碳酸盐型卤水Li+， Na+， K+， CO32--H2O体系热力学与相图模型化

doi:10.11949/0438-1157.20250218

摘要/Abstract

摘要：

碳酸盐型卤水广泛存在于自然界和各种工业过程，新型资源和过程的开发同样需要相图和热力学模型的支持。碱金属（Li，Na，K）的碳酸盐卤水体系是典型和普遍的，补充必要的相图数据完善卤水体系热力学模型是亟需的。为此，本研究首先对多温相图数据缺乏的Li₂CO₃-K₂CO₃-H₂O体系实验补充了273.15、323.15、348.15 K的相图数据；而后在完善Li₂CO₃、Na₂CO₃、K₂CO₃三个二元体系热力学模型的基础上，重新获得CO $32$ ^-离子多温等压摩尔热容参数；构建了Li₂CO₃-Na₂CO₃-H₂O、Li₂CO₃-K₂CO₃-H₂O、Na₂CO₃-K₂CO₃-H₂O三个体系的多温热力学模型，获得了Li⁺，Na⁺，K⁺，CO $32$ ^--H₂O体系全部多温液相特征参数（3组离子对与水、3组离子对之间的交互作用参数）和9个固相物种热力学参数；预测得到三元体系的完整相图结构。对相图数据一致性较差的Na₂CO₃-K₂CO₃-H₂O体系，给出了各种盐类稳定平衡相区的判断。结果表明，所获得热力学参数对碳酸盐卤水体系的溶液物性和固液相平衡规律表达具有合理性和热力学一致性，可满足计算准确性的要求。

关键词: 碳酸盐型卤水, 相图, 热力学模型, Li⁺，Na⁺，K⁺，CO $32$ ^--H₂O体系

Abstract:

Carbonate-type brines are widely distributed in natural environments and industrial processes, where the development of novel resources and processes requires the supporting of systematic phase diagram and thermodynamic model. The alkali metal (Li, Na, K) carbonate brine systems represent typical and universal cases, necessitating supplementary phase diagram data to refine comprehensive thermodynamic models. This study first experimentally determined the phase diagrams of the Li₂CO₃-K₂CO₃-H₂O system at 273.15, 323.15 and 348.15 K to address data scarcity. Subsequently, on the basis of improving the thermodynamic models of the three binary systems of Li₂CO₃, Na₂CO₃ and K₂CO₃, the multi-temperature isobaric molar heat capacity parameters of the CO $32$ ^- ion were re-obtained. Multi-temperature thermodynamic models were developed for three ternary systems: Li₂CO₃-Na₂CO₃-H₂O, Li₂CO₃-K₂CO₃-H₂O and Na₂CO₃-K₂CO₃-H₂O. All the multitemperature liquid-phase characteristic parameters of the Li⁺, Na⁺, K⁺ and CO $32$ ^--H₂O systems (interaction parameters between three groups of ion pairs and water, and among three groups of ion pairs) and thermodynamic parameters of nine solid-phase species were obtained. The complete phase diagram structure of the ternary system was predicted. For the Na₂CO₃-K₂CO₃-H₂O system with poor consistency of phase diagram data, the judgments of the stable equilibrium phase regions of various salts were given. The results show that the obtained thermodynamic parameters are reasonable and thermodynamically consistent in expressing the solution properties and solid-liquid phase equilibrium laws of the carbonate brine system, which can meet the requirements of calculation accuracy.

Key words: carbonate-type brine, phase diagram, thermodynamic model, Li⁺, Na⁺, K⁺, CO $32$ ^--H₂O system

中图分类号:

O 642

王偲凡, 栗一帆, 陈江波, 周桓. 碳酸盐型卤水Li⁺， Na⁺， K⁺， CO $32$ ^--H₂O体系热力学与相图模型化[J]. 化工学报, 2025, 76(9): 4770-4785.

