Rate equation theory of gas-solid reaction kinetics for calcium

looping and chemical looping

Zhenshan Li, Hongming Sun, Jinhua Bao, Ningsheng Cai Department of Thermal Engineering Tsinghua University 2012/08/20

4th IEAGHG Network Meeting and Technical Workshop On High Temperature Solid Looping Cycles

Tsinghua University 20th-21st of August, 2012

Outline

Kinetics model for gas solid reaction Solid product nucleation and growth Rate equation method Results and discussions Conclusions

Kinetics model for gas solid reaction

(1) Two stages: fast and slower stages (2) High T increase the critical conversion (3) Most G-S reactions behave similarly

CaO + CO2 = CaCO3

Vasilije Manovic. Ind. Eng. Chem. Res. Yuran Li et al. Fuel, 2007, 86, 785–792. Garcia F et al. Ind. Eng. Chem. Res. 2004, 43, 8168-8177.

CaO/fly ash , 5 vol% O2, 2000 ppm SO2

CuO ~1000µm, 5% CO, 95% N2

Why the critical conversion increases with the temperature increasing?

CaO

CaCO3

Kinetics model for gas solid reaction

(1) Gas external mass transfer

(2) Pore diffusion

(3) Adsorption

(4) Product layer diffusion

(5) Reaction and product growth

(a)缩核模型 (b)晶粒模型 (d)成核与和生长模型(a) shrinking core model (b) grain model (c) pore model (d) nucleation and growth固体反应物

固体产物

孔

product

reactant

pore

(a)缩核模型 (b)晶粒模型 (d)成核与和生长模型(a) shrinking core model (b) grain model (c) pore model (d) nucleation and growth固体反应物

固体产物

孔

product

reactant

pore

However, the nucleation and growth of solid product was not considered in detailed in these models.

Kinetics model for gas solid reaction

Two famous theories for product growth

Wagner theory: focuses on the slower product layer diffusion stage;

Cabrera-Mott theory: focuses on initial oxidation stage; A critical assumption in the Cabrera-Mott model is that the oxide film grows in a uniform layer-by-layer fashion.

However, the nucleation and growth of solid product occur during the initial reaction stage, and the critical assumption of the Cabrera–Mott model is not valid, micro-structural information must be considered in detailed oxidation modeling.

Solid product nucleation and growth

5.3min 8.6min 13min

700oC 800oC 900oC

Fe oxidation 1020ppm O2

Fe oxidation at 700oC, 1020ppm O2

MgO surfaces reacting with 200 ppm of SO2 and 5 vol% O2 for 10 min

550oC 650oC 750oC

Solid product nucleation and growth

NiO reduction by H2 at 800oC, (a) 2s; (b) 5s; (c) 5s.

Hidayat T et al. Metall Mater Trans B. 2009, 40B, 474-489

Solid product nucleation and growth

CaCO3 sulfation with SO2 (3516 ppm) at 600oC for 30min, after 15min,10vol% steam was added

Cu2O islands at constant oxygen partial pressure of 3×10-4 and temperature of 1000oC.

Oxide islands formed on Cu(110) at different oxidation temperatures, the oxygen pressure is 0.1 torr.

Zhou GW. PhD thesis. University of Pittsburgh, 2003.

The formation and growth of the solid product is the most critical step

Solid product shows three-dimensional island shaped morphology . High density groups of islands with smaller size are formed at lower temperature while low density, larger sizes of islands are formed at high temperatures. How to describe the island growth in gas-solid reaction model is not clear in previous work

Solid product nucleation and growth

CaOCaO CaO

(1) layer growth; (2) island growth; (3) island-layer growth

There are three growth modes for solid products

Rate Equation Method

成核

R成核 > R生长R成核 < R生长

不稳定核

晶界迁移烧结

成核

R成核 > R生长R成核 < R生长

不稳定核

晶界迁移烧结

物理吸附、化学吸附解离、成键

物理吸附、化学吸附解离、成键

reaction

nucleation growth

Ostwald ripening

Grain boundary and lattice diffusion

成核

R成核 > R生长R成核 < R生长

不稳定核

晶界迁移烧结

成核

R成核 > R生长R成核 < R生长

不稳定核

晶界迁移烧结

物理吸附、化学吸附解离、成键

物理吸附、化学吸附解离、成键

reaction

nucleation growth

Ostwald ripening

Grain boundary and lattice diffusion

The nucleation and growth of solid products are controlled by both the chemical reaction rate and surface diffusion.

