# Theoretical Methodology of a High-Flux Coal-Direct Chemical Looping Combustion System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}capture [1,2]. The CDCLC concept is typically implemented in two interconnected reactors, the so-called fuel reactor (FR) and the air reactor (AR), with an oxygen carrier (OC) circulating in between to transfer oxygen and heat. Specifically, in the FR, the fuel is first devolatilized and gasified by the gasification agent steam, and then the gasification products (mainly CO, H

_{2}, and CH

_{4}) are further oxidized to CO

_{2}and H

_{2}O by the OC. In the AR, the reduced OC from the FR is oxidized by the air for regeneration, and then will be recirculated back to the FR. By means of the OC particles that deliver oxygen from the AR to FR, the direct mixing of the fuel and air can be avoided, and further highly purified CO

_{2}, without the dilution of N

_{2}, can be acquired at the outlet of the FR via the condensation of steam [3,4,5,6,7,8,9,10,11,12].

_{th}[3] and 100 kW

_{th}[9] units at Chalmers University of Technology (Sweden), the 10 kW

_{th}[4] and 50 kW

_{th}[5] units at Southeast University (China), the 1 MW

_{th}unit from Technische Universität Darmstadt (Germany) [10], the 25 kW

_{th}unit at Hamburg University of Technology (Germany) [11], the 25 kW

_{th}unit from Ohio State University (America) [12], the 50 kW

_{th}unit at Instituto de Carboquimica (ICB-CSIC) (Spain) [16], and the 5 kW

_{th}CDCLC reactor at Huazhong University of Science and Technology (China) [17]. However, despite promising experimental results obtained in pilot-scale units, the CDCLC technology for CO

_{2}capture has to be further developed towards large-scale commercial applications. In this aspect, it is essential to develop theoretical methodologies, beside experimental studies, for a better understanding of hydrodynamic and reaction mechanisms in CDCLC processes, which can provide vital references to the design, operation, and process optimization of the future large-scale CDCLC power plants. By far, compared to the extensive experimental studies, few studies are available in the literature on the development of theoretical methodologies in terms of hydrodynamics and/or reaction mechanisms for CDCLC processes. Su et al. [18], based on the hydrodynamic equations for fluidized beds and the reaction kinetics, simulated the CDCLC process in a dual circulating fluidized bed (DCFB) system. Ohlemüller et al. [19] developed a process simulation model to predict the flow and reaction performances of a 1 MW

_{th}unit at Technische Universität Darmstadt.

## 2. Materials and Methods

#### 2.1. Visualization Experimental Device

_{1,sta}, Q

_{2,sta}, Q

_{3,sta}, and Q

_{4,sta}represent the inlet air flow rate of the FR, the fluidizing air flow rate of the J-valve, the aeration air flow rate of the J-valve, and the inlet air flow rate of the AR, respectively. Q

_{a}

_{,sta}and Q

_{b}

_{,sta}represent the outlet air flow rates of the FR and the AR, respectively.

#### 2.2. Materials

^{3}. The minimum fluidization gas velocity under the cold condition was 0.187 m/s [20].

#### 2.3. Performance Indicators

_{1}/H

_{1}) represents the pressure gradient between the AR and the carbon stripper, which was expressed as Equation (1). The lower pressure gradient (ΔP

_{2}/H

_{2}) represents the pressure gradient between the J-valve and the AR, which was expressed as Equation (2) [20].

_{s}, represents the solid circulation ratio (kg/s) per unit area of the FR, which was estimated by [20,21]

_{s}, could be estimated according to the local pressure drop [13,14,21,22,23,24].

_{1}, represents the gas leakage ratio from the FR to the AR. During the experimental process, the FR leakage ratio was measured by using tracer gas 1 [14,20].

_{2}, represents the gas leakage ratio from the AR to the FR, which could be measured by using tracer gas 2 [14,20].

_{3}, represents the gas leakage ratio of the J-valve aeration air into the AR, which was measured by using tracer gas 3 [20].

