Thermodynamic Analysis of Calcium Carbide ... - ACS Publications

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Thermodynamic Analysis of Calcium Carbide Production Leiming Ji, Qingya Liu, and Zhenyu Liu* State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: CaC2 production is studied from the viewpoint of thermodynamics using an equilibrium composition model with total Gibbs free energy minimization. It is found that CaC2 is formed directly from the reaction of C and CaO without an intermediate step under the conditions of industrial practice. The different reaction mechanisms reported in the literature can be attributed to the difference in reaction conditions. The model determines equilibrium composition of the reaction system under various conditions, including those applicable to the autothermal CaC2 production process.

1. INTRODUCTION Calcium carbide (CaC2) is an important coal-derived platform chemical produced via a reaction of CaO with coke (C), reaction 1. It is mainly used to produce acetylene and acetylenederived products, such as polyethylene (PE), polyvinyl chloride (PVC), vinylacetic acid, and 1,4-butyl glycol.1 In 2012, the annual production of CaC2 in China is more than 18 million tons.2 3C + CaO → CaC2 + CO (1)

lower than 1733 K and the appearance of CO in the gas and CaC2 in the solid at temperatures higher than 1733 K suggested the occurrence of reaction 1. Mu and Hard10 also reported similar findings. These inconsistencies in mechanism seem to indicate that the reaction passway to CaC2 varies with the reaction conditions. It should be noted that a reaction mechanism can not only be determined by experiments, but also can be evaluated by the thermodynamic state of the system and the equilibrium compositions. For example, El-Naas11 studied the equilibrium composition of a C−CaO−CaC2 system at a C/Ca ratio of 3 and reported CaC2 formation at temperatures of higher than 2150 K under the ambient pressure. Erasmus12 studied the CaC2 yield and the amounts of Ca vapor in a temperature range of 1973−2773 K at C/CaO ratios of 1.72−2.85 under the ambient pressure. Zhu et al.13 reported a relationship between the CaC2 equilibrium composition and the Ar content in a plasma system at a C/CaO ratio of 3. However, these studies did not address the CaC2−CaO eutectic that forms at temperatures about 1973 K,10,14,15 which may play an important role in determination of the equilibrium composition. Furthermore, the autothermal process may not be limited to the ambient pressure operation and changes in pressure may affect the reaction mechanism. In this work, a thermodynamic analysis involving the formation of the CaC2−CaO eutectic is carried out to understand the CaC2 formation mechanism and the calculation results, including the chemical reactions and the equilibrium compositions, which are compared with those in the literature. Additionally, operating parameters suitable for the autothermal production of CaC2 are predicted.

To overcome the high energy consumption inherited in the one-century-old electric arc method for CaC2 production, about 3250 kw·h·t−1 for CaC2 of 80% purity,3 research on autothermal production of CaC2 with oxygen-fuel heating4,5 was carried out to avoid the energy loss in coal fired power generation, about 60% with modern technologies. In the autothermal process, oxygen and a portion of coke react to form CO to supply the energy needed for the production of CaC2. Since the autothermal process is different from the electric arc process, thorough understanding of the reaction mechanism, including the phase change, is very important. The reaction mechanism for the CaC2 production in the literature varies. Tagawa and Sugawara studied the reaction in a thermobalance in a temperature range of 1873−2073 K. They proposed that reaction 1 proceeded via a two-step mechanism, reactions 2 and 3,6 without analyzing the volatile products. Wang et al.7 also studied the reaction in a thermobalance under an high Ar purging rate, 800 mL/min. On the basis of the CO generation at temperatures of 1223−1723 K, they reported the occurrence of reaction 2. Rai et al.8 studied the reaction using a graphite and CaO under high vacuum at various C/CaO ratios and temperatures of 1423−1523 K. They discovered Ca in the vapor prior to the formation of CaC2, which supported the twostep mechanism.

