promising technique due to the cost

effectiveness and the wide availability of the reactant. In this process, the CaO reacts with CO2 based on the following reaction in a reactor called a Carbonator. (

)

(

)

(

)

The reacted particles may then be conducted to another reactor (Calciner) to regenerate the CaO and yield pure CO2 for further storage. Regenerated CaO particles are returned back to the carbonator to reuse in the capturing process. After an initial rapid kineticallycontrolled reaction, the formation of a critical product layer on the particles results in a sudden change in reaction rate to a slow diffusion-controlled phase (Ping Sun 2008). The reaction is endothermic as showns by the heat of reaction below:

The maximum capture capacity decreases with the number of carbonation/calcination cycles. This phenomenon is related to sintering and growing of grains after the first few calcinations that result in decreasing of the pores inside the particles and consequently reduction of the active surface area by the number of cycles (C. Salvador 2003, Gemma S. Grasa 2007, Robert T.Symondsa 2009, Juan Carlos 2002, N. Rodríguez 2010). In order to keep the operating system at a reasonable conversion rate of CO2 capture, fresh particles must be replaced as a make-up flow (Luis M. Romeo 2009) to cover the decay of capturing efficiency. Carbonation and calcination takes place at high temperature (around 650˚C and 950˚C respectively), although under certain conditions (see review by Bertos et al. 2004) carbonation can be achieved at room temperature. In comparison with low temperature capturing systems, the process is still cost effective and a worthwhile option especially if the CO2 is to be recovered,, because in low temperature systems the energy supplied for regeneration cannot be recovered efficiently (Rao 2002, Juan C. Abanades 2004). Due to the high reaction rate of carbonation, a fluidized bed is an attractive candidate for CO2 capture. On the other hand, recycling the well-reacted particles after regeneration though a calcinator indicates the intrinsic benefit of the process as a complete self-generating system. At present there is no comprehensive information available on the performance of a realistic fluidized bed reactor to capture CO2 with a solid sorbent. A good understanding of the gas-solid interactions, mass transfer potential and throughput capacity would be essential in designing a novel carbonator with optimum operating conditions.

Fluidized beds have been widely utilized in many different applications including combustion, gasification, catalytic cracking, etc. Many literature studies and mathematical models have been devoted to the subject, to understand the fluid and particle behaviour in fluidized bed reactors (Ding and Gidaspow, 1990, Gidaspow et al., 1994; Benyahia et al. (2000), Neri and Gidaspow (2000), Zheng et al. (2001), Enwald et al., 1996; Patil et al., 2005). There are two different classes of models for gas-solid fluidized bed modelling: Eulerian/Eulerian (continuum) models and Eulerian/Lagrangian (discrete particle) models. Lagrangian models solve the Newtonian equations of motion for each individual particle using effects of particle collisions and forces acting on the particle by the gas. Eulerian models consider all phases to be continuous and fully interpenetrating. The equations employed are a generalization of the Navier–Stokes equations for interacting continua. Owing to the continuum representation of the particle phases, Eulerian models require additional closure laws to describe the rheology of particles [Huilin and Gidaspow; 2003]. In this study, the Eulerian/Lagrangian approach of particle tracking with heterogeneous gas-solid reaction has been used to get a good understanding of this phenomenon in carbon capture in a fluidized bed reactor. The reactor has been modelled and simulated by the CFD technique using the finite volume method. Different particle sizes were investigated to find out the most suitable hydrodynamic operating conditions to handle fluidization and to keep the reactor operating at an appropriate gas-solid contact, considering the possibility of a high reaction rate and maximum utilisation of all the particles.

2- Modelling The CFD code PHYSICA developed at Greenwich was used as the framework to determine the behaviour of a fluidized bed reactor with a heterogeneous gas-solid reaction. Particle tracking in PHYSICA is based on the momentum interaction and mass transfer between the gas continuous phase and the solid particles. The connection between the continuous phase and solid particles is through source terms, transferred from the particle phase to the gas equations and conversely, forces acting on the particles by the surrounding gas. The particle equation of motion is then solved to determine the progression of the particle in time, until it leaves the calculation domain. The particles respond to the mean velocity field, but also to turbulent fluctuations in the gas.

