裂缝性低渗透碳酸盐岩储层酸压改造油井动态压力特征
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摘要
裂缝性低渗透碳酸盐岩储层具有基质低孔隙度低渗透率、天然裂缝和溶蚀孔洞发育的三重介质特征。在考虑基质低速非达西渗流和裂缝应力敏感特征的基础上,针对裂缝性低渗透碳酸盐岩储层酸压改造油井建立了动态压力响应模型。利用对数变换和摄动法得到考虑井筒储集效应和表皮效应的实空间井底压力解,并绘制了典型图版,同时讨论了基质非达西渗流、裂缝应力敏感大小、储层物性改造强弱、储层流道改造程度、酸压改造范围等参数对动态压力响应的影响。结果表明:基质低速非达西程度越强压力及压力导数曲线上翘越明显,裂缝应力敏感性越大压力及压力导数曲线向上弯曲越剧烈。模型可用于裂缝性低渗透碳酸盐岩类油藏油井酸压改造效果评价和不稳定产能分析,得到的酸压有效改造面积和酸压改造程度对油井后期酸化解堵、重复酸压等增产措施具有重要的指导意义。
Fractured low permeability carbonate reservoirs are triple porosity media with low porosity and low permeability,but there are natural dissolved vugs and natural fractures in the reservoir rock.Considering low speed non-Darcy seepage in reservoir rocks and stress sensitivity of natural fractures and acid fracturing fractures,a transient pressure behavior model of acid fracturing oil well in fractured low permeability carbonate reservoirs is established.Using logarithmic transformation and perturbation method,the transient pressure solution of real space is obtained,further,it analyzes the effect of low speed non-Darcy in reservoir rock,stress sensitivity of fractures,rock property improvement degree,flow channel improvement degree,acid fracturing area.The result shows the more obvious the low speed non-Darcy flow and stress sensitivity is,the more warping and bending the type curve is.The model can be used to evaluate the effect of the acid fracturing and evaluation of unstable productivity on carbonate reservoirs,identification and judgment of acid fracturing area and acid fracturing degree is of guiding significance to oil well increasing production measures,such as repeated fracturing,acidification and plugging,in fractured low permeability carbonate reservoirs.
Fractured low permeability carbonate reservoirs are triple porosity media with low porosity and low permeability,but there are natural dissolved vugs and natural fractures in the reservoir rock.Considering low speed non-Darcy seepage in reservoir rocks and stress sensitivity of natural fractures and acid fracturing fractures,a transient pressure behavior model of acid fracturing oil well in fractured low permeability carbonate reservoirs is established.Using logarithmic transformation and perturbation method,the transient pressure solution of real space is obtained,further,it analyzes the effect of low speed non-Darcy in reservoir rock,stress sensitivity of fractures,rock property improvement degree,flow channel improvement degree,acid fracturing area.The result shows the more obvious the low speed non-Darcy flow and stress sensitivity is,the more warping and bending the type curve is.The model can be used to evaluate the effect of the acid fracturing and evaluation of unstable productivity on carbonate reservoirs,identification and judgment of acid fracturing area and acid fracturing degree is of guiding significance to oil well increasing production measures,such as repeated fracturing,acidification and plugging,in fractured low permeability carbonate reservoirs.
引文
[1]Miller-Bownlie T A.Subsoil water in relation to tube wells[J].Indian&Eastern Engineer,1919,42(2):116-131.
[2]Terzaghi K.Theoretical Soil Mechanics[M].New York:Chapman and Hall,1959:325-327.
[3]Mapxacин.ИЛ.Physical and Chemical Mechanism of Oil Layer[M].Li Dianwen.Beijing:Petroleum Industry Press,1987:1-3.马尔哈辛.油层物理化学机理[M].李殿文译.北京:石油工业出版社,1987:1-3.
[4]ГopbyнoвA T,Zhang Shubao.Abnormal Oil and Gas Field[M].Beijing:Petroleum Industry Press,1987:3.戈尔布诺夫A T.异常油田开发[M].张树宝译.北京:石油工业出版社,1987:3.
[5]Miller R J,Low P F.Threshold gradient for water flow in clay systems[J].Soil Science Society of America Journal,1963,27(6):605-609.
[6]Vairogs J,Hearn C L,Dareing D W,et al.Effect of rock stress on gas production from low-permeability reservoirs[J].Society of Petroleum Engineers,1971,23(9):1161-1167.
[7]Pascal F,Pascal H,Murray D W.Consolidation with threshold gradients[J].International Journal for Numerical&Analytical Methods in Geomechanics,1981,5(3):247-261.
