页岩气非线性渗流的有限元模拟方法
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摘要
基于考虑解吸、扩散和滑移作用的页岩气非线性渗流理论模型,构建了以压力为自变量的页岩气非线性渗流的三维有限元方程.通过一个忽略解吸效应的页岩气稳定渗流算例和一个考虑解吸附效应的页岩气非稳定渗流算例,求解井筒附近压力场,以及压力和气井产量随时间的变化,并与文献中的理论解进行对比,验证数值方法的合理性.结果表明,本文提供的页岩气非稳定渗流数值计算方法,其结果与理论解吻合,且收敛性好,可用于页岩气开发中气井周围压力变化和气井产量的预测,为页岩气井设计和页岩气开采提供重要的手段.
On the basis of nonlinear shale gas flow model considering the diffusion, slippage and desorption effects, a three-dimensional general numerical algorithm in the context of finite element scheme with pressure as the independent variable was developed. Two examples were investigated to illustrate the accuracy of this finite element scheme. One was to solve the steady pressure field of one shale gas reservoir without considering desorption effect. The other was to study transient pressure and flux of the shale gas reservoir with desorption effect considered. Compared with the analytical solutions from references, it can be seen that numerical solutions of the algorithm were consistent with the analytical solutions, and the convergence was easy to approach. The numerical algorithm in this paper can be used to forecast the pressure field and the flux of the gas reservoirs, and provides an important method for designing and developing shale gas reservoirs.
On the basis of nonlinear shale gas flow model considering the diffusion, slippage and desorption effects, a three-dimensional general numerical algorithm in the context of finite element scheme with pressure as the independent variable was developed. Two examples were investigated to illustrate the accuracy of this finite element scheme. One was to solve the steady pressure field of one shale gas reservoir without considering desorption effect. The other was to study transient pressure and flux of the shale gas reservoir with desorption effect considered. Compared with the analytical solutions from references, it can be seen that numerical solutions of the algorithm were consistent with the analytical solutions, and the convergence was easy to approach. The numerical algorithm in this paper can be used to forecast the pressure field and the flux of the gas reservoirs, and provides an important method for designing and developing shale gas reservoirs.
引文
1 Curtis M E,Ambrose R J,Sondergeld C H,et al.Structural characterization of gas shales on the micro-and nano-scales.In:Canadian Unconventional Resources and International Petroleum Conference,19–21 October,Calgary,Alberta,Canada.SPE 137693
2 姚军,孙海,黄朝琴,等.页岩气藏开发中的关键力学问题.中国科学:物理学力学天文学,2013,43:1527–1547
3 邹才能,朱如凯,白斌,等.中国油气储层中纳米孔首次发现及其科学价值.岩石学报,2011,27:1857–1864
4 Javadpour F,Fisher D,Unsworth M.Nanoscale gas flow in shale sediments.J Can Petrol Technol,2007,46:55–61
5 Karniadakis G E,Beskok A.Microflows and Nanoflows:Fundamentals and Simulation.Berlin:Springer,2001
6 Beskok A,Karniadakis G E.A model for flows in channels,pipes,and ducts at micro-and nano-scales.Microscale Therm Eng,1999,3:43 –77
