Novel Lime Calcination System for CO₂ Capture and Its Thermal–Mass Balance Analysis

Abstract

In conventional lime calcination processes, because of fuel combustion in the kiln, the carbon dioxide (CO₂) from limestone decomposition is mixed with the flue gas, which results in energy requirement for gas separation in the carbon capture process. Here, a novel lime calcination system with carrier gas (CO₂) heating and air cooling is proposed to avoid the mixing problem of the CO₂ and the flue gas. This system consists of a new shaft kiln with four processing zones and a furnace system, where fuel combustion, limestone reaction, and lime cooling are carried out separately. Therefore, while obtaining qualified lime products, the CO₂ from limestone decomposition can be captured without a gas separation process, which accounts for 70% of the total carbon emission in lime production. Furthermore, a thermal–mass balance model was developed for the new system. Based on the model calculation, the energy consumption level of the new system was clarified via a case study. Moreover, parametric analyses were performed to examine the influence of the coefficient of excess air, the coefficient of lost carrier gas, and the calorific value of coal gas on the system performance such as the energy consumption and the CO₂ captured.

1. Introduction

Lime is an important industrial raw material and is widely used in major industries such as iron- and steel-making, flue gas desulfurization, construction, and paper-making industries.¹⁻³ Lime is generally obtained by thermal decomposition of limestone into quicklime and carbon dioxide (CO₂) in a shaft kiln⁴ or a rotary kiln;⁵ thus, lime production is a significant source of carbon emissions.^5,6 China is currently the largest lime producer in the world with an annual output of more than 200 million tons, accounting for about 70% of the world’s total output.⁷ In China, the greenhouse gas emissions caused by lime production increased from 35 million tons of equivalent CO₂ in 1979 to 140 million tons of equivalent CO₂ in 2009; Chinese emissions in 2009 accounted for more than 60% of the world’s emissions related to lime.^8,9 Thus, there is a pressing need to decrease the emissions of this carbon-intensive sector.

The thermal decomposition reaction equation¹⁰ of limestone is as follows

1

The reaction formula of eq 1 shows that there are two kinds of CO₂ emission during the lime production: (1) the CO₂ from limestone decomposition (the mass accounts for 42% of the mass of limestone)¹¹ and (2) the CO₂ from fuel combustion. This is because the decomposition of limestone is an endothermic reaction, and the industry generally uses fossil fuels to heat the raw materials. Of these, limestone decomposition dominates the carbon emission, accounting for about 70%⁵ of the total carbon emission during lime production.

For the conventional calcination process widely used in lime production, as shown in Figure 1a, because of the fuel combustion in the kiln, the above two parts of CO₂ are emitted as flue gas after mixing.^12,13 Thus, the purity required for CO₂ transportation and storage cannot be achieved because the flue gas contains a large amount of nitrogen, and CO₂ capture requires a gas separation device that consumes a considerable amount of separation energy.

Figure 1.

Comparison of principles: (a) conventional limestone calcination process and (b) new lime calcination process.

This work proposes a novel lime calcination process with carrier gas heating and air cooling, as shown in Figure 1b. On the one hand, to avoid mixing the CO₂ from limestone decomposition with the flue gas of fuel combustion, the CO₂ used as the circulating carrier gas is employed for heating the limestone. On the other hand, to avoid the carbonation of lime as well as to recover the heat carried by the lime, the air is used for cooling the hot lime. Thus, while obtaining qualified lime products, the tail gas of the new process is expected to be pure CO₂. As a result, the CO₂ from limestone decomposition, which accounts for 70% of the total carbon emission in lime production, can be directly captured without separation of nitrogen and CO₂.

The principle of the reduction in CO₂ emissions of the new process is obvious, but its energy consumption needs to be clarified. In the new process, the partial pressure of CO₂ in the kiln is about five times that of conventional calcination, which means the new process has a greater initial temperature of limestone decomposition. Then, the temperature of the carrier gas discharged from the kiln roof would increase and may increase energy consumption. Therefore, to understand the energy consumption level of the new process and clarify its feasibility, it is necessary to establish the thermal–mass balance model of the new process.

The thermal–mass balance analysis is a common method for calculating energy consumption and thermal efficiency in the industry. There is considerable literature on thermal–mass balance modeling. Among them, some literature works on the shaft lime kiln are as follows.

