Article pubs.acs.org/IECR
Simulation of the Effect of Various Operating Parameters for the Effective Separation of Carbon Dioxide into an Aqueous Caustic Soda Solution in a Packed Bed Using Lattice Boltzmann Simulation Dwaipayan Sen,†,‡ Santanu Sarkar,† Sangita Bhattacharjee,§ Sibdas Bandopadhya,⊥ Sourja Ghosh,⊥ and Chiranjib Bhattacharjee*,† †
Department of Chemical Engineering, Jadavpur University, Kolkata, India Heritage Institute of Technology, Kolkata, India ⊥ Central Glass and Ceramic Research Institute, Kolkata, India §
ABSTRACT: Nowadays, reduction of the carbon footprint in the environment is one of the most challenging issues, and thus several technologies have been adopted for the effective arrest of carbon dioxide (CO2). Among these, packed-bed absorption using caustic soda is one of the simplest and widely accepted separation strategies for CO2. However, the intricate issues that make the process a bit complicated are the selection of operational parameters such as gas velocity or the caustic concentration for efficient separation. Moreover, the most significant one is the blockage of the pores within the packed-bed column that lead to a reduction in the effective mass-transfer area and, therefore, less separation. In order to analyze these operational paradigms, one needs to explore the process internal fluid dynamics pattern for long-term operation. In this present work, an attempt was made to enumerate this flow field in a packed bed using a lattice Boltzmann simulation technique, an extended concept of lattice gas automata. Moreover, using the simulation technique, the gas inlet velocity to the column and the caustic soda concentration were estimated for effective CO2 capture. The model shows a minimum absolute percentage error of 0.0005 between the predicted and experimental CO2 outlet concentration.
1. INTRODUCTION Pollutants’ emissions to the environment from industries and refineries are one of the major contemporary potential threats that are globally recognized. Considering the demand for primary energy needs, the burning of fossil fuel, and thereby inheritance of energy from it, occupies more than 80% of the global energy market.1 The burning of fossil fuel, primarily hydrocarbons, emits carbon dioxide (CO2), which is accounting for nearly 40% of the total global CO2 emissions.2 Moreover, CO2 exhibits 60% of all of the greenhouse gases to the global warming issue and, therefore, demands the arrest of CO2 from the effluent stream before release to the environment.3 Over the past 2 decades, its concentration in the atmosphere has significantly increased1 and, therefore, initiates a proper strategy development to capture CO2 along with its storage. This approach attributing to CO2 capture and storage is universally called CCS technology.1 Several methods have been adopted so far by the research fraternities to capture CO2 from an industrial effluent gas stream that primarily includes absorption, adsorption, cryogenic separation, and membrane-based separation.4−7 Among these several methodologies, absorption-based separation is one of the frequently used technologies8 that has been adopted by a number of industries to capture CO2. Packed-bed absorption is one the most convenient schemes9 that is still running in several industrial sectors even with a constant search for constant economical technologies such as biological or membrane routes to CO2 capture. One of the intricate issues in any packed-bed system is the residence time of gas−liquid contact within the column, which mainly depends © 2013 American Chemical Society
on the type of packing along with other operational parameters. Moreover, its performance toward the arrest of CO2 has been enumerated by the actual flow dynamics through the interstitial spaces and the kinetics of the system.8 Random and structured packed-bed columns are mainly two broad classifications of packing geometries that are universally accepted. Compared to the random-packing element, structured packing is of regular geometry with low pressure drop. However, it is obvious that, with the unordered geometry, the gas−liquid contact time with random packing is more compared to the structured one. Now, to evaluate the mass-transfer operation, modeling of the process is of paramount interest for the researchers. Especially, the flow dynamics, and thereby its effect on the absorption process along the packed-bed column, necessitates the development of a mathematical approach toward the separation process analysis. Aroonwilas and Tontiwachwuthikul9 and Sun et al.10 developed a mechanistic model to predict the absorption process performance for structured and random packed-bed columns, respectively. However, these models were more inclined toward analysis of the solvent distribution inside the column instead of absorption due to a chemical reaction. Especially, in the case of a multiphase system, as during CO2 absorption using a basic solvent, the development of a mechanistic model is complex and depends on several assumptions that reduce the prediction accuracy. Multiphase Received: Revised: Accepted: Published: 1731
July 23, 2012 November 22, 2012 January 7, 2013 January 7, 2013 dx.doi.org/10.1021/ie301954c | Ind. Eng. Chem. Res. 2013, 52, 1731−1742
