煤层气藏全流固耦合数学模型
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摘要
为准确表征煤层复杂的地质力学效应,根据多重孔隙介质力学特征和多过程运移特点,来构建煤层气藏三孔双渗全流固耦合数学模型,并基于所研发的全隐式有限体积数值模拟器,进一步研究地质力学效应对孔渗参数和煤层气产能的影响。结果表明,有效应力效应与基质收缩作用均可影响裂缝渗透率,且作用方向相反:有效应力效应的作用强度在开发初期大于基质收缩作用,但在后期发生逆转,导致渗透率先减小后增大,最终值甚至可达初始值的数倍;随着煤岩杨氏模量增大,有效应力效应减弱,煤层气日产量增大,产气高峰出现时机提前,随着Langmuir体应变量增大,基质收缩作用增强,同样煤层气日产量增大,产气高峰出现时机提前。全流固耦合数学模型能够更准确地刻画煤层复杂流固耦合作用,这对煤层气产能预测具有重要意义。
To more accurately characterize the complex geomechanical effects in coalbed methane reservoir,a fully coupled triple porosity dual permeability fluid flow and geomechanics model was established with consideration of poroelastic properties and multi-process transportation. The corresponding numerical solver was constructed by the fully implicit finite volumetric method,and the impacts of geomechanics on porosity and permeability and methane production were investigated. The results show that both effective stress effect and matrix shrinkage can significantly affect fracture permeability,but in opposite direction. The dominate factor is effective stress effect compared with matrix shrinkage at the early stage of primary production,but latter turns to matrix shrinkage,which makes fracture permeability firstly decreases and then rebound. The final permeability can even reach several times of its original value. As Young's modulus increases,the effective stress effect recedes,which creates bigger and earlier peak gas production. As the Langmuir strain increases,the matrix shrinkage is strengthened,which creates bigger and earlier peak gas production. The fully coupled fluid flow and geomechanics model can describe the complex fluid-structure interaction of coalbed methane reservoir more accurately,which is of great significance to the prediction of CBM productivity.
To more accurately characterize the complex geomechanical effects in coalbed methane reservoir,a fully coupled triple porosity dual permeability fluid flow and geomechanics model was established with consideration of poroelastic properties and multi-process transportation. The corresponding numerical solver was constructed by the fully implicit finite volumetric method,and the impacts of geomechanics on porosity and permeability and methane production were investigated. The results show that both effective stress effect and matrix shrinkage can significantly affect fracture permeability,but in opposite direction. The dominate factor is effective stress effect compared with matrix shrinkage at the early stage of primary production,but latter turns to matrix shrinkage,which makes fracture permeability firstly decreases and then rebound. The final permeability can even reach several times of its original value. As Young's modulus increases,the effective stress effect recedes,which creates bigger and earlier peak gas production. As the Langmuir strain increases,the matrix shrinkage is strengthened,which creates bigger and earlier peak gas production. The fully coupled fluid flow and geomechanics model can describe the complex fluid-structure interaction of coalbed methane reservoir more accurately,which is of great significance to the prediction of CBM productivity.
引文
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[2] WEI Z J,ZHANG D X. A fully coupled multiphase multicomponent flow and geomechanics model for enhanced coalbedmethane recovery and CO2storage. SPE Journal,2013,18(3):448-467.
[3]孙超群,李术才,李华銮,等.煤层气藏应力—渗流流固耦合模型及SPH求解.天然气地球科学,2017,28(2):305-312.SUN C Q,LI S C,LI H L,et al. Stress-seepage hydro-mechanical coupling model of coal-bed methane reservoir and its SPH analysis. Natural Gas Geoscience,2017,28(2):305-312.
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[6] PALMER I. Permeability changes in coal:Analytical modeling.International Journal of Coal Geology,2009,77(2):119-126.
[7] SHI J Q,DURUCAN S. Exponential growth in San Juan Basin Fruitland coalbed permeability with reservoir drawdown:Model match and new insights. SPE Reservoir Evaluation&Engineering,2010,13(6):914-925.
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[9]李传亮,朱苏阳,彭朝阳,等.煤层气井突然产气机理分析.岩性油气藏,2017,29(2):145-149.LI C L,ZHU S Y,PENG C Y,et al. Mechanism of gas production rate outburst in coalbed methane wells. Lithologic Reservoirs,2017,29(2):145-149.
