岩性油气藏  2018, Vol. 30 Issue (4): 113-119       PDF    
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CPA方程对CO2-水体系相态研究
涂汉敏1, 郭平1 , 贾钠2, 汪周华1, 王千3    
1. 油气藏地质及开发工程国家重点实验室·西南石油大学, 成都 610500;
2. 里贾纳大学 工程与应用科学学院石油工程系, 里贾纳 S4S0A2, 加拿大;
3. 中海石油 (中国) 有限公司天津分公司, 天津 300452
摘要: CO2作为酸性气体之一,其热力学性质对石油、天然气开发至关重要。水通常在地层中与烃类共生,由于地层盐水的存在使得与烃类混合的气体量减少,并且这种效应将随着压力和水相量的增加而增加(随盐度的降低而减小)。因此,弄清CO2-水体系的热力学性质将对理解这些过程具有重要的指导意义。通过运用SRK-CPA状态方程结合CR-1混合规则对CO2-水体系的相平衡特征进行计算,研究CO2在水中的溶解度和水在CO2气相中的溶解度,并对308 K,373 K和473 K等3种温度下,CO2-水体系不同缔合模型相互作用的模拟结果与实验数据进行分析,结果表明:在CO2的临界温度和临界压力附近,由于发生了由气-液到液-液的相态转变,CO2和水的溶解度在此温度和压力点将发生显著的变化;当CO2作为非缔合物与缔合模型为4 C的水发生溶剂化交叉缔合时,运用CPA方程计算的溶解度结果与实验数据拟合较好。CPA方程在工程应用中能够满足含CO2和水体系的热力学性质预测需求。
关键词: CPA状态方程      CO2-水体系      热力学性质      溶解度      缔合模型     
Calculation of phase behavior for CO2-water mixtures using CPA EoS
TU Hanmin1, GUO Ping1, JIA Na2, WANG Zhouhua1, WANG Qian3     
1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China;
2. Program of Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina S4S0A2, Canada;
3. CNOOC China Co. Ltd. Tianjing Company, Tianjing 300452, China
Abstract: Carbon dioxide(CO2)is an acid gas, and its thermodynamic properties are vital to numerous processes in the oil and gas. Water always coexists with hydrocarbons in petroleum reservoirs, and the presence of brine may reduce the amount of gas to be mixed with hydrocarbons. This effect increases with increasing pressure and the amount of aqueous phase(while decreases with the decreasing of salinity). Hence, the understanding of the thermodynamics of CO2-water mixtures is quite crucial for the rational design and operation of many processes. The characteristics of phase behavior for CO2-water mixtures were studied by using Cubic-Plus-Association (CPA)Equation of State(EoS)to combine with the CR-1 mixing rule to assess the mutual solubility of CO2 and water. CO2 can be treated in three different ways:(1)as a non-associating molecule; (2)as an associating molecule that can be cross-associate with water(solvation); (3)as a self and cross associating molecule. As water is considered as an associating molecule, it has three association schemes of 2 B, 3 B and 4 C. The performance of CPA EoS using different interaction models was evaluated and discussed at three temperatures of 308 K, 373 K and 473 K, and also was compared to various recent published investigations. It demonstrates the complicated phase behavior of CO2 and water, especially when they are close to the critical point of CO2, where thermodynamic properties sudden changed. The results show that good agreement with experimental data can be achieved when CO2 is considered as a non-associating molecule and 4 C association scheme is considered in the calculation model.
Key words: Cubic-Plus-Association Equation of State      CO2-water mixtures      thermodynamic properties      solubility      association scheme     
0 引言

