大斜度井砾石充填数值模拟研究
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摘要
大斜度井砾石充填受井斜角的影响,其充填机理与垂直井和水平井完全不同,充填过程更为复杂。目前关于砾石充填的研究依然集中在水平井砾石充填,而大斜度井砾石充填的研究基本上以小型物理模拟为主,数模研究相对比较薄弱,并且仅有的一些研究也主要集中在局部的分析模型上。由于目前尚缺乏深入的机理研究和完善的数学模型,难以建立有效的参数优化方法,其充填作业中易发生砂堵现象,使作业失败。因此,针对上述问题有必要开展对大斜度井砾石充填系统深入的研究工作。
本论文首先研究了大斜度井砾石充填机理和特征。在此基础上,将砂床表面砾石颗粒的运动分为静止、推移和悬移三种形式,考虑井斜角的影响,引入颗粒无因次沉没度随机变量,通过颗粒的力矩平衡分析,研究了颗粒运动形式之间相互转换的临界条件,建立了考虑颗粒起动随机性的临界流速公式,包括临界起动条件、止动条件以及基于颗粒群体沉速的悬浮条件。利用临界起动流速公式,首次推导了给定参数下能够形成稳定α波平衡砂床的临界井斜角计算模型,该模型可用于判断已知井斜角和各施工参数下充填过程中能否形成稳定砂床。
应用随机分析理论研究了砂床表面颗粒的状态概率及其数字特征。根据颗粒状态概率代表其运动趋势的原理,将平衡砂床高度的变化归结为颗粒运动状态变化的结果,建立了特定水流条件和给定井筒倾角下平衡砂床高度的计算模型。利用实验结果对上述模型进行验证,结果吻合较好。
考虑携砂液向地层的滤失,推导了斜井砾石充填筛套环空、冲筛环空两个流动系统中流体与砾石的质量和动量守恒方程。研究携砂液向地层的滤失特征,结合砂床平衡高度计算方法,建立了时间相关的描述斜井砾石充填α充填过程的数学模型。该模型描述了斜井砾石充填的各个特征,可用于顺利充填和提前堵塞等各种情况,从而为大斜度井砾石充填工艺设计提供理论依据,为砾石充填在大斜度井中的广泛应用奠定良好的基础,对提高大斜度井开采水平具有实际意义。
Influenced by hole deviation angle, mechanism of gravel packing in highly deviated wells is different from vertical wells and horizontal wells, which is more complex. The current research regarding gravel packing is still concentrated in the horizontal well gravel packing, while highly deviated wells gravel packing is basically oriented to small-scale physical simulation, and mathematical model study is relatively weak, only some studies have mainly concentrated in the local analysis model. Because of lack of in-depth study and perfect mathematical model, it is difficult to set up an effective optimization method of parameters, which leads to the premature plugging, so that operation failed. Therefore, response to these questions there is a need for researching high angle wells gravel packing.
In this paper, mechanism of gravel packing in highly deviated wells is studied at first. Then the behavior of the grains on the bed surface is classified as three statues: station, slippage and suspension. A random variable of dimensionless submergence was introduced to denote the location randomness. Considering the deviation angle, a calculation model for critical velocity of solid grain was established by means of mechanical analysis, which includes critical starting, stopping and suspension conditions, by which the critical deviation angle calculation model, under given parameters can form a stableα-wave equilibrium bed, is derived for the first time.
Random analysis theory is used to investigate the final status probability and its numerical character of the grains. According to the principle that status probability indicates the feature movement trend, the change of the equilibrium bed’s height is ascribe to the change of surface grains behavior and a new model for the equilibrium bed’s height calculation is set up. The results obtained from this formula,which are in satisfactory agreement with the experimental data.
The mass and momentum conservation of fluid and gravel grains are evolved, considering the fluid filtration to the formation. Combined with the bed height model, a time-dependent mathematical model describes the process of gravel packing in highly deviated wells. The model can be used any situations such as full packing and premature plugging. All of the above provide theoretical basis for the technological design of gravel packing in highly deviated wells, and lay a good foundation for the extensive application, which have practical significance for improving the level of exploitation in highly deviated wells.
