表 1 某混合物各组分平衡常数(K值)的计算值与实验值
Table 1 Caculation and experimental data of K-values for each component of the fluid
图 1 孔隙半径为10、30、50 nm时和无毛细管力情况下地层油的性质
Fig.1 Black-oil properties of the Middle Bakken formation with pore sizes of 10, 30, 50 nm, and infinity(the infinite pore size means there is no capillary pressure), respectively
ZHANG Yuan,DI Yuan,ZHANG Yun,et al.Investigation into effects of nanoporous capillary pressure on well performance of tight oil reservoirs[J].Journal of Zhejiang University of Science and Technology,2017,29(05):328-333.[doi: 10.3969/j.issn.1671-8798.2017.05.002 ]
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传统的相平衡计算模型无法准确计算纳米孔隙中的油气相态变化,因此须对传统的闪蒸计算模型进行改进。今通过计算油气两相压力不相等情况下油气的相平衡,得到考虑毛细管力效应的油气黏度、密度及溶解气油比等物性。毛细管力采用Young-Laplace公式进行计算,计算了某多组分混合物的相态平衡常数,结果与实验值符合良好,从而验证了本文算法计算相平衡的准确性。还以Bakken致密油藏为例,基于黑油模型研究毛细管力对相平衡影响时的油藏产量预测,结果表明忽略毛细管力的影响,会使预测的油气产量低于实际的油气产量。本研究较好地解释了毛细管力对油气的相态平衡及其对致密油藏产能预测的影响。
In response to failure of the conventional phase equilibrium calculation model to precisely evaluate the vapor-liquid phase behavior of nanopore, the conventional flash calculation model was modified to calculate the vapor-liquid phase equilibrium in case of inequalities between liquid and vapor phases, which subsequently obtained values of properties including viscosity, density and solution gas-oil ratio. Afterwards, the Young-Laplace equation was employed to evaluate the capillary pressure by calculating the phase equilibrium constants of a multicomponent mixture. And the calculated results fairly accorded with the experimental data, which verified accuracy of this calculation. Finally, the black oil model was applied to predict the effects of capillary pressure upon well performance for an actual well from the Bakken tight oil reservoirs. Results show that the predicted well performance is lower than the actual one when the nanoporous capillary pressure is neglected. This study has provided a better understanding of the effects of capillary pressure upon vapor-liquid phase equilibrium and well performance of tight oil reservoirs.
非常规油气藏的特点是低孔、低渗,孔隙尺寸大多在2.5～103 nm,储集层中纳米级孔隙发育[1-2]。大量研究表明,纳米级孔隙中的高毛细管力不仅影响油气在孔隙中的流动过程,也影响油气的相态平衡,进而影响油气的最终采收率。