[10] WARPINSKI N R,TEUFEL L W. Determination of the effective-stress law for permeability and deformation in low-permeability rocks. SPE Formation Evaluation,1992,7(2):123-131.
[11] SHI J Q,DURUCAN S. A model for changes in coalbed permeability during primary and enhanced methane recovery. SPE Reservoir Evaluation&Engineering,2005,8(4):291-299.
[12]张海茹,李昊.煤层气峰值产量拟合及产量动态预测方法研究.岩性油气藏,2013,25(4):116-118.ZHANG H R,LI H. Study on coalbed methane peak production fitting and production forecast by different dynamic analysis methods. Lithologic Reservoirs,2013,25(4):116-118.
[13]吴雅琴,邵国良,徐耀辉,等.煤层气开发地质单元划分及开发方式优化:以沁水盆地郑庄区块为例.岩性油气藏,2016,28(6):125-133.WU Y Q,SHAO G L,XU Y H,et al. Geological unit division and development model optimization of coalbed methane:a case study from Zhengzhuang block in Qinshui Basin. Lithologic Reservoirs,2016,28(6):125-133.
[14]高为,金军,易同生,等.黔北小林华矿区高阶煤层气藏特征及开采技术.岩性油气藏,2017,29(5):140-147.GAO W,JIN J,YI T S,et al. Enrichment mechanism and mining technology of high rank coalbed methane in Xiaolinhua coal mine,northern Guizhou. Lithologic Reservoirs,2017,29(5):140-147.
[15] SAKAI H,KURIHARA M. Development of double-permeability type compositional simulator for predicting enhanced coalbed methane recovery. The 24th Formation Evaluation Symposium of Japan,Chiba,2018.
[16] ZIMMERMAN R W. Coupling in poroelasticity and thermoelasticity. International Journal of Rock Mechanics and Mining Sciences,2000,37(2):79-87.
[17] KLINKENBERG L J. The permeability of porous media to liquids and gases. API Drilling and Production Practices,1941:200-213.
[18] CHEN H Y,TEUFEL L W. Coupling fluid-flow and geomechanics in dual-porosity modeling of naturally fractured reservoirs-model description and comparison. SPE 59043,2000.
[19] CARMAN P C,MALHERBE P R. Routine measurement of surface of paint pigments and other fine powders. I. Journal of the Society of Chemical Industry,1950,69(5):134-143.
[20] HARPALANI S,CHEN G. Influence of gas production induced volumetric strain on permeability of coal. Geotechnical and Geological Engineering,1997,15(4):303-325.
[21]李国庆,孟召平,王保玉.高煤阶煤层气扩散-渗流机理及初期排采强度数值模拟.煤炭学报,2014,39(9):1919-1926.LI G Q,MENG Z P,WANG B Y. Diffusion and seepage mechanisms of high rank coal-bed methane reservoir and its numerical simulation at early drainagerate. Journal of China Coal Society,2014,39(9):1919-1926.
[22]尹帅,丁文龙,高敏东.樊庄北部3号煤层现今应力场分布数值模拟.西南石油大学学报(自然科学版),2017,39(4):81-89.YIN S,DING W L,GAO M D. The in-situ stress field distribution numerical simulation of No.3 coal seam in the north of Fanzhuang CBM well blocks. Journal of Southwest Petroleum University(Science&Technology Edition),2017,39(4):81-89.
[23]张益,沈磊,田喜军,等.考虑采动影响的煤层气储层数值模拟方法研究.西安石油大学学报(自然科学版),2017,32(6):61-65.ZHANG Y,SHEN L,TIAN X J,et al. Research on numerical simulation method of coal bed gas reservoir under mining condition. Journal of Xi'an Shiyou University(Natural Science Edition),2017,32(6):61-65.
[24]孙政,李相方,徐兵祥,等.一种表征煤储层压力与流体饱和度关系的数学模型.中国科学:技术科学,2018,48(5):457-464.SUN Z,LI X F,XU B X,et al. A mathematic model for characterizing the relationship between coal reservoir pressure and fluid saturation. Scientia Sinica Technologica,2018,48(5):457-464.
[25]颜志丰,琚宜文,唐书恒,等.沁水盆地南部煤层气储层压裂过程数值模拟研究.地球物理学报,2013,56(5):1734-1744.YAN Z F,JU Y W,TANG S H,et al. Numerical simulation study of fracturing process in coalbed methane reservoir in southern Qinshui Basin. Chinese Journal of Geophysics,2013,56(5):1734-1744.