The driven force for Ostwald ripening

Diffusion coefficient

Rate Equation Method

①

③②

④

③④

...气体反应物

固体反应物

固体生成物

②

③

CO2

CaO

CaCO3

①

③②

④

③④

...气体反应物

固体反应物

固体生成物

②

③

CO2

CaO

CaCO3

(1) surface reaction and the formation of solid product:

(2)surface diffusion of single molecule:

(3) single molecule captured by islands:

sσ)

sσ

(4) single molecule escape from islands:

(5) grain boundary and lattice diffusion:

2 2CO CO ,e molecular( )F k C C N= −

1/ 2.712.0 ( / )s sr rσ = +

1e,s s sD Nη = 1e, e1exp( )s

s

N NRT dγΩ

=

s GB L(1 )k fD f D= + −

0 exp( )ii i

ED DRT−

=

An island can grow due to the capture of molecules from small islands. Or an island can shrink due to the escaping of molecules to larger islands.

①

③②

④

③④

...气体反应物

固体反应物

固体生成物

②

③

CO2

CaO

CaCO3

①

③②

④

③④

...气体反应物

固体反应物

固体生成物

②

③

CO2

CaO

CaCO3

Rate Equation Method

grain boundary and lattice diffusion molecule captured by island

molecule esca

d + -d

pe from i slan (2 )d s

sNt=

≤ ≤ ∞

1 reaction captured by island escape fd rom d

islandNt= − +

Ns: islands composed of s molecules

N1: islands composed of one molecule

Island density changing depends on surface reaction, surface diffusion, nucleation and island growth, grain boundary and lattice diffusion

Rate equation for N1:

Rate equation for Ns:

①

③②

④

③④

...气体反应物

固体反应物

固体生成物

②

③

CO2

CaO

CaCO3

①

③②

④

③④

...气体反应物

固体反应物

固体生成物

②

③

CO2

CaO

CaCO3

Rate Equation Method

1 1 1 1 1 1 1 1d ( ) (2 s )d

ss s s s s s s s s s s s s s

N F k N k N D N N D N N N Nt

σ σ η η− − − − + += − + − − + ≤ ≤ ∞

11 1 1 2 2

2 3

d (2 ) (2 )d s s s s s s

s s

N F D N N N N Nt

θ σ σ η η∞ ∞

= =

= − + + +∑ ∑

Ns: islands composed of s molecules

N1: islands composed of one molecule

Surface reaction

Loss of single molecule due to capture by other islands

single molecule escapes from other islands

Grain boundary & lattice diffusion

Island density changing depends on surface reaction, surface diffusion, nucleation and island growth, grain boundary and lattice diffusion

2s s

sN sθ

∞

=

= ∑Surface coverage:

Rate equation for N1:

Results and Discussions

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15 20

Time (min)

CaO

Con

vers

ion

calculated resutls

690oC

515oC

590oC

640oC

743oC

The output parameters of rate equation are islands density (Ns), and the macroscopic behavior such as solid conversion can be calculated with the islands density. Rate equation can be validated by both microscopic AFM & SEM and macroscopic TGA experiments.

~20µm CaO carbonation, 14vol% CO2

More detail can be found in the paper published by Li ZS et al, Energy Fuels, 2012,

Results and Discussions

700 800 900

Fe oxidation 1020ppm O2

Fe oxidation at 900oC, 5vol% O2

Submitted to Combustion and Flame.

Conclusions

A rate equation theory was developed to provide information on the variations in island size distribution with time evolution. The elemental steps of surface reaction, surface diffusion, and grain boundary and lattice diffusion were included in these rate equations. The macroscopic solid conversion can be calculated by use of the island size distribution information.

Achieved:

Next step: Mechanism of the effect of H2O on gas solid reaction. Effect of impurity and support on islands nucleation, growth and morphology – (surface diffusion, capture number or grain boundary diffusion). Sintering of oxygen carrier or sorbent- (Ostwald ripening & islands diffusion & neck sintering ).

This research is supported by the National Natural Science Funds of China (50806038, 51061130535 ) and by the National Basic

Research Program of China (No.2011CB707301). .