[8]Pedrosa O A.Pressure Transient Response in Stress-sensitive Formations[R].SPE15115,1986.
[9]Feng Wenguang,Ge Jiali.Dynamic characteristics of the pressure curve of a single medium and double medium non darcy low velocity seepage[J].Petroleum Exploration and Development,1986(5):52-57.冯文光,葛家理.单一介质、双重介质非达西低速渗流的压力曲线动态特征[J].石油勘探与开发,1986(5):52-57.
[10]Cheng Shiqing,Li Yaogang.Numerical solution of well testing model for low-speed non-darcy flow and its application[J].Natural Gas Industry,1996,16(3):27-30.程时清,李跃刚.低速非达西渗流试井模型的数值解及其应用[J].天然气工业,1996,16(3):27-30.
[11]Cheng Shiqing,Li Gongquan,Lu Tai,et al.Mathematical model and typical curve for calculating effective hole diameter in the low velocity non-darcy flow testing of dual-media reservoirs[J].Natural Gas Industry,1997,17(2):35-37.程时清,李功权,卢涛,等.双重介质油气藏低速非达西渗流试井有效井径数学模型及典型曲线[J].天然气工业,1997,17(2):35-37.
[12]Tong Dengke,Ge Jiali.A seepage flow model with non-darcy low velocity for fractal reservoirs and its solution[J].Petroleum Geology&Oilfield Development in the Daqing,1996,15(3):18-23.同登科,葛家理.分形油藏非达西低速渗流模型及其解[J].大庆石油地质与开发,1996,15(3):18-23.
[13]Tong Dengke,Jiang Dongmei,Chen Qinlei.Dynamic characteristics of reservoir with deformed double-porosity medium[J].Journal of the University of Petroleum,China,2001,25(5):53-56,5.同登科,姜东梅,陈钦雷.变形双重介质油藏动态特征[J].石油大学学报:自然科学版,2001,25(5):53-56,5.
[14]Tong Dengke.Zhang Fengqin.Wang Ruihe.Exact solution and its behavior characteristic of the nonlinear dual porosity model[J].Applied Mathematics and Mechanics,2005,26(10):1161-1167.同登科,张鸿庆,王瑞和.非线性双重介质模型的精确解及动态特征[J].应用数学和力学,2005,26(10):1161-1167.
[15]Liao Xinwei,Feng Jilei.Well test model of stress sensitive gas reservoirs with super high pressure and low permeability[J].Natural Gas Industry,2005,25(2):110-112,213-214.廖新维,冯积累.超高压低渗气藏应力敏感试井模型研究[J].天然气工业,2005,25(2):110-112,213-214.
[16]Wang Zisheng,Yao Jun.Study of pressure transient characteristic for stress sensitive triply medium reservoirs with fractures and vugs conveying fluids to wellbore[J].Journal of Hydrodynamics,2006,21(1):84-89.王子胜,姚军.缝洞向井筒供液时三重压敏介质油藏压力响应特征研究[J].水动力学研究与进展,2006,21(1):84-89.
[17]Zhang Liehui,Zhang Jinliang,Xu Bingqing.A nonlinear seepage flow model for deformable double media fractal gas reservoirs[J].Chinese Journal of Computational Physics,2007,24(1):90-94.张烈辉,张锦良,徐冰青.变形双重介质分形气藏非线性渗流理论模型及数值研究[J].计算物理,2007,24(1):90-94.
[18]Zhang Yun,Wang Zisheng,Yao Jun,et al.Study and application of pressure transient of naturally fractured reservoirs with stress-sensitive and start pressure grade[J].Journal of Hydrodynamics,2007,22(3):332-337.张允,王子胜,姚军,等.带启动压力梯度的双孔压敏介质压力动态及其应用研究[J].水动力学研究与进展,2007,22(3):332-337.
[19]Tian Leng,He Shunli,Li Xiusheng.Study of well test of stress-sensitive sandstone in low permeability gas reservoir[J].Petroleum Drilling Techniques,2007,35(6):89-92.田冷,何顺利,李秀生.低渗透气田砂岩储层应力敏感试井模型研究[J].石油钻探技术,2007,35(6):89-92.
[20]Xue Lili.Tong Dengke.Fluid characteristics of triple-medium double permeability consider quadratic gradient term effects[J].Chinese Quarterly of Mechanics,2008,29(3):412-417.薛莉莉,同登科.考虑二次梯度项影响的三孔双渗模型渗流特征[J].力学季刊,2008,29(3):412-417.