[26]杨新乐,任常在,张永利,等.低渗透煤层气注热开采热-流-固耦合数学模型及数值模拟.煤炭学报,2013,38(6):1044-1049.YANG X L,REN C Z,ZHANG Y L,et al. Numerical simulation of the coupled thermal-fluid-solid mathematical models during extracting methane in low-permeability coal bed by heat injection. Journal of China Coal Society,2013,38(6):1044-1049.
[27]吴金涛,侯健,陆雪皎,等.注气驱替煤层气数值模拟.计算物理,2014,31(6):681-689.WU J T,HOU J,LU X J,et al. Numerical simulation of coalbed methane displacement with gas injection. Chinese Journal of Computational Physics,2014,31(6):681-689.
[28]范超军,李胜,罗明坤,等.基于流-固-热耦合的深部煤层气抽采数值模拟.煤炭学报,2016,41(12):3076-3085.FAN C J,LI S,LUO M K,et al. Deep CBM extraction numerical simulation based on hydraulic-mechanical-thermal coupled model. Journal of China Coal Society,2016,41(12):3076-3085.
[2] WEI Z J,ZHANG D X. A fully coupled multiphase multicomponent flow and geomechanics model for enhanced coalbedmethane recovery and CO2storage. SPE Journal,2013,18(3):448-467.
[3]孙超群,李术才,李华銮,等.煤层气藏应力—渗流流固耦合模型及SPH求解.天然气地球科学,2017,28(2):305-312.SUN C Q,LI S C,LI H L,et al. Stress-seepage hydro-mechanical coupling model of coal-bed methane reservoir and its SPH analysis. Natural Gas Geoscience,2017,28(2):305-312.
[4]倪冬,王延斌,韩文龙,等.沁水南部柿庄南区块3号煤层现今地应力特征及其与渗透率的关系研究.河南理工大学学报(自然科学版),2019,38(1):68-75.NI D,WANG Y B,HAN W L,et al. Characteristic of in-situ stress in No. 3 coal seams of southern Shizhuang block,southern Qinshui Basin,and its influence on permeability. Journal of Henan Polytechnic University(Natural Science),2019,38(1):68-75.
[5] PEKOT L J,REEVES S R. Modeling the effects of matrix shrinkage and differential swelling on coalbed methane recovery and carbon sequestration. Proceedings of the 2003 International Coalbed Methane Symposium. University of Alabama,Tuscaloosa,Alabama,2003.
[6] PALMER I. Permeability changes in coal:Analytical modeling.International Journal of Coal Geology,2009,77(2):119-126.
[7] SHI J Q,DURUCAN S. Exponential growth in San Juan Basin Fruitland coalbed permeability with reservoir drawdown:Model match and new insights. SPE Reservoir Evaluation&Engineering,2010,13(6):914-925.
[8] WARREN J E,ROOT P J. The behavior of naturally fractured reservoirs. SPE Journal,1963,3(3):245-255.
[9]李传亮,朱苏阳,彭朝阳,等.煤层气井突然产气机理分析.岩性油气藏,2017,29(2):145-149.LI C L,ZHU S Y,PENG C Y,et al. Mechanism of gas production rate outburst in coalbed methane wells. Lithologic Reservoirs,2017,29(2):145-149.
[10] WARPINSKI N R,TEUFEL L W. Determination of the effective-stress law for permeability and deformation in low-permeability rocks. SPE Formation Evaluation,1992,7(2):123-131.
[11] SHI J Q,DURUCAN S. A model for changes in coalbed permeability during primary and enhanced methane recovery. SPE Reservoir Evaluation&Engineering,2005,8(4):291-299.
[12]张海茹,李昊.煤层气峰值产量拟合及产量动态预测方法研究.岩性油气藏,2013,25(4):116-118.ZHANG H R,LI H. Study on coalbed methane peak production fitting and production forecast by different dynamic analysis methods. Lithologic Reservoirs,2013,25(4):116-118.
[13]吴雅琴,邵国良,徐耀辉,等.煤层气开发地质单元划分及开发方式优化:以沁水盆地郑庄区块为例.岩性油气藏,2016,28(6):125-133.WU Y Q,SHAO G L,XU Y H,et al. Geological unit division and development model optimization of coalbed methane:a case study from Zhengzhuang block in Qinshui Basin. Lithologic Reservoirs,2016,28(6):125-133.