2.1 Hydrodynamics of the reactor

You need to add the equations solved for the gas field here, showing in particular the location of the sources linking the gas with the particle field The continuity equation in gas phase is given as below: (

)

(1)

The conservation equation for the Cartesian velocity component can be written in the form: (

)

(

)

(

) (2)

Where the S terms are the sources into the equations. Solution of this set of equations determines both the velocity field, u, and the pressure field, P.The motion of any individual particle is calculated from the equation of motion: (3) (

)

(4)

Where mp refers to the mass of the particle and up,i indicates the velocity of the particle in i direction, uf,i is the gas velocity and CD is the drag coefficient. In Physica, calculation on of the particle track uses a time step that is independent of that which may be used by the continuous phase. This time step is determined by the user specifying the number of time steps a particle should take in moving across an element, calculated using the following equation: (5) (∑

)

(6)

Where d is the smallest face to element centroid distance for the element containing the particle, pe is the number of steps per element and Vp is the particle speed. The position of the particle is updated through the following equation: (7)

and

indicate the previous and current

particle velocity in the i direction. previous particle position and

is the

is the time step used.

Standard model used to as a turbulence model to consider the fluctuations in gas phase. The k-e model consists of the turbulent kinetic energy equation and the dissipation rate equation. The following constant values used in this application:

2.2 Carbonation kinetic model The following equation used to predict the conversion of CaO inside the computing domain [Gemma et al. 2009]. ( (

are given respectively the values 0.09, 1.0, 1.3, 1.44 and 1.92.

(

√

̅

(9)

The particle velocities are calculated through the momentum equations. Solving the particle momentum equation will give the following equation to update particle velocities: (

)

(

)

)

( (10)

)

Where and are the gravity acceleration in x and y direction ( equals to zero here), is the fluid viscous stress acting on the particle and is given as below: (11) Where dP indicates the particle diameter and , are the density of particle and fluid respectively. is the drag coefficient and Re the slip velocity Reynolds number (

)

(12)

(13) √(

)

(

)

(14)

) )

]

(15)

)

(

)

(17)

(18)

(8)

Where the is a random Gaussian number and k is gas turbulent kinetic energy calculated from gas flow field with kin calculation the gas velocity at particle position.

(

( (

(16)

To simulate the interaction of particles with the turbulent eddies in the gas flow field, a stochastic turbulence model is used, generating fluctuating velocities using a standard deviation based on the gas turbulent kinetic energy calculated in equation (6). ̃

)√ √

)[

(

) (19)

Where X represents the conversion of CaO and DP refers to the apparent product layer diffusion coefficient. D and ks are obtained by the Arrhenius equation. The parameter is a structural parameter and can be expressed as in the following equation: (

)

(20) Where S0 indicates the initial surface area per unit of volume, L0 refers to the initial total pore length in the porous system per unit volume and represents the porosity. 2.3 Boundary conditions Table (1) shows the boundary conditions applied for the 2-D simulation of a fluidized bed reactor. Particles’ initial position is located between 0.7m to 1.0m from the bottom of the reactor. The reactor with a 0.2m diameter has been expanded at 3m height to 0.4m diameter. The total height of the reactor is 8m. The gas flow containing 10% CO2 and 90% inert gas with the physical properties of feeds into the reactor near its base. The outlet is ventilated to the atmosphere, as a pressure outlet boundary condition.. The following exothermic reaction is considered inside the reactor, in which CO2 is diffusing through the gas phase to the particles surface and the reaction product is accumulated on the particles surface and porosity . Formation of product layer on the surface gradually

reduces the diffusion rate. This phenomenon is considered in the simulation with a linear reduction in the reaction rate. Since the product layer on the particles is only 50nm [Gemma et., al 2008] thick, it is safe to assume that the particle size remains constant. The reaction however increases the density of the particles, because the reaction product is accumulating inside the particle pores with no change on the particle size.

seems still carbonation reaction is going on nearly the outlet. This could be explained by solid volume fraction counter that indicates presence of middle size of particles fluidizing nearly outlet of the reactor. As a result, the size of this reactor must be longer than the one used in this simulation to achieve maximum possibility of CO2 capture.

