缝洞型油藏波动和流动耦合模型井底压力分析
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摘要
缝洞型油藏储集介质包括基质、裂缝和溶洞.在缝洞型油藏的研究中,由于其复杂的孔隙结构和流动机理,裂缝-溶洞-基质之间的相互作用通常被简化为粒间窜流,然而实际地层中如果溶洞体积很大,会导致流动过程中压力变化很大,所以溶洞并不能被简化为一种介质.通过联立力学三大守恒方程,洞中的压力是以波的形式在溶洞中传播(类似于一种压力降的形式)的理论首次被提出,进而形成了波动和流动耦合的缝洞型油藏新的试井模型,并与外部地层渗流方程相结合形成新的完备的控制方程组,再通过Laplace变换和数值反演,得到了井底压力及压力导数的双对数曲线典型图版.结果表明,井底压力曲线形态受流动和波动相关的无量纲参数以及与外部地层性质有关的无量纲参数的影响,针对各个参数进行了敏感性分析.同时与新疆油田的某实例井相拟合,发现曲线拟合效果很好,地质解释结果与实际结果符合.
Fractured vuggy reservoirs consist of matrix, fractures and vugs. Researchers usually treat the matrix-fracture-vug interaction as inter-porosity flow due to their complex pore system and flow mechanism. In fact, vugs play an important role in fractured vuggy reservoirs and can't be simplified to one homogeneous medium. The idea that pressure spreading in vugs is in form of wave, which is similar to pressure decline, was proposed. Based on that, an analytical well test model for fractured vuggy reservoirs combined with seepage equations for outer formation was presented. Then the log-log type curves of the wellbore pressure and its derivative were obtained through the Laplace transform and numerical inversion. The results show that, the pressure curve forms were influenced by dimensionless parameters related to flow and wave propagation, also by dimensionless parameters related to the outer formation. Sensitivity analysis of these parameters were done. Lastly, a field example was demonstrated to validate the accuracy of the proposed model, which matched the real geological data well.
Fractured vuggy reservoirs consist of matrix, fractures and vugs. Researchers usually treat the matrix-fracture-vug interaction as inter-porosity flow due to their complex pore system and flow mechanism. In fact, vugs play an important role in fractured vuggy reservoirs and can't be simplified to one homogeneous medium. The idea that pressure spreading in vugs is in form of wave, which is similar to pressure decline, was proposed. Based on that, an analytical well test model for fractured vuggy reservoirs combined with seepage equations for outer formation was presented. Then the log-log type curves of the wellbore pressure and its derivative were obtained through the Laplace transform and numerical inversion. The results show that, the pressure curve forms were influenced by dimensionless parameters related to flow and wave propagation, also by dimensionless parameters related to the outer formation. Sensitivity analysis of these parameters were done. Lastly, a field example was demonstrated to validate the accuracy of the proposed model, which matched the real geological data well.
引文
[1] 李阳. 塔河油田碳酸盐岩缝洞型油藏开发理论及方法[J]. 石油学报, 2013, 34(1): 115-121. (LI Yang. The theory and method for development of carbonate fractured-cavity reservoirs in Tahe oilfield[J]. Acta Petrolei Sinica, 2013, 34(1): 115-121.(in Chinese))
[2] 邢翠巧, 尹洪军, 李兴科, 等. 缝洞型碳酸盐岩油藏试井分析模型研究[J]. 河北工业科技, 2018, 35(1): 31-36.(XING Cuiqiao, YIN Hongjun, LI Xingke, et al. Research of the fractured vuggy type carbonate reservoirs well test analysis model[J]. Hebei Journal of Industrial Science and Technology, 2018, 35(1): 31-36.(in Chinese))
[3] BARENBLATT G, ZHELTOV I, KOCHINA I. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks(strata)[J]. Journal of Applied Mathematics & Mechanics, 1960, 24(5): 1286-1303.
[4] WARREN J, ROOT P. The behavior of naturally fractured reservoirs[J]. Society of Petroleum Engineers Journal, 1963, 3(3): 245-255.
[5] KAZEMI H. Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution[J]. Society of Petroleum Engineers Journal, 1969, 9(4): 451-462.
[6] ABDASSAH D, ERSHAGHI I. Triple-porosity systems for representing naturally fractured reservoirs[J]. SPE Formation Evaluation, 1986, 1(2): 113-127.