Zuideveld et al.¹⁴ studied the calculation methods for the design of the preheating zone, reacting zone, and cooling zone of shaft kilns. Zhou et al.¹⁵ established a thermal and material balance model in the lime kiln and performed the thermal process analysis in terms of the main influence factors on the thermal equilibrium state of the lime kiln. Zhou et al.¹⁶ also developed a mathematical model of the reaction and heat-transfer process in a lime shaft kiln based on the material and energy balance relationship and studied the influence of various operating parameters on the limestone calcination process. Piringer¹⁷ studied the applications of the low calorific value gas in the lime kilns of the iron and steel enterprises. Schwertmann^18,19 studied the balance calculation of each zone of the lime kiln and obtained heat consumption of the entire kiln through an accurate balance calculation of the reacting zone. Yi et al.²⁰ established a mathematical model of limestone decomposition and heat transfer based on the principles of thermal and material balance. The influence of operating parameters on the calcination process was then analyzed and optimized. Lang et al.²¹ performed a thermal balance analysis of the cooling and heating zones of the shaft kiln and proposed a method to reduce energy consumption. Tong²² proposed a thermal balance model of the lime kiln and optimized the related process parameters based on the thermal balance analysis. Gutiérrez et al.⁶ developed a mass, energy, and exergy balance model to evaluate the performance of a vertical shaft kiln. Rong et al.¹ conducted a comprehensive model analysis to improve the thermal performance of annular shaft kilns with opposite burners.

While the above-mentioned literature is important for energy consumption calculations, operation conditions of the new process are quite different from conventional limestone calcination processes. For instance, the CO₂ pressure of the gas phase in the reacting zone of the new process is about five times that of the conventional process. The literature models cannot be applied directly to the new process. Therefore, a thermal–mass balance model for the new process has been developed.

2. Process Description

To facilitate modeling and analysis, the new process was envisioned to a new system from the standpoint of industrial practice in Figure 2, which consists of a new shaft kiln with four processing zones and a furnace system. The shaft kiln is used to convert limestone to lime, and the furnace system is used to provide the heat required for the conversion process. Compared with a conventional one, the new shaft kiln includes a soaking zone. Limestone particles enter the shaft kiln from the kiln roof and slowly drop under gravity. Lime particles are formed and discharged from the bottom of the shaft kiln after preheating, reacting (decomposition), soaking, and cooling. The heat required for the limestone decomposition reaction is carried into the shaft kiln from the furnace system by a circulating carrier gas. Most of the circulating carrier gas enters the reacting zone, and a small part of the circulating carrier gas enters the soaking zone.

Figure 2.

Flow scheme of the new lime calcination system.

In the reacting zone, the rising carrier gas heats the particles, and the limestone in the particles is heated to convert to lime and release CO₂. As a result, the temperature of the carrier gas along its flow direction gradually decreases and the mass flow rate gradually increases. Then, the rising carrier gas continues to enter the preheating zone and heat the limestone particles, but the particle temperature has not reached the limestone’s initial decomposition temperature. Thus, in the preheating zone, the temperature of the carrier gas gradually decreases along its flow direction but the mass flow rate remains unchanged. At the kiln roof, part of the carrier gas is discharged as the tail gas and the rest of the carrier gas is recovered by a high-temperature blower and sent to the furnace system (stove-A in Figure 2) as the circulating carrier gas.

In the soaking zone, the heat conduction occurs in the particles due to the temperature gradient in the particle. The temperature gradient in the particle gradually decreases until the temperature is evenly distributed. The carrier gas flows along the direction of the movement of the particles and exchanges heat with the particles. As a result, the carrier gas temperature gradually decreases to equal to the particle temperature and finally exits the shaft kiln from the bottom of the soaking zone. In the cooling zone, the air cools the particles, and the air temperature gradually increases but its mass flow rate remains unchanged and finally exits the shaft kiln from the top of the cooling zone. The carrier gas discharged from the bottom of the soaking zone and the hot air discharged from the top of the cooling zone are mixed to form an oxidant gas and sent to the furnace system (stove-B in Figure 2), thereby completing the entire cycle.

The new system has several advantages over the conventional process: (1) The CO₂ generated from the limestone decomposition process is used as the carrier gas; thus, a tail gas with high-purity CO₂ can be obtained and captured, while the lime particles are cooled by the air to avoid carbonation. (2) The heat is provided by combustion outside the shaft kiln, and therefore, the flame and the harmful products of the fuel combustion do not contact the particles, which improves the quality of the lime products. (3) By including the soaking zone, the cooling air is prevented from being mixed with the carrier gas in the reacting and cooling zones, thereby ensuring the purity of carrier gas.