## 3. Results and Discussion

#### 3.1. Gas–Solid Flow Characteristics

_{2}leakage from the carbon stripper into the AR, and hence the great reduction of CO

_{2}capture efficiency. In the second state, the positive differential pressure between the top and bottom becomes much smaller, and the gas velocity is only slightly higher than the solids velocity, indicating a modest gas leakage from the FR to the AR. In the third state, when the differential pressure between the two ends of the upper dipleg becomes zero, the solids downward flow is controlled by gravity and the gas–solid relative velocity becomes zero. Then in the fourth state, the bottom pressure of the upper dipleg starts to outpace the top pressure, and the gas–solid flow becomes negative pressure gradient flow, leading to a further reduction of the downward velocity of gas phase. When the downward gas velocity further decreases to zero, it comes to the fifth state, so-called the ideal sealing state. At this point, the gas–solid relative velocity is equal to the absolute value of the solids descending velocity, indicating the ideal suppression of the gas leakages between the FR and AR. In the sixth state, with the further enhancement of the negative pressure gradient, the gas begins to flow upward with a low velocity, indicating a small amount of gas leakage from the AR to the FR. Finally, when a large amount of gas flow moves upward in terms of visible large bubbles, the upper dipleg will enter into the last state, so-called the critical sealing state, meaning that the whole-system particle circulation is about to be broken together with a dramatical leakage of N

_{2}from the AR into FR. In general, States 1 and 2 belong to the positive pressure gradient flow, State 3 belongs to the zero pressure gradient flow, and States 4 to 7 belong to the negative pressure gradient flow.

_{1}/H

_{1}, the FR leakage ratio f

_{1}had a linear drop until extinction while the AR leakage ratio f

_{2}firstly stayed at zero and then had a linear increase [20]. Thus, the variations of gas–solid flow state in the upper dipleg corresponding to the upper pressure gradient could be further deduced, as shown in Figure 4. It can be found that the gas flow direction in the upper dipleg changed from downward to upward. By referring to Figure 3, it can be concluded that the gas–solid flow in the upper dipleg had gone through States 2 to 6, demonstrating the feasibility of the selection of optimal operation region for the gas leakage control and solid circulation by means of the adjustment of the upper pressure gradient ΔP

_{1}/H

_{1}. Consistent with the experimental studies [20], we set −3% and 3% as the limit values of the two gas leakages f

_{1}and f

_{2}, respectively, and as the selection criteria of the upper pressure gradient. Thus, we can get the optimal region of ΔP

_{1}/H

_{1}corresponding to States 2 to 6 under the involved operation conditions: State 2 (−2.1 kPa/m < ΔP

_{1}/H

_{1}< 0 kPa/m), State 3 (ΔP

_{1}/H

_{1}= 0 kPa/m), State 4 (0 kPa/m < ΔP

_{1}/H

_{1}< 1.6 kPa/m), State 5 (ΔP

_{1}/H

_{1}= 1.6 kPa/m), and State 6 (1.6 kPa/m < ΔP

_{1}/H

_{1}< 3.0 kPa/m).

_{2}into the FR, and further the reduction of CO

_{2}capture concentration, State 4 should also better be avoided during the CDCLC process. Moreover, an excess gas leakage (i.e., State 7 shown in Figure 3) will cause serious damage on the stability of the solids downward flow, and further the solid circulation. Therefore, only States 5 and 6 were regarded as the preferred gas–solid flow states in the lower dipleg. Consistent with our previous experimental studies [20], we set 20% as the upper limit value of the gas leakage f

_{3}, and as the selection criterion of optimal region under the involved operation conditions.

#### 3.2. Theoretical Methodology for Gas Leakage Restraint

#### 3.2.1. Semi-Theoretical Formulas of the Upper Pressure Gradient

^{2}·s, the value of the theoretical ideal pressure gradient was about 1.6 kPa/m which was almost the same with the experimental value. Then, when the solid circulation flux increased to 300 kg/m

^{2}·s, the theoretical and measured values of the ideal pressure gradient were increased to about 2.5 and 2.8 kPa/m, respectively. In general, the relative errors between the measured and predicted values of the ideal pressure gradient were kept to be lower than 15%, demonstrating the application feasibility of the modified Ergun equation in the prediction of the ideal pressure gradient of the high-flux CDCLC system.