[7] CAMACHO-VELAZQUEZ R, VASQUEZ-CRUZ M, CASTREJON-AIVARA R, et al. Pressure transient and decline curve behaviors in naturally fractured vuggy carbonate reservoirs[J]. SPE Reservoir Evaluation & Engineering, 2005, 8(2): 95-112.
[8] 薛承瑾, 戴卫华, 张皎生. 裂缝与井筒连通的三重介质油藏试井解释方法[J]. 油气地质与采收率, 2003, 10(3): 39-41.(XUE Chengjin, DAI Weihua, ZHANG Jiaosheng. Well test interpretation method for triple media oil reservoir in which fracture communicated with wellbore[J]. Petroleum Geology and Recovery Efficiency, 2003 , 10(3): 39-41.(in Chinese))
[9] WU Y S, LIU H H, BODVARSSON G S. A triple-continuum approach for modeling flow and transport processes in fractured rock[J]. Journal of Contaminant Hydrology, 2004, 73(1): 145-179.
[10] 常学军, 姚军, 戴卫华, 等. 裂缝和洞与井筒连通的三重介质油藏试井解释方法研究[J]. 水动力学研究与进展, 2004, 19(3): 339-346.(CHANG Xuejun, YAO Jun, DAI Weihua, et al. The study of well test interpretation method for a triple medium reservoir[J]. Journal of Hydrodynamics, 2004, 19(3): 339-346.(in Chinese))
[11] 王子胜, 姚军, 张凯. 三重介质油藏非牛顿液不稳定渗流压力变化特征研究[J]. 中外能源, 2006, 11(2): 13-17.(WANG Zisheng, YAO Jun, ZHANG Kai. The characteristic of transient pressure of non-Newtonian fluid’s transient flow in triple-media reservoirs[J]. China Foreign Energy, 2006, 11(2): 13-17.(in Chinese))
[12] 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.(WANG Zisheng, YAO Jun. Study of pressure-transient characteristic for stress-sensitive triple-medium reservoirs with fractures and vugs conveying fluids to wellbore[J]. Journal of Hydrodynamics, 2006, 21(1): 84-89.(in Chinese))
[13] 李成勇, 刘启国, 张燃, 等. 三重介质油藏水平井试井解释模型研究[J]. 西南石油大学学报(自然科学版), 2006, 28(4): 32-35.(LI Chengyong, LIU Qiguo, ZHANG Ran, et al. The research of well test of horizontal well in triple medium reservoir[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2006, 28(4): 32-35.(in Chinese))
[14] KANG Z J, WU Y S, LI J L, et al. Modeling multiphase flow in naturally fractured vuggy petroleum reservoirs[C]//Proceedings of SPE Annual Technical Conference and Exhibition. San Antonio, 2006.
[15] WU Y S, EHLIG-ECONOMIDES C, QIN G, et al. A triple-continuum pressure-transient model for a naturally fractured vuggy reservoir[C]//Proceedings of SPE Annual Technical Conference and Exhibition. Anaheim, 2007.
[16] 蔡明金, 贾永禄. 三重介质有限导流垂直裂缝井压力动态分析[J]. 油气井测试, 2007, 16(5): 12-15.(CAI Mingjin, JIA Yonglu. Dynamic analysis for pressure in limit conductivity vertical fracture wells of triple-porosity reservoir[J]. Well Testing, 2007, 16(5): 12-15.(in Chinese))
[17] 张冬丽, 李江龙. 缝洞型油藏流体流动数学模型及应用进展[J]. 西南石油大学学报(自然科学版), 2009, 31(6): 66-70.(ZHANG Dongli, LI Jianglong. Application progress of fluid flow mathematic model for fracture-vug type reservoir[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2009, 31(6): 66-70.(in Chinese))
[18] 张冬丽, 李江龙, 吴玉树. 缝洞型油藏三重介质数值试井模型影响因素[J]. 西南石油大学学报(自然科学版), 2010, 32(2): 113-120.(ZHANG Dongli, LI Jianglong, WU Yushu. Influencing factors of the numerical well test model of the triple-continuum in fractured vuggy reservoir[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2010, 32(2): 113-120.(in Chinese))
[19] 李江龙, 张冬丽, 吴玉树. 缝洞型油藏三重介质数值试井解释方法研究[J]. 水动力学研究与进展, 2012, 27(6): 640-648.(LI Jianglong, ZHANG Dongli, WU Yushu. Triple-continuum numerical well test interpretation method for a naturally fractured vuggy reservoir[J]. Journal of Hydrodynamics, 2012, 27(6): 640-648.(in Chinese))
[20] WU Y S, YUAN D, KANG Z J, et al. A multiple-continuum model for simulating single-phase and multiphase flow in naturally fractured vuggy reservoirs[J]. Journal of Petroleum Science & Engineering, 2011, 78(1): 13-22.