Sifan WANG, Yifan LI, Jiangbo CHEN, Huan ZHOU. Thermodynamics and phase diagram modeling of carbonate-type brines Li⁺, Na⁺, K⁺, CO $32$ ^--H₂O system[J]. CIESC Journal, 2025, 76(9): 4770-4785.

图/表 22

表1 Li+， Na+， K+， CO32--H2O相关体系相图的相关文献汇总

Table 1 Solubility data in the Li+， Na+， K+， CO32--H2O system

体系	T/K	文献
Li₂CO₃-H₂O	271.04~575.15	[34-36]
Na₂CO₃-H₂O	273.15~368.15	[37-39]
K₂CO₃-H₂O	262.15~499.15	[40-42]
Li₂CO₃-Na₂CO₃-H₂O	278.15~373.15	[4-6,43-44]
Na₂CO₃-K₂CO₃-H₂O	273.15~373.15	[10,16,45-49]
Li₂CO₃-K₂CO₃-H₂O	288.15,298.15	[8,50]
Li₂CO₃-Na₂CO₃-K₂CO₃-H₂O	288.15,298.15	[11,17]

表 2 Li2CO3-K2CO3-H2O 三元体系固-液相平衡数据

Table 2 Solid-liquid phase equilibrium data of Li2CO3-K2CO3-H2O ternary system

序号	液相组成w(B)/%		密度 ρ/(kg·L^-1)	pH	湿固相组成w(B)/%			固相
序号	K₂CO₃	Li₂CO₃	密度 ρ/(kg·L^-1)	pH	K₂CO₃	Li₂CO₃		固相
T=273.15 K
1, A	0	1.51	1.0263	11.09	0		65.25	S₁
2	8.27	1.40	1.1450	11.58	4.00		62.58	S₁
3	16.63	1.28	1.2153	11.72	6.32		63.43	S₁
4	24.37	1.07	1.3037	11.94	8.97		64.58	S₁
5	31.69	0.88	1.3561	12.36	12.21		62.33	S₁
6	37.91	0.71	1.4014	12.56	16.61		56.56	S₁
7	44.85	0.53	1.4255	12.67	20.53		54.86	S₁
8, E	51.32	0.43	1.4547	12.89	36.30		47.03	S₁+S₂
9	51.22	0.28	1.4482	12.86	60.32		22.15	S₂
10	51.13	0.14	1.4506	12.85	67.96		6.54	S₂
11, B	51.05	0	1.4512	12.88	73.00		0	S₂
T=323.15 K
1, C	0	1.07	1.0212	11.01	0		67.50	S₁
2	9.31	0.92	1.1437	11.67	4.52		58.20	S₁
3	15.83	0.89	1.1983	11.83	7.04		60.15	S₁
4	22.94	0.79	1.2731	12.16	9.21		63.32	S₁
5	29.06	0.71	1.3253	12.43	10.46		62.72	S₁
6	34.18	0.63	1.3776	12.58	12.11		65.54	S₁
7	39.62	0.47	1.4015	12.66	15.54		60.45	S₁
8	44.53	0.39	1.4359	13.20	17.62		61.13	S₁
9	49.83	0.32	1.4720	13.37	16.78		65.68	S₁
10, F	55.53	0.24	1.5393	13.51	37.55		45.15	S₁+S₂
11	55.32	0.13	1.5322	13.49	60.48		21.29	S₂
12	55.14	0.07	1.5363	13.43	66.70		12.13	S₂
13, D	54.98	0	1.5331	13.45	73.35		0	S₂
T=348.15 K
1, M	0	0.88	1.0188	10.96	0		63.58	S₁
2	9.16	0.79	1.1386	11.39	3.09		65.73	S₁
3	18.87	0.69	1.2285	11.63	7.33		63.31	S₁
4	28.28	0.51	1.3109	11.79	10.11		64.12	S₁
5	35.49	0.41	1.3860	12.15	14.76		58.58	S₁
6	40.96	0.33	1.4091	12.41	16.11		61.26	S₁
7	47.36	0.26	1.4533	12.55	20.02		58.33	S₁
8	53.12	0.19	1.5117	12.98	23.18		57.19	S₁
9, G	57.75	0.16	1.5677	13.68	42.36		39.35	S₁+S₂
10	57.73	0.10	1.5619	13.67	68.59		10.12	S₂
11, N	57.71	0	1.5601	13.63	72.63		0	S₂