_{1}/H

_{1}under a high-flux condition of 200 kg/m

^{2}·s, which ranged between −2.1 kPa/m and 3.0 kPa/m. Thus, by associating the optimal region with the ideal pressure gradient (1.6 kPa/m), a semi-theoretical formula of gas leakages between the two reactors (i.e., Equation (11)) could be deduced, which includes two conterminal linear equations with the ideal pressure gradient chosen as the boundary point. This formula successfully established the important mapping relationships between the gas–solid flow states in the upper dipleg and the upper pressure gradient, which should be important coupling criteria of selecting design parameters and operating conditions.

#### 3.2.2. Semi-Theoretical Formulas of the Lower Pressure Gradient

_{2}/H

_{2}under a high-flux condition of 200 kg/m

^{2}·s should be limited within 6.0 kPa/m in order to guarantee the J-valve leakage ratio lower than 20%. Thus, by associating the optimal region of the lower pressure gradient with the ideal pressure gradient, a semi-theoretical formula of J-valve gas leakage (i.e., Equation (13)) could be deduced, in which the coefficient β was used as the slope. Similarly, with Equation (11), this formula established the mapping relationships between the J-valve gas leakage and the lower pressure gradient, enabling a coupling criterion of selecting design parameters and operating conditions during the CDCLC process.

#### 3.3. Theoretical Methodology for Circulation Stability

^{2}·s, the experimental value of the critical sealing gradient was 10.7 kPa/m under an upper dipleg height of 1.07 m [20]. In order to ensure the accuracy of test measurement, another dipleg height (0.87 m) was adopted for the measure of the critical sealing gradient while the other operating conditions were kept constant. It can be seen that these two experimental results (10.9 kPa/m for 0.87 m height, and 10.7 kPa/m for 1.07 m height) were very close to each other, demonstrating the constancy of the critical sealing gradient. On the other hand, the calculation value of the critical sealing gradient based on Equation (14) was between 8.5 kPa/m and 9.9 kPa/m. Thus, the relative error between the measured and predicted values of the critical sealing gradient could be further calculated to be lower than 21% for γ of 0.6, and 8% for γ of 0.7, demonstrating the application feasibility of Chang et al. [32] equation in the prediction of the critical pressure gradient of the high-flux CDCLC system. Moreover, the value of 0.7 for the coefficient γ seems to be more suitable for this system, in view of the least relative error with the experimental values. Therefore, the semi-theoretical formula for the circulation stability of this high-flux system can be finally expressed as Equation (15).

#### 3.4. Theoretical Methodology Application to Condition Designs of the Cold System

^{2}·s as the solid circulation flux G

_{s}while the corresponding FR superficial gas velocity U

_{f}

_{,sta}and the inlet air flow rate of the AR Q

_{4,sta}were set to be 10.7 m/s and 44 m

^{3}/h, respectively. Thus, according to Equations (10) and (12), the theoretical ideal pressure gradients of the upper dipleg and the lower dipleg should be about 2.5 kPa/m and 1.9 kPa/m, respectively. Then, on the basis of the above semi-theoretical formulas (i.e., Equations (11) and (13)), we could further deduce that the optimal regions for gas leakage restraint were about −1.3 to 3.9 kPa/m for the upper pressure gradient ΔP

_{1}/H

_{1}, and about 1.9 to 6.6 kPa/m for the lower pressure gradient ΔP

_{2}/H

_{2}. Under this premise, we selected 3.8 kPa/m and 5.2 kPa/m as the proposed values of ΔP

_{1}/H

_{1}and ΔP

_{2}/H

_{2}, respectively.

_{1}/H

_{1}close to the upper limit of the optimal region, the FR leakage ratio f

_{1}(−0.1%) and the AR leakage ratio f

_{2}(2.5%) can still be limited within their limits (i.e., −3% for f

_{1}and 3% for f

_{2}), demonstrating the feasibility of the semi-theoretical Equation (11) for the prediction of the optimal region for gas leakage control. On the other hand, the lower pressure gradient ΔP

_{2}/H

_{2}was located at a value of 5.2 kPa/m, in which the J-valve leakage ratio f

_{3}(15.2%) could be kept within a proposed region (<20%) in order to ensure a favorable solid circulation.

