_{2}Capture from Coal Syngas

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Gasification of coal or biomass with _{2} capture is an emerging technology aiming to address the problem of climate change. Development of a CO_{2} sorbent with desirable properties and understanding the behavior of such a material in carbonation/calcination reactions is an important part of developing the technology. In this paper, we report experimental results describing the carbonation behavior of three synthetic CaO-based sorbents. We also present a physically-based model of the reactive transport processes in sorbent particles, which have complicated pore structures. This modeling is based on the conditional approach (

_{2}capture

Extensive efforts have been devoted worldwide to developing CO_{2} mitigation technologies in order to address the problem of climate change. Gasification of coal/biomass with _{2} capture is an emerging technology aimed at addressing this issue. The technology simultaneously allows production of clean hydrogen at relatively low cost while reducing the release of CO_{2} into the atmosphere. The process is carried out using two reactors: the gasifier and the calciner. Coal/biomass reacts with steam in the gasifier to produce hydrogen (H_{2}). The heat required for this reaction is supplied by the exothermic carbonation reaction (CaO + CO_{2} = CaCO_{3}), in which CO_{2} is also consumed. In this way, high purity H_{2} is generated. The reacted sorbent particles are separated from the product gas and transferred into the calciner for regeneration.

Carbonation/calcination of CaO-based sorbents, which is also known as the calcium looping cycle, is considered to be an economically viable CO_{2}-capture technology [_{2} sorption capacity over cycles, synthetic CaO based sorbents have been developed [

In order to assist in selecting optimal parameters of the carbonation process, which is an illustrative example of a reactive flow through complex porous media, a comprehensive, physically-based model of such processes is required. Traditionally, a porous medium is characterised by two phases: the fluid β-phase and the solid σ-phase [

The regime of the heterogeneous reaction is determined by the balance between the reaction kinetics and the rate of transport of the reactant to the reactive surface. This balance is described in terms of the Damköhler number

Another approach is one—which, by analogy with other areas of Fluid Mechanics, we call direct numerical simulation (DNS). In this approach, the reactive flow is simulated over the gas phase only, while the boundary conditions are defined on gas-solid interface. The prerequisite for this approach is the ability to represent the pore structure in a way suitable for such simulations. This approach does not include averaging and allows simulating reactive flows as accurately as possible. Clearly, exact simulation of real porous media is problematic. As a result, some models have to be used. Accuracy of DNS method comes at an enormous computational cost. This cost makes the DNS method practically inapplicable for large domains and for porous media with complicated porous structures. Determining and simulating the structure of pores in such media, where the pore size can vary over many orders of magnitude, is an extremely difficult problem by itself.

Practically, the exact pore structure can be approximated by an artificially created system of relatively simple pores, which is intended to reproduce some characteristics of the realistic pores. Such simulations, which can be referred to as incomplete DNS (IDNS), still deal with non-averaged quantities and should be distinguished from the methods based on averaging. IDNS allows for a substantial reduction in computational cost. In this case, however, one could not expect the same accuracy due to incomplete reproduction of the realistic pore structure and, possibly, other simplifications.

An alternative approach, which addresses these challenges, has been recently introduced [

Conditional models become the most effective when traditional volume averaging is replaced by more mathematically sound and convenient ensemble averaging. The ensemble-spatial averaging theorem, which is the ensemble analogue of the spatial averaging theorem [

It is important to note that the presented CMC methodology is general and independent of the sub-models used to describe diffusive characteristics of a porous medium or kinetics of heterogeneous and homogeneous reactions. In fact, one can use virtually any sub-models, which are dictated by real conditions or regarded as appropriate from separate considerations. The approach is applicable to a variety of reacting flows through porous media.

Below we present a spectrum of models that can be effectively used to accurately model a wide range of reacting flows through porous media. In this paper, we briefly summarise theoretical developments of the previous studies and also present the results of computational modelling of the carbonation process in sorbent particles, while comparing these results to experimental data. Before presenting the conditional approach we briefly discuss the phenomena involved in the carbonation process.