Table1: boundary conditions Description Value Particle density(kg/m3) Particle diameter( m) Particles initial velocity(m/s) Gas inlet velocity(m/s) Gas initial temperature(ºC) Bed width(m) Bed high(m) Particles sphericity

3340 0.0 3.79 650 0.1-0.2 8.0 1.0

3- Results and discussion Simulation results show that there are different high density regions inside the reactor allocated to the different particle sizes (Figure 1). For large particles, the associated dense region is located in lower middle of the reactor by the expansion area. For middle-size particles, it is situated in lower top of the reactor, while accumulation zone. This simulation indicates that for a range of particle diameters there is a strong correlation between hydrodynamic parameters such as the geometry of the reactor and particle concentration that could be a key factor in using all the available capacity of the load to capture CO2 and obtain the fastest reaction conversion inside the reactor. The residence time of particles can be controlled by the gas fluidization velocity which depends on the particles density and diameter in a balance between the drag force and gravity. Separation of particles by dividing the reactor into a set of zones of different gas velocity can be an important aspect of energy saving and allowing operation at a maximum achievable capture capacity. Figure 2 shows CO2 volume fraction along the centre of the reactor with an initial concentration of 10 % CO2 in the view of the fact that CO2 produced in coal combustion amounts to 10-12% of generated flue gases (Bhurisa Thitakamol 2007, Carlo Giavarini 2010). The simulation predicted a sharp reduction in between the expansion area occupied by heavier solid particles. It

Figure 1: Solid volume fraction inside the reactor (vfrac) all particles together (vfrac1) particles with 200 in diameter (vfrac2) particles with 150 in diameter and (vfrac3) particles with 100 in diameter.

Comparison between two different geometries shows that the expanded reactor can remove much more CO2 against the straight reactor with no expansion. The simulation results shows that the expanded reactor could capture around 36% of CO2 entered in inlet gas flow, while with same concentration of inlet flow and solid mass the capture could reach to 27% of CO2 removal. Using an expanded reactor not only can handle floatation of various range of particle sizes, but also will increase the capture capacity allowing the particles remain inside the reactor to be well reacted before leaving the reactor. In this case it increases 25% the capture capacity in comparison with a straight reactor and a uniform particle size.

0.1

CO2 Volume Fraction

0.095 Straight

0.09 0.085

Expanded

0.08 0.075

Figure 3. solid volume fraction profile along the centre of the reactor (top), gas velocity (bottom)

0.07 0.065

Figure 4 shows the normalized particle residence time at each cell in the computational domain.

0.06 0

1

2

3

4

5

6

7

8

(21)

Centre Line of the Reactor (m) Figure 2. comparison of CO2 concentration profile along the centre of the reactor in two different geomteries. Figure 3 (top) shows the Normalized particle’s volume fraction along the centre of the reactor. It slightly shows two maximum points that the first one refers to particle’s injection area but the second and global maximum indicates the transient region in expansion area that heavier particles stay in that portion of the reactor. The fluid velocity goes (Figure 3 (bottom)) down in expansion area and will do stop heavier particles in that region and smaller particle’s are fluidized above that region.

.

Where indicates the normalized residence time, is the maximum residence time in a cell and is the residence time at each cell. In Figure 3 there are 3 significant zones occupied by the particles. The one in the lowest section designates the position of fresh particles supplied to the reactor. The second zone is located in the middle of the reactor, just below the expansion area, representing big particles that cannot move up due to the reduction in gas velocity as the flow area expands, leading to a decrease of drag force against the gravity. Consequently those particles reside in that region until they get fully converted. The third dense zone corresponds to the middle size particles (150 ) that nearly reach the outlet but still remain in the reactor. Due to the carbonate building into the particles, the largest gradually sink to the bottom of the reactor where they may be collected. Medium size particles have the longest residence time, since they cannot escape below the expansion zone even on full conversion. The smallest size particles mostly leave the reactor without reaching getting ultimate conversion. However, since they also increase the reaction area per unit mass considerably, they still contribute to its collection efficiency. Particles travelling from their

initial position in the bottom to the top of the reactor undergo a fast initial carbonation reaction stage.