图1 Li2CO3-K2CO3-H2O三元体系273.15 K的相图

Fig.1 Phase diagram of Li2CO3-K2CO3-H2O ternary system at 273.15 K

图2 Li2CO3-K2CO3-H2O三元体系323.15 K的相图

Fig.2 Phase diagram of Li2CO3-K2CO3-H2O ternary system at 323.15 K

图3 Li2CO3-K2CO3-H2O三元体系348.15 K的相图

Fig.3 Phase diagram of Li2CO3-K2CO3-H2O ternary system at 348.15 K

图4 Li2CO3-K2CO3-H2O体系的多温相图数据

Fig.4 Phase diagram data of Li2CO3-K2CO3-H2O ternary system at multi temperature

表3 二元体系的溶液物性与溶解度数据

Table 3 Physical property and solubility data of solution in binary systems

System	Property	T/K	m/(mol·kg^-1)	Ref.	MRD/%
Li₂CO₃-H₂O	Solubility(Li₂CO₃)	273.14—575.15	0.2128—0.0206	[34-36]	0.69
Na₂CO₃-H₂O	P_vap	283.14—573.15	0.3921—2.6611	[51]	2.46
	C_p	283.13—403.15	0.1924—4.0436	[52]	0.94
	Solubility(Na₂CO₃)	271.04—305.15	0.5703—4.3186	[37-38]	0.51
	Solubility(Na₂CO₃·H₂O)	305.14—308.52	4.2834—4.6703	[37-38]	0.60
	Solubility(Na₂CO₃·7H₂O)	305.52—377.95	4.6681—4.1994	[37-38]	0.55
	Solubility(Na₂CO₃·10H₂O)	377.94—453.15	4.1994—3.1450	[37-39]	0.67
K₂CO₃-H₂O	P_vap	313.15—333.15	0.1477—3.4050	[53]	2.15
	C_p	283.15—353.15	0.1477—7.2356	[54]	0.95
	Solubility(K₂CO₃)	446.15—499.15	17.1628—19.0007	[42]	0.56
	Solubility(K₂CO₃·1.5H₂O)	268.15—426.15	7.7015—17.1913	[40-42]	0.64
	Solubility(K₂CO₃·6H₂O)	243.15—266.95	5.3035—7.5179	[40-41]	1.94

图5 二元体系饱和蒸气压的计算效果

Fig.5 The calculated results of saturated vapor pressure for binary systems

表4 Li+， Na+， K+， CO32--H2O体系液相特征参数

Table 4 Liquid parameters of Li+， Na+， K+， CO32--H2O system

离子对（水）		$A I J$	$B I J$	$C I J$
I	J	$A I J$	$B I J$	$C I J$
(Li⁺,CO $32$ ^-)	H₂O	0	0	0
H₂O	(Li⁺,CO $32$ ^-)	0	0	0
(Na⁺,CO $32$ ^-)	H₂O	-3.79	154.56	0.90
H₂O	(Na⁺,CO $32$ ^-)	7.41	-621.23	0.31
(K⁺,CO $32$ ^-)	H₂O	-4.69	67.11	0.91
H₂O	(K⁺,CO $32$ ^-)	9.54	-667.88	-1.94
(Li⁺,CO $32$ ^-)	(Na⁺,CO $32$ ^-)	0.60	-620.77	0
(Na⁺,CO $32$ ^-)	(Li⁺,CO $32$ ^-)	-5.32	1451.19	0
(Li⁺,CO $32$ ^-)	(K⁺,CO $32$ ^-)	0.10	-139.11	0
(K⁺,CO $32$ ^-)	(Li⁺,CO $32$ ^-)	-8.23	160.24	0
(Na⁺,CO $32$ ^-)	(K⁺,CO $32$ ^-)	-0.45	-980.33	0
(K⁺,CO $32$ ^-)	(Na⁺,CO $32$ ^-)	2.88	1611.80	0