#### 3.5. Hot State Application Assessment of the Theoretical Methodology

^{2}·s so as to keep consistent with the proposed cold-state operation condition mentioned above. The only difference was that under the hot state, the operating temperature was as high as 1243 K with the corresponding dynamic viscosity μ

_{g}

_{,hot}= 4.7 × 10

^{−5}Pa·s. Table 3 details the parameters for the calculation of ideal pressure gradients under the hot state.

_{1}/H

_{1}, and about 5 to 9.7 kPa/m for ΔP

_{2}/H

_{2}. On the other hand, according to Equation (15), the critical pressure gradient for the circulation stability could be deduced to be about 9.9 kPa/m. It can be found that the upper limit of the optimal region of ΔP

_{2}/H

_{2}(9.7 kPa/m) for gas leakage restraint was very close to the critical pressure gradient for the circulation stability (9.9 kPa/m), demonstrating the rationality of the choice of 20% as the upper limit standard of the J-valve leakage. Certainly, it should be noted that the approach of the optimal pressure gradients for gas leakages to the critical pressure gradient for circulation stability also means the increase in the risk of circulation collapse during the hot-state operation process.

## 4. Conclusions

- (1)
- During the CDCLC process, the dipleg flow can situate at a pressure region across the positive and negative pressure gradients, which can be categorized into seven flow states. Considering the gas leakages and the circulation stability, the upper dipleg of the AR was recommended to be operated among State 2 to 6 while the lower dipleg of the AR should better run between States 5 and 6.
- (2)
- The gas leakages between the two reactors were expressed as two conterminal linear equations with the ideal pressure gradient chosen as the boundary point, which can be used to predict the optimal regions of the upper pressure gradient. Similarly, the J-valve leakage within the optimal region was expressed as a linear function of the lower pressure gradient of the AR. In addition, an empirical formula of critical sealing was developed for this high-flux CDCLC system, which can be used to identify the advent of circulation collapse so as to guarantee the operation stability.
- (3)
- The theoretical methodology for gas leakages and solid circulation was successfully applied to the condition design and operation of the cold system, achieving favorable gas–solid flow and circulation together with good control of gas leakages in the whole system.
- (4)
- The theoretical methodology was adopted to carry out a capability assessment of the high-flux CDCLC system under a hot state in terms of the restraint of gas leakages and the stability of solid circulation. The ideal pressure gradients under the hot state of 1243 K were about 2.6 times than those under the cold state, implying a lower requirement of sealing height in the hot state. However, on the other hand, the increase of the ideal pressure gradients also led to the approach of the optimal pressure gradients for gas leakages to the critical pressure gradients for circulation stability, which would increase the risk of circulation collapse during the operation process.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A_{ud} | sectional area of the upper downcomer (m^{2}) |

A_{f} | sectional area of the upper FR (m^{2}) |

d_{s} | mean diameter of the OC particles (mm) |

D_{f} | FR diameter (m) |

D_{ud} | upper downcomer diameter (m) |

f_{1} | FR leakage ratio |

f_{2} | AR leakage ratio |

f_{3} | J-valve leakage ratio |

f_{i} | gas leakage ratio between the two reactors (i = 1 or 2) |

g | acceleration due to gravity (9.8 m/s^{2}) |

g_{c} | conversion coefficient (9.8 N/kg) |

G_{s} | solid circulation flux (kg/m^{2}·s) |

H_{1} | solid-seal height of the upper dipleg of the AR (m) |

H_{2} | solid-seal height of the lower dipleg of the AR (m) |

∆H | scale height in the upper dipleg of the AR (m) |

L_{ld} | side length of the lower downcomer (m) |

P_{b} | pressure of the AR outlet (kPa) |

P_{c} | pressure of the AR inlet (kPa) |

P_{d} | top pressure of the lower dipleg of the AR (kPa) |

P_{i} | pressure at the interface of the dense phase and dilute phase of the upper downcomer (kPa) |

P_{11} | pressure at the underside of the separator (kPa) |

P_{12} | pressure at the top position of the lower dipleg (kPa) |

$\Delta {P}_{Z}$ | local pressure drop at two adjacent elevations of the FR (kPa) |

${\left(\Delta P/H\right)}_{c}$ | critical pressure gradient for circulation stability (kPa/m) |