Sigmund等[3]以实验仪器来研究C1-C4和C1-nC5混合物的泡点及露点压力,发现界面效应会影响平衡压力及各相的组分含量。理论分析也显示出泡点压力会随着孔隙尺寸的减小而降低[4-8],并且油藏条件距离临界点越远,泡点压力下降得越显著。由于传统的PVT(pressure-volume-temperature)分析无法对毛细管力效应的相态问题给出准确的预测,因此,需要改进传统的计算方法来计算流体性质,从而对非常规油气藏进行产能预测[9]。Wang等[10]通过加入孔隙压实效应项,研究了该效应对油藏产量的影响。Teklu等[11]引入了流体组分临界性质的转换因子来计算流体的相平衡,结果表明,毛细管力效应对相包络线的影响显著。Rezaveisi等[12]将毛细管力项的相平衡计算模型与组分模拟器相结合,用来预测非常规油藏的产能变化。在前人研究的基础上,笔者提出了一个能够考虑毛细管力效应的计算储层流体相平衡的数值方法,将此法对某多组分混合物的相平衡进行计算,并把计算结果与实验结果进行对比; 还以Bakken致密油藏中一口生产井为例,基于黑油模型研究了毛细管力对油藏产量预测的影响。
1 理论模型1.1 相平衡计算模型当液相和气相中各组分的逸度相等时,体系达到相平衡[11],即:
fiL(T,PL,xi)=fiV(T,PV,yi),i=1,…,Nc。(1)
根据质量守恒定律,可得式(2)～(4):
∑Nci=1xi=∑Nci=1yi=1,(2)
Fzi=xiL+yiV,i=1,…,Nc,(3)
∑Nci=1((Kic-1)zi)/(1+(V/F)(Kic-1))=0。(4)
式(1)～(4)中:fiL、fiV分别为液相、气相中组分i的逸度; PV和PL分别为气相和液相的压力; Nc为体系中的组分数; zi为体系中组分i的总摩尔分数; xi和yi分别为液相和气相的摩尔分数; F为总摩尔数; L和V分别为液相和气相的摩尔数; Kic为考虑毛细管力情况下的平衡常数。采用式(5)[11]进行计算:
Kic=(1-(Pc)/(PV))Ki=((PL)/(PV))Ki,i=1,…,Nc。(5)
式(5)中:Ki为传统相平衡计算中的平衡常数; Pc为毛细管力。采用Young-Laplace方程[13]来计算:
Pc=(2σcosθ)/r。(6)
式(6)中:r为毛细管半径,目前的研究中,常将r近似为孔隙半径[7]; θ为接触角; σ为气相与液相间的界面张力,采用Macleod-Sugden方程[13]计算。
利用Peng-Robinson状态方程[14]可求得液相和气相的压缩因子。采用Newton-Raphson迭代来解式(2)～(4)的非线性方程组,可求得组分i在气相和液相中的逸度,最终求得xi,yi等参数[15]。
1.2 流体性质的计算采用前述相平衡计算方法,可求得考虑毛细管力效应时的溶解气油比、体积系数、黏度等物性参数(均为压力的函数)。
溶解气油比的计算公式如下:
Rs=((nVVmV)SC)/((nLVmL)SC)。(7)
式(7)中:nV和nL分别为气体和液体的摩尔分数; VmV和VmL分别为气体和液体的摩尔体积; SC表示标准状态(20 ℃,101.3 kPa)。
地层油的体积系数Bo用公式表示为:
Bo=((nLVmL)RC)/((nLVmL)SC)。(8)
式(8)中,RC表示油藏条件。
黏度[16]的计算如下:
[(μ-μ*)ξ+10-4]1/4=a0+a1ρr+a2ρ2r+a3ρ3r+a4ρ4r。(9)
式(9)中:μ为原油在地层条件下的黏度; μ*为低压下混合物的黏度; ξ为混合物的黏度; 参数a0～a4分别为0.102 3、0.0233 64、0.058 533、-0.040 758和0.009 332 4; ρr为视摩尔密度; 各参数的计算可参见文献[17]。
2 相平衡计算方法的验证
表1 某混合物各组分平衡常数(K值)的计算值与实验值
Table 1 Caculation and experimental data of K-values for each component of the fluid
通过计算某混合物在71.7 ℃、426.1 kPa条件下的平衡常数,来验证本文相平衡计算方法的准确性。具体的计算结果如表1所示,由此可知,计算而得的平衡常数值的平均误差为2.5%,计算值与实验值[10]的误差较小,从而验证了本文相平衡计算方法的准确性。
3 相平衡算法的应用3.1 毛细管力效应对流体性质的影响本研究中将油相作为润湿相,油相的压力设为参考压力。分别计算了Bakken致密油藏中,孔隙半径为10、30、50 nm及无毛细管力情况下地层油的体积系数与油的黏度及溶解气油比,油藏温度为115.6 ℃。计算结果如图1所示。
图1 孔隙半径为10、30、50 nm时和无毛细管力情况下地层油的性质
Fig.1 Black-oil properties of the Middle Bakken formation with pore sizes of 10, 30, 50 nm, and infinity(the infinite pore size means there is no capillary pressure), respectively