表4 Li+， Na+， K+， CO32--H2O体系液相特征参数

Table 4 Liquid parameters of Li+， Na+， K+， CO32--H2O system

离子对（水）		$A I J$	$B I J$	$C I J$
I	J	$A I J$	$B I J$	$C I J$
(Li⁺,CO $32$ ^-)	H₂O	0	0	0
H₂O	(Li⁺,CO $32$ ^-)	0	0	0
(Na⁺,CO $32$ ^-)	H₂O	-3.79	154.56	0.90
H₂O	(Na⁺,CO $32$ ^-)	7.41	-621.23	0.31
(K⁺,CO $32$ ^-)	H₂O	-4.69	67.11	0.91
H₂O	(K⁺,CO $32$ ^-)	9.54	-667.88	-1.94
(Li⁺,CO $32$ ^-)	(Na⁺,CO $32$ ^-)	0.60	-620.77	0
(Na⁺,CO $32$ ^-)	(Li⁺,CO $32$ ^-)	-5.32	1451.19	0
(Li⁺,CO $32$ ^-)	(K⁺,CO $32$ ^-)	0.10	-139.11	0
(K⁺,CO $32$ ^-)	(Li⁺,CO $32$ ^-)	-8.23	160.24	0
(Na⁺,CO $32$ ^-)	(K⁺,CO $32$ ^-)	-0.45	-980.33	0
(K⁺,CO $32$ ^-)	(Na⁺,CO $32$ ^-)	2.88	1611.80	0

表5 Li+， Na+， K+， CO32--H2O体系的物种热力学参数

Table 5 Thermodynamic parameters of species in Li+， Na+， K+， CO32--H2O system

物种	$∆ f G 􀱈$ /（kJ·mol^-1）	$∆ f H 􀱈$ /（kJ·mol^-1）	$C p (298.15 K)$ /（J·mol^-1·K^-1）	c₁	c₂	c₃	文献
CO $32$ ^-	-527.46	-677.48	-130.58	-344.85	1759.55	-3491.17	本文
Li₂CO₃	-1130.56	-1219.27	99.12	104.76	177.32	0.00	本文
	-1132.06	-1215.90	99.12	—	—	—	NBS^[55]
Na₂CO₃	-1043.25	-1130.03	112.30	12.01	244.01	24.48	本文
	-1044.44	-1130.00	112.30	—	—	—	NBS^[55]
Na₂CO₃·H₂O	-1285.37	-1435.20	145.60	45.31	244.01	24.48	本文
	-1285.31	-1431.26	145.60	—	—	—	NBS^[55]
Na₂CO₃·7H₂O	-2712.19	-3178.93	374.56	274.27	244.01	24.48	本文
	-2714.20	-3199.96	—	—	—	—	NBS^[55]
Na₂CO₃·10H₂O	-3425.64	-4088.86	550.29	450.00	244.01	24.48	本文
	-3427.66	-4081.32	550.32	—	—	—	NBS^[55]
K₂CO₃	-1064.04	-1169.21	114.25	97.91	92.05	-9.87	本文
	-1063.5	-1151.02	114.43	—	—	—	NBS^[55]
K₂CO₃·1.5H₂O	-1434.55	-1630.27	198.76	198.76	0	0	本文
	-1432.5	-1609.20	—	—	—	—	NBS^[55]
K₂CO₃·6H₂O	-1434.64	-1630.63	107.74	28.57	302.80	-9.87	本文
Li₂CO₃·Na₂CO₃	-2179.86	-2371.48	269.93	116.77	421.33	24.48	本文
Na₂CO₃·K₂CO₃	-2125.32	2335.81	226.55	109.92	336.06	14.61	本文
Na₂CO₃·K₂CO₃·H₂O	-2363.36	-2629.56	379.77	379.77	0	0	本文
Na₂CO₃·K₂CO₃·6H₂O	-3560.81	-4160.11	476.44	476.44	0	0	本文
Na₂CO₃·K₂CO₃·12H₂O	-5013.40	-5559.91	-7404.63	-7404.63	0	0	本文
NaKCO₃·6H₂O	-2494.87	-2972.26	207.81	207.81	0	0	本文