ΔP_{1}/H_{1} | upper pressure gradient of the AR (kPa/m) |

${\left(\Delta {P}_{1}/{H}_{1}\right)}_{i}$ | upper pressure gradient of the AR under the ideal sealing state (kPa/m) |

${\left(\Delta {P}_{1}/{H}_{1}\right)}_{t}$ | transient upper pressure gradient of the AR (kPa/m) |

ΔP_{2}/H_{2} | lower pressure gradient of the AR (kPa/m) |

${\left(\Delta {P}_{2}/{H}_{2}\right)}_{i}$ | lower pressure gradient of the AR under the ideal sealing state (kPa/m) |

${\left(\Delta {P}_{2}/{H}_{2}\right)}_{t}$ | transient lower pressure gradient of the AR (kPa/m) |

Q_{1,sta} | inlet air flow rate of the FR distributor (m^{3}/h) |

Q_{2,sta} | fluidizing air flow rate of the J-valve (m^{3}/h) |

Q_{3,sta} | aeration air flow rate of the J-valve (m^{3}/h) |

Q_{4,sta} | inlet air flow rate of the AR (m^{3}/h) |

Q_{a,sta} | outlet air flow rate of the FR (m^{3}/h) |

Q_{b,sta} | outlet air flow rate of the AR (m^{3}/h) |

t | measured duration of the OC particles passing through the scale height (s) |

T | operation temperature (K) |

u_{s} | velocity of the OC particles in the upper dipleg (m/s) |

U_{f,sta} | FR superficial gas velocity (m/s) |

U_{s} | solids velocity (m/s) |

${x}_{a,CO}$ | concentration of tracer gas 1 measured at the outlet of the separator (ppm) |

${x}_{b,CO}$ | concentration of tracer gas 1 measured at the AR outlet (ppm) |

${x}_{a,CO}^{\prime}$ | concentration of tracer gas 2 measured at the outlet of the separator (ppm) |

${x}_{b,CO}^{\prime}$ | concentration of tracer gas 2 measured at the AR outlet (ppm) |

${x}_{a,CO}^{\u2033}$ | concentration of tracer gas 3 measured at the outlet of the separator (ppm) |

${x}_{b,CO}^{\u2033}$ | concentration of tracer gas 3 measured at the AR outlet (ppm) |

$\Delta Z$ | height difference between two adjacent elevations of the FR (m) |

${\alpha}_{1}$ | slope of the linear fitting equation of FR leakage ratio |

${\alpha}_{2}$ | slope of the linear fitting equation of AR leakage ratio |

$\beta $ | slope of the linear fitting equation of J-valve leakage ratio |

$\gamma $ | dimensionless coefficient of the fitting equation of critical sealing gradient |