3. Thermal–Mass Balance Model

The new lime calcination system includes a shaft kiln and a furnace system (as shown in Figure 2). To analyze the thermal–mass balance of the shaft kiln, Figure 3 shows the temperature distribution schematic curves of each zone in the shaft kiln. Particle processing in the shaft kiln is divided into four zones: preheating, reacting, soaking, and cooling. In the preheating zone, the limestone particles from the kiln roof are preheated to the initial decomposition temperature. In the reacting zone, the limestone is decomposed. In the soaking zone, the heat can homogenize throughout the particle, so that when the particle is discharged from the soaking zone it has a uniform temperature distribution throughout its radius. In the cooling zone, the particles are discharged from the kiln bottom after being cooled. The particle temperature at the junction of the preheating and reacting zones should be equal to the limestone’s initial decomposition temperature. The circulating carrier gas is injected into the kiln at the junction of the reaction and soaking zones, the cooling air is introduced into the bottom of the cooling zone, and the hot air is drawn from the junction of the soaking and cooling zones. Besides, the establishment of the thermal–mass balance model requires the following assumptions: (1) the system is operated under steady-state conditions, (2) the limestone particles only contain CaCO₃, (3) the carrier gas contains only CO₂, (4) heat loss of the shaft kiln and the furnace system is negligible, and (5) the kinetic and potential energies of the gas and solid streams are negligible.

Figure 3.

Principle temperature profiles in the shaft kiln.

Based on the above conditions, Figure 4 further shows the thermal–mass input and output of the new system. Based on Figure 4, the thermal–mass balance model for the shaft kiln and the furnace system can be established. Especially, the thermal–mass balance of the shaft kiln is discussed in four parts, namely, the preheating, reacting, soaking, and cooling zones.

Figure 4.

Thermal–mass balance diagram of the new lime calcination system.

3.1. Mass Balance Equations of the Shaft Kiln

The mass streams in the shaft kiln include the carrier gas, particle, and air streams. In the preheating, soaking, and cooling zones, the mass flow rate of each stream remains unchanged. In the reacting zone, the limestone decomposes into lime and CO₂ so that the mass flow rate of the particle stream decreases and the mass flow rate of the carrier gas stream increases. The mass balance equation of the carrier gas stream in the reacting zone is

2

The mass balance equation of the particle stream in the reacting zone is

3

where x is the CO₂ content in the limestone particle (mass fraction).

3.2. Thermal Balance Equations of the Shaft Kiln

3.2.1. Preheating Zone

As shown in Figure 4, the heat outputs in the preheating zone include the heat taken away by the carrier gas and the limestone particles and the heat inputs include the heat brought by the carrier gas and the limestone particles. The heat balance equation of the preheating zone is

4

where m_L is the mass flow rate of the limestone particles, m_g is the mass flow rate of the carrier gas, T is the temperature, T_r is the temperature of the carrier gas entering the preheating zone (leaving the reacting zone), T_a is the environmental temperature, T_t is the tail gas temperature, T_e is the limestone’s initial decomposition temperature, and C_p^CO₂ and C_p are the specific heat capacities of the carrier gas and the limestone particles, respectively. In eq 4, T_r must be greater than T_e, and the difference between these two temperatures is the pinch temperature difference of the shaft kiln, that is

5

In practice, the value of ΔT_re depends on factors such as gas–solid heat-transfer characteristics, particle size, and height of the preheating zone. Therefore, in the model calculation, ΔT_re is a given parameter in Table 2.

Table 2. Parameters for Model Calculations.

no.	parameter	unit	value
1	mL	t·d–1	345.0
2	P	bar	1.013
3	Ta	K	300
4	Th	K	1623
5	Tref	K	300
6	α		1.0
7	β		0
8	qce	MJ·kg–1	29.307
9	yfCO2	%	10.00
10	yfCO	%	35.62
11	yfN2	%	54.38
12	yaO2	%	21.00
13	yaN2	%	79.00
14	P0	bar	2.150 × 107
15	ΔTre	K	5
16	x	%	42
17	ηQ	%	98
18	ΔhQ	kJ·kg–1	2946.4
19	ΔhrL	kJ·mol–1	165.0
20	ΔhrCO	kJ·mol–1	283.0
21	ΔTpa	K	30
22	ΔTsf	K	30
23	ΔTst	K	30

3.2.2. Reacting Zone

As shown in Figure 4, the main heat output in the reacting zone is the decomposition heat of limestone, and the remaining output includes the heat taken away by the carrier gas and the lime particles. The heat inputs include the heat brought by the circulating carrier gas and the limestone particles. The heat balance equation of the reacting zone is

6

where m_h is the mass flow rate of the circulating carrier gas entering the reacting zone, m_Q is the mass flow rate of the lime particles leaving the reacting zone, η_Q is the conversion ratio of limestone, Δh_Q is the reaction enthalpy required for generating a unit mass of lime, T_ref is the reference temperature, T_h is the temperature of the circulating carrier gas entering the reacting zone (from the furnace system), C_p^Q is the specific heat capacity of the lime particles, and T_b is the average temperature of the lime particles leaving the reacting zone.