近年来,CO2埋存、捕集、输运、注CO2等是油气藏提高采收率的重要工艺流程[1-4]。对于油气藏储层而言,多孔介质中不可避免地存在大量的地层水[5-6],含CO2和极性物质(水)的烃类体系势必引起越来越多的关注[7-9]。准确地描述CO2 -水体系的热力学性质,对制订油气开采工艺具有重要的意义。目前,石油和化工行业常用的状态方程为立方型的SRK,PR和维里状态方程等[10-11],这些方程不能仅用一个可调参数来正确地描述极性和缔合作用的物质相态。如果用这些方程来关联流体,则需要2个或者更多的可调参数并结合vdW混合规则或者更加复杂的混合规则。因此,为了满足该类物质体系热力学性质的计算需求,例如,水、醇、CO2与H2S等,阿姆斯特丹壳牌研究中心首先提出了CPA(Cubic-Plus-Association)状态方程[12]。该方程不仅保留了传统状态方程的物理项,同时增加了考虑氢键作用的缔合项,提高了具有分子间缔合作用的分子物性计算精度[13-14]。对于含有极性和缔合作用的物质,CPA方程目前是热力学性质计算的首选。

众多学者[15-16]研究表明,非极性物质CO2既可以作为非缔合物也可以作为缔合物。作为缔合物,CO2与水一样具有2 B,3 B和4 C的缔合模型。Voutsas等[17],Pappa等[18]和Perakis等[19]运用PRCPA和SRK-CPA状态方程模拟了CO2混合物的热力学性质,发现当缔合模型为4 C时计算结果较好,而Olivera等[20]则通过研究发现CO2作为2 B和4 C模型时计算结果较好。CO2作为非缔合物可以与水等低分子物质相互作用溶剂化,由于此相互作用是由色散和偶极力共同引起的,溶剂化的过程有时相当强烈。Kontogeorgis等[21]运用CPA方程模拟CO2和水的溶剂化过程,计算结果表明,在较高的压力下CO2与水的溶解度计算结果与实验数据拟合良好。上述研究表明,对于不同的研究体系最佳的缔合模型不同。同时CO2与水体系的模拟是直接基于水为4 C缔合模型的计算。为准确预测含CO2和水混合物的热力学性质,运用CPA方程研究CO2和水之间的不同缔合模型,对308 K,373 K和473 K等3种温度下物质的溶解度进行计算,同时与文献实验数据进行对比和分析,确定CO2与水的最佳缔合方案,以期为包含此2类物质的烃类体系热力学性质分析奠定基础。

1 模型与理论

由Derawi等[22]提出的CPA状态方程主要由物理项和基于热力学微扰理论的缔合项2部分组成[12, 23-24]。物理项是解释分子间的物理作用,通常为SRK立方型状态方程或者PR立方型状态方程,缔合项是描述分子氢键的缔合作用。对于非缔合物,CPA状态方程可简化为SRK状态方程[15, 25]

$ {Z_{{\text{CPA}}}} = {Z_{{\text{SRK}}}} + {Z_{{\text{Association}}}} $ (1)

式中:ZSRK[26]ZAssociation[27]可分别表示为

$ {Z_{{\text{SRK}}}} = \frac{{{V_m}}}{{{V_m}-b}}-\frac{\alpha }{{RT\left( {{V_m} + b} \right)}} $ (2)

$ {Z_{{\text{Association}}}} = \rho \sum\limits_i {{x_i}} \sum\limits_{{A_i}} {\left[{\left( {\frac{1}{{{X_{{A_i}}}}}-\frac{1}{2}} \right)\frac{{\partial {X_{{A_i}}}}}{{\partial \rho }}} \right]} $ (3)

式(2)~ (3)中:Vm为摩尔体积,m3/mol;ρ为摩尔密度,mol/m3T为绝对温度,K;R是气体常数,通常取值8.314×10-6,m3· MPa/(K· mol);αb均是SRK状态方程的能量和体积参数,m3/mol;xi是组分i的摩尔分数。

XAi是分子i的活性A位没有与其他活性位缔合的摩尔分数,可以表示为分子i的活性A位与分子j的活性B位之间缔合能ΔAiBj的函数[26]