ε | void fraction in the downcomer |

ε_{s} | cross-sectional average solids holdup in the FR |

φ_{s} | sphere coefficient of the OC particles |

ρ_{b} | bulk density of the OC particles (kg/m^{3}) |

ρ_{g} | density of air (kg/m^{3}) |

ρ_{s} | apparent density of the OC particles (kg/m^{3}) |

μ_{g} | dynamic viscosity of air (Pa·s) |

## References

- Kim, H.R.; Wang, D.; Zeng, L.; Bayham, S.; Tong, A.; Chung, E.; Kathe, M.V.; Luo, S.; McGiveron, O.; Wang, A.; et al. Coal direct chemical looping combustion process: Design and operation of a 25-kWth sub-pilot unit. Fuel
**2013**, 108, 370–384. [Google Scholar] [CrossRef] - Bayham, S.C.; Kim, H.R.; Wang, D.; Tong, A.; Zeng, L.; McGiveron, O.; Kathe, M.V.; Chung, E.; Wang, W.; Wang, A.; et al. Iron-based coal direct chemical looping combustion process: 200-h continuous operation of a 25-kWth subpilot unit. Energy Fuels
**2013**, 27, 1347–1356. [Google Scholar] [CrossRef] - Berguerand, N.; Lyngfelt, A. Design and operation of a 10 kW
_{th}chemical-looping combustor for solid fuels-testing with South African coal. Fuel**2008**, 87, 2713–2726. [Google Scholar] [CrossRef] - Shen, L.H.; Wu, J.H.; Xiao, J. Experiments on chemical looping combustion of coal with a NiO based oxygen carrier. Combust. Flame
**2009**, 156, 721–728. [Google Scholar] [CrossRef] - Xiao, R.; Chen, L.; Saha, C.; Zhang, S.; Bhattacharya, S. Pressurized chemical-looping combustion of coal using an iron ore as oxygen carrier in a pilot-scale unit. Int. J. Greenh. Gas Control
**2012**, 10, 363–373. [Google Scholar] [CrossRef] - Abad, A.; Gayán, P.; de Diego, L.F.; García-Labiano, F.; Adánez, J. Fuel reactor modelling in chemical-looping combustion of coal: 1. Model formulation. Chem. Eng. Sci.
**2013**, 87, 277–293. [Google Scholar] [CrossRef] - García-Labiano, F.; de Diego, L.F.; Gayán, P.; Abad, A.; Adánez, J. Fuel reactor modelling in chemical-looping combustion of coal: 2-simulation and optimization. Chem. Eng. Sci.
**2013**, 87, 173–182. [Google Scholar] [CrossRef] - Wang, X.; Jin, B.; Zhang, Y.; Zhang, Y.; Liu, X. Three dimensional modeling of a coal-fired chemical looping combustion process in the circulating fluidized bed fuel reactor. Energy Fuels
**2013**, 27, 2173–2184. [Google Scholar] [CrossRef] - Markström, P.; Linderholm, C.; Lyngfelt, A. Operation of a 100 kW chemical-looping combustor with Mexican petroleum coke and Cerrejón coal. Appl. Energy
**2014**, 113, 1830–1835. [Google Scholar] [CrossRef] - Ströhle, J.; Orth, M.; Epple, B. Design and operation of a 1 MW
_{th}chemical looping plant. Appl. Energy**2014**, 113, 1490–1495. [Google Scholar] [CrossRef] - Thon, A.; Kramp, M.; Hartge, E.-U.; Heinrich, S.; Werther, J. Operational experience with a system of coupled fluidized beds for chemical looping combustion of solid fuels using ilmenite as oxygen carrier. Appl. Energy
**2014**, 118, 309–317. [Google Scholar] [CrossRef] - Bayham, S.; McGiveron, O.; Tong, A.; Chung, E.; Kathe, M.; Wang, D.; Zeng, L.; Fan, L.S. Parametric and dynamic studies of an iron-based 25-kW
_{th}coal direct chemical looping unit using sub-bituminous coal. Appl. Energy**2015**, 145, 354–363. [Google Scholar] [CrossRef] - Wang, X.; Jin, B.; Liu, X.; Zhang, Y.; Liu, H. Experimental investigation on flow behaviors in a novel in situ gasification chemical looping combustion apparatus. Ind. Eng. Chem. Res.
**2013**, 52, 14208–14218. [Google Scholar] [CrossRef] - Wang, X.; Jin, B.; Liu, H.; Wang, W.; Liu, X.; Zhang, Y. Optimization of in situ gasification chemical looping combustion through experimental investigations with a cold experimental system. Ind. Eng. Chem. Res.
**2015**, 54, 5749–5758. [Google Scholar] [CrossRef] - Wang, X.; Jin, B.; Zhu, X.; Liu, H. Experimental evaluation of a novel 20 kW
_{th}in situ gasification chemical looping combustion unit with an iron ore as the oxygen carrier. Ind. Eng. Chem. Res.**2016**, 55, 11775–11784. [Google Scholar] [CrossRef] - Adánez, J.; Abad, A.; Perez-Vega, R.; Luis, F.; García-Labiano, F.; Gayán, P. Design and operation of a coal-fired 50 kW