The lime particles leaving the reacting zone for the soaking zone have just completed the reaction, and there is a temperature gradient in the particle. Therefore, T_b in eq 6 is estimated by further assumptions. Indeed, the surface temperature of lime particles can be approximately equal to T_h, and the center temperature is approximately equal to T_e. By assuming that the lime particles are spherical and the temperature from the surface to the center is linearly distributed (Iliuta et al.²³ pointed out that the temperature within the lime particle is slightly different from a linear distribution), then, according to the conservation of energy, T_b satisfies the following formula

where r is the radial coordinate and r₀ is the radius of the lime particles. Then, we have

7

3.2.3. Soaking Zone

As shown in Figure 4, the heat outputs in the soaking zone include the heat taken away by the carrier gas and the lime particles and the heat inputs include the heat brought by the circulating carrier gas and the lime particles. Given that the temperatures of the gas and particles at the bottom of the soaking zone are equal and there is no temperature gradient in the particle, the heat balance equation of the soaking zone is

8

where T_q is the temperature of the carrier gas and the lime particles at the bottom of the soaking zone and m_c is the mass flow rate of the circulating carrier gas entering the soaking zone.

Under the ideal design condition, no circulating carrier gas should enter the soaking zone (because it will reduce the amount of CO₂ captured) and no cooling air should be entering the reacting zone through the soaking zone (because it will reduce the CO₂ purity of the tail gas). However, in actual operation, it is difficult to maintain the above ideal state through pressure balance. As a compromise, a small part of the circulating carrier gas can be lost to ensure the purity of CO₂ captured, that is, a small part of the circulating carrier gas can enter the soaking zone.

Since the circulating carrier gas entering the soaking zone is finally discharged from the system after passing through the furnace system, m_c should not be greater than the mass flow rate of the CO₂ generated in the reacting zone to ensure the mass balance of the system. The larger the m_c, the less the CO₂ captured through the tail gas recovery. Therefore, the coefficient of lost carrier gas β with a value range of 0–1 is further defined to measure the amount of circulating carrier gas entering the soaking zone, namely, β = m_c/(m_L – m_Q). In practice, the value of β depends on the pressure characteristic of each zone in the shaft kiln. Therefore, in the model calculation, β is a given parameter in Table 2.

3.2.4. Cooling Zone

As shown in Figure 4, the heat outputs of the cooling zone include the heat taken away by the hot air and the lime particles and the heat inputs include the heat brought by the cooling air and the lime particles. The heat balance equation of the cooling zone is

9

where m_a is the mass flow rate of the cooling air, T_c is the temperature of the hot air, T_p is the temperature of the lime product discharged from the bottom of the shaft kiln, and C_p^air is the specific heat capacity of the air. In eq 9, the lime particle temperature T_p at the kiln bottom must be higher than the cooling air temperature T_a. The difference between these two temperatures is the bottom temperature difference of the shaft kiln, that is

10

In practice, the value of ΔT_pa depends on factors such as heat-transfer characteristics and the height of the cooling zone. Therefore, in the model calculation, ΔT_pa is a given parameter in Table 2.

3.3. Decomposition Temperature of Limestone

Solving these thermal–mass balance equations also requires the decomposition temperature of limestone, which is a function of the partial pressure of CO₂. The formula of limestone decomposition temperature is given as follows²⁴

11

where Δh_r^L is the reaction enthalpy, R is the gas constant, P is the partial pressure of CO₂, and P₀ is the equation constant. In the new system, the carrier gas is regarded as pure CO₂, so the partial pressure of CO₂ is equal to the gas-phase pressure in the kiln.

3.4. Thermal Balance Equations of the Furnace System

The furnace system is equipped with a preheater and two identical regenerative hot stoves (stove-A and stove-B). Stove-A and stove-B are switched for use. When stove-A is in the heat storage step, stove-B is in the heat release step, and vice versa. In the following discussion, stove-A is assumed to be in the heat release step, and stove-B is in the heat storage step. The fuel of the furnace system is the coal gas, which is common in iron- and steel-making mills, such as the blast furnace gas (BFG) and the Linze–Donawitz gas (LDG), and the combustible component of the coal gas is assumed to be carbon monoxide and completely burned. Then, the thermal balance analysis is performed.

3.4.1. Stove-A

In stove-A, the circulating carrier gas from the shaft kiln roof absorbs the heat released by stove-A to increase its temperature. The heat balance equation of stove-A is

12

where Q_s is the heat-releasing load of stove-A.