The CaO based sorbents are porous materials with complicated porous structures with fractal properties. Such media are characterised by geometrical similarity of pore structures at different scales (micro-, meso- and macro-pores) and by the predominant location of the reactive surface (CaO) within the smallest pores. Transport in such porous media involves complex cascade diffusion through pores of different sizes (micro-, meso- and macro-pores). In the experiments described in Section 4.1, the pressure at the outer border of spherical sorbent particles remains approximately constant. However, the convective transport could not be neglected a priori. Indeed, the consumption of CO_{2} at the reactive surfaces inside a sorbent particle can cause non-zero pressure gradients and, therefore, non-zero gas velocities. Although convective transport predominantly occurs through the largest pores and fractures, the convective term should also be taken into account.

Traditionally [

The traditional approach is suitable for modelling the reactive transport if the heterogeneous reaction is in the kinetics-controlled regime (

The reactive transport in porous sorbent particles is complicated by the formation of the product layer (CaCO_{3}) over the reactive surface. Such a layer alters the pore structure and, more importantly, substantially reduces the apparent rate of the carbonation reaction by slowing down the transport of the gaseous reactant to the reactive surface [

The conditional moment closure (CMC) methodology was proposed in the early nineties [

As discussed above, the traditional approach [

The conditional approach distinguishes two types of fractality in porous media: interface and network (see Section 10 in [

We note, however, that the regime of the heterogeneous reaction is not known a priori. Furthermore, the true rate of the carbonation reaction (on clean CaO surface) is, practically, not accessible to measurements. Instead, information about the true rate can be inferred from modeling of the carbonation behavior of real samples. Below we describe the conditional modeling of the carbonation behavior of the sample CaAlWM.

The main idea utilised in the PCMC model is linking transport of different reactive scalars to and from the phase interface to a single scalar—the tracer scalar

The reactive flow within the β-phase is governed by the continuity:

Here, ρ and _{i}_{i}

The diffusive tracer _{Z}

This ensures that _{Z}_{Z}

The tracer is instantaneously consumed at the reactive surface, so that

The equations of the PCMC model are expressed in terms of conditional Favre averages. For an arbitrary function _{z}_{z}

Averaging _{i} ≡ (Ȳ_{1})_{z}, we arrive at the following equations of the PCMC model:
_{Z}

If the reactive surface is not resolved by the conditioning variable, the source terms _{i}_{z}_{i}_{Z}

Thus, _{i}_{i}

Note that consistent modelling of both _{Z}_{z}_{Z}

Alternatively, the distance to the phase interface can be parameterised by the distance tracer

The PDCMC model equations are formulated in terms of conditional averages [_{r}_{r}_{r}_{r}_{r}_{R}_{R}_{R}^{α}

In terms of the averages conditioned on

A superficial PDF, normalised as in _{i}_{l}

The last terms in

In the case of interface fractality, the PCMC and PDCMC models are equivalent at the modeling level. This means that with a consistent choice of the parameters of the models, PCMC and PDCMC can be obtained from each other by replacement of variables. The interface-resolving versions of the models (

Determining transport coefficients for conditional models is a problem, which can be solved by performing DNS on a small test volume or by adjusting the coefficients in according with experimental data. The NEMA-DCA approach, which can constructively determine transport coefficients for network fractality while taking into account percolation effects for arbitrary irregular networks of pores, seems most promising.

Determining transport coefficients in realistic porous media is a challenging problem, especially under conditions when network fractality plays a significant role and percolation effects may become prominent. The goal of determining transport properties in porous media with irregular structure and varying percolations can be achieved by using NEMA-DCA, which represents a merger of a DCA with a generalized, NEMA. The generalisation is needed since Kirkpatrick's original single-bond EMA [

For this approach, the porous medium is seen as a random network, in which the pores are the nodes of the network; each pore has an associated random vector of properties _{i}_{1},_{2},_{3}), and can also contain other pore properties. In particular, the inclusion of pore size as one of the properties denoted by _{1},_{2},_{3},_{i}_{j}