[14]高为,金军,易同生,等.黔北小林华矿区高阶煤层气藏特征及开采技术.岩性油气藏,2017,29(5):140-147.GAO W,JIN J,YI T S,et al. Enrichment mechanism and mining technology of high rank coalbed methane in Xiaolinhua coal mine,northern Guizhou. Lithologic Reservoirs,2017,29(5):140-147.
[15] SAKAI H,KURIHARA M. Development of double-permeability type compositional simulator for predicting enhanced coalbed methane recovery. The 24th Formation Evaluation Symposium of Japan,Chiba,2018.
[16] ZIMMERMAN R W. Coupling in poroelasticity and thermoelasticity. International Journal of Rock Mechanics and Mining Sciences,2000,37(2):79-87.
[17] KLINKENBERG L J. The permeability of porous media to liquids and gases. API Drilling and Production Practices,1941:200-213.
[18] CHEN H Y,TEUFEL L W. Coupling fluid-flow and geomechanics in dual-porosity modeling of naturally fractured reservoirs-model description and comparison. SPE 59043,2000.
[19] CARMAN P C,MALHERBE P R. Routine measurement of surface of paint pigments and other fine powders. I. Journal of the Society of Chemical Industry,1950,69(5):134-143.
[20] HARPALANI S,CHEN G. Influence of gas production induced volumetric strain on permeability of coal. Geotechnical and Geological Engineering,1997,15(4):303-325.
[21]李国庆,孟召平,王保玉.高煤阶煤层气扩散-渗流机理及初期排采强度数值模拟.煤炭学报,2014,39(9):1919-1926.LI G Q,MENG Z P,WANG B Y. Diffusion and seepage mechanisms of high rank coal-bed methane reservoir and its numerical simulation at early drainagerate. Journal of China Coal Society,2014,39(9):1919-1926.
[22]尹帅,丁文龙,高敏东.樊庄北部3号煤层现今应力场分布数值模拟.西南石油大学学报(自然科学版),2017,39(4):81-89.YIN S,DING W L,GAO M D. The in-situ stress field distribution numerical simulation of No.3 coal seam in the north of Fanzhuang CBM well blocks. Journal of Southwest Petroleum University(Science&Technology Edition),2017,39(4):81-89.
[23]张益,沈磊,田喜军,等.考虑采动影响的煤层气储层数值模拟方法研究.西安石油大学学报(自然科学版),2017,32(6):61-65.ZHANG Y,SHEN L,TIAN X J,et al. Research on numerical simulation method of coal bed gas reservoir under mining condition. Journal of Xi'an Shiyou University(Natural Science Edition),2017,32(6):61-65.
[24]孙政,李相方,徐兵祥,等.一种表征煤储层压力与流体饱和度关系的数学模型.中国科学:技术科学,2018,48(5):457-464.SUN Z,LI X F,XU B X,et al. A mathematic model for characterizing the relationship between coal reservoir pressure and fluid saturation. Scientia Sinica Technologica,2018,48(5):457-464.
[25]颜志丰,琚宜文,唐书恒,等.沁水盆地南部煤层气储层压裂过程数值模拟研究.地球物理学报,2013,56(5):1734-1744.YAN Z F,JU Y W,TANG S H,et al. Numerical simulation study of fracturing process in coalbed methane reservoir in southern Qinshui Basin. Chinese Journal of Geophysics,2013,56(5):1734-1744.
[26]杨新乐,任常在,张永利,等.低渗透煤层气注热开采热-流-固耦合数学模型及数值模拟.煤炭学报,2013,38(6):1044-1049.YANG X L,REN C Z,ZHANG Y L,et al. Numerical simulation of the coupled thermal-fluid-solid mathematical models during extracting methane in low-permeability coal bed by heat injection. Journal of China Coal Society,2013,38(6):1044-1049.
[27]吴金涛,侯健,陆雪皎,等.注气驱替煤层气数值模拟.计算物理,2014,31(6):681-689.WU J T,HOU J,LU X J,et al. Numerical simulation of coalbed methane displacement with gas injection. Chinese Journal of Computational Physics,2014,31(6):681-689.
[28]范超军,李胜,罗明坤,等.基于流-固-热耦合的深部煤层气抽采数值模拟.煤炭学报,2016,41(12):3076-3085.FAN C J,LI S,LUO M K,et al. Deep CBM extraction numerical simulation based on hydraulic-mechanical-thermal coupled model. Journal of China Coal Society,2016,41(12):3076-3085.