3.4.2. Stove-B

In stove-B, the coal gas from the preheater and the oxidant gas from the shaft kiln are mixed and combusted. The high-temperature flue gas stores its heat in stove-B, then flows into the preheater for heat recovery, and finally leaves the system. As shown in Figure 4, the heat outputs of stove-B include the heat taken away by the flue gas and the heat stored. The heat inputs of stove-B include the heat brought by the oxidant gas and the coal gas and the heat generated by combustion. The heat-storing load of stove-B should be equal to the heat-releasing load of stove-A. The heat balance equation of stove-B is

13

where N_f is the molar flow rate of the coal gas, N_d is the molar flow rate of the flue gas, Δh_r^CO is the combustion reaction enthalpy of carbon monoxide (the calorific value of carbon monoxide), y_f is the mole fraction of carbon monoxide in the coal gas, C_p,m^f and C_p,m are the molar specific heat capacities of the coal gas and the flue gas, respectively, T_f is the temperature of the coal gas entering stove-B, and T_s is the temperature of the flue gas discharged from stove-B. Because the stoves are regenerative heat exchangers, T_s is close to T_t. The difference between these two temperatures is the cold-end temperature difference of the stoves, that is

14

In practice, the value of ΔT_st depends on the heat-transfer performance of the stoves. Therefore, in the model calculation, ΔT_st is a given parameter in Table 2.

In the flue gas, the mole fraction of CO₂, the mole fraction of oxygen, and the mole fraction of nitrogen (y_d^CO₂, y_d, and y_d^N₂) are calculated by eqs 15 –17, respectively.

15

where N_c is the molar flow rate of CO₂ in the oxidant gas, N_f is the molar flow rate of the coal gas, N_d is the molar flow rate of the flue gas, and y_f^CO₂ and y_f are the mole fractions of CO₂ and carbon monoxide in the coal gas, respectively.

16

where N_a is the molar flow of the air and y_a^O₂ is the molar fraction of oxygen in the air.

17

where y_a^N₂ is the molar fraction of nitrogen in the air and y_f is the mole fractions of nitrogen in the coal gas.

The N_c in eq 15 is obtained by

18

where M_CO2 is the molecular weight of CO₂.

The N_a in eq 16 is obtained by

19

where M_air is the molecular weight of air.

The N_f in eq 15 is obtained by

20

where α is the coefficient of excess air and S_o is the stoichiometric amount of oxidant for the coal gas combustion, which is calculated by

21

The N_d in eq 15 is obtained by

22

3.4.3. Preheater

The heat balance equation of the preheater is

23

where T_d is the final discharge temperature of the flue gas. In eq 23, T_f is less than T_s. The difference between these two temperatures is the hot-end temperature difference of the preheater, that is

24

In practice, the value of ΔT_sf depends on the design of the preheater. Therefore, in the model calculation, ΔT_sf is a given parameter in Table 2.

3.5. Calculation of Energy Consumption

As shown in Figure 4, the only energy consumption of the system is the coal gas passed into the furnace system, so the energy consumption per unit of lime product (or to be called “unit energy consumption” for short) is defined and calculated by

25

Furthermore, according to Figure 4, the unit energy consumption of the system is composed of four parts, namely, the heat requirement of the limestone decomposition reaction, the waste heat taken away by the tail gas, the waste heat taken away by the flue gas, and the waste heat taken away by the lime product. To examine the proportions of different parts in the unit energy consumption and their changing laws, the expressions for the different parts in the unit energy consumption are also given below.

The expression of the limestone’s decomposition heat is

26

where q_ce is the calorific value of a unit kilogram standard coal.

The expression of the waste heat taken away by the tail gas is

27

The expression of the waste heat taken away by the flue gas is

28

The expression of the waste heat taken away by the lime product is

29

4. Results and Discussion

A new system with an output of 200 t·d^–1 to be used in an iron- and steel-making mill was taken as a case study. First, the system under typical operating conditions is calculated. Second, based on typical working conditions, the following three parameters have been changed to analyze their influence on energy consumption (e₁, e₂, e₃, and e₄), on the flue gas temperatures T_d, on the tail gas temperature T_t, on the flue gas amount m_d, and on the CO₂ captured m_t (the tail gas amount): the coefficient of excess air α (Section 4.1), the coefficient of lost carrier gas β (Section 4.2), and the calorific value of coal gas q_c (Section 4.3).

The q_c is obtained by

30

The m_d is obtained by

31

where M_N2 is the molecular weight of nitrogen.

The m_t is obtained by

32

The C_p,m^f in eq 13 is calculated by

33

where M_CO is the molecular weights of carbon monoxide and C_p^N₂ and C_p are the specific heat capacities of nitrogen and carbon monoxide, respectively.