[21]Feng Guoqin,Liu Qiguo,Shi Guanglzhi.et al.An unsteady seepage flow model considering kick off pressure gradient for low-permeability gas reservoirs[J].Petroleum Exploration and Development,2008,35(4):457-461.冯国庆,刘启国,石广志,等.考虑启动压力梯度的低渗透气藏不稳定渗流模型[J].石油勘探与开发,2008,35(4):457-461.
[22]Cai Jinming,Chen Fangyi,Zhang Lixuan,et al.A nonlinear seepage flow model for deformable double media fractal gas reservoirs[J].Special Oil and Gas Reservoir,2008,15(2):69-72,109.蔡明金,陈方毅,张利轩,等.考虑启动压力梯度低渗透油藏应力敏感模型研究[J].特种油气藏,2008,15(2):69-72,109.
[23]Zhang Lei,Tong Dengke,Ma Xiaodan.Pressure dynamic analysis of triple permeability model in deformed triple porosity reservoirs[J].Engineering Mechanics,2008,25(10):103-109.张磊,同登科,马晓丹.变形三重介质三渗模型的压力动态分析[J].工程力学,2008,25(10):103-109.
[24]Tong Dengke,Liu Wenchao,Xue Lili.Flow characteristics of triple-permeability model in low permeability reservoir with deformed triple porosity medium[J].Chinese Quarterly of Mechanics,2010.31(3):334-341.同登科,刘文超,薛莉莉.变形三重介质低渗透油藏三渗模型流动特征[J].力学季刊,2010,31(3):334-341.
[25]Zhang L H,Guo J J,Liu Q G.A well test model for stresssensitive and heterogeneous reservoirs with non-uniform thicknesses[J].Petroleum Science,2010,7(4):524-529.
[26]Ren Dong,Liu Qiguo,Tang Yong,et al.A dual porosity model for transient well tests in volcanic gas reservoirs considering threshold pressure gradient[J].Natural Gas Industry,2011,31(10):50-53.任东,刘启国,汤勇,等.基于启动压力梯度的火山岩气藏多重介质试井模型[J].天然气工业,2011,31(10):50-53.
[27]Luo Erhui,Wang Xiaodong.A study on transient flow under threshold pressure gradient in dual-pore media with low permeability[J].China Offshore Oil and Gas,2011,23(5):318-321.罗二辉,王晓冬.双重低渗介质含启动压力梯度不定常渗流研究[J].中国海上油气,2011,23(5):318-321.
[28]Luo Erhui,Hu Yongle.A study of non-Darcy transient flow with low permeability in triple porosity media reservoir[J].Journal of China University of Mining&Technology,2013,42(1):100-104.罗二辉,胡永乐.三重介质低渗油藏非达西非稳态渗流研究[J].中国矿业大学学报,2013,42(1):100-104.
[29]Ai Shuang,Yao Yuedong.Flow model for well test analysis of low-permeability and stress-sensitive reservoirs[J].Special Topic&Reservoir in Porous Media,2012,3(2):125-138.
[30]Ren J,Guo P.Anew mathematical model for pressure transient analysis in stress-sensitive reservoirs[J].Mathematical Problems in Engineering,2014,(1):759-765.
[31]Feng N,Cheng S,Lan W,et al.Variable-permeability welltesting models and pressure response in low-permeability reservoirs with non-darcy flow[J].Earth Sciences Research Journal,2016,20(1):1-6.
[32]Kikani J,Pedrosa O A.Perturbation analysis of stress-sensitive reservoirs(includes associated papers 25281and 25292)[J].Society of Petroleum Engineers,1991,6(3):379-386.
[33]Lin Jingwei,Jin Qiuming.Perturbation analysis of pressure transient response in stress-sensitive reservoirs[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(supplement 2):2422-2428.梁景伟,金裘明.压敏油藏的压力动态摄动分析[J].岩石力学与工程学报,2002,21(增刊2):2422-2428.
[2]Terzaghi K.Theoretical Soil Mechanics[M].New York:Chapman and Hall,1959:325-327.
[3]Mapxacин.ИЛ.Physical and Chemical Mechanism of Oil Layer[M].Li Dianwen.Beijing:Petroleum Industry Press,1987:1-3.马尔哈辛.油层物理化学机理[M].李殿文译.北京:石油工业出版社,1987:1-3.
[4]ГopbyнoвA T,Zhang Shubao.Abnormal Oil and Gas Field[M].Beijing:Petroleum Industry Press,1987:3.戈尔布诺夫A T.异常油田开发[M].张树宝译.北京:石油工业出版社,1987:3.