_{th}chemical looping combustor. Energy Procedia**2014**, 63, 63–72. [Google Scholar] [CrossRef] - Ma, J.; Zhao, H.; Tian, X.; Wei, Y.; Rajendran, S.; Zhang, Y.; Bhattacharya, S.; Zheng, C. Chemical looping combustion of coal in a 5 kW
_{th}interconnected fluidized bed reactor using hematite as oxygen carrier. Appl. Energy**2015**, 157, 304–313. [Google Scholar] [CrossRef] - Su, M.; Zhao, H.; Ma, J. Computational fluid dynamics simulation for chemical looping combustion of coal in a dual circulation fluidized bed. Energy Convers. Manag.
**2015**, 105, 1–12. [Google Scholar] [CrossRef] - Ohlemüller, P.; Alobaid, F.; Abad, A.; Adanez, J.; Ströhle, J.; Epple, B. Development and validation of a 1D process model with autothermal operation of a 1 MW
_{th}chemical looping pilot plant. Int. J. Greenh. Gas Control**2018**, 73, 29–41. [Google Scholar] [CrossRef] - Wang, X.; Liu, X.; Jin, B.; Wang, D. Hydrodynamic study of AR coupling effects on solid circulation and gas leakages in a high-flux in situ gasification chemical looping combustion system. Processes
**2018**, 6, 196. [Google Scholar] [CrossRef] - Wang, X.; Jin, B.; Zhong, W.; Zhang, M.; Huang, Y.; Duan, F. Flow behaviors in a high-flux circulating fluidized bed. Int. J. Chem. React. Eng.
**2008**, 6, A79. [Google Scholar] [CrossRef] - Issangya, A.S.; Bai, D.; Bi, H.T.; Lim, K.S.; Zhu, J.; Grace, J.R. Suspension densities in a high-density circulating fluidized bed riser. Chem. Eng. Sci.
**1999**, 54, 5451–5460. [Google Scholar] [CrossRef] - Namkung, W.; Kim, S.W.; Kim, S.D. Flow regimes and axial pressure profiles in a circulating fluidized bed. Chem. Eng. J.
**1999**, 54, 245–252. [Google Scholar] [CrossRef] - Li, Z.Q.; Wu, C.N.; Wei, F.; Jin, Y. Experimental study of high-density gas-solids flow in a new coupled circulating fluidized bed. Powder Technol.
**2004**, 139, 214–220. [Google Scholar] [CrossRef] - Jing, S.; Li, H. Study on the flow of fine powders from hoppers connected to a moving-bed standpipe with negative pressure gradient. Powder Technol.
**1999**, 101, 266–278. [Google Scholar] [CrossRef] - Nagashima, H.; Ishikura, T.; Ide, M. Flow characteristics of a small moving bed downcomer with an orifice under negative pressure gradient. Powder Technol.
**2009**, 192, 110–115. [Google Scholar] [CrossRef] - Wang, J.; Bouma, J.H.; Dries, H. An experimental study of cyclone dipleg flow in fluidized catalytic cracking. Powder Technol.
**2000**, 112, 221–228. [Google Scholar] [CrossRef] - Wang, Q.; Yang, H.; Wang, P.; Lu, J.; Liu, Q.; Zhang, H.; Wei, L.; Zhang, M. Application of CPFD method in the simulation of a circulating fluidized bed with a loop seal, part I—Determination of modeling parameters. Powder Technol.
**2014**, 253, 814–821. [Google Scholar] [CrossRef] - Wang, Q.; Yang, H.; Wang, P.; Lu, J.; Liu, Q.; Zhang, H.; Wei, L.; Zhang, M. Application of CPFD method in the simulation of a circulating fluidized bed with a loop seal Part II—Investigation of solids circulation. Powder Technol.
**2014**, 253, 822–828. [Google Scholar] [CrossRef] - Yin, S.; Jin, B.; Zhong, W.; Lu, Y.; Shao, Y.; Liu, H. Gas-solid flow behavior in a pressurized high-flux circulating fluidized bed riser. Chem. Eng. Commun.
**2014**, 201, 352–366. [Google Scholar] [CrossRef] - Wang, Z.; Zhao, T.; Yao, J.; Liu, K.; Takei, M. Influence of particle size on the exit effect of a full-scale rolling circulating fluidized bed. Part. Sci. Technol.
**2018**, 36, 541–551. [Google Scholar] [CrossRef] - Chang, G.; Yang, G.; Yang, S.; Li, S.; Li, H. Gas solid flow in a moving bed under negative pressure difference. J. Chem. Ind. Eng.
**1980**, 31, 229–240. [Google Scholar] - Ergun, S. Fluid flow through packed columns. Chem. Eng. Prog.
**1952**, 48, 89–94. [Google Scholar] - Leung, L.S.; Jones, P.J. Flow of gas—Solid mixtures in standpipes. A review. Powder Technol.
**1978**, 20, 145–160. [Google Scholar] [CrossRef] - Ozahi, E.; Gundogdu, M.Y.; Carpinlioglu, M.Ö. A modification on Ergun’s correlation for use in cylindrical packed beds with non-spherical particles. Adv. Powder Technol.
**2008**, 19, 369–381. [Google Scholar] [CrossRef]