The proposed method derives a continuous transport equation from this model via an averaging approach, but with two steps. The first step employs an effective medium approximation in order to account for the network's connectivity in a continuous model. If this step was skipped, the continuous model would simply neglect such effects, resulting in significant inaccuracy. The latter step consists of a conditional ensemble average over possible realizations of the network structure; as with the CMC approaches discussed in other sections, this average is conditional and retains dependence on parameters of the pore network. Most notably, the distance tracer

For the EMA, each throat conductance distribution _{i}_{j}_{i}_{j}_{i}_{j}_{i}_{j}_{i}_{j}_{i}_{j}_{in}

After taking the generalised effective medium approximation, conditional ensemble averaging gives the effective diffusion tensor _{2}(Δ

The NEMA-DCA approach has been shown to give accurate results even under conditions when a conventional diffusional approximation would become highly inaccurate due to percolation effects, or diverge without producing a finite value for the coefficients [

Three synthetic CaO sorbents denoted as CaCSG, CaCPM and CaAlWM were studied here. The samples CaCSG and CaCPM were made from calcium hydroxide and high aluminate cement by the simplified sol-gel and physical mixing methods respectively. They both contain around 15% CaO in the final sorbent. The sample CaAlWM was made from calcium _{12}Al_{14}O_{33} as inert support. The chemical compositions of the cement and the detailed preparation procedure used to make the sorbents are given in [

Adsorption of N_{2} on a sorbent was performed on a TriStar 3000 instrument (Micromeritics Instrument Corporation, Norcross, GA, USA) in order to evaluate its Brunauer, Emmett and Teller (BET) surface area and pore volume, parameters of which were used to calculate the initial surface area and porosity of CaO and CaCO_{3}. Before the test, the fresh sorbent was degassed at 250 °C overnight. Then adsorption of N_{2} was accomplished at −196 °C in liquid nitrogen. The properties of the samples are summarised in

The carbonation behavior of the samples was measured using a Cahn-131 thermogravimetric analyser (TGA) (Thermo Fisher Scientific, Newington, NH, USA) at five different temperatures in the range of 550–750 °C. The schematic diagram of the experimental setup is shown in _{2} stream with volumetric flow rate of 85 mL/min. After 10 min holding at 900 °C, the furnace was cooled down to the desired temperature for carbonation under 15 vol% CO_{2} (N_{2} balance) for 30 min. A thermocouple was placed about 5 mm below the sample hold to represent the solid temperature. The mass of the sample was recorded by the balance every 10 s.

The experimental results are presented in

The carbonation of CaAlWM sample has been simulated using the PCMC model. In this simulation, the parameters of the sorbent particles and initial conditions were selected to match those in experiments (see

As discussed above, the carbonation reaction results in a formation of a product layer over the reactive surface. Such a layer imposes additional resistance to the transport of gaseous species towards the reaction surface. This effect has been taken into account in the present treatment, as described in [

The rate-controlling mechanisms of the carbonation reaction have been discussed in [^{P} is given by:
_{a} is the activation energy;

The above described PCMC model has been implemented in the form of MATLAB code that utilises the Newton–Raphson method. The code allows for simulation of the reactive transport within spherical porous particles, while taking into account the formation of the product layer over the reactive surface. The usage of spherical symmetry of the particles reduces the dimension of the problem to one spatial coordinate ξ (radial direction) and one additional coordinate (

The PDF _{Z}_{z} is modelled as described in [_{z}. See Reference [

The _{i}_{i}_{max}. The boundary conditions at the reactive surface _{max}) are defined as follows. We note that the gas exchange between the inner space of the particle and the surrounding atmosphere occurs mainly through the largest pores. To simulate this, _{i}

The algorithm used in this code can be briefly described as follows:

As the preliminary step, all the necessary variables are initialised and the values of the model parameters as well as initial and boundary conditions are assigned to match those in experiment. Then, the time advancing procedure is carried out.

Firstly, the values of _{i}

Secondly, the obtained values of _{i}_{Z}

Thirdly, the new values of the gas velocity in radial direction _{ξ} are recalculated from the continuity _{ξ} and both previous and new values of the gas density. In _{Z}_{ξ}.