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flow coupled with a chemical reaction requires mathematical modeling at the macroscopic level where the continuum assumption relates the mesoscopic insight of the process. Moreover, the approach is more realistic for the packed-bed system, where all mass-transfer phenomena occur at a porous length scale. To understand such fluid flow behavior within the packed-bed column and, hence, mass transfer in the case of a reaction-coupled multiphase process, computational fluid dynamics (CFD) is one of the convenient simulation tools appreciated by several researchers.11 However, according to Yoshino and Inamuro12 and Joshi and Ranade,13 the adaptation of CFD introduces numerical instability in the case with finitevolume analysis for complex boundary conditions related to a packed bed. Furthermore, the CFD technique to solve the flow domain from a macroscopic viewpoint sometimes makes the solution process complicated in dealing with the complicated boundary conditions or molecular-level interaction. Therefore, to counteract the limitations in CFD, a new method, called the “lattice Boltzmann method” (LBM), was proposed by McNamara and Zanetti14 in the late 1980s. In the case for prediction of the fluid flow behavior in a microsystem, it is essential to correlate the thermodynamics and boundary conditions as a consequence of the dynamics in this physical microsystem. However, upon incorporation of such mathematics in the computational domain to solve the flow dynamics, the number of degrees of freedom overpopulates, which might not be necessary in solving the flow field. Therefore, it is quite convenient to construct an artificial microsystem that is easy to simulate but yet encompasses all of the physics that actually describes a realistic fluid system. The LBM is based on the construction of such an artificial microsystem15 and bridging of the lattice gas automation (LGA)16 with the conventional computational strategy. In the LGA, the algorithm is based on the concept called “bit democracy”,17 where the particle’s presence at a particular position in the computational domain at a specific time instant was represented by “1” or “0”. However, the LBM extends the LGA with an improvement toward the elimination of statistical noise by replacing the concept of “bit democracy” with an ensemble averaging.17 One of the primal features in the LBM is the information passing at a mesoscale level to solve the system’s thermodynamic properties and complex boundary conditions locally (Shan and Chen, 1993).15 Moreover, the LBM recovers fully the Navier−Stokes equation at a macroscopic level, and thus it correlates the mesolevel computation with the continuum assumption.18 Unlike CFD, in LBM simulation, the computational domain was disintegrated into several lattice blocks. In the case with a packed-bed absorber for CO2 capture, the absorber can be considered as a combination of microreactors and the system requires a powerful tool to investigate the problem at a pore-scale level. Hence, the LBM, which deals an ensemble averaging technique at mesoscale, demands more attention to simulate a packed-bed column compared to a continuum-based CFD technique that solves Navier−Stokes at a macroscopic scale. Several studies had already been reported on the applicability of the LBM to simulate the fluid flow dynamics within a porous structure. Especially, the LBM is a very well-known application tool among researchers who are pursuing their investigation on geosciences.19 The percolation of fluid through the porous soil structure and, thereafter, simulation of the process to investigate their flow dynamics using the LBM is a very common topic of investigation among researchers. Kang et al.20
had developed a mathematical model based on the LBM for the oceanic depletion of CO2 to make a thorough study on the pattern of storage, chances of hydrate formation, and fate of the porosity due to hydrate formation. Manjhi et al.21 made a study on the applicability of the LBM for a packed-bed absorber. According to the author, use of the LBM provides an option to investigate the radial and axial dependences of the examined parameters without incorporating any existing correlations that could lead to an assumption. Khirevich et al.22 had simulated the flow field for a solvent within a packed-bed column, and the effect of porosity on the flow was analyzed using a LBM technique. However, the LBM simulations that have been done so far for packed-bed systems emphasize primarily the structured packing. Therefore, limited literature on randompacking simulation initiates the present work to develop a mathematical model based on the LBM on a packed-bed absorber for CO2 arrest. The current study applies the LBM to simulate a packed-bed column with random-packing elements in three dimensions, where the local kinetics of the fluid have been coupled with the reaction. A Bhatnagar−Gross−Krook (BGK) collision operator23 was applied for the collision step following streaming of the particles when streaming was initiated because of the developed local concentration gradient due to reaction. Unlike CFD, the whole three-dimensional (3D) computational domain was divided into four-dimensional (4D) face-centered cubes.14 Specifically, the problem was analyzed for variation of the Peclet number (Pe), solvent concentration, and bed porosity because these are the parameters that fully describe the reactive flow dynamics within the packed-bed column. One of the simplest aspects in this current model is the coupling of the reaction term as an external force field with the diffusional gradient term represented here as collision−streaming sequences, a basic approach toward the formulation of a kinetic LBM model, instead of formulating another stochastic equation for the reaction term. This reduces the computational effort and also conceptually establishes the fact that the concentration gradient because of the reaction promotes streaming of the particles, leading to collisions.