[5]Miller R J,Low P F.Threshold gradient for water flow in clay systems[J].Soil Science Society of America Journal,1963,27(6):605-609.
[6]Vairogs J,Hearn C L,Dareing D W,et al.Effect of rock stress on gas production from low-permeability reservoirs[J].Society of Petroleum Engineers,1971,23(9):1161-1167.
[7]Pascal F,Pascal H,Murray D W.Consolidation with threshold gradients[J].International Journal for Numerical&Analytical Methods in Geomechanics,1981,5(3):247-261.
[8]Pedrosa O A.Pressure Transient Response in Stress-sensitive Formations[R].SPE15115,1986.
[9]Feng Wenguang,Ge Jiali.Dynamic characteristics of the pressure curve of a single medium and double medium non darcy low velocity seepage[J].Petroleum Exploration and Development,1986(5):52-57.冯文光,葛家理.单一介质、双重介质非达西低速渗流的压力曲线动态特征[J].石油勘探与开发,1986(5):52-57.
[10]Cheng Shiqing,Li Yaogang.Numerical solution of well testing model for low-speed non-darcy flow and its application[J].Natural Gas Industry,1996,16(3):27-30.程时清,李跃刚.低速非达西渗流试井模型的数值解及其应用[J].天然气工业,1996,16(3):27-30.
[11]Cheng Shiqing,Li Gongquan,Lu Tai,et al.Mathematical model and typical curve for calculating effective hole diameter in the low velocity non-darcy flow testing of dual-media reservoirs[J].Natural Gas Industry,1997,17(2):35-37.程时清,李功权,卢涛,等.双重介质油气藏低速非达西渗流试井有效井径数学模型及典型曲线[J].天然气工业,1997,17(2):35-37.
[12]Tong Dengke,Ge Jiali.A seepage flow model with non-darcy low velocity for fractal reservoirs and its solution[J].Petroleum Geology&Oilfield Development in the Daqing,1996,15(3):18-23.同登科,葛家理.分形油藏非达西低速渗流模型及其解[J].大庆石油地质与开发,1996,15(3):18-23.
[13]Tong Dengke,Jiang Dongmei,Chen Qinlei.Dynamic characteristics of reservoir with deformed double-porosity medium[J].Journal of the University of Petroleum,China,2001,25(5):53-56,5.同登科,姜东梅,陈钦雷.变形双重介质油藏动态特征[J].石油大学学报:自然科学版,2001,25(5):53-56,5.
[14]Tong Dengke.Zhang Fengqin.Wang Ruihe.Exact solution and its behavior characteristic of the nonlinear dual porosity model[J].Applied Mathematics and Mechanics,2005,26(10):1161-1167.同登科,张鸿庆,王瑞和.非线性双重介质模型的精确解及动态特征[J].应用数学和力学,2005,26(10):1161-1167.
[15]Liao Xinwei,Feng Jilei.Well test model of stress sensitive gas reservoirs with super high pressure and low permeability[J].Natural Gas Industry,2005,25(2):110-112,213-214.廖新维,冯积累.超高压低渗气藏应力敏感试井模型研究[J].天然气工业,2005,25(2):110-112,213-214.
[16]Wang Zisheng,Yao Jun.Study of pressure transient characteristic for stress sensitive triply medium reservoirs with fractures and vugs conveying fluids to wellbore[J].Journal of Hydrodynamics,2006,21(1):84-89.王子胜,姚军.缝洞向井筒供液时三重压敏介质油藏压力响应特征研究[J].水动力学研究与进展,2006,21(1):84-89.
[17]Zhang Liehui,Zhang Jinliang,Xu Bingqing.A nonlinear seepage flow model for deformable double media fractal gas reservoirs[J].Chinese Journal of Computational Physics,2007,24(1):90-94.张烈辉,张锦良,徐冰青.变形双重介质分形气藏非线性渗流理论模型及数值研究[J].计算物理,2007,24(1):90-94.
[18]Zhang Yun,Wang Zisheng,Yao Jun,et al.Study and application of pressure transient of naturally fractured reservoirs with stress-sensitive and start pressure grade[J].Journal of Hydrodynamics,2007,22(3):332-337.张允,王子胜,姚军,等.带启动压力梯度的双孔压敏介质压力动态及其应用研究[J].水动力学研究与进展,2007,22(3):332-337.