表5 Li+， Na+， K+， CO32--H2O体系的物种热力学参数

Table 5 Thermodynamic parameters of species in Li+， Na+， K+， CO32--H2O system

物种	$∆ f G 􀱈$ /（kJ·mol^-1）	$∆ f H 􀱈$ /（kJ·mol^-1）	$C p (298.15 K)$ /（J·mol^-1·K^-1）	c₁	c₂	c₃	文献
CO $32$ ^-	-527.46	-677.48	-130.58	-344.85	1759.55	-3491.17	本文
Li₂CO₃	-1130.56	-1219.27	99.12	104.76	177.32	0.00	本文
	-1132.06	-1215.90	99.12	—	—	—	NBS^[55]
Na₂CO₃	-1043.25	-1130.03	112.30	12.01	244.01	24.48	本文
	-1044.44	-1130.00	112.30	—	—	—	NBS^[55]
Na₂CO₃·H₂O	-1285.37	-1435.20	145.60	45.31	244.01	24.48	本文
	-1285.31	-1431.26	145.60	—	—	—	NBS^[55]
Na₂CO₃·7H₂O	-2712.19	-3178.93	374.56	274.27	244.01	24.48	本文
	-2714.20	-3199.96	—	—	—	—	NBS^[55]
Na₂CO₃·10H₂O	-3425.64	-4088.86	550.29	450.00	244.01	24.48	本文
	-3427.66	-4081.32	550.32	—	—	—	NBS^[55]
K₂CO₃	-1064.04	-1169.21	114.25	97.91	92.05	-9.87	本文
	-1063.5	-1151.02	114.43	—	—	—	NBS^[55]
K₂CO₃·1.5H₂O	-1434.55	-1630.27	198.76	198.76	0	0	本文
	-1432.5	-1609.20	—	—	—	—	NBS^[55]
K₂CO₃·6H₂O	-1434.64	-1630.63	107.74	28.57	302.80	-9.87	本文
Li₂CO₃·Na₂CO₃	-2179.86	-2371.48	269.93	116.77	421.33	24.48	本文
Na₂CO₃·K₂CO₃	-2125.32	2335.81	226.55	109.92	336.06	14.61	本文
Na₂CO₃·K₂CO₃·H₂O	-2363.36	-2629.56	379.77	379.77	0	0	本文
Na₂CO₃·K₂CO₃·6H₂O	-3560.81	-4160.11	476.44	476.44	0	0	本文
Na₂CO₃·K₂CO₃·12H₂O	-5013.40	-5559.91	-7404.63	-7404.63	0	0	本文
NaKCO₃·6H₂O	-2494.87	-2972.26	207.81	207.81	0	0	本文