Fourthly, the new values of the gas pressure

Finally, the new value of the product layer thickness δ, as well as the parameters _{Z}_{z}, are calculated as described in [

The value for the diffusivity in the gas phase (

The results of the modeling and their comparison with experimental data are presented in

It is important to investigate the regime of the heterogeneous reaction in order to clarify which type of fractality dominates in this particular case. To do this, we examine the variation of the gaseous reactant (CO_{2}) mass fraction in _{2} mass fraction varies substantially in the ξ-direction. Due to diffusion toward the centre of a sorbent particle, this variation decreases with time. In contrast, the CO_{2} mass fraction varies insignificantly as functions of the diffusive tracer even at the initial stage of the process. This implies that, under the conditions used in the experiments, the heterogeneous carbonation reaction is in the kinetics-controlled regime (

The paper expose the family of conditional models specifically designed to simulate reacting flows in complex porous media. The presented methods—PCMC, PDCMC and NEMA-DCA—allow for the simultaneous and consistent treatment of both homogeneous reactions in the gas phase and heterogeneous reactions on complex phase interface in various reaction regimes coupled with the transport through an irregular pore networks. The methods are designed to take into account percolation effects, irregular or fractal natures of porous media, fast heterogeneous reactions, and transport between pores of very different sizes. In contrast to previously used models, which utilize the volume averaging technique and, therefore, neglect inter-pore variations in gaseous reactant concentrations, the new models utilize conditional averaging and take these variations into account. The conditional models are computationally affordable and should escape the prohibitive computational cost associated with DNS.

The carbonation behavior of the CaO-based sorbents has been experimentally investigated and simulated using the discussed conditional approach. The simulation results are in a good agreement with the experimental data. The carbonation process is an important instrumental part of the gasification technology with _{2} capture and the ability to accurately model this process is important for optimization of this emerging gasification technology.

The authors gratefully acknowledge the financial support of the Department of Resources, Energy and Tourism under the Australia-China Joint Coordination Group on Clean Coal Technology grant scheme and the Australian Research Council.

The authors declare no conflict of interest.

_{2}capture from power generation, cement manufacture and hydrogen production

_{2}capture

_{2}capture

_{2}capture by the synthetic CaO sorbent in a 1 kV dual fluidised-bed reactor

_{2}capture

_{3}⇄ CaO+CO

_{2}

_{2}-lime reaction

_{2}separation

Schematic diagram of the experimental setup.

Carbonation behavior of the sample CaAlWM.

Carbonation behavior of the sample CaCSG.

Carbonation behavior of the sample CaCPM.

Validation of the model prediction against the experimental data.

Properties of the studied CaO based sorbents.

CaO Content (%) | 6.5 | 15 | 15 |

Sorbent density (g/cm^{3}) |
2.73 | 1.965 | 1.965 |

Porosity | 0.327 | 0.186 | 0.565 |

Surface area of CaO (m^{2}/cm^{3}) |
0.47 | 0.88 | 0.47 |

Total surface area of solid (m^{2}/cm^{3}) |
11.49 | 10.0 | 5.35 |

Pore volume (cm^{3}/g) |
0.024 | 0.031 | 0.016 |

Particle diameter (mm) | 0.54 | 0.54 | 0.54 |

Adjustable parameters of the model.

Diffusivity in ^{2}/s) |
1.6 × 10^{−5} | |

Effective diffusivity in ξ-direction (m^{2}/s) |
5.0 × 10^{−4} | |

Excess fractal dimension | 0.9 | |

Permiability (d) | 0.001 | |

Gas viscosity (Pa s) | 2.93 × 10^{−5} | |

Size of the largest pores (mm) | 0.54 | |

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Diffusivity through the product layer | Pre-exponential factor (m^{2}/s) |
0.065 |

Activation energy (J/mol) | 1.94 × 10^{5} | |

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Intrinsic rate of the carbonation reaction | Pre-exponential factor (kg/m^{2}) |
0.7773 |

Activation energy (J/mol) | 4.3 × 10^{4} |