本论文首先研究了大斜度井砾石充填机理和特征。在此基础上,将砂床表面砾石颗粒的运动分为静止、推移和悬移三种形式,考虑井斜角的影响,引入颗粒无因次沉没度随机变量,通过颗粒的力矩平衡分析,研究了颗粒运动形式之间相互转换的临界条件,建立了考虑颗粒起动随机性的临界流速公式,包括临界起动条件、止动条件以及基于颗粒群体沉速的悬浮条件。利用临界起动流速公式,首次推导了给定参数下能够形成稳定α波平衡砂床的临界井斜角计算模型,该模型可用于判断已知井斜角和各施工参数下充填过程中能否形成稳定砂床。
应用随机分析理论研究了砂床表面颗粒的状态概率及其数字特征。根据颗粒状态概率代表其运动趋势的原理,将平衡砂床高度的变化归结为颗粒运动状态变化的结果,建立了特定水流条件和给定井筒倾角下平衡砂床高度的计算模型。利用实验结果对上述模型进行验证,结果吻合较好。
考虑携砂液向地层的滤失,推导了斜井砾石充填筛套环空、冲筛环空两个流动系统中流体与砾石的质量和动量守恒方程。研究携砂液向地层的滤失特征,结合砂床平衡高度计算方法,建立了时间相关的描述斜井砾石充填α充填过程的数学模型。该模型描述了斜井砾石充填的各个特征,可用于顺利充填和提前堵塞等各种情况,从而为大斜度井砾石充填工艺设计提供理论依据,为砾石充填在大斜度井中的广泛应用奠定良好的基础,对提高大斜度井开采水平具有实际意义。
Influenced by hole deviation angle, mechanism of gravel packing in highly deviated wells is different from vertical wells and horizontal wells, which is more complex. The current research regarding gravel packing is still concentrated in the horizontal well gravel packing, while highly deviated wells gravel packing is basically oriented to small-scale physical simulation, and mathematical model study is relatively weak, only some studies have mainly concentrated in the local analysis model. Because of lack of in-depth study and perfect mathematical model, it is difficult to set up an effective optimization method of parameters, which leads to the premature plugging, so that operation failed. Therefore, response to these questions there is a need for researching high angle wells gravel packing.
In this paper, mechanism of gravel packing in highly deviated wells is studied at first. Then the behavior of the grains on the bed surface is classified as three statues: station, slippage and suspension. A random variable of dimensionless submergence was introduced to denote the location randomness. Considering the deviation angle, a calculation model for critical velocity of solid grain was established by means of mechanical analysis, which includes critical starting, stopping and suspension conditions, by which the critical deviation angle calculation model, under given parameters can form a stableα-wave equilibrium bed, is derived for the first time.
Random analysis theory is used to investigate the final status probability and its numerical character of the grains. According to the principle that status probability indicates the feature movement trend, the change of the equilibrium bed’s height is ascribe to the change of surface grains behavior and a new model for the equilibrium bed’s height calculation is set up. The results obtained from this formula,which are in satisfactory agreement with the experimental data.
The mass and momentum conservation of fluid and gravel grains are evolved, considering the fluid filtration to the formation. Combined with the bed height model, a time-dependent mathematical model describes the process of gravel packing in highly deviated wells. The model can be used any situations such as full packing and premature plugging. All of the above provide theoretical basis for the technological design of gravel packing in highly deviated wells, and lay a good foundation for the extensive application, which have practical significance for improving the level of exploitation in highly deviated wells.
引文
[1] Hyun Cho. A Three-Layer Modeling for Cuttings Transport with Coiled Tubing Horizontal Drilling. SPE 63269, 2000: 1-14.
[2] J.X.Forrest, Horizontal Gravel Packing Studies in a Full-Scale Model Wellbore. SPE20681, 1999.