7 Florence F A,Rushing J A,Newsham K E,et al.Improved permeability prediction relations for low-permeability sands.In:Rocky Mountain Oil and Gas Technology Symposium.Denver,2007,16
8 朱维耀,马千,邓佳,等.纳微米级孔隙气体流动数学模型及应用.北京科技大学学报,2014,36:710–715
9 Deng J,Zhu W Y,Ma Q.A new seepage model for shale gas reservoir and productivity analysis of fractured well.Fuel,2014,124:232 –240
10 Deng J,Zhu W Y.Study on the steady and transient pressure characteristics of shales gas reservoirs.Nat Gas Sci Eng,2015,24:210–216
11 刘嘉璇,尚新春,朱维耀.页岩气直井非稳态非线性渗流的数值计算及产能预测.中国科学:技术科学,2015,45:737–746
12 尹虎,王新海,刘洪,等.考虑启动压力梯度的页岩气藏数值模拟.油气田开发,2012,30:43–45,57
13 糜利栋,姜汉桥,李俊键.页岩气离散裂缝网络模型数值模拟方法研究.天然气地球科学,2014,25:1795–1803
14 糜利栋,姜汉桥,李俊键.基于有限元分析的页岩气扩散数值模拟.科学技术与工程,2014,14:70–75
15 郭小哲,周长沙.页岩气藏压裂水平井渗流数值模型的建立.西南石油大学学报(自然科学版),2014,36:90–96
16 任飞,王新海,任凯,等.考虑压裂区渗透率变化的页岩气井产能评价.断块油气田,2013,20:649–651
17 任飞,王新海,谢玉银.考虑滑脱效应的页岩气井底压力特征.石油天然气学报,2013,35:124–126
18 盛茂,李根生,黄中伟,等.页岩气藏流固耦合渗流模型及有限元求解.岩石力学与工程学报,2013,32:1894–1900
19郭为,熊伟,高树生,等.温度对页岩等温吸附/解吸特征影响.石油勘探与开发,2013,40:481–485
20 孔祥言.高等渗流力学(第二版).合肥:中国科学技术大学出版社,2010
21 Wu M.A finite-element algorithm for modeling variably saturated flows.J Hydrol,2010,394:315–323
22 Neuman S P.Saturated-unsaturated flow seepage by finite element.J Hydraul Division,2015,99:2233–2250
2 姚军,孙海,黄朝琴,等.页岩气藏开发中的关键力学问题.中国科学:物理学力学天文学,2013,43:1527–1547
3 邹才能,朱如凯,白斌,等.中国油气储层中纳米孔首次发现及其科学价值.岩石学报,2011,27:1857–1864
4 Javadpour F,Fisher D,Unsworth M.Nanoscale gas flow in shale sediments.J Can Petrol Technol,2007,46:55–61
5 Karniadakis G E,Beskok A.Microflows and Nanoflows:Fundamentals and Simulation.Berlin:Springer,2001
6 Beskok A,Karniadakis G E.A model for flows in channels,pipes,and ducts at micro-and nano-scales.Microscale Therm Eng,1999,3:43 –77
7 Florence F A,Rushing J A,Newsham K E,et al.Improved permeability prediction relations for low-permeability sands.In:Rocky Mountain Oil and Gas Technology Symposium.Denver,2007,16
8 朱维耀,马千,邓佳,等.纳微米级孔隙气体流动数学模型及应用.北京科技大学学报,2014,36:710–715
9 Deng J,Zhu W Y,Ma Q.A new seepage model for shale gas reservoir and productivity analysis of fractured well.Fuel,2014,124:232 –240
10 Deng J,Zhu W Y.Study on the steady and transient pressure characteristics of shales gas reservoirs.Nat Gas Sci Eng,2015,24:210–216
11 刘嘉璇,尚新春,朱维耀.页岩气直井非稳态非线性渗流的数值计算及产能预测.中国科学:技术科学,2015,45:737–746
12 尹虎,王新海,刘洪,等.考虑启动压力梯度的页岩气藏数值模拟.油气田开发,2012,30:43–45,57
13 糜利栋,姜汉桥,李俊键.页岩气离散裂缝网络模型数值模拟方法研究.天然气地球科学,2014,25:1795–1803
14 糜利栋,姜汉桥,李俊键.基于有限元分析的页岩气扩散数值模拟.科学技术与工程,2014,14:70–75
15 郭小哲,周长沙.页岩气藏压裂水平井渗流数值模型的建立.西南石油大学学报(自然科学版),2014,36:90–96
16 任飞,王新海,任凯,等.考虑压裂区渗透率变化的页岩气井产能评价.断块油气田,2013,20:649–651
17 任飞,王新海,谢玉银.考虑滑脱效应的页岩气井底压力特征.石油天然气学报,2013,35:124–126
18 盛茂,李根生,黄中伟,等.页岩气藏流固耦合渗流模型及有限元求解.岩石力学与工程学报,2013,32:1894–1900
19郭为,熊伟,高树生,等.温度对页岩等温吸附/解吸特征影响.石油勘探与开发,2013,40:481–485
20 孔祥言.高等渗流力学(第二版).合肥:中国科学技术大学出版社,2010
21 Wu M.A finite-element algorithm for modeling variably saturated flows.J Hydrol,2010,394:315–323
22 Neuman S P.Saturated-unsaturated flow seepage by finite element.J Hydraul Division,2015,99:2233–2250