Abstract：The sand production for loose sandstone reservoirs is studied. The stress conditions from the microscopic scale are analyzed with a clear understanding of the mechanical condition. Three geometrical constraints for the sand production are considered. For the reservoir to produce sands, the geometrical conditions and mechanical conditions must simultaneously be satisfied. The formation pore is expressed by the capillary bundle. The capillary bundle model for the sand production is established by analyzing the stress conditions between the fluid and the sand particles. A formula for the critical velocity is obtained. The critical velocity increases with the increase of the sand diameter, the porosity and the sand particle frictional angle. The critical velocity decreases with the increase of the viscosity. The formula gives results in a good agreement with experiments,and the average error is only 15.9%. This geometrical constraints are proposed which may help the mechanism of the sand production. The formula of the critical velocity presented in this paper can be used conveniently in the oil field.
聂向荣, 杨胜来, 章星, 丁景辰, 陈浩. 颗粒尺度下砂岩出砂几何约束条件及毛管束模型[J]. 科技导报, 2014, 32(6): 54-58.
NIE Xiangrong, YANG Shenglai, ZHANG Xing, DING Jingchen, CHEN Hao. Geometrical Constraints and Capillary Bundle Model for Sand Production in Sandstone Reservoir at Particle Scale. journal1, 2014, 32(6): 54-58.
[1] 卢宝荣, 蔡明俊, 刘树明, 等. 羊三木油田馆一油组油层出砂影响因素 探讨[J]. 石油勘探与开发, 2004, 31(3): 146-147. Lu Baorong, Cai Mingjun, Liu Shuming, et al. Influencing factors of reservoir sand flow in the Guan No. 1 oil group, Yangsanmu Oilfield[J]. 图6 不同孔隙度下砂粒直径和临界流速关系曲线 (μ =1 mPa·s, θ =10o) Fig. 6 Sandstone particle and critical velocity curves at different φ (μ =1 mPa·s, θ =10o) 图7 不同摩擦角下流体黏度和临界流速关系曲线 (dp=20 μm, φ =0.2) Fig. 7 Viscosity and critical velocity curves at different θ (dp=20 μm, φ =0.2) 岩心号 P2-207-4 P2-245-4 P2-X591-4 空气渗透率/ (10-3μm2) 1009 357 548 孔隙度/ % 33.42 28.84 29.63 临界流速/ (m·d-1) 2.935 1.761 1.467 表1 砂岩出砂规律实验研究 Table 1 Experimental study of sandstone production 表2 临界流速计算结果与实验结果对比 Table 2 Comparison of calculation results and experimental results 岩心号 P2-207-4 P2-245-4 P2-X591-4 临界流速/(m·d-1) 实验 2.935 1.761 1.467 计算 2.83 1.94 1.98 相对误差/% 3.5 10.1 34.9 平均误差/% 15.9 57 科技导报2014, 32(www.kjdb.org 6) Petroleum Exploration and Development, 2004, 31(3): 146-147.
[2] 张本艳, 张继超, 涂文利. 胜利油田注水现状及对储集层的影响[J]. 石 油勘探与开发, 2007, 34(3): 364-368. Zhang Benyan, Zhang Jichao, Tu Wenli. Current situation of water injection and its influence on reservoirs in Shengli Oilfield[J]. Petroleum Exploration and Development, 2007, 34(3):364-368.
[3] 汪永利, 张保平. Fula油田稠油油藏地层出砂机理实验研究[J]. 石油 勘探与开发, 2002, 29(4): 109-110. Wang Yongli, Zhang Baoping. A laboratory research for the sandproduction mechanism of viscous oil reservoirs in Fula Oilfield[J]. Petroleum Exploration and Development, 2002, 29(4): 109-110.
[4] Essam I. Effect of water injection on sand production associated with oil production in sandstone reservoirs[C]//SPE/IADC Middle East Drilling and Technology Conference 2007. Cairo, Egypt: Society of Petroleum Engineers Inc, 2007: 1-9.
[5] Zhang L W, Dusseault M B. Sand-production simulation in heavy-oil reservoirs[J]. SPE Reservoir Evaluation & Engineering, 2004, 7(6): 399-407.
[6] 王利华, 邓金根, 周建良, 等. 弱固结砂岩气藏出砂物理模拟实验[J]. 石油学报, 2011, 32(6): 1007-1011. Wang Lihua, Deng Jingen, Zhou Jianliang, et al. A physical simulation experiment on sanding in weakly consolidated sandstone gas reservoirs[J]. Acta Petrolei Sinica, 2011, 32(6): 1007-1011.
[7] 曾祥林, 何冠军, 孙福街, 等. SZ36-1油藏出砂对渗透率影响及出砂 规律实验模拟[J]. 石油勘探与开发, 2005, 32(6): 105-107. Zeng Xianglin, He Guanjun, Sun Fujie, et al. Influences of sand production on permeability and experiments on sand production characters in SZ36-1 Oilfield[J]. Petroleum Exploration and Development, 2005, 32(6): 105-107.
[8] 刘建军, 裴桂红, 李继祥, 等. 弱胶结油藏大孔道出砂的渗流与管流耦 合模型[J]. 岩石力学与工程学报, 2004, 32(S2): 4726-4730. Liu Jianjun, Pei Guihong, Li Jixiang, et al. Coulpld model of seepage and pipe-flow for sand production from big channel in unconsolidated reservoir[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 32(S2): 4726-4730.
[9] Boutt D F, Cook B K, Williams J R. A coupled fluid-soild model for problems in geomechanics: Application to sand production[J]. International Journal for Numerical and Analytical in Geomechanics, 2011, 35: 997-1018.
[10] 薛世峰, 马国顺, 于来刚, 等. 流固耦合模型在定量预测油水井出砂 过程中的应用[J]. 石油勘探与开发, 2007, 34(8): 750-754. Xue Shifeng, Ma Guoshun, Yu Laigang, et al. A fluid-solid coupling model and its application in quantitative sand production prediction of oil and water wells[J]. Petroleum Exploration and Development, 2007, 34(8): 750-754.
[11] Wang Y L. Coupled reservoir-geomechanics model with sand erosion for sand rate and enhanced production prediction[C]//The SPE International Symposium and Exhibition on Formation Damage Control 2002. Lafayette, USA: Society of Petroleum Engineers Inc, 2002: 1-11.
[12] 万志清, 秦四清, 李志刚, 等. 土洞形成的机理及起始条件[J]. 岩石力 学与工程学报, 2003, 22(8): 1377-1382. Wan Zhiqing, Qin Siqing, Li Zhigang, et al. Formation mechanism and initial condition of soil cavity[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(8): 1377-1382.
[13] 李宾元. 油层出砂机理研究[J]. 西南石油学院学报, 1994, 16(1): 23-27. Li Binyuan. Study of mechanism of oil reservoir sand production[J]. Journal of Southwestern Petroleum Institute, 1994, 16(1): 23-27.
[14] 王新东, 凌明友, 李三起, 等. 临盘油田盘二块沙三下出砂规律试验 研究[J]. 断块油气田, 2003, 10(3): 67-70. Wang Xindong, Ling Mingyou, Li Sanqi, et al. Experimental study of sand producing law of lower S3, Pan'er Area in Linpan Oilfield[J]. Fault-bock Oil & Gas Field, 2003, 10(3): 67-70.
2014, Vol. 32 