**Figure 1.**Schematic of the high-flux coal-direct chemical looping combustion (CDCLC) system (OC: oxygen carrier).

**Figure 2.**Schematic diagram of the cold-state experimental device of the high-flux CDCLC system. P: pressure; Q: gas flow; AR: air reactor; FR: fuel reactor.

**Figure 5.**Comparison of predicted and experimental upper pressure gradients under ideal sealing states with different solid circulation fluxes.

**Figure 6.**Comparison of predicted and experimental upper pressure gradients under the critical sealing state.

**Figure 7.**The pressure profile of the whole system and the apparent solids holdup along the FR under the proposed pressure gradient condition: (

**a**) pressure profile, and (

**b**) apparent solids holdup.

**Table 1.**Parameters for the calculation of the ideal upper pressure gradient (OC: oxygen carrier; FR: fuel reactor).

Description | Value |
---|---|

Density of air ρ_{g} (kg/m^{3}) | 1.29 |

Dynamic viscosity of air μ_{g} (Pa·s) | 1.78 × 10^{−5} |

Apparent density of the OC ρ_{s} (kg/m^{3}) | 3015 |

Void fraction in the downcomer ε (-) | 0.477 |

Mean diameter of the OC d_{s} (mm) | 0.43 |

Sphere coefficient of the OC φ_{s} (-) | 0.7 |

Diameter of the FR D_{f} (m) | 0.06 |

Diameter of the upper downcomer D_{ud} (m) | 0.10 |

**Table 2.**Pressure gradients and gas leakage ratios under the proposed operation condition (AR: air reactor).

Description | Parameter | Measured Value (%) | Calculation Value (%) | Relative Error (%) |
---|---|---|---|---|

ΔP_{1}/H_{1} = 3.8 kPa/m | FR leakage ratio f_{1} | −0.1 | 0 | - |

AR leakage ratio f_{2} | 2.5 | 2.9 | 14 | |

ΔP_{2}/H_{2} = 5.2 kPa/m | J-valve leakage ratio f_{3} | 15.2 | 14.2 | 7 |

Description | Value |
---|---|

Temperature (K) | 1243 |

Solid circulation flux G_{s} (kg/m^{2}·s) | 300 |

Gas dynamic viscosity under the hot state μ_{g,hot} (Pa·s) | 4.7 × 10^{−5} |

Apparent density of the OC ρ_{s} (kg/m^{3}) | 3015 |

Void fraction in the downcomer ε (-) | 0.477 |

Mean diameter of the OC d_{s} (mm) | 0.43 |

Sphere coefficient of the OC φ_{s} (-) | 0.7 |

FR diameter D_{f} (m) | 0.06 |

Upper downcomer diameter D_{ud} (m) | 0.10 |

Side length of the lower downcomer L_{ld} (m) | 0.10 |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Liu, X.; Jin, Z.; Zhu, J.; Jin, B.
Theoretical Methodology of a High-Flux Coal-Direct Chemical Looping Combustion System. *Processes* **2018**, *6*, 251.
https://doi.org/10.3390/pr6120251

**AMA Style**

Wang X, Liu X, Jin Z, Zhu J, Jin B.
Theoretical Methodology of a High-Flux Coal-Direct Chemical Looping Combustion System. *Processes*. 2018; 6(12):251.
https://doi.org/10.3390/pr6120251

**Chicago/Turabian Style**

Wang, Xiaojia, Xianli Liu, Zhaoyang Jin, Jiewen Zhu, and Baosheng Jin.
2018. "Theoretical Methodology of a High-Flux Coal-Direct Chemical Looping Combustion System" *Processes* 6, no. 12: 251.
https://doi.org/10.3390/pr6120251