[21] GUO J C, NIE R S, JIA Y L. Dual permeability flow behavior for modeling horizontal well production in fractured-vuggy carbonate reservoirs[J]. Journal of Hydrology, 2012, 464/465(13): 281-293.
[22] 刘启国, 徐有杰, 刘义成, 等. 夹角断层多段压裂水平井试井求解新方法[J]. 应用数学和力学,2018, 39(5): 558-567.(LIU Qiguo, XU Youjie, LIU Yicheng, et al. A new well test analysis method for multi-stage fractured horizontal wells with angle faults[J]. Applied Mathematics and Mechanics, 2018, 39(5): 558-567.(in Chinese))
[23] DOUGLAS J F, GASIOREK J M, SWAFFILED J A. 流体力学[M]. 北京: 世界图书出版社, 1995.(DOUGLAS J F, GASIOREK J M, SWAFFIELD J A. Fluid Dynamics[M]. Beijing: World Publishing Corporation, 1995.(in Chinese))
[24] XING C Q, YIN H J, LIU K X, et al. Well test analysis for fractured and vuggy carbonate reservoirs of well drilling in large scale cave[J]. Energies, 2018, 11(1): 80-94.
[25] STEHFEST H. Numerical inversion of Laplace transform-algorithm[J]. Communications of the ACM, 1970,13(1): 47-49.
[2] 邢翠巧, 尹洪军, 李兴科, 等. 缝洞型碳酸盐岩油藏试井分析模型研究[J]. 河北工业科技, 2018, 35(1): 31-36.(XING Cuiqiao, YIN Hongjun, LI Xingke, et al. Research of the fractured vuggy type carbonate reservoirs well test analysis model[J]. Hebei Journal of Industrial Science and Technology, 2018, 35(1): 31-36.(in Chinese))
[3] BARENBLATT G, ZHELTOV I, KOCHINA I. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks(strata)[J]. Journal of Applied Mathematics & Mechanics, 1960, 24(5): 1286-1303.
[4] WARREN J, ROOT P. The behavior of naturally fractured reservoirs[J]. Society of Petroleum Engineers Journal, 1963, 3(3): 245-255.
[5] KAZEMI H. Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution[J]. Society of Petroleum Engineers Journal, 1969, 9(4): 451-462.
[6] ABDASSAH D, ERSHAGHI I. Triple-porosity systems for representing naturally fractured reservoirs[J]. SPE Formation Evaluation, 1986, 1(2): 113-127.
[7] CAMACHO-VELAZQUEZ R, VASQUEZ-CRUZ M, CASTREJON-AIVARA R, et al. Pressure transient and decline curve behaviors in naturally fractured vuggy carbonate reservoirs[J]. SPE Reservoir Evaluation & Engineering, 2005, 8(2): 95-112.
[8] 薛承瑾, 戴卫华, 张皎生. 裂缝与井筒连通的三重介质油藏试井解释方法[J]. 油气地质与采收率, 2003, 10(3): 39-41.(XUE Chengjin, DAI Weihua, ZHANG Jiaosheng. Well test interpretation method for triple media oil reservoir in which fracture communicated with wellbore[J]. Petroleum Geology and Recovery Efficiency, 2003 , 10(3): 39-41.(in Chinese))
[9] WU Y S, LIU H H, BODVARSSON G S. A triple-continuum approach for modeling flow and transport processes in fractured rock[J]. Journal of Contaminant Hydrology, 2004, 73(1): 145-179.