2. EXPERIMENTAL AND SUBSEQUENT THEORETICAL CONSIDERATION FOR MODEL FORMULATION 2.1. Experimental Procedure. The experimental setup for a packed-bed column (make: borosilicate glass of diameter 0.055 m and length 0.75 m) with a packing of raschig rings (make: borosilicate glass of different nominal diameters for varying porosity given in Table 1) was procured from K.C. Engineers, Haryana, India, and was used to selectively absorb CO2 from an air−CO2 gas mixture using a caustic soda (NaOH) solution (a flow rate of 150 L h−1 measured by a rotameter having the range 0−200 L h−1 and calibrated with ±10% accuracy) according to the following chemical reaction at Table 1. Size and Number of the Raschig Rings Loaded within the Column for Different Bed Porosities
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bed porosity
nominal diameter of the raschig ring (m)
number of packing elements
0.1 0.3 0.5 0.7
0.0010 0.0015 0.0020 0.0025
3062813 697641 212695 66361
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a column temperature of 308 K (35 °C). One of the primary reasons for using a caustic soda solution as a solvent to absorb CO2 is its simple kinetics and its low-cost regeneration technique to reutilize in the process again compared to other solvents such as amine.24,25
the sample without any interference of Na2CO3 during acid titration. Equation 1 shows enumeration for the percentage of CO2 absorbed. Na 2CO3 + BaCl 2 = BaCO3 ↓ + 2NaCl
2NaOH + CO2 = Na 2CO3 + H 2O
percentage of CO2 reacted =
Figure 1 shows the setup of the experimental procedure. NaOH solutions of 0.25, 0.5, 1, and 2 N were fed at the top of
(1)
2.3. Assumptions Taken during Simulation of the Packed Bed for CO2 Absorption Using the LBM. The LBM, a computational paradigm, was adopted here to simulate the CO2 absorption process using NaOH in a packed-bed absorber. In most of contexts, where the LBM is usually simulating a reaction domain, the flow field requires two different sets of differential forms. One simulates the hydrodynamics of the fluid flow, and the other simulates mass transport of the reactive species.28 This might be because of two different time scales for reactive mass transport and flow dynamics.29 However, in this case, the rapid reaction between CO2 and NaOH dictates a relevant assumption of a comparable time scale between the momentum and reaction. Moreover, it is assumed here that the change in the mass density or concentration within the packed bed due to reaction creates a concentration gradient, which results in the particles streaming and, henceforth, collisions formulated by a BGK collision operator. Assumptions that were considered during the formulation of the simulation model are given below: (a) The corners of the cubic lattice blocks of type D3Q19 were assumed to be the nodes representing the solid packing elements. These nodes are considered as spheres resembling the raschig rings (sphericity = 1). The distance between the spherical corner nodes is proportional to the porosity of the bed. Therefore, if the porosity of the bed decreases, the distance between two neighboring nodes will also decrease and vice versa. A representative computational domain was stripped out from the packed bed, as shown in Figure 1, and was discretized with Nx × Ny × Nz, the number of grids along the x, y, and z axes that are adjusted according to the porosity of the bed. (b) No external body forces are acting on the fluid particle. (c) The effects of viscous dissipation are negligible because of the flow execution in the low-Reynolds-number regime (100 < Re < 500). (d) The reaction does not release or absorb sensible energy that could change the temperature along or across the bed. (e) The reaction is assumed to be the pseudo-first-order system where a change in the NaOH concentration along or across the bed is negligible. Therefore, the production rate of CO2 is given as follows:
Figure 1. Experimental setup showing the packed-bed column for the separation of CO2 from a CO2−air mixture using a NaOH solution.
