_{2}Emissions under Fast Fluidized Bed Conditions Using One Dimensional Model

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Fluidized bed combustion behavior of coal and biomass is of practical
interest due to its significant involvement in heating systems and power plant
operations. This combustion behavior has been studied by many experimental
techniques along with different kinetic models. In this study, SO_{2} emissions have been studied out in a pilot scale test facility of Circulating
Fluidized Bed combustor (70 KW) under fast fluidized bed conditions burning
coal with Pakistani wheat straw. One dimensional Mathematical model is being
developed to predict the SO_{2} emissions under different operating
conditions like bed temperature, Ca/S molar ratio, solids circulation rate,
excess air ratio and secondary to primary air ratio. These parameters are
varied to validate the model and encouraging correlation is found between the
experimental values and model predictions.

Biomass as an alternative energy source is getting a lot of attention due to the environmental and cost benefits. Globally, attention has been diverted for the replacement of fossil fuels with biomass. In UK, utilization of the fossil fuels will be replaced with renewables by 10% up to 2010 and 20% up to 2020 [_{2} and SO_{2} emis- sions from coal fired power plants can effectively be reduced by co-firing the CO_{2} neutral fuels with coal. About 534.23 million tons of wheat straw is produced worldwide in 2011 [_{2} emissions have been reported during the combustion of coal and Pakistani wheat straw under fast fluidized bed conditions [_{th} are in operation worldwide [_{2}, biomass also reduces NOx, SO_{2} and CO emissions in co- combustion with coal [

The objective of the present study is to model the CFB rig for the estimation of SO_{2} emissions under different oper- ating conditions and compare the model values to the experimental values. The values of bed temperature, Ca/S molar ratio, solids circulation rate, excess air ratio and secondary to primary air were varied to validate the model.

Hannes classified the different types of model based on complexity as global models, one dimensional model, multi-dimensional model (computational fluid dynamics) and scaling and expert systems [_{x} formation [_{2}, and NO_{x} [

Hannes developed a very detail and comprehensive model for the coal combustion in CFB boiler [

CFB combustor used in this investigation is shown in

. Comparison of some models given in literature

Fluid Dynamics | State | Coal Comb. | Size Distrib. | SO_{2} | NO_{x} | Re-Circulat | |
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Mori | Block | Dyn | a | a | |||

Basu | 1.5-dim | Std | a | a | |||

Lin | 1-dim | Std | a | a | a | ||

Halder | 1-dim | Std | a | ||||

IST | 1-dim | Std | a | a | a | ||

Alstrom | 1-dim | Dyn | a | ||||

Haider | 1.5-dim | Std | a | a | |||

IEA | 1.5-dim | Std | a | a | a | a | a |

Std = steady state; Dyn = dynamic.

PLC view of CFB rig

coal and wheat straw were supplied from gravimetric hoppers with screw feeders coupled with variable speed motors. More detail regarding the experimental setup and operation can be seen elsewhere [^{3} is used as the circulating bed material. Wheat straw (SMD = 0.85 mm) and Pakistani subbituminous coal (SMD = 0.49 mm) are used as the fuel in this study. Analyses and heating values of the feed materials are given in _{2}, NO_{x} and CO in flue gas are measured by on line gas analyzers. Dry flue gas is also sampled in Teflon bags to analyze in gas chromatograph, Perkin Elmer Auto system GC Arnel. All reported values are corrected to 6% O_{2} in the flue gas. Limestone (98.8% CaCO_{3}, SMD= 129 µm and ρ = 2730 kg/m^{3}) is also added as the sulfur capture sorbent through feeder.

Coal combustion model developed by Hannes [

All main reactions were assumed to take place in the riser as in the return leg, temperature dropped and the availability of oxygen was small. For the use of matrix solver, it was reasonable to continue the annular phase into the dense bed, so that bed and freeboard could be solve together and continuously. The lateral mixing be- tween core and annulus in the dense bed region was set high enough to equalize both phases to a common dense bed. All balances were setup by setting the time dependent term to zero to achieve steady state conditions. The gas flows were split using the values from the pre-calculations of the bubble holdup and the annulus width. The gas flow was balanced as molar flow. Changes caused by reactions which were not equimolar were assumed to have no influence on fluidization. The balanced flows were the convective flow in each phase (cor, ann, bub), cross flows from core to annulus (cor-ann), core to bubble (cor-bub) and vice versa, and mixing flows between the phases (corannx, corbubx).