[10] 常学军, 姚军, 戴卫华, 等. 裂缝和洞与井筒连通的三重介质油藏试井解释方法研究[J]. 水动力学研究与进展, 2004, 19(3): 339-346.(CHANG Xuejun, YAO Jun, DAI Weihua, et al. The study of well test interpretation method for a triple medium reservoir[J]. Journal of Hydrodynamics, 2004, 19(3): 339-346.(in Chinese))
[11] 王子胜, 姚军, 张凯. 三重介质油藏非牛顿液不稳定渗流压力变化特征研究[J]. 中外能源, 2006, 11(2): 13-17.(WANG Zisheng, YAO Jun, ZHANG Kai. The characteristic of transient pressure of non-Newtonian fluid’s transient flow in triple-media reservoirs[J]. China Foreign Energy, 2006, 11(2): 13-17.(in Chinese))
[12] 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.(WANG Zisheng, YAO Jun. Study of pressure-transient characteristic for stress-sensitive triple-medium reservoirs with fractures and vugs conveying fluids to wellbore[J]. Journal of Hydrodynamics, 2006, 21(1): 84-89.(in Chinese))
[13] 李成勇, 刘启国, 张燃, 等. 三重介质油藏水平井试井解释模型研究[J]. 西南石油大学学报(自然科学版), 2006, 28(4): 32-35.(LI Chengyong, LIU Qiguo, ZHANG Ran, et al. The research of well test of horizontal well in triple medium reservoir[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2006, 28(4): 32-35.(in Chinese))
[14] KANG Z J, WU Y S, LI J L, et al. Modeling multiphase flow in naturally fractured vuggy petroleum reservoirs[C]//Proceedings of SPE Annual Technical Conference and Exhibition. San Antonio, 2006.
[15] WU Y S, EHLIG-ECONOMIDES C, QIN G, et al. A triple-continuum pressure-transient model for a naturally fractured vuggy reservoir[C]//Proceedings of SPE Annual Technical Conference and Exhibition. Anaheim, 2007.
[16] 蔡明金, 贾永禄. 三重介质有限导流垂直裂缝井压力动态分析[J]. 油气井测试, 2007, 16(5): 12-15.(CAI Mingjin, JIA Yonglu. Dynamic analysis for pressure in limit conductivity vertical fracture wells of triple-porosity reservoir[J]. Well Testing, 2007, 16(5): 12-15.(in Chinese))
[17] 张冬丽, 李江龙. 缝洞型油藏流体流动数学模型及应用进展[J]. 西南石油大学学报(自然科学版), 2009, 31(6): 66-70.(ZHANG Dongli, LI Jianglong. Application progress of fluid flow mathematic model for fracture-vug type reservoir[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2009, 31(6): 66-70.(in Chinese))
[18] 张冬丽, 李江龙, 吴玉树. 缝洞型油藏三重介质数值试井模型影响因素[J]. 西南石油大学学报(自然科学版), 2010, 32(2): 113-120.(ZHANG Dongli, LI Jianglong, WU Yushu. Influencing factors of the numerical well test model of the triple-continuum in fractured vuggy reservoir[J]. Journal of Southwest Petroleum University(Science & Technology Edition), 2010, 32(2): 113-120.(in Chinese))
[19] 李江龙, 张冬丽, 吴玉树. 缝洞型油藏三重介质数值试井解释方法研究[J]. 水动力学研究与进展, 2012, 27(6): 640-648.(LI Jianglong, ZHANG Dongli, WU Yushu. Triple-continuum numerical well test interpretation method for a naturally fractured vuggy reservoir[J]. Journal of Hydrodynamics, 2012, 27(6): 640-648.(in Chinese))
[20] WU Y S, YUAN D, KANG Z J, et al. A multiple-continuum model for simulating single-phase and multiphase flow in naturally fractured vuggy reservoirs[J]. Journal of Petroleum Science & Engineering, 2011, 78(1): 13-22.
[21] GUO J C, NIE R S, JIA Y L. Dual permeability flow behavior for modeling horizontal well production in fractured-vuggy carbonate reservoirs[J]. Journal of Hydrology, 2012, 464/465(13): 281-293.
[22] 刘启国, 徐有杰, 刘义成, 等. 夹角断层多段压裂水平井试井求解新方法[J]. 应用数学和力学,2018, 39(5): 558-567.(LIU Qiguo, XU Youjie, LIU Yicheng, et al. A new well test analysis method for multi-stage fractured horizontal wells with angle faults[J]. Applied Mathematics and Mechanics, 2018, 39(5): 558-567.(in Chinese))
[23] DOUGLAS J F, GASIOREK J M, SWAFFILED J A. 流体力学[M]. 北京: 世界图书出版社, 1995.(DOUGLAS J F, GASIOREK J M, SWAFFIELD J A. Fluid Dynamics[M]. Beijing: World Publishing Corporation, 1995.(in Chinese))
[24] XING C Q, YIN H J, LIU K X, et al. Well test analysis for fractured and vuggy carbonate reservoirs of well drilling in large scale cave[J]. Energies, 2018, 11(1): 80-94.
[25] STEHFEST H. Numerical inversion of Laplace transform-algorithm[J]. Communications of the ACM, 1970,13(1): 47-49.
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