the column with a flow rate of 4.2 × 10−5 m3 s−1 (150 L h−1) through a liquid distributor. The concentration of CO2 introduced to the column was 0.164 kg m−3 (≈9.0 mol %), a typical CO2 content in the flue gas from a coal-fired power plant,26 and it was adjusted by the flowmeters (measured by a rotameter having the range 0−100 L m−1 and calibrated with ±10% accuracy) attached to both air−CO2 feed lines. The flow rate for CO2 and air has been provided in Table 2 for a bed Table 2. Flow Rate of CO2 and Air Fed into a Column of Porosity 0.5 during the Experiment bed porosity
CO2 flow rate (×105 m3 s−1)
air flow rate (×105 m3 s−1)
0.5
2.4 3.2 3.9 5.0 6.5 11.2
23.9 31.9 39.8 51.0 65.3 113.2
in out S C NaOH − C NaOH × 100 in G 2CCO 2
porosity of 0.5. The liquid collected at the bottom of the column was analyzed for CO2 absorbed by titration using barium chloride,27 which is elaborated on in the following subsection. 2.2. Analytical Procedure for Detection of the Percentage of CO2 Absorbed. A total of 10−5 m3 (10 mL) of a CO2-enriched solvent was collected as a sample from several sample locations along the length of the packed tower followed by the addition of 3 × 10−6 m3 (3 mL) of 1 N barium chloride (BaCl2), 0.2 N hydrochloric acid (HCl), and one drop of phenolpthalein to the sample. Primarily, sodium carbonate (Na2CO3) present in the sample because of CO2 absorption in a NaOH solution will precipitate out as barium carbonate (BaCO3) according to the following chemical reaction. This ensures only the reaction between HCl and residual NaOH in
dCCO2 dt
= (kIIC NaOH)CCO2 = kIpseudoCCO2
(2)
(f) The motion of a fluid particle was induced by both collision and the concentration gradient developed because of the reaction. (g) There is no interaction force between the molecules due to phase separation that could influence the flow field. 2.4. Simulation Strategy Using the LBM for CO2 Absorption by NaOH in a Packed Bed. Figure 2 describes the algorithm followed for the present LBM simulation. In the LBM, the probabilistic mass density distribution function is expressed as f i,j(x,t) at a location x and at a time instant t. Here, 1733
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Figure 3. D3Q19 lattice block.
collision operator manifests the relaxation of f i,j(x,t) toward the equilibrium distribution f eq i,j (x,t) with a single characteristic time ω. The macroscopic concentration (ρi) and velocity (Ui) are evaluated from eqs 7 and 8, respectively. 19
ρi =
∑ fi ,j (x , t )
mass conservation equation (8)
j=1 19
∑ ejfi ,j (x , t )
Uiρi =
momentum conservation equation
j=1
(9) Figure 2. Algorithm for the LBM simulation.
The concentration gradient that was developed within the packed-bed system, because of CO2 absorption, induced the flow of CO2 in the bed along with the kinetic collision factor. However, the movement and reaction phenomena are expressed here by two dimensionless numbers: the Peclet number (Pe; eq 10) and the second Damkohler number (DaII; eq 11), respectively.20
i refers to the fluid component and j refers to a particular node of the D3Q19 lattice. Simulation of the domain was exclusively guided by two subsequent phenomena: streaming of the particles (eq 4) and thereafter collision of the particles (eq 5) with a velocity ej (eq 3) toward the neighboring node.23 Figure 3 shows the schematic diagram of the lattice block.