2. THEORY AND METHODOLOGY 2.1. Thermodynamic Data. On the basis of the reports in the literature11−13 and in industry, six substances, including coke, Ca, CO, CaO, CaC2, and O2, are used for the thermodynamic analysis. Although it has been found that the

(2)

C + CaO → Ca + CO Ca + 2C → CaC2

(3) 9

The study Li et al. recently reported, however, does not support the two-step mechanism. They also carried out the reaction in a thermobalance, but with a low Ar purging rate, 50 mL/min, and an online mass spectrometer (MS). The little mass loss and the absence of CO and Ca vapor at temperatures © 2014 American Chemical Society

Received: Revised: Accepted: Published: 2537

November 24, 2013 January 17, 2014 January 22, 2014 January 22, 2014 dx.doi.org/10.1021/ie403981j | Ind. Eng. Chem. Res. 2014, 53, 2537−2543

Industrial & Engineering Chemistry Research

Article

Table 1. Thermodynamic Properties of Pure Substances Used in the Study17,18 Hi298.15K

T range

−1 a

K C(graphite)

298.15−1100 1100−4073 298.15−2800 298.15−2500 298.15−2845 298.15−2845 298.15−1275 1275−3000 298.15−3000 298.15−3000

Ca(g) CO(g) CaO(s) CaO(l) CaC2(s, IV) CaC2(l) O2(g) a

(J·mol )

Si298.15K

Cpi

(J·mol−1·K−1)

(J·mol−1·K−1)

0 178146 −110 541 −635 090 −555 594 −53 030.3 3802.2 0

5.74

0.084 24.435 20.832 28.409 58.7912 58.7912 64.4336 75.1028 75.1028 29.957

154.674 197.527 37.75 65.690 76 79.1553 96.8246 205.04

+ 0.038 911(T/K) − 146 400(T/K)−2 − 0.000 017 364(T/K)2 + 0.000 418(T/K) − 3 163 100(T/K)−2 + 0.0041(T/K) − 46 000(T/K)−2 − 1 147 146(T/K)−2 −133.904(T/K)−0.5 + 102 978 787.9(T/K)−3 − 1 147 146(T/K)−2 −133.904(T/K)−0.5 + 102 978 787.9(T/K)−3 + 0.008 368(T/K)

+ 0.00418 (T/K) − 167400(T/K)−2

Standard molar enthalpy of formation, the standard state is at 298.15 K.

mechanism for the CaC2 production should be the one with a higher equilibrium CO partial pressure under the same conditions since it is easier to occur.21

quality of carbon affects the rates of the reactions involved in CaC2 production,16,17 graphite is used as the carbon source because the effect of carbon quality is limited at equilibrium. CaO and CaC2 are in the solid or the liquid states. Since CaC2 is produced only at high temperatures, its properties are those of CaC2 (IV).18 All of the thermodynamic data (Hi298.15K, Si298.15K, Cpi) are listed in Table 1 or determined by eqs 4, 5, and 6. Hi =

Hi298.15K

⎛p ⎞ ⎟ ΔG = ΔG1° + RT ln⎜⎜ CO ° ⎟ ⎝ p ⎠ °

pCO = eΔG1 / −RT

T

+

Si = Si298.15K +

∫298.15 Cpi dT T

∫298.15

Cpi T

dT

(7) (8)

⎛p × p ⎞ ⎛ p ⎞2 ⎟ ΔG = ΔG2° + RT ln⎜ CO ° Ca ⎟ = ΔG2° + RT ln⎜ CO ⎝ P° ⎠ ⎝ ⎠ P

(4)

(9)

(5) °

Gi = Hi − TSi

pCO = eΔG2 / −2RT

(6)

There are a number of reports on the phase diagram of CaO−CaC2 eutectics. The one reported by Juza and Schuster19 was regarded to be more reliable15,20 and is adopted in this work. Figure 1 shows the phase diagram where the minimum eutectic temperature is 2103 K at an x(CaC2) of 0.48.

(10)

2.3. Equilibrium Composition Calculation. The equilibrium composition of a reaction system is the composition that has the minimal Gibbs free energy. To simplify the calculation hypotheses are made, including that the solid phase is a pure solid, the gas phase is an ideal gas, the liquid phases are ideal liquids, and the melting point varies little with pressure. The dot lines in Figure 1 are the liquidus lines that can be represented by eqs 11 and 12, which are determined by linear regression. T (K ) = 2703.41 − 1374.80x

0 < x < 0.48 |r | = 0.979 (11)

T (K ) = 1799.62 + 629.72x

0.48 < x < 1 |r | = 0.997 (12)

Since the fugacity coefficients of the components in the gas mixture and the activity coefficients of the components in the liquid mixture can all be set to 1, the Gibbs free energy of the gas, liquid and solid phases can then be represented by eqs 13, 14 and 15, respectively, and the total Gibbs free energy of the reaction system by eq 16. Figure 1. CaO−CaC2 phase diagram of experimental data.18