[3] Gruesbeck C, W. M. Salathiel, E. Echols. Design of Gravel Packs in Deviated Wellbores. SPE 6805, 1989.
[4] W.L. Penberthy. Gravel Placement in Horizontal Wells, SPE 31147, 1995: 1-12.
[5] M.W. Gravel Pack Designs of Highly-Deviated Well with an Alternative Flow-Path Concept, SPE 73743, 2002: 1-16.
[6]杨具瑞,曹叔尤.坡面非均匀沙起动规律研究[J].水力发电学报. 2004(3):102-106.
[7]胥锐一等.水平井砾石充填防砂模拟研究.油气采收技术,1998.6.
[8]李爱芬,王世虎,王文玲.地层砂粒在液体中的沉降规律研究.油气地质与采收率.2001(2):29-32.
[9]窦国仁.再论泥沙起动流速[J].泥沙研究.1999(6):1-9.
[10] P.H. Winterfield. Numerical Simulator of Gravel Packing, SPE 19753, 1992: 1-12.
[11] A.F.L. Aragao, L.Quinter. A Novel Approach for Drilling and Gravel Packing Horizontal Wells in the Presentce of Reactive Shales Using a Solids-Free Synthetic Fluid, SPE102295, 2005: 1-8.
[12] E. Harold Vickery. Through-Tubing Gravel Pack With Small Clearance: The Important Factors, SPE 73773, 2002: 1-6.
[13] E. Davidson. Successful Deployment of a New Stimulation Chemical, Post- Horizontal-Openhole Gravel Pack in Wells Drilled With Both Water-Based and Oil-Based Drill-In Fluid, SPE 101964, 2006: 1-12.
[14] F.O. Stanley. Rotating Jet Technology Improves Stimulation Fluid Placement to Effectively Treat Horizontal and Gravel Packed Wells-Lab model tests and global results are reviewed, SPE 90174, 2004: 1-16.
[15] P.D. Nguyen. Analysis of Gravel Packing Using 3-D Numerical Simulation, SPE 23792, 1992: 1-12.
[16] L.G. Jones. Gravel Packing Horizontal Wellbore with Leak-Off Using Shunts, SPE 38604, 1997: 1-12.
[17] Gruesbeck C. Design of Gravel Packs in Deviated Wellbores. JPT, January 1979.
[18] Penden.J.M. A Numerical Approach to the Design of Gravel Pack for Effective Sand Control in Deviated Wells. SPE 13048, 1984: 1-12.
[19] Wahlmeier M.A. Mechanics of Gravel Placement and Packing: A Design and Evaluation Approach. SPE Prod. &Eng, Feb.1988: 1-12.
[20] Shayock S G. Gravel Packing Studies in a Full-Scale Deviated Wellbore. JPT, March 1983.
[21] Doron P, Granica D. Slurry Flow in Horizontal Pipes-Experimental and Modeling. Int.J.Multiphase Flow Vol.13, No.4, 1987.
[22] Doron P, Barnea D. Effect of the No-Slip Assumpation on the Prediction of Solid-Liquid Flow Characteristics. Int.J.Multiphase Flow Vol.18, No.4, 1992.
[23] Doron P, Barnea D. A Three-Layer Model for Solid-Liquid Flow in Horizontal Pipes. Int.J.Multiphase Flow Vol.19, 1993.
[24] Doron P. Pressure Drop and Limit Deposition Velocity for Solid-Liquid Flow in Pipes. Chem. Engng. Sci., Vol.50, No. 10, 1995.
[25] Doron P. Flow Pattern Maps for Solid-Liquid Flow in Pipes. Int.J. Multiphase Flow, Vol.22, No.2, 1996.
[26] Doron P. Flow of Solid-Liquid Mixtures in Inclined Pipes. Int.J. Multiphase Flow, Vol.23, No.2, 1997.
[27] I J Soboy. Modle Aids Cuttings Transport Prediction. JPT, September 1989.9.
