基于反常扩散模型的页岩气藏压裂水平井产能研究
|
摘要
页岩气藏体积压裂后,由于气体渗流孔隙尺度的突变以及基质与裂缝性质的显著差异,使渗流速度场表现出急剧的不连续性,致使连续介质假设条件不成立。为清楚认识页岩气藏渗流规律并进行产能研究,基于页岩气压裂水平井三线性流模型,耦合分形多孔介质的反常扩散方程,建立页岩气压裂水平井产能模型,运用Laplace变换和Stehfest数值反演得到无因次产量,结合实例计算分析并绘制出无因次产量递减曲线。研究结果表明:页岩气流动阶段分为人工裂缝线性流阶段、人工裂缝和天然裂缝双线性流阶段、天然裂缝线性流阶段、天然裂缝和基质双线性流阶段、基质线性流阶段;基于所建立的产能模型,研究了反常扩散指数、拟渗透率、储容比、裂缝间距等对产能的影响;结果表明:反常扩散指数越小,基质的非均质性越强,生产后期产能递减越明显;天然裂缝拟渗透率主要影响天然裂缝线性流期时间长短,而人工裂缝拟渗透率对页岩气藏的影响覆盖了生产周期的中后期;弹性储容比越大,产能的增加幅度越明显。研究为页岩气藏产能分析及评价提供了一个新的思路及方法。
After the volume fracturing of shale gas reservoirs, due to the abrupt variations in the pore scale of the gas seepage andthe severe difference between the characteristics of shale matrix and fractures, the seepage velocity field showed a sharp discontinu-ity, resulting in the failure of continuum assumption. In order to accurately understand the flow pattern of shale gas reservoirs andanalyze the productivity, based on the trilinear flow model of fractured horizontal wells in shale gas reservoirs and coupled with theanomalous diffusion equation of fractal porous media, we established a fractured horizontal well productivity model of shale gas res-ervoirs. The dimensionless production was obtained by Laplace transform and Stehfest numerical inversion. Finally, we analyzed itsresult combining specific example and obtained a dimensional production curve. The analysis results showed that five flow regionsfor shale gas could be identified, including the linear flow stage of hydraulic fractures, the bilinear flow in hydraulic fractures andnatural fractures, the linear flow stage of natural fractures, the bilinear flow in natural fractures and matrices, and the phase of ma-trix linear flow. Based on the production model, we also studied the influence of anomalous diffusion exponent, pseudo-permeabili-ty, storability ratio, fracture spacing and the like. on the production of shale gas reservoirs. The results indicated that the smaller ab-normal diffusion exponent and the stronger matrix heterogeneity were, the more obvious decrease of productivity would be, and thenatural fractures pseudo-permeability had great impact on the length of time in the linear flow of the natural fractures. Further-more, the hydraulic fracture pseudo-permeability could influence the productivity in the whole middle-late production cycle. Thelarger the storability ratio was, the more obvious increase amplitude of productivity would be. The research provided a new idea andmethod for productivity analysis and evaluation of shale gas reservoirs.
After the volume fracturing of shale gas reservoirs, due to the abrupt variations in the pore scale of the gas seepage andthe severe difference between the characteristics of shale matrix and fractures, the seepage velocity field showed a sharp discontinu-ity, resulting in the failure of continuum assumption. In order to accurately understand the flow pattern of shale gas reservoirs andanalyze the productivity, based on the trilinear flow model of fractured horizontal wells in shale gas reservoirs and coupled with theanomalous diffusion equation of fractal porous media, we established a fractured horizontal well productivity model of shale gas res-ervoirs. The dimensionless production was obtained by Laplace transform and Stehfest numerical inversion. Finally, we analyzed itsresult combining specific example and obtained a dimensional production curve. The analysis results showed that five flow regionsfor shale gas could be identified, including the linear flow stage of hydraulic fractures, the bilinear flow in hydraulic fractures andnatural fractures, the linear flow stage of natural fractures, the bilinear flow in natural fractures and matrices, and the phase of ma-trix linear flow. Based on the production model, we also studied the influence of anomalous diffusion exponent, pseudo-permeabili-ty, storability ratio, fracture spacing and the like. on the production of shale gas reservoirs. The results indicated that the smaller ab-normal diffusion exponent and the stronger matrix heterogeneity were, the more obvious decrease of productivity would be, and thenatural fractures pseudo-permeability had great impact on the length of time in the linear flow of the natural fractures. Further-more, the hydraulic fracture pseudo-permeability could influence the productivity in the whole middle-late production cycle. Thelarger the storability ratio was, the more obvious increase amplitude of productivity would be. The research provided a new idea andmethod for productivity analysis and evaluation of shale gas reservoirs.