图6 二元体系溶液比热容

Fig.6 The calculated results of liquid heat capacity for binary systems

图7 Li2CO3-H2O，Na2CO3-H2O，K2CO3-H2O二元体系溶解度全图

Fig.7 Solubility diagrams for binary systems Li2CO3-H2O，Na2CO3-H2O and K2CO3-H2O

表6 二元体系和三元体系零变量点的预测结果

Table 6 The predicted invariant points in binary and ternary systems

体系		固相	T/K	液相组成 / %
体系		固相	T/K	LC	NC	KC
Na₂CO₃–H₂O	A	冰+ NC10	270.78	—	5.81	—
	B	NC10 + NC7	300.00	—	29.83	—
	C	NC7 + NC1	308.91	—	33.44	—
	D	NC1 + NC	385.09	—	30.99	—
K₂CO₃-H₂O	E	冰+ KC6	242.95	—	—	42.30
	F	KC6+ KC1.5	266.01	—	—	50.96
	G	KC1.5 + KC	429.75	—	—	70.38
Li₂CO₃–K₂CO₃–H₂O	H	冰+ LC + KC1.5	223.15	0.14	—	45.08
Li₂CO₃–Na₂CO₃–H₂O	I	冰+ LC + NC10	269.83	1.28	6.46	—
	J	LC + NC10 + LNC	300.72	0.97	32.77	—
	K	NC10+NC7+LNC	301.27	0.90	34.62	—
	L	NC7+NC1+LNC	308.02	0.72	39.67	—
Na₂CO₃–K₂CO₃–H₂O	M	冰+ KC6 + NKC6	236.15	—	0.04	40.28
	N	冰+ NC10 + NKC6	251.51	—	1.70	27.27
	O	KC6+NKC6+KC1.5	262.15	—	0.25	49.75
	P	NC10 + NKC6 + NC1	295.32	—	21.05	17.24
	Q	NC10 + NC7 + NC1	296.03	—	21.74	16.11
	R	NKC6 + KC1.5 + NKC	304.24	—	4.77	49.18
	S	NKC6 + NC1 + NKC	310.67	—	11.71	37.48

图8 Li2CO3-Na2CO3-H2O三元体系在273.15 K 和323.15 K的等温相图

Fig.8 Isothermal solubility diagrams for Li2CO3-Na2CO3-H2O ternary system at 273.15 K and 323.15 K

图9 Li2CO3-Na2CO3-H2O三元体系298.15 K和373.15 K的等温溶解度

Fig. 9 Isothermal solubility for Li2CO3-Na2CO3-H2O ternary system at 298.15 K and 373.15 K

图10 Na2CO3-K2CO3-H2O三元体系在298.15 K和373.15 K下的等温溶解度

Fig. 10 Calculated results of isothermal solubility for Na2CO3-K2CO3-H2O ternary system at 298.15 K and 373.15 K

图11 Li2CO3-K2CO3-H2O体系348.15 K 以下温度的完整相图和拓扑结构

Fig.11 Complete phase diagrams and topology diagrams of Li2CO3-K2CO3-H2O system at temperature under 348.15 K

图12 Li2CO3-Na2CO3-H2O体系的完整相图和拓扑结构

Fig.12 Complete phase diagrams and topology diagrams of Li2CO3-Na2CO3-H2O system at temperature under 373.15 K

图13 Na2CO3-K2CO3-H2O体系在共晶点至373.15 K温度的完整相图和拓扑结构图

Fig. 13 Calculated isothermal solubility and predicted complete topology phase diagrams of Na 2CO3-K2CO3-H2O system at temperature range from eutectic point to 373.15 K

图s1 三元体系Li2CO3-K2CO3-H2O 273.15 K 零变量点XRD 谱图（S1+S2）

Fig. s1 X-ray diffraction patterns of invariant points in Li2CO3-K2CO3-H2O ternary system at 273.15 K S1—Li2CO3; S2—K2CO3·1.5 H2O

图s2 三元体系Li2CO3-K2CO3-H2O 323.15 K 零变量点XRD 谱图（S1+S2）

Fig. s2 X-ray diffraction patterns of invariant points in Li2CO3-K2CO3-H2O ternary system at 323.15 K S1—Li2CO3; S2—K2CO3·1.5 H2O

图s3 三元体系Li2CO3-K2CO3-H2O 348.15 K 零变量点XRD 谱图（S1+S2）

Fig. s3 X-ray diffraction patterns of invariant points in Li2CO3-K2CO3-H2O ternary system at 348.15 K S1—Li2CO3; S2—K2CO3·1.5 H2O

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碳酸盐型卤水Li⁺， Na⁺， K⁺， CO $32$ ^--H₂O体系热力学与相图模型化

Thermodynamics and phase diagram modeling of carbonate-type brines Li⁺, Na⁺, K⁺, CO $32$ ^--H₂O system

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