[28] Martins A L. Evalua the Transport of Solids Generated by Shale Instabilities in ERW Drilling. SPE Drilling&Completion, Vol.14, No.4, 1999.
[29] Nguyen P D. A Three-Layer Hydraulic Program of Effective Cuttings Transport and Hole Cleaning in High Deviated and Horizontal Wells. SPE 36383 Presented at the IADC SPE 1996 Asia Pacific Drilling Technology Conference, Kuala Lumpur, 9-11 September.
[30] Penden.J.M. Comprehensive Experimental Investigation of Drilled Cuttings Transport in Inclined Wells Including the Effects of Rotation and Eccentricity. SPE 20925, 1990: 1-12.
[31] Upchurch E R. Horizontal Gravel Packing Technique for Slim, Case-Holes in Highly in Highly Permeable Zones: A Single-Well Case Hitory. SPE Drilling&Completion, Vol.15, No.3, 2000.9.
[32]董长银,张琪.水平井砾石充填过程实时数值模拟研究.石油学报,2004,25(6):96-100.
[33]赵东伟,董长银,张琪.考虑位置随机性的固体颗粒启动临界流速研究.石油大学学报,2004,28(4):59-66.
[34]李爱芬.地层砂粒在液体中的沉降规律研究.油气地质与采收率.2001,8(1):70-74.
[35]董长银,张琪,曲占庆等.筛套环空砾石层压降的简化计算模型.石油大学学报:自然科学版,2001,25(2):28-30.
[36]赵东伟,董长银,张琪.砾石充填防砂砾石尺寸优选方法.石油钻探技术,2004,32(4):63-65.
[37]薄启炜,董长银,张琪等.砾石充填层孔喉结构可视化模拟.石油勘探与开发,2003,30(4):108-110.
[38]孙堡维.斜井砾石充填过程数学和计算机模拟研究.天然气工业,1994,14 (2) : 40~43.
[2] J.X.Forrest, Horizontal Gravel Packing Studies in a Full-Scale Model Wellbore. SPE20681, 1999.
[3] Gruesbeck C, W. M. Salathiel, E. Echols. Design of Gravel Packs in Deviated Wellbores. SPE 6805, 1989.
[4] W.L. Penberthy. Gravel Placement in Horizontal Wells, SPE 31147, 1995: 1-12.
[5] M.W. Gravel Pack Designs of Highly-Deviated Well with an Alternative Flow-Path Concept, SPE 73743, 2002: 1-16.
[6]杨具瑞,曹叔尤.坡面非均匀沙起动规律研究[J].水力发电学报. 2004(3):102-106.
[7]胥锐一等.水平井砾石充填防砂模拟研究.油气采收技术,1998.6.
[8]李爱芬,王世虎,王文玲.地层砂粒在液体中的沉降规律研究.油气地质与采收率.2001(2):29-32.
[9]窦国仁.再论泥沙起动流速[J].泥沙研究.1999(6):1-9.
[10] P.H. Winterfield. Numerical Simulator of Gravel Packing, SPE 19753, 1992: 1-12.
[11] A.F.L. Aragao, L.Quinter. A Novel Approach for Drilling and Gravel Packing Horizontal Wells in the Presentce of Reactive Shales Using a Solids-Free Synthetic Fluid, SPE102295, 2005: 1-8.
[12] E. Harold Vickery. Through-Tubing Gravel Pack With Small Clearance: The Important Factors, SPE 73773, 2002: 1-6.
[13] E. Davidson. Successful Deployment of a New Stimulation Chemical, Post- Horizontal-Openhole Gravel Pack in Wells Drilled With Both Water-Based and Oil-Based Drill-In Fluid, SPE 101964, 2006: 1-12.
[14] F.O. Stanley. Rotating Jet Technology Improves Stimulation Fluid Placement to Effectively Treat Horizontal and Gravel Packed Wells-Lab model tests and global results are reviewed, SPE 90174, 2004: 1-16.