引文
[1]董大忠,邹才能,戴金星,等.中国页岩气发展战略对策建议[J].天然气地球科学,2016,27(3):397-406.
[2]邱中建,邓松涛.中国非常规天然气的战略地位[J].天然气工业,2012,32(1):1-5.
[3]江怀友,鞠斌山,李治平,等.世界页岩气资源现状研究[J].中外能源,2014,19(3):14-22.
[4]郑军卫,孙德强,李小燕,等.页岩气勘探开发技术进展[J].天然气地球科学2011,22(3):511-517.
[5]苏玉亮,盛广龙,王文东,等.页岩气藏多重介质耦合流动模型[J].天然气工业,2016,36(2):52-59.
[6]姚同玉,黄延章,李继山.页岩气在超低渗介质中的渗流行为[J].力学学报,2012,44(6):990-995.
[7]Al-Ahmadi H A,Wattenbarger R A.Triple-porosity models:one further step towards capturing fractured reservoirs heterogeneity[C]//paper SPE-149054-MS presented at the SPE/DGSSaudi Arabia Section Technical Symposium and Exhibition,15-18 May 2011,Al-Khobar,Saudi Arabia.
[8]Ezulike D O,Dehghanpour H.A model for simultaneous matrix depletion into natural and hydraulic fracture networks[J].Journal of Natural Gas Science&Engineering,2014,16(17):57-69.
[9]Tian L,Xiao C,Liu M,et al.Well testing model for multi-fractured horizontal well for shale gas reservoirs with consideration of dual diffusion in matrix[J].Journal of Natural Gas Science&Engineering,2014,21(21):283-295.
[10]Thorstenson D C,Pollock D W.Gas transport in unsaturated porous media:The adequacy of Fick's law[J].Reviews of Geophysics,1989,27(1):61-78.
[11]田冷,肖聪,刘明进,等.考虑页岩气扩散的多级压裂水平井产能模型[J].东北石油大学学报,2014,38(5):93-102.
[12]李勇明,彭瑀,王中泽.页岩气压裂增产机理与施工技术分析[J].西南石油大学学报(自然科学版),2013,35(2):90-96.
[13]钱斌,张俊成,朱炬辉,等.四川盆地长宁地区页岩气水平井组“拉链式”压裂实践[J].天然气工业,2015,35(1):81-84.
[14]Raghavan R.Fractional diffusion:Performance of fractured wells[J].Journal of Petroleum Science&Engineering,2012,92-93(4):167-173.
[15]孙洪广,常爱莲,陈文,等.反常扩散:分数阶导数建模及其在环境流动中的应用[J].中国科学:物理学力学天文学,2015,45(10):8-22.
[16]庞国飞,陈文,张晓棣,等.复杂介质中扩散和耗散行为的分数阶导数唯象建模[J].应用数学和力学,2015,36(11):1117-1134.
[17]Obembe A D,Hossain M E,Abu-Khamsin S A.Variable-order derivative time fractional diffusion model for heterogeneous porous media[J].Journal of Petroleum Science&Engineering,2017,152:391-405.
[18]Albinali A,Ozkan E.Analytical modeling of flow in highly disordered,fractured nano-porous reservoirs[C]//paper SPE-180440-MS presented at the SPE Western Regional Meeting,23-26 May 2016,Anchorage,Alaska,USA.
[19]Holy R W,Ozkan E.A practical and rigorous approach for production data analysis in unconventional wells[C]//paper SPE-180240-MS presented at the SPE Low Perm Symposium,5-6May 2016,Denver,Colorado,USA.
[20]Obembe A D,Hossain M E,Mustapha K,et al.A modified memory-based mathematical model describing fluid flow in porous media[J].Computers&Mathematics with Applications,2016,73(6):1385-1402.
[21]Ozcan O,Sarak H,Ozkan E,et al.A trilinear flow model for a fractured horizontal well in a fractal unconventional reservoir[C]//paper SPE-170971-MS presented at the SPE Annual Technical Conference and Exhibition,27-29 October 2014,Amsterdam,The Netherlands.
[22]Caputo M.Linear Models of Dissipation whose Q is almost Frequency Independent-II[J].Geophysical Journal International,1967,13(5):529-539.
[23]Stehfest,H.Algorithm 368:Numerical inversion of Laplace transforms[J].Communications of the Acm,1970,13(1):47-49.