( )

(23)

Figure 4 shows a good agreement in both the simulation result and carbonation model by Gemma et., al 2009, but there is an initial overprediction by Gemma’s model of the reaction controlled model, while the simulation result shows a much closer agreement. Both models under-predict the maximum conversion in the reaction-controlled stage. 0.8 0.7

X (CO2 Conversion)

0.6 0.5

Experimental data by Gemma et., al 2009 Simulation result

0.4 0.3

Carbonation model by Gemma et., al 2009

0.2 0.1 0 0

20

40

60

80

100

120

140

t (sec) Figure 5. comparison on conversion curves: a simulation result (Left) and those predicted by Grasa et al. (2009) in different Cycles via experimental work. Figure 4. Normalized particles residence time inside the reactor

Figure 5 shows a particle conversion curve, until leaving the computational domain. It shows that at first a fast carbonation reaction is followed by a slow diffusion-controlled mechanism. It seems operating at the fast reaction-controlled stage would be much more efficient rather than trying to achieve the fullest possible conversion, that needs much more time and incurs an energy penalty, since after a fast carbonation stage the reaction rate is not really significant. Comparison between the simulation result and experimental data gives a good agreement. In the simulation, the experimental model by Grasa (2009) has been modified considering the sintering effect on diffusion and active surface area using an exponential correlation: (22)

4- Conclusions A fluidized bed reactor has been modelled using an Eulerian/Lagrangian CFD model that considers particle tracking and heterogeneous reaction associated with the carbonation reaction between CaO and CO2. The study highlights the importance of several key factors in a fluidized bed reactor that are key to a successful design. This simple expanding design was shown to yield a 36 % reduction of the inlet flue gas stream. The gas-solid contact has been studied with regard to the hydrodynamics of particle fluidization and mass transfer due to the carbonation reaction. The results indicate that different solid zones exist inside the reactor corresponding to different particle seizes. The simulation can predict the correct reactor dimensions based on the ultimate conversion required. The particle residence time is another important parameter in the design and this model has the capability to give enough detail of the residence time and collection of particles depending on size. This is still a preliminary result and research is still ongoing to investigate other key factors

affecting carbonation. However, the evidence given by the model is that such a design is possible and a practical menas of removing CO2 emissions from large sources with existing technology.

̃: fluctuation velocity : velocity of particle [m/s] : direction of i [m] : conversion of CaO

Nomenclature

: previous position of particle at i direction [m]

: stoichiometric coefficients for carbonation reaction : Concentration of CO2, [kmol/m3] : drag coefficient : Effective product layer diffusivity, [m2/s]

: current position of particle at i direction [m] : ratio volume fraction after and before reaction : time step [sec] : Residence time

: Pre-exponential factor in Eq. 10, [m2/s]

: structural factor of particle

: Particle diameter [m]

: porosity of particle

: Activation Energy [kj/mole]

: density [kg/m3)

: Reaction correlation factor

: viscosity [kg/(m2s)]

: Gravity [m/s2]

: random Gaussian number

: Rate constant for surface reaction, [m4/kmols] : Pre-exponential factor in Eq. 7, [m4/kmols] : Initial total length of pore system, [m/m3] : Molecular weight of CaO, [kg/kmol] : Mass of particle [kg] : Gas constant [m3 Pa K−1 mol−1] : Reynolds number : Time [sec] : Temperature [

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] Carbon8 Systems, http://www.c8s.co.uk/technology.php

: gas velocity at i direction[m/s] : particle velocity at x direction[m/s] : velocity at i direction ̅ : average gas velocity at particle position [m/s] : particle velocity at y direction[m/s] : particle velocity at i direction : slip velocity [m/s] : previous velocity of particle at i direction [m/s]

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