For mass balance, gaseous flows were balanced based on the following differential equation:

An overall population balance was done to get the size distribution of the bed inventory. Then size classes

. Analysis of coal and wheat straw

Proximate analysis | Elemental analysis | GCV | |||||||
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VM | FC | Ash | C | H | N | S | O | MJ/kg | |

Salt range Coal (%)^{db} | 38.60 | 43.90 | 17.50 | 68.90 | 9.8 | 0.56 | 4.2 | 16.54 | 25.55 |

Wheat Straw (%)^{db} | 73.12 | 19.98 | 6.90 | 47.50 | 7.35 | 1.20 | - | 43.95 | 18.20 |

db = dry basis.

of the different materials (m), (coal, limestone, sand and ash) were balanced separately for each cell (L). The following differential equation was discretized for each phase (cr, anl) considering size, materials and location (cell) of the solids.

In the lowest cell of the riser, all annular material had to be returned to the core to conserve the mass balance.

Reactive species such as CaO and the combustibles in the coal were modelled as solid fractions. For better system solubility, the mass flow of the particles was kept constant, only the species fractions might vary. The fluidization pattern and char holdup was assumed not to be influenced by these changes. Coal mass was treated as virtual fraction, it did not influence the flow pattern but delivered the source terms for evaporated water and released volatiles. Only the ash residue in the char was balanced in the size distribution calculation. The fixed carbon was treated as ash load. The fraction balance was based on the following equation:

Where the last term represents the release or reaction influence. “k” is a release or reaction constant depend- ing on local gas concentrations and temperature. Drying and devolatilization are time dependent processes. The time dependent fraction was determined and averaged for each cell (L) and class (i) as under:

All these equations were written as first order equations for concentrations. The solution of the concentration equations is done analogue to the enthalpy balances.

The enthalpy balance delivered the average cell temperature. Enthalpy balance was based on the convective flows of gas and solids, changes in formation enthalpies due to reactions and the heat transfer to the walls. Fol- lowing differential equation was used for the energy balance.

The total balance system was consisted of the first order and solved through the matrix mechanism by ar- ranging core and annular cells in the form of arrays. More detail about the sequence of calculations can be seen elsewhere [

Lime stone is added into the CFB combustor to capture SO_{2} directly. It is very tough to model the self-desul- phurization of the coal, done by the mineral and metallic fractions in coal. The self-desulphurization of the coal is not explicitly modelled, however it can be taken into account by reducing the sulphur content in the coal by the amount of available calcium [

1) calcination:

2) oxidation:

3) sulphation:

Overall reaction can be written as under:

Thus, the sulphur capture capability strongly depends on the residence time, the fragmentation behaviour, and the pore structure of the sorbent. Calcium-sulphur compounds do not only exist as CaSO_{4} but may also exist as CaS, depending upon oxidizing or reducing boundary conditions, respectively. Since in fluidized beds the resi- dence times of the particles are high and the sulphation reaction is slow, particle tracking is nearly impossible to distinguish in reducing and oxidizing zones as they mix within short times. Therefore, only the oxidizing condi- tions are considered in the following model.

During the calcination, the equilibrium between CaCO_{3} and CaO is dependent on the partial pressure of CO_{2} in the surrounding gas, and on temperature. Baker [

For a given partial pressure of CO_{2}, calcination will only take place above the corresponding temperature. Dennis and Fieldes [_{calc} by:

With k_{0} = 207 (mol/bar×m^{2}×s) and an empirical variable describing a constant molar fraction of CO_{2} which is 0.065 at 825˚C, 0.1 at 875˚C and 0.17 at 925˚C.

For a kinetically controlled shrinking-core model, Kunii and Levenspiel [

The combination with residence time of the particles is done with a residence time distribution:

Where the average residence time is the quotient of limestone mass in the furnace and limestone feed flow. The average calcination degree is

On integration

During calcination, the released CO_{2} leaves the limestone with No. of pores which increases the inner surface area and subsequently sulphation reactions. Shrinking core model was used for the sulphation reaction due to its validity [

Gas-solid reaction model, describing the reactions taking place at the individual particles is combined with the hydrodynamic model delivering the particle flow rates and concentrations. This model has differentials in time and radius, which are to be solved properly. So Wolff approach is implemented into the sulphation model, based on an analytical way to solve the radius dependent integral, so that only a forward integration in time remains [

Where the equilibrium between SO_{2} and SO_{3} can be expressed by:

The reaction rate at the core surface can be stated as [

Equation (18) can be solved as follows:

Integration over the reacted shell and the gas film leads to the concentration of SO_{2} on the core surface de- pendent on the bulk SO_{2} concentration.

Substitution back into Equation (16) and rewriting yields:

From the integration of left side of Equation (16) over the gas shell and over the reacted shell, the diffusion functions f_{film} and f_{shell} can be derived [

The conversion α _{lime} can be understood as reacted volume fraction of the particle

Averaged conversion is approached with a residence time distribution function [

Above equation can be solved analytically using a substitution of Equation (24) into Equation (21).