$ {X_{Ai}} = \frac{1}{{1 + \rho \sum\limits_j {{x_j}} \sum\limits_{{B_j}} {{X_{{B_j}}}{\Delta ^{{A_i}{B_j}}}} }} $ (4)

式中:Bj表示缔合位。

缔合能ΔAiBj可表示为[26]

$ {\Delta ^{{A_i}{B_j}}} = g{\left( \rho \right)^{ref}}\left[{\exp \left( {\frac{{{\varepsilon ^{{A_i}{B_j}}}}}{{RT}}} \right)-1} \right]{b_{ij}}{\beta ^{{A_i}{B_j}}} $ (5)

式中:βε分别为缔合体积和能量,MPa·m3/mol;εAiBj为分子i和分子j的交叉缔合能,MPa·m3/mol;βAiBj为分子i和分子j的交叉缔合体积。

径向分布函数g[24]可以表达为

$ g{\left( \rho \right)^{ref}} = \frac{1}{{1-1.9\eta }}, \;\eta = \frac{1}{4}b, \;\rho = \frac{b}{{4{V_m}}} $ (6)

式(2)不是XAi的显示表达式,它的取值是由缔合模型确定。使用CR-1混合规则,交叉缔合能和体积参数的表达式为

$ {\varepsilon ^{{A_i}{B_j}}} = \frac{{{\varepsilon ^{{A_i}{B_i}}} + {\varepsilon ^{{A_j}{B_j}}}}}{2}, {\beta ^{{A_i}{B_j}}} = \sqrt {{\beta ^{{A_i}{B_i}}}{\beta ^{{A_j}{B_j}}}} $ (7)

当CO2为非缔合物与其他组分交叉缔合溶剂化时,上述混合规则可修改为[28]

$ {\varepsilon ^{{A_i}{B_j}}} = \frac{{{\varepsilon _{association}}}}{2}, {\beta ^{{A_i}{B_j}}} = {\beta _{across}}\left( {实验数据拟合} \right) $ (8)

在缔合项中,εAiBj为分子i和分子j的交叉缔合能,βAiBj为分子i和分子j间的交叉缔合体积。

2 缔合模型与参数

Huang等[29]提出了7种取决于缔合位的1 A,2 B,3 B和4 C缔合模型。CO2和H2O的缔合模型结构如表 1所列,表 1给出了CO2的4种缔合模型与水缔合的结构图以及CO2与水的自缔合结构。从表 1可以看出,CO2作为非缔合物与水溶剂化时,CO2中的C原子仅接受水中O原子供出的电子,形成H2 O…CO2,如表 1中“1”所示;当CO2为缔合物时,CO2中的C原子接受水中O原子供出的电子,CO2中的O原子将C原子得到的电子供出给水中的H原子形成氢键,O=C=O…HOH,如表 1中“2”所示,此氢键不同于水中的H…O键[1730-31] (表 1中箭头表示电子转移方向,虚线表示原子间的相互作用)。

下载CSV 表 1 CO2和H2O的缔合模型结构 Table 1 Association structure of CO2 and H2O

通常通过拟合蒸汽压和饱和液体密度实验数据得到CPA状态方程有5个纯组分参数:3个非缔合参数(α0bc1)和2个缔合参数(εAiBjβAiBj)。前人对这些参数作了详细研究,如表 2所列。对于非缔合的3个参数既可以通过拟合实验数据得到也可以通过传统的方法由临界压力、临界温度和偏心因子计算得到[32-33]。文中所涉及的实验数据来自已发表文献中的数据[34-37]