The C_p,m^d in eq 13 is calculated by

34

where C_p^O₂ is the specific heat capacity of oxygen and M_O2 is the molecular weight of oxygen.

The specific heat capacities mentioned above depend on the temperature, which is calculated by the following expression^25,26

35

where C_p0, T₀, and n are the equation constants. The equation constants for calculating the specific heat capacities of gases and solids used in this work come from the literature^25,26 and are listed in Table 1.

Table 1. Constants for the Heat Capacity Equation.

material	Cp0 (kJ·kg–1·K–1)	T0 (K)	n (−)
CO2	0.84	273	0.30
CO	1.00	273	0.12
O2	0.90	273	0.15
N2	1.00	273	0.11
air	1.00	273	0.10
lime	0.84	373	0.13
limestone	0.97	373	0.25

In addition to the above specific heat calculation equations (from eqs 33 to 35) and equation constants in Table 1, the main parameters used in this model are listed in Table 2. In Table 2, the 1st to 13th parameters are the operating conditions of the kiln, the 14th to 20th parameters come from the literature,^25,26 and the 21st to 23rd parameters are given parameters (namely, the three heat exchange temperature differences, which are set to a reasonable value of 30 °C). In this model, there are 31 unknown variables to be determined by solving 31 equations (from eqs 2 to 32). These variables as well as their calculation results under typical operating conditions are listed in Table 3.

Table 3. Model Unknown Variables and Their Calculation Results under Typical Operating Conditions.

no.	parameter	unit	value
1	mQ	t·d–1	200.0
2	mg	t·d–1	1139
3	mh	t·d–1	994.4
4	mc	t·d–1	0
5	ma	t·d–1	203.0
6	mt	t·d–1	144.8
7	md	t·d–1	448.7
8	So		0.848
9	Te	K	1176.4
10	Tb	K	1511.4
11	Tc	K	1290.2
12	Tt	K	942.0
13	Tp	K	330.0
14	Tq	K	1511.3
15	Ts	K	972.0
16	Tf	K	942.0
17	Td	K	635.7
18	qc	MJ·m–3	4.5
19	Qs	kW	10 446
20	Nc	mol·s–1	0
21	Na	mol·s–1	81.47
22	Nf	mol·s–1	96.06
23	Nd	mol·s–1	160.4
24	ydCO2	%	27.32
25	ydO2	%	0
26	ydN2	%	72.68
27	e	kgce·t–1	142.7
28	e1	kgce·t–1	98.53
29	e2	kgce·t–1	16.88
30	e3	kgce·t–1	26.49
31	e4	kgce·t–1	0.841

4.1. Influence Analysis of the Coefficient of Excess Air

The coefficient of excess air is an important operating indicator of fuel combustion. In general, the coefficient of excess air should be as small as possible, but the premise is that the fuel must be completely burned. As shown in Figures 5 and 6, we analyzed the influence of the coefficient of excess air in the range of 1.0–1.35 on the energy consumption, the flue gas temperature, the tail gas temperature, the flue gas amount, and the CO₂ captured (the tail gas amount).

Figure 5.

Influence of the coefficient of excess air on energy consumption.

Figure 6.

Influence of the coefficient of excess air on the (a) flue gas temperature and tail gas temperature and (b) flue gas amount and CO₂ captured.

Figure 5 shows that as the coefficient of excess air increases, the waste heat of tail gas e₂ and the waste heat of lime product e₄ remain unchanged but the waste heat of flue gas e₃ increases. Overall, the larger the excess air coefficient, the higher the unit energy consumption. Since the limestone’s decomposition heat e₁ is fixed and the waste heat of tail gas e₂ remains unchanged, the increase in unit energy consumption is caused by an increase in the waste heat of flue gas e₃.

Figure 6 shows that as the coefficient of excess air increases, both the flue gas temperature and the flue gas amount increase, while the tail gas temperature and the CO₂ captured (the tail gas amount) keep unchanged. It can be seen that the reason for the increase in the waste heat of flue gas e₃ is that the flue gas amount and the flue gas temperature both increase, and the reason that the waste heat of tail gas e₂ keeps unchanged is that the tail gas temperature and the tail gas amount both remain unchanged.

In summary, to reduce the unit energy consumption of the system, the coefficient of excess air should be controlled as low as possible.

4.2. Influence Analysis of the Coefficient of Lost Carrier Gas

The lost carrier gas means the circulating carrier gas entering the soaking zone. Allowing a small amount of the circulating carrier gas to enter the soaking zone is a compromise in actual operation. By sacrificing some of the CO₂ capture capacity as the expense, the air in the cooling zone will not enter the reacting zone through the soaking zone, which ensures the high purity of the tail gas to facilitate the direct capture of CO₂. As shown in Figures 7 and 8, we analyzed the impact of the coefficient of lost carrier gas in the range of 0–0.35 on energy consumption, the flue gas temperature, the flue gas amount, the tail gas temperature, and the CO₂ captured (the tail gas amount).