[19]Tian Leng,He Shunli,Li Xiusheng.Study of well test of stress-sensitive sandstone in low permeability gas reservoir[J].Petroleum Drilling Techniques,2007,35(6):89-92.田冷,何顺利,李秀生.低渗透气田砂岩储层应力敏感试井模型研究[J].石油钻探技术,2007,35(6):89-92.
[20]Xue Lili.Tong Dengke.Fluid characteristics of triple-medium double permeability consider quadratic gradient term effects[J].Chinese Quarterly of Mechanics,2008,29(3):412-417.薛莉莉,同登科.考虑二次梯度项影响的三孔双渗模型渗流特征[J].力学季刊,2008,29(3):412-417.
[21]Feng Guoqin,Liu Qiguo,Shi Guanglzhi.et al.An unsteady seepage flow model considering kick off pressure gradient for low-permeability gas reservoirs[J].Petroleum Exploration and Development,2008,35(4):457-461.冯国庆,刘启国,石广志,等.考虑启动压力梯度的低渗透气藏不稳定渗流模型[J].石油勘探与开发,2008,35(4):457-461.
[22]Cai Jinming,Chen Fangyi,Zhang Lixuan,et al.A nonlinear seepage flow model for deformable double media fractal gas reservoirs[J].Special Oil and Gas Reservoir,2008,15(2):69-72,109.蔡明金,陈方毅,张利轩,等.考虑启动压力梯度低渗透油藏应力敏感模型研究[J].特种油气藏,2008,15(2):69-72,109.
[23]Zhang Lei,Tong Dengke,Ma Xiaodan.Pressure dynamic analysis of triple permeability model in deformed triple porosity reservoirs[J].Engineering Mechanics,2008,25(10):103-109.张磊,同登科,马晓丹.变形三重介质三渗模型的压力动态分析[J].工程力学,2008,25(10):103-109.
[24]Tong Dengke,Liu Wenchao,Xue Lili.Flow characteristics of triple-permeability model in low permeability reservoir with deformed triple porosity medium[J].Chinese Quarterly of Mechanics,2010.31(3):334-341.同登科,刘文超,薛莉莉.变形三重介质低渗透油藏三渗模型流动特征[J].力学季刊,2010,31(3):334-341.
[25]Zhang L H,Guo J J,Liu Q G.A well test model for stresssensitive and heterogeneous reservoirs with non-uniform thicknesses[J].Petroleum Science,2010,7(4):524-529.
[26]Ren Dong,Liu Qiguo,Tang Yong,et al.A dual porosity model for transient well tests in volcanic gas reservoirs considering threshold pressure gradient[J].Natural Gas Industry,2011,31(10):50-53.任东,刘启国,汤勇,等.基于启动压力梯度的火山岩气藏多重介质试井模型[J].天然气工业,2011,31(10):50-53.
[27]Luo Erhui,Wang Xiaodong.A study on transient flow under threshold pressure gradient in dual-pore media with low permeability[J].China Offshore Oil and Gas,2011,23(5):318-321.罗二辉,王晓冬.双重低渗介质含启动压力梯度不定常渗流研究[J].中国海上油气,2011,23(5):318-321.
[28]Luo Erhui,Hu Yongle.A study of non-Darcy transient flow with low permeability in triple porosity media reservoir[J].Journal of China University of Mining&Technology,2013,42(1):100-104.罗二辉,胡永乐.三重介质低渗油藏非达西非稳态渗流研究[J].中国矿业大学学报,2013,42(1):100-104.
[29]Ai Shuang,Yao Yuedong.Flow model for well test analysis of low-permeability and stress-sensitive reservoirs[J].Special Topic&Reservoir in Porous Media,2012,3(2):125-138.
[30]Ren J,Guo P.Anew mathematical model for pressure transient analysis in stress-sensitive reservoirs[J].Mathematical Problems in Engineering,2014,(1):759-765.
[31]Feng N,Cheng S,Lan W,et al.Variable-permeability welltesting models and pressure response in low-permeability reservoirs with non-darcy flow[J].Earth Sciences Research Journal,2016,20(1):1-6.
[32]Kikani J,Pedrosa O A.Perturbation analysis of stress-sensitive reservoirs(includes associated papers 25281and 25292)[J].Society of Petroleum Engineers,1991,6(3):379-386.
[33]Lin Jingwei,Jin Qiuming.Perturbation analysis of pressure transient response in stress-sensitive reservoirs[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(supplement 2):2422-2428.梁景伟,金裘明.压敏油藏的压力动态摄动分析[J].岩石力学与工程学报,2002,21(增刊2):2422-2428.