[24]同登科,陈钦雷.关于Laplace数值反演Stehfest方法的一点注记[J].石油学报,2001,22(6):91-92.
[2]邱中建,邓松涛.中国非常规天然气的战略地位[J].天然气工业,2012,32(1):1-5.
[3]江怀友,鞠斌山,李治平,等.世界页岩气资源现状研究[J].中外能源,2014,19(3):14-22.
[4]郑军卫,孙德强,李小燕,等.页岩气勘探开发技术进展[J].天然气地球科学2011,22(3):511-517.
[5]苏玉亮,盛广龙,王文东,等.页岩气藏多重介质耦合流动模型[J].天然气工业,2016,36(2):52-59.
[6]姚同玉,黄延章,李继山.页岩气在超低渗介质中的渗流行为[J].力学学报,2012,44(6):990-995.
[7]Al-Ahmadi H A,Wattenbarger R A.Triple-porosity models:one further step towards capturing fractured reservoirs heterogeneity[C]//paper SPE-149054-MS presented at the SPE/DGSSaudi Arabia Section Technical Symposium and Exhibition,15-18 May 2011,Al-Khobar,Saudi Arabia.
[8]Ezulike D O,Dehghanpour H.A model for simultaneous matrix depletion into natural and hydraulic fracture networks[J].Journal of Natural Gas Science&Engineering,2014,16(17):57-69.
[9]Tian L,Xiao C,Liu M,et al.Well testing model for multi-fractured horizontal well for shale gas reservoirs with consideration of dual diffusion in matrix[J].Journal of Natural Gas Science&Engineering,2014,21(21):283-295.
[10]Thorstenson D C,Pollock D W.Gas transport in unsaturated porous media:The adequacy of Fick's law[J].Reviews of Geophysics,1989,27(1):61-78.
[11]田冷,肖聪,刘明进,等.考虑页岩气扩散的多级压裂水平井产能模型[J].东北石油大学学报,2014,38(5):93-102.
[12]李勇明,彭瑀,王中泽.页岩气压裂增产机理与施工技术分析[J].西南石油大学学报(自然科学版),2013,35(2):90-96.
[13]钱斌,张俊成,朱炬辉,等.四川盆地长宁地区页岩气水平井组“拉链式”压裂实践[J].天然气工业,2015,35(1):81-84.
[14]Raghavan R.Fractional diffusion:Performance of fractured wells[J].Journal of Petroleum Science&Engineering,2012,92-93(4):167-173.
[15]孙洪广,常爱莲,陈文,等.反常扩散:分数阶导数建模及其在环境流动中的应用[J].中国科学:物理学力学天文学,2015,45(10):8-22.
[16]庞国飞,陈文,张晓棣,等.复杂介质中扩散和耗散行为的分数阶导数唯象建模[J].应用数学和力学,2015,36(11):1117-1134.
[17]Obembe A D,Hossain M E,Abu-Khamsin S A.Variable-order derivative time fractional diffusion model for heterogeneous porous media[J].Journal of Petroleum Science&Engineering,2017,152:391-405.
[18]Albinali A,Ozkan E.Analytical modeling of flow in highly disordered,fractured nano-porous reservoirs[C]//paper SPE-180440-MS presented at the SPE Western Regional Meeting,23-26 May 2016,Anchorage,Alaska,USA.
[19]Holy R W,Ozkan E.A practical and rigorous approach for production data analysis in unconventional wells[C]//paper SPE-180240-MS presented at the SPE Low Perm Symposium,5-6May 2016,Denver,Colorado,USA.
[20]Obembe A D,Hossain M E,Mustapha K,et al.A modified memory-based mathematical model describing fluid flow in porous media[J].Computers&Mathematics with Applications,2016,73(6):1385-1402.
[21]Ozcan O,Sarak H,Ozkan E,et al.A trilinear flow model for a fractured horizontal well in a fractal unconventional reservoir[C]//paper SPE-170971-MS presented at the SPE Annual Technical Conference and Exhibition,27-29 October 2014,Amsterdam,The Netherlands.
[22]Caputo M.Linear Models of Dissipation whose Q is almost Frequency Independent-II[J].Geophysical Journal International,1967,13(5):529-539.
[23]Stehfest,H.Algorithm 368:Numerical inversion of Laplace transforms[J].Communications of the Acm,1970,13(1):47-49.
[24]同登科,陈钦雷.关于Laplace数值反演Stehfest方法的一点注记[J].石油学报,2001,22(6):91-92.