Figure 7.

Influence of the coefficient of lost carrier gas on energy consumption.

Figure 8.

Influence of the coefficient of lost carrier gas on the (a) flue gas temperature and tail gas temperature and (b) flue gas amount and CO₂ captured.

Figure 7 shows that as the coefficient of lost carrier gas increases, the waste heat of lime product remains unchanged, the waste heat of flue gas increases, and the waste heat of tail gas decreases. Since the limestone’s decomposition heat e₁ is fixed, and the increase in the waste heat of flue gas e₃ offsets the decrease in the waste heat of tail gas e₂, the coefficient of lost carrier gas does not significantly influence the unit energy consumption.

Figure 8 shows that as the coefficient of lost carrier gas increases, both the flue gas temperature and the flue gas amount increase, the tail gas temperature remains unchanged, and the CO₂ captured (the tail gas amount) decreases. Therefore, the reason for the increase in the waste heat of flue gas e₃ is the increase of both the flue gas amount and the flue gas temperature, and the reason for the decrease of the waste heat of tail gas e₂ is the decrease in the tail gas amount.

In summary, although the coefficient of lost carrier gas does not influence the unit energy consumption of the system, the increase in the coefficient of lost carrier gas means a decrease in the CO₂ captured (the tail gas amount). Therefore, to capture more CO₂, the coefficient of lost carrier gas should be controlled as low as possible.

4.3. Influence Analysis of the Calorific Value of Coal Gas

The coal gas, such as BFG or LDG, is a relatively abundant energy source in iron- and steel-making enterprises, whose main combustible component is carbon monoxide. Because different types of coal gas have different carbon monoxide contents, the calorific value of coal gas varies. As shown in Figures 9 and 10, we analyzed the impact of the calorific value of coal gas in the range of 4.5–8.0 MJ·m^–3 (from BFG to LDG) on energy consumption, the flue gas temperature, the flue gas amount, the tail gas temperature, and the CO₂ captured (the tail gas amount).

Figure 9.

Influence of the calorific value of coal gas on energy consumption.

Figure 10.

Influence of the calorific value of coal gas on (a) flue gas temperature and tail gas temperature and (b) flue gas amount and CO₂ captured.

Figure 9 shows that as the calorific value of coal gas increases, the waste heat of lime product e₄, the waste heat of flue gas e₃ and the waste heat of tail gas e₂ all have not changed significantly. Since the limestone’s decomposition heat e₁ is fixed, the calorific value of coal gas does not influence the unit energy consumption of the system.

Figure 10 shows that as the calorific value of coal gas increases, the tail gas temperature and the CO₂ captured (the tail gas amount) remain unchanged, the flue gas temperature increases, and the flue gas amount decreases. The increase of the flue gas temperature offsets the decrease of the flue gas amount, so the waste heat of flue gas e₃ remains unchanged.

In summary, the calorific value of coal gas does not influence the unit energy consumption of the system.

5. Conclusions

In this work, a lime calcination process with the CO₂ heating and the air cooling was proposed to avoid mixing the CO₂ from limestone decomposition with the flue gas of fuel combustion. This new process was extended to a new system from the standpoint of industrial practice, which consists of a new shaft kiln and a furnace system. Since the fuel combustion and the limestone decomposition reaction are performed separately, the CO₂ from limestone decomposition can be directly captured without separation of nitrogen and CO₂. Furthermore, a thermal–mass balance model was developed for the new system, and the energy consumption level of the new system was understood via a case study. The model-based analysis was performed to examine the influence of the key parameters on the performance of the new system. Based on the case study of the new lime calcination system, the main conclusions derived are as follows:

• (1)Under typical operation conditions, the unit energy consumption of the new system using BFG as fuel is 142.7 kgce·t^–1 and the CO₂ captured is 144.8 t·d^–1 (the lime output of the system is 200 t·d^–1).
• (2)The greater the air excess coefficient (ranges from 1.0 to 1.35), the higher the unit energy consumption.
• (3)The coefficient of lost carrier gas (ranges from 0 to 0.35) does not influence the unit energy consumption.
• (4)The calorific value of coal gas (ranges from 4.5 to 8.0) does not influence the unit energy consumption.