由曲线的拐点可以看出,当孔隙半径降低为10 nm时,受毛细管力的影响,泡点压力降低约1 379 kPa,毛细管力对相态平衡影响显著。孔隙半径为50 nm时,计算地层油的性质与不考虑毛细管力条件下的计算结果基本相同。因此,对于本算例的情况,当孔隙半径大于50 nm时,可忽略毛细管力对相平衡的影响。
3.2 生产数据历史拟合历史拟合作为油藏数值模拟过程中的重要环节,通过数值模拟的方法及油藏的动态数据对油藏参数进行修正,并通过不断修改地层的静态参数,使模拟计算结果达到允许的误差范围,以提高数值模拟的准确性。
表2 Middle Bakken油藏模型的相关参数
Table 2 Parameters of Middle Bakken reservoir model
油藏三维模型如图2所示,长、宽、高分别为3 200.4、792.5、15.2 m。油藏中心有一口水平井,并伴有30条人工裂缝,裂缝宽度设为0.003 m,井底流压为6 894.8 kPa。油藏及裂缝的性质[19]如表2所示。网格采用了局部加密方法,以便准确描述基质到裂缝之间的流体流动。由于地层中孔隙分布并非单一的孔隙半径分布,因此,根据实验测得的实际孔隙分布数据[20]最终将孔隙半径划分为5个区域,即小于10 nm(27%),10～20 nm(26%),20～30 nm(30%),30～50 nm(13%)及大于50 nm(4%)的区域。不同区域的流体具有不同的PVT性质,并将其随机分布于油藏模型中,结果如图3所示。该油藏模型的渗透率分布如图4所示。
图2 油藏的三维模型(x、y和z方向的网格尺寸为12.2 m×12.2 m×15.2 m)
Fig.2 A three-dimensional(3D)reservoir model for the base case(The block size is set to 12.2 m× 12.2 m×15.2 m in x, y, and z directions, respectively)
图3 油藏模型中孔隙半径随机分布示意(1～5分别表示5个不同的PVT区域)
Fig.3 Random distribution of pore sizes in the reservoir model(Color bar of 1—5 respresents five different PVT regions, respectively)
图4 油藏模型的渗透率分布示意
Fig.4 Permeability distribution of the reservoir model
利用Kurtoglu和Kazemi提供的Bakken致密油藏450 d的生产数据[18],首先对油的产量进行拟合,结果如图5(a)所示。保持油的产量不变,考虑毛细管力对相平衡的影响,分别将井底流压和气的产量作为拟合对象进行拟合,结果如图5(b)和(c)所示。由图5(b)和(c)可知,在不考虑毛细管力对相平衡影响的情况下,当基质渗透率调整为0.037 mD(毫达西),裂缝传导率为50 mD-ft(毫达西英尺)时,与生产数据能够较好地拟合; 而考虑毛细管力对相平衡的影响,拟合后基质渗透率调整为0.032 mD,裂缝传导率由50 mD-ft(毫达西英尺)变为48 mD-ft(毫达西英尺)。
图5 Bakken致密油藏生产历史拟合的结果
Fig.5 History matching results of the Bakken tight oil reservoir
3.3 单井产能预测
通过3.2节的生产历史拟合过程,对油藏的数值模拟模型进行了修正,现采用黑油模型研究毛细管力效应影响的相平衡对致密油藏实际开发的影响。如图6所示,计算结果表明,毛细管力效应使累积产油量、累积产气量和最终采收率分别提高7%、8%和6%。这是因为考虑毛细管力效应时,泡点压力降低,两相区的区域变小,从而使单一油相的生产时间变长,产量提高。此外,油相黏度降低,也是产量升高的另一个原因。
图6 有无考虑毛细管力影响相平衡情况下生产井30年的累积产量变化
Fig.6 Comparison of well performance in a 30-year period with and without the capillarity effect
4 结 论
本研究给出了考虑纳米孔隙中毛细管力效应的相平衡计算及产能预测的方法。通过某混合物平衡常数计算值与实验值的对比,验证了本研究方法计算相平衡的准确性。计算结果表明,考虑毛细管力的影响时,原油体积系数和溶解气油比升高,而黏度降低。对Bakken致密油藏某生产井进行产能预测的计算表明,毛细管力效应使累积产油量、产气量及最终采收率分别提高7%、8%和6%。这说明在致密油藏的产能预测中,应当考虑毛细管力对相平衡的影响,否则会对产能预测造成误差。
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