Gg =

2.2. Criteria for Reaction Mechanism Validation. The Gibbs free energy of formation of reaction 1 can be expressed as eq 7, which may take another form to show the dependence of the equilibrium CO partial pressure on temperature, eq 8. Similarly, the Gibbs free energy of formation and the equilibrium CO partial pressure of reaction 2 can be expressed by eqs 9 and 10, respectively. The dominant reaction

∑

n ig Gi +

Gl =

∑

n ilGi +

Gs =

∑ nisGi

⎛ yp⎞ n ig RT ln⎜⎜ i ° ⎟⎟ ⎝p ⎠

∑ ∑

n ilRT ln x i

Gtotal = G g + Gl + Gs 2538

(13) (14) (15) (16)

dx.doi.org/10.1021/ie403981j | Ind. Eng. Chem. Res. 2014, 53, 2537−2543


Article

Figure 2. Flow diagram for calculation of chemical equilibrium in calcium carbide system. EC stands for equilibrium compositions.

In the presence of a liquid phase, at temperatures higher than 2103 K in Figure 1, the Gibbs free energy minimization and the equilibrium composition calculation for the three regions (A, B, and C in Figure 1) are performed separately. The fractions of the solid and the liquid phases in regions A and C are determined by the lever principle, while the fractions of CaO and CaC2 in region B are determined assuming an ideal liquid. The composition that yields the minimum Gibbs free energy for the whole system is the equilibrium composition. It is determined by eq 16 using the constraint set by eq 17.22,23

∑

n ia ik = bk

(17)

Figure 2 shows the flow diagram for the equilibrium composition calculation determined by the Matlab software. Figure 3. CO equilibrium partial pressure of reactions 1 and 2.

3. RESULTS AND DISSUSSION 3.1. Mechanism of CaC2 Formation. Figure 3 shows the equilibrium CO pressures of reactions 1 and 2, determined by eqs 8 and 10, respectively, in a temperature range of 1273− 2473 K. At temperatures lower than 1573 K, reaction 2 yields equilibrium CO pressures higher than that of reaction 1, indicating its dominance in the reaction mechanism. However, the very low CO pressures, lower than 10−4 atm, suggest that both reactions do not occur to a significant level in the temperature range, especially when the reaction system is at a pressure much higher than 10−4 atm, the ambient pressure 1 atm, for example, or under a low purging rate. This is because the low diffusion rate of the low pressure CO generated from the reaction surface limits the reaction rate. This further suggests that reaction 2 is observable only at a very low operating pressure, under vacuum or a high purging rate, for example. This agrees with the findings of Rai et al. and Wang et al., the formerly observed Ca vapor at 1423−1523 K under

vacuum,8 while the latter observed CO at 1223−1723 K under a high Ar purging rate (800 mL/min).7 At temperatures higher than 1573 K, reaction 1 yields equilibrium CO pressures higher than reaction 2, indicating its dominance in the reaction mechanism. For example, the equilibrium CO pressures of reactions 1 and 2 are 0.006 and 0.002 atm, respectively, at 1773 K or 6.06 and 0.33 atm, respectively, at 2273 K. This behavior agrees with that reported by Li et al.9,14,24 where the reaction was carried out in a thermobalance under a low Ar purging rate (50 mL/min). The discussion presented above suggests that the difference in reaction mechanisms reported in the literature are not contradicted with each other and can be attributed to the difference in operating conditions. Since the CaC2 production is usually operated at temperatures around 2273 K for high reaction rates and the ambient pressure for easy operation, the main reaction mechanism should be reaction 1. 2539



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Figure 4. Equilibrium compositions of the CaC2 reaction system at 0.005 atm and different C/CaO molar ratios. (a) C/CaO = 3.6 and (b) C/CaO = 2.

3.2. Equilibrium Composition. Thermodynamic calculations are performed for the reaction system under various pressures, temperatures, and initial C/CaO ratios. Figure 4 shows the results obtained in a temperature range of 1460− 2300 K at a pressure of 0.005 atm and initial C/CaO molar ratios of 3.6 (a) and 2.0 (b). Compared with the stoichiometry of reaction 1, the former is in excess of C, whereas the latter is in excess of CaO. It seems that the C/CaO molar ratio has little affect on the initial reaction temperature because it is 1740 K in both cases. Since this temperature is very close to that reported by Li et al., 1733 K, for experiments carried out in a thermobalance,9 the calculation results are compared with the data reported by the authors. Figure 4(a) shows that at an initial C/CaO molar ratio of 3.6, the whole process behaves as a two-stage process should it be operated in a temperature-ramping mode. At temperatures of 1740−1760 K, the disappearances of CaO and C correspond to large increases in CaC2 and CO and small increases in Ca, indicating the major reaction being reaction 1. In the temperature range of 1760−1940 K, the mechanism seems to follow reaction 18, i.e., a decrease in CaC2 corresponds to increases in both C and Ca. CaC2 → Ca + 2C