With values of C_{1}, C_{2}, C_{3} and C_{4} as

Final integration of Equation (26) is,

This equation is replaced with residence time distribution function and numerically integrated using a modified Euler method. The function has as very steep gradient for very small values of

The diffusion coefficients consist of the Knudsen diffusion effects in the pores and the diffusion of a binary mixture of gases [

In the gas film, only binary diffusion occurs [

The calculation of the thickness of the gas film layer d is estimated by the mass transport coefficient

where

So the reaction rates and concentrations were calculated and following parameters were used in the model,

K_{0} = 0.154 (SO_{4}/SO_{3} equilibrium constant) [

t_{tort} = 3 (tortuosity factor) [

α_{max} = 0.5 (maximum conversion degree) [

k_{sulf} = 0.15 (sulphation constant m/s) [

Since the residence time of limestone particles and their sulphation takes place over hours, while gas resi- dence time is in seconds, the sorbent is balanced as a homogenous phase. This is done by considering fragmen- tation and attrition of the sorbent which enlarges the available reactive surface. The conversion rate is calculated with an averaged SO_{2} bulk concentration. The gas reaction is calculated depending on local holdup of sorbent in the riser. Weighing the local SO_{2} concentrations with the local hold-up of sorbent provides the average gas con- centration for the calculation to determine the conversion of the sorbent. The steady state sorbent conversion and gas concentration is established during the overall mass balance in the program.

To see the synergy effects and validate the model, its predictions were compared with the experimental data taken from the CFB test rig.

Typical results obtained through the model and experimental studies are shown from Figures 2-6. There is a good agreement between the model predictions and the experimental results in accordance with the synergy ef- fects of coal and biomass combustion, on emissions of SO_{2}. Model was run with a series of input values but re- ported values are, for bed temperature, excess air factor, secondary to primary air ratio, solid circulation rate and Ca/S molar ratio, for 5%, 10% and 20% blends of wheat straw with coal on weight basis.

It was believed that an increase in bed temperature can accelerate the calcination reaction resulting in low SO_{2} concentration. High bed temperature also resulted in low CO concentrations which adversely affect the decom- positions reactions of CaSO_{4}. Model predictions were in agreement when compared to the experimental values for different bed temperatures as shown in

Agreement between model predictions and experimental results were found to be very encouraging for the effect of Ca/S molar ration on SO_{2} emission as shown in

Bed temperature vs. SO_{2} concentration, experimental results and model predictions

Ca/S molar ratio vs. SO_{2} concentration, experimental results and model predictions

Excess air factor vs. SO_{2} concentration, experimental results and model predictions

Solids circulation rate vs. SO_{2 }concentration, experimental results and model predictions

Secondary air to primary air ratio vs. SO_{2} concentration, experimental results and model predictions

Effect of variation of excess air factor on the SO_{2} emission, predicted by the model is shown in _{2} emission. With an excess air factor of 1.20, reaction rate of sulphation increased due to higher oxygen concentration in the riser. Based on the same scenario, SO_{2} emission deceased in the actual ex- perimental work.

Experimental and model results related to the effect of solids circulation rate on SO_{2} emissions have been compared and reported in ^{2}∙s, the error was small and model has given the good predictions especially at higher wheat straw ratio.

In _{2} emission have been com- pared with the experimental results. As clear from the results, model was unable to produce good correlation for the variation in secondary to primary air ratio for the SO_{2} emission. Model predictions have given a positive er- ror for lower secondary to primary air ratio while a negative error was observed for the higher values of second- dary to primary air ratio. This might be due to the complex hydrodynamics inside the riser produced after the secondary air injection which could not be accounted in the present correlations used for the hydrodynamic modelling of the riser. As by the injection of secondary air, temperature of that region will be low and more oxi- dizing conditions would be made available making a precarious region regarding the model. Especially variation in the secondary to primary air ratio produced the undesired effect on the hydrodynamics of the riser that ulti- mately affected the SO_{2} concentration.

A fluidized bed model for the steady state combustion and sulphation in a CFB was used to predict the SO_{2} con- centrations in the exit flue gases. It was based on the shrinking core model. Agreement between model predic- tion and experimental results was found encouraging for the parameters like bed temperature, fluidizing air ve- locity, excess air ratio and solids circulation rate. However for secondary to primary air ratio, some short com- ings in the model were observed.

Authors wish to thank the Higher Education Commission of Pakistan for their financial support to this project. (Project No. 1380-HEC).