Pe =
ej = ⎧ (0, 0, 0) j=0 ⎪ ⎪ ⎨ (± 1, 0, 0) (0, ± 1, 0) (0, 0, ± 1) j = 1, ..., 6 ⎪ ⎪(± 1, ± 1, 0) (± 1, 0, ± 1) (0, ± 1, ± 1) j = 7, ..., 18 ⎩ (3)
fi , j (x + ejΔt , t + Δt ) = fi , j (x , t )
DaII =
fi , j *(x + ejΔt , t + Δt ) = fi , j (x + ejΔt , t + Δt ) + Ω (5)
where Ω is the collision operator given by a BGK collision operator (Bhatnagar et al., 1954)23 described by eq 6. 1 Ω = [f ieq (x , t ) − fi , j (x , t )] (6) ω ,j 2 2⎤ ⎡ ejUi 1 ⎛ ejUi ⎞ 1 ⎛ Ui ⎞ ⎥ ⎢ t ) = wjρi 1 + 2 + ⎜ 2 ⎟ − ⎜ ⎟ ⎢⎣ 2 ⎝ cs ⎠ 2 ⎝ cs ⎠ ⎥⎦ cs
kIpseudoLc 2 reaction velocity of the solute = D molecular diffusion of the solute (11)
(4)
(x , f ieq ,j
(10)
Pe and DaII were again recombined to get another dimensionless number that relates the advection of the solutes with the reaction velocity and is called the Damkohler number (DaI; eq 12). Equation 13 describes the mass density distribution change due to reaction. DaII DaI = (12) Pe
streaming operation
collision operation
UL advection of the solute i c = D molecular diffusion of the solute
fi , j (x , t ) = fi , j (x , t − Δt )[1 − wDa j I]
(13)
However, it is evident from the concept of the particle’s migration that the reaction happens in accordance with the migration of the particles on different nodes of a lattice block, and this migration depends on the probability at which the particle moves toward the different lattice nodes from its rest position. Hence, eq 13 includes the probability term wj multiplied by the rate term DaI. It was assumed that the whole packed bed was primarily at a steady state and filled with gas only. Therefore, at t = 0, the macroscopic velocity is 0 and the concentration throughout the bed is uniform. This
(7)
f eq i,j (x,t)
where is the equilibrium mass density distribution and ω is the BGK relaxation term that needs to be set between 0 and 2 to obtain a stable solution for the system.30 Here the 1734
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assumption leads to an initial estimation of f i,j(x,t) (eq 14) and f eq i,j (x,t) (eq 15). ρ fi , j (x , t ) = where ρ = ρ0 = ρ1 = .... = ρ18 (14) 19 f ieq (x , t ) = wjρi ,j
optimized condition, one needs to understand the packed-bed dynamics at a mesoscaled level. The LBM provides an opportunity for such analysis or, more specifically, to judge the computational domain from a local view instead of the global one. Thus, understanding the local variation in the computational domain helps to analyze the packed bed at pore scale, which, in turn, portrays the inherent hydrodynamics of the system to the researcher. However, the primal intricacy of such a simulation is to accurately represent the packing domain that exists in reality. The flow field within the packed-bed column is more unordered for a random packing compared to a structured one. Now inclusion of such an unordered scenario in the simulation model makes the model complicated and difficult to solve. Moreover, the occurrence of a multiphase system, where mass transport of CO2 gas happens through a chemical reaction with a caustic soda solution makes the system more complicated to analyze through the development of a mathematical simulation technique. However, a sensible effort on the proper design of the lattice Boltzmann simulation environment will reduce the complicacy and can address all aspects of paramount interest during the simulation. Therefore, the current section is an attempt to analyze the system’s dynamics and feasibility using the lattice Boltzmann simulation technique to make a guess on the operating parameters that are preferred to be maintained. In subsection 3.1, the effect of the porosity on the CO2 arrest has been studied to understand how mass transfer is affected by the reduction in the pore sizes. Here the porosity reduction was compared with a common fact in the packed bed, called “pore blocking”. Figure 5 is a schematic representation of the various
(15)
No-slip boundary condition at the wall had been represented here by the bounce-back boundary condition31 in the LBM. At the entry and outlet zone of the packed-bed column, a periodic boundary condition was applied. In the present context, the bounce-back condition is applied against a curved boundary that is actually the boundary created by the solid wall of the column according to the algorithm proposed by Mei et al.32 According to them, the solid curved boundary must lie between the lattice nodes of spacing Δh. Figure 4 shows the actual idea
Figure 4. Layout of the regularly spaced lattices and curved boundary wall for the packed-bed column.
behind the consideration of the curved solid boundary between the nodes. After streaming of the particle, the bounce-back velocity from the wall toward the node is given by eq 16. ub, j =
Δ−1 ej Δ
(16)
where 0