Figure 5 shows the initial temperatures of the reaction of the CaC2 formation at various pressures and an initial C/CaO

Figure 5. The initial reaction temperature as a function of reaction pressure.

molar ration of 3. The trend is also applicable to other initial C/ CaO molar ratios since they have little affect on the initial temperature as demonstrated in Figure 4. It is clear that a higher pressure results in a higher initial temperature of the reaction, about 1640 K at 0.001 atm and about 2100 K at 1.0 atm, for example. This inhibition effect of pressure on the reaction agrees with that reported by Mu et al.10 and can be attributed to the gaseous CO formed in reaction 1, which is reversible, and a higher pressure means a stronger reverse driving force. This trend is important because it indicates that the initial reaction temperatures reported in the literature are meaningless unless the CO pressure is provided. It is important to note that the high quality product of industrial CaC2 production is a CaC2−CaO eutectic with good fluidity and a CaC2 molar content greater than 78.1% (China’s Nation Standard GB 10665−2004, corresponding to an acetylene generation of 300 L/kg). This composition requirement corresponds to a reaction temperature of higher than 2273 K as shown in Figure 1. To understand the effect of pressure on the temperature−composition relation calculation is performed at an initial C/CaO molar ratio of 2.8, a feed composition frequently found in industry, and the results are shown in Figure 6 and Table 2. It is found that the yields of CaC2 and Ca generally decrease with an increase in pressure or a decrease in temperature. The CaC2 molar contents are higher

(18)

Figure 4(b) shows that at an initial C/CaO molar ratio of 2, the whole process behaves as a three-stage process should it be operated in a temperature-ramping mode. At temperatures of 1740−1760 K, the result is similar to the first stage observed at a C/CaO ratio of 3.6, i.e., the occurrence of reaction 1. At temperatures of 1760−1800 K, the decreases in CaO and CaC2 correspond to the increases in CO and Ca, which can be described by reaction 19. In the temperature range of 1860− 1940 K, the result is similar to the second stage observed at a C/CaO ratio of 3.6. Clearly, these thermodynamic calculations presented above for the two initial C/CaO ratios agree well with the experimental behaviors reported by Li et al.,9 with the exception of the presence of a small amount of Ca in the first stage. Although the reason for the discrepancy is not clear at present, it is likely, however, that the small amount of Ca was not detectible by experiment or the Ca vapor formed reacts quickly with C to form CaC2 due to the nonuniform mixing of the C and CaO powder in the thermobalance crucible. CaC2 + 2CaO → 3Ca + 2CO

(19) 2540



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compositions of the products are calculated. Figure 7 shows the Ca containing substances, CaC2, CaO, and Ca, at various temperatures and pressures, assuming the sum of them being 1

Figure 6. Yields of CaC2 and Ca at a C/CaO ratio of 2.8 and different temperatures and pressures.

Table 2. Molar Content of CaC2 (%) in the Product Calculated at Different Temperatures and Pressures T (K) pressure (atm)

2100

2200

2273

2400

0.5 1 1.5 2 2.5 3 3.5 4

92.6 0 0 0 0 0 0 0

90.8 92.6 93.0 93.1 63.8 62.8 60.4 57.9

90.0 92.0 92.7 93.0 93.1 80.1 76.5 72.8

90.0 91.7 92.4 92.7 92.8 92.0 91.2 90.3

than 78.1% at pressures lower than 2 atm and temperatures higher than 2200 K or at a pressure of 3 atm and temperatures higher than 2273 K. The Ca yield is minimal and can be neglected at pressures higher than 1 atm. Clearly, the conditions adopted by the industrial electric arc process, ambient pressure, and temperatures higher than 2273 K warrant production of high quality CaC2. The calculation data and the discussion presented above indicate that the model, with the inclusion of CaC2−CaO eutectic, predicts the equilibrium compositions well, even though some hypotheses are made. 3.3. Conditions Predicted for Autothermal CaC2 Production. On the basis of the feed compositions reported in the literature for the autothermal production of CaC2, CaO/ O2/C = 1:4.11:11.11 in molar ratio,5,25 the equilibrium

Figure 7. Equilibrium compositions of CaC2, CaO, and Ca vapor as a function of temperature and pressure with oxygen-fuel heating (a, CaC2; b, CaO; and c, Ca vapor). 2541