下载CSV 表 2 CO2和H2O的物性参数 Table 2 Physical parameters of CO2 and H2O
3 结果与讨论

图 1~6为不同温度下水为4 C缔合模型时与CO2相互作用的气液平衡计算结果。CO2与水体系的热力学特征非常复杂,尤其是当体系温度在CO2的临界温度和临界压力附近时(308 K,75.3 bar)。图 1图 2为临界温度附近CO2在水中的溶解度和水在CO2中的溶解度随压力的变化曲线。从图图 1图 2可以看出,随着压力的增加,CO2在水中的溶解度先快速增加后缓慢增加,而水在CO2中的溶解度则随着压力的增加先快速减小,后缓慢减小,然后再快速增加,最后缓慢增加。CO2临界压力点附近的溶解度突变,主要是由于此时发生了由气-液平衡到液-液平衡的相态转变。这种水在CO2中溶解度随压力的变化曲线并不是唯一的,在其他体系中也常见,例如,沥青在CO2中的溶解度曲线以及固体在CO2中的溶解度曲线。在更高的温度下(373 K和473 K),随着压力的逐渐增大CO2和水的溶解度曲线逐渐趋于光滑并且呈现出单调变化的特征(图 3~6),或单调增加或单调递减。当压力超过CO2的临界压力时,溶解度的值基本上不变或者变化的幅度很小。

下载eps/tif图 图 1 308 K时CO2在H2O中的溶解度 Fig. 1 Solubility of CO2 in H2O at 308 K
下载eps/tif图 图 2 308 K时H2O在CO2中的溶解度 Fig. 2 Solubility of H2O in CO2 at 308 K
下载eps/tif图 图 3 373 K时CO2在H2O中的溶解度 Fig. 3 Solubility of CO2 in H2O at 373 K
下载eps/tif图 图 4 373 K时H2O在CO2中的溶解度 Fig. 4 Solubility of H2O in CO2at 373 K
下载eps/tif图 图 5 473 K时CO2在H2O中的溶解度 Fig. 5 Solubility of CO2 in H2O at 473 K
下载eps/tif图 图 6 473 K时H2O在CO2中的溶解度 Fig. 6 Solubility of H2O in CO2 at 473 K

表 3为CO2与水相互作用时不同缔合模型计算的平均误差结果。从表 3可以看出,308 K时当CO2被模拟为缔合物,低压下较小的压力范围内水在CO2中的溶解度计算结果与实验数据和吻合良好,当压力超出一定范围时,曲线的形状特征发生改变。在更高的温度下,计算的CO2在水中的溶解度曲线变化趋势虽然与实验结果的变化趋势一样,但是两者之间的偏差较大。在308 K时,CO2在水中的溶解度的平均偏差为25.04%,而水在CO2中的溶解度平均偏差则大于100%。

下载CSV 表 3 CO2-H2O的溶解度计算结果 Table 3 Result analysis of solubility calculation of CO2 and H2O

当CO2被模拟为非缔合物时,它还可以与水发生交叉缔合溶剂化。当水为4 C缔合模型与CO2交叉缔合溶剂化时,计算结果与实验结果之间的误差最小为13.94%,其曲线的变化趋势与实验结果的变化趋势基本一致。这表明CO2溶剂化的结果比缔合模型时更能模拟含CO2体系的热力学平衡性质。

4 结论

(1) 非极性物质CO2的缔合模型不同于水,有3种不同的缔合方式:①非缔合,既不自缔合也不与水发生交叉缔合;②非缔合,仅够与水发生交叉缔合(溶剂化);③缔合,不仅能发生自缔合还能与水发生交叉缔合。

(2) CO2与水体系的相态特征非常复杂,在CO2的临界温度和临界压力附近,由于发生了相态的变化,水和CO2的溶解度将发生突变;随着温度的升高,这种溶解度值发生突变的现象将逐渐消失。

(3) 通过对CO2与水所有缔合模型结构的模拟分析,得出当CO2被模拟为非缔合物与缔合模型为4 C的水交叉缔合溶剂化时,CPA方程的计算结果与实验数据偏差较小。

(4) 当CO2与水交叉缔合溶剂化时,CR-1混合规则发生改变,其缔合能和缔合体积参数将由实验数据拟合得到。溶解度的计算结果虽能满足工程应用要求但理论上偏差较大,在后续的研究中可以开展其他混合规则对该体系相态特征计算的敏感性研究。

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