[15] P.D. Nguyen. Analysis of Gravel Packing Using 3-D Numerical Simulation, SPE 23792, 1992: 1-12.
[16] L.G. Jones. Gravel Packing Horizontal Wellbore with Leak-Off Using Shunts, SPE 38604, 1997: 1-12.
[17] Gruesbeck C. Design of Gravel Packs in Deviated Wellbores. JPT, January 1979.
[18] Penden.J.M. A Numerical Approach to the Design of Gravel Pack for Effective Sand Control in Deviated Wells. SPE 13048, 1984: 1-12.
[19] Wahlmeier M.A. Mechanics of Gravel Placement and Packing: A Design and Evaluation Approach. SPE Prod. &Eng, Feb.1988: 1-12.
[20] Shayock S G. Gravel Packing Studies in a Full-Scale Deviated Wellbore. JPT, March 1983.
[21] Doron P, Granica D. Slurry Flow in Horizontal Pipes-Experimental and Modeling. Int.J.Multiphase Flow Vol.13, No.4, 1987.
[22] Doron P, Barnea D. Effect of the No-Slip Assumpation on the Prediction of Solid-Liquid Flow Characteristics. Int.J.Multiphase Flow Vol.18, No.4, 1992.
[23] Doron P, Barnea D. A Three-Layer Model for Solid-Liquid Flow in Horizontal Pipes. Int.J.Multiphase Flow Vol.19, 1993.
[24] Doron P. Pressure Drop and Limit Deposition Velocity for Solid-Liquid Flow in Pipes. Chem. Engng. Sci., Vol.50, No. 10, 1995.
[25] Doron P. Flow Pattern Maps for Solid-Liquid Flow in Pipes. Int.J. Multiphase Flow, Vol.22, No.2, 1996.
[26] Doron P. Flow of Solid-Liquid Mixtures in Inclined Pipes. Int.J. Multiphase Flow, Vol.23, No.2, 1997.
[27] I J Soboy. Modle Aids Cuttings Transport Prediction. JPT, September 1989.9.
[28] Martins A L. Evalua the Transport of Solids Generated by Shale Instabilities in ERW Drilling. SPE Drilling&Completion, Vol.14, No.4, 1999.
[29] Nguyen P D. A Three-Layer Hydraulic Program of Effective Cuttings Transport and Hole Cleaning in High Deviated and Horizontal Wells. SPE 36383 Presented at the IADC SPE 1996 Asia Pacific Drilling Technology Conference, Kuala Lumpur, 9-11 September.
[30] Penden.J.M. Comprehensive Experimental Investigation of Drilled Cuttings Transport in Inclined Wells Including the Effects of Rotation and Eccentricity. SPE 20925, 1990: 1-12.
[31] Upchurch E R. Horizontal Gravel Packing Technique for Slim, Case-Holes in Highly in Highly Permeable Zones: A Single-Well Case Hitory. SPE Drilling&Completion, Vol.15, No.3, 2000.9.
[32]董长银,张琪.水平井砾石充填过程实时数值模拟研究.石油学报,2004,25(6):96-100.
[33]赵东伟,董长银,张琪.考虑位置随机性的固体颗粒启动临界流速研究.石油大学学报,2004,28(4):59-66.
[34]李爱芬.地层砂粒在液体中的沉降规律研究.油气地质与采收率.2001,8(1):70-74.
[35]董长银,张琪,曲占庆等.筛套环空砾石层压降的简化计算模型.石油大学学报:自然科学版,2001,25(2):28-30.
[36]赵东伟,董长银,张琪.砾石充填防砂砾石尺寸优选方法.石油钻探技术,2004,32(4):63-65.
[37]薄启炜,董长银,张琪等.砾石充填层孔喉结构可视化模拟.石油勘探与开发,2003,30(4):108-110.
[38]孙堡维.斜井砾石充填过程数学和计算机模拟研究.天然气工业,1994,14 (2) : 40~43.