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optimum conditions for the autothermal process are about 2.5 atm at 2200−2273 K and 4 atm or higher at 2373 K.

mol. Figure 7(a) shows that the optimal conditions for the autothermal CaC2 production are temperatures higher than 2273 K and pressures about 2−3 atm. A higher pressure inhibits the CaC2 production and leads to a low CaO conversion (Figure 7(b)). A lower pressure promotes the formation of Ca vapor (Figure 7(c)). Figure 8 is another form of Figure 7. The isothermal lines of 2200, 2273, and 2373 K follow a similar path when the CaC2

■

AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +86 10 64421073. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the Major State Basic Research Project (2011CB201306) and the National Natural Science Foundation of China (21121064 and 20976011) is acknowledged. We thank Mr. Lun Li for his valuable suggestions about the MATLAB software.

■ Figure 8. Equilibrium compositions of CaO, CaC2, and Ca vapor for autothermal production of CaC2 at a feed composition of CaO/O2/C = 1:4.11:11.11.

mole fraction is higher than 0.6 (a lower CaC2 fraction is meaningless for CaC2 production). These lines locate mainly in an area with Ca fractions around 0.1, indicating the main product being the CaC2−CaO eutectic. The optimum conditions for CaC2 production is the area covered by the dotted circle, which centers at CaC2/CaO/Ca = 0.8:0.15:0.05 with a radium of 0.05. This area warrants the products being in the eutectic form for easy discharge and the CaC2 content being sufficiently high to meet the national standard of the top grade product. The temperature−pressure relation of the optimum conditions is around 2.5 atm at 2200 and 2273 K, and greater than 4 atm at 2373 K. At a pressure of 1 atm, the products are CaC2 and Ca at all temperatures with no CaO, indicating that the products cannot be discharged from the reactor because the melting point of CaC2 is around 2433 K.19

4. CONCLUSIONS A thermodynamic method was used to study the CaC2 production from CaO and coke. The results show that the different reaction mechanisms reported in the literature may not contradict each other and can be attributed to the differences in reaction pressure and temperature. The dominant mechanism at temperatures higher than 1573 K is the CaC2 formation directly from CaO and coke. The equilibrium composition calculation based on the total Gibbs free energy minimization, with the inclusion of the CaC2−CaO eutectic, show that the initial C/CaO ratio influences the reaction mechanism. An initial C/CaO ratio of less than 3 results in a three-stage mechanism, while an initial C/CaO ratio greater than 3 results in a two-stage mechanism, if the reaction is carried out in a temperature-ramping mode. The optimum conditions for the electric arc process are the ambient pressure and temperatures higher than 2273 K. The suggested

■

NOMENCLATURE aik=Numbers of atoms of the kth element present in each molecule of species i bk=Total mass of kth element in the system Cpi=Heat capacity of species i (J·mol−1·K−1) Gi=Standard molar Gibbs free energy of species i (kJ·mol−1) Gg=Total Gibbs free energy in gas phase (kJ) Gl=Total Gibbs free energy in liquid phase (kJ) Gs=Total Gibbs free energy in solid phase (kJ) Gtotal=Total Gibbs free energy in the system (kJ) ΔG=Standard molar Gibbs free energy of formation at different temperatures and pressures (kJ·mol−1) ΔG°1 =Standard molar Gibbs free energy of formation for reaction 1 at different temperatures (kJ·mol−1) ΔG2°=Standard molar Gibbs free energy of formation for reaction 2 at different temperatures (kJ·mol−1) Hi=Molar enthalpy of species I (J·mol−1) H298.15K =Molar enthalpy of species i at 298.15 K (J·mol−1) i ni=Mole of species I (mol) ngi =Mole of species i in gas phase (mol) nli=Mole of species i in liquid phase (mol) nsi =Mole of species i in solid phase (mol) p=Pressure of the reaction system (atm) pCa=Pressure of Ca in the system (atm) pCO=Pressure of CO in the system (atm) po=Standard-state pressure (1 atm) R=Molar gas constant (J·mol−1·K−1) r=Coefficient of correlation Si=Molar entropy of species i (J·mol−1·K−1) S298.15K =Molar entropy of species i at 298.15 K (J·mol−1·K−1) i T=Temperature of the system (K) x(CaC2)=Mole fraction of CaC2 in the CaC2−CaO phase diagram xi=Mole fraction of species i in a liquid phase yi=Mole fraction of species i in a gas phase REFERENCES

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