Glossary

Nomenclature

C_p0

constant for eq 35, kJ·kg^–1·K^–1

C_p^air

specific heat capacity of air, kJ·kg^–1·K^–1

C_p^CO

specific heat capacity of carbon monoxide, kJ·kg^–1·K^–1

C_p^CO₂

specific heat capacity of the carrier gas (CO₂), kJ·kg^–1·K^–1

C_p,m^d

molar specific heat capacity of the flue gas, kJ·mol^–1·K^–1

C_p,m^f

molar specific heat capacity of the coal gas, kJ·mol^–1·K^–1

C_p^N₂

specific heat capacity of nitrogen, kJ·kg^–1·K^–1

C_p^O₂

specific heat capacity of oxygen, kJ·kg^–1·K^–1

e

unit energy consumption (kilogram standard coal per ton lime), kgce·t^–1

e₁

limestone’s decomposition heat, kgce·t^–1

e₂

waste heat taken away by the tail gas, kgce·t^–1

e₃

waste heat taken away by the flue gas, kgce·t^–1

e₄

waste heat taken away by the lime product, kgce·t^–1

m_a

mass flow rate of the air in the cooling zone, t·d^–1

m_c

mass flow rate of the circulating carrier gas entering the soaking zone, t·d^–1

m_d

mass flow rate of the flue gas, t·d^–1

m_g

mass flow rate of the carrier gas entering the preheating zone, t·d^–1

m_h

mass flow rate of the circulating carrier gas entering the reacting zone, t·d^–1

m_L

mass flow rate of limestone particles entering the preheating zone, t·d^–1

m_Q

mass flow rate of lime particles in the cooling zone, t·d^–1

m_t

mass flow rate of the tail gas (CO₂ captured), t·d^–1

M_N2

molecular weight of nitrogen, kg·mol^–1

M_CO2

molecular weight of carbon dioxide, kg·mol^–1

M_CO

molecular weight of carbon monoxide, kg·mol^–1

M_O2

molecular weight of oxygen, kg·mol^–1

n

constant for eq 35

N_c

molar flow rate of the circulating carrier gas entering the soaking zone, mol·s^–1

N_a

molar flow rate of the cooling air, mol·s^–1

N_f

molar flow rate of the coal gas, mol·s^–1

N_d

molar flow rate of the flue gas, mol·s^–1

P

gas-phase pressure in the shaft kiln, bar

P₀

constant for eq 11, bar

q_c

calorific value of coal gas, MJ·m^–3

q_ce

calorific value of standard coal, MJ·kg^–1

Q_s

heat-releasing load of stove-A, kW

r

radial coordinate, m

r₀

radius of the lime particle, m

R

ideal gas constant, R = 0.008314, kJ·mol^–1·K^–1

S_o

stoichiometric amount of the oxidant

T

temperature, K

T₀

constant for eq 35, K

T_a

environmental temperature, K

T_b

average temperature of the lime particles leaving the reacting zone, K

T_c

temperature of the air leaving the cooling zone, K

T_d

temperature of the flue gas discharged from the preheater, K

T_e

limestone’s initial decomposition temperature, K

T_f

temperature of the coal gas discharged from the preheater, K

T_h

temperature of the circulating carrier gas entering the shaft kiln, K

T_p

temperature of the lime product, K

T_q

temperature of the gas and solid at the bottom of the soaking zone, K

T_r

temperature of the carrier gas leaves the racting zone, K

T_ref

reference temperature, K

T_s

temperature of the flue gas discharged from stove-B, K

T_t

temperature of the tail gas, K

x

CO₂ mass fraction of limestone %

y_a^O₂

O₂ molar fraction of air, %

y_a^N₂

N₂ molar fraction of air, %

y_d^CO₂

CO₂ molar fraction of the flue gas, %

y_d^O₂

O₂ molar fraction of the flue gas, %

y_d^N₂

N₂ molar fraction of the flue gas, %

y_f^CO₂

CO₂ molar fraction of the coal gas, %

y_f^CO

CO molar fraction of the coal gas, %

y_f^N₂

N₂ molar fraction of the coal gas, %

Glossary

Greek Letters

Δh_Q

reaction enthalpy of generating a unit mass of lime, kJ·kg^–1

Δh_r^L

reaction enthalpy of generating a unit mole of lime, kJ·mol^–1

Δh_r^CO

reaction enthalpy of CO combustion, kJ·mol^–1

ΔT_pa

bottom temperature difference of the shaft kiln, K

ΔT_re

pinch temperature difference of the shaft kiln, K

ΔT_sf

hot-end temperature difference of the preheater, K

ΔT_st

cold-end temperature difference of the stove, K

η_Q

conversion ratio of limestone, %

α

coefficient of excess air

β

coefficient of the carrier gas

Glossary

Abbreviations Used

BFG

blast furnace gas

LDG

Linze–Donawitz gas

The authors declare no competing financial interest.