130 2017 2 PETROLEUM EXPLORATION AND DEVELOPMENT Vol.44 No.1 文章编号 :1000-0747(2017)01-0130-07 DOI: 10.11698/PED.2017.01.16 应用电容电阻模型研究大型成熟油田井间连通性 JAMALI Ali,ETTEHADTAVAKKOL Amin (Texas Tech University, Lubbock, TX 79409, USA) 摘要 : 针对电容电阻模型在大型成熟油田应用时存在的问题, 选用了生产井电容电阻模型 (CRMP), 提出了其在大型成熟油田的简化应用方法, 并进行了实例分析 结合大型成熟油田的特征, 给出了 CRMP 简化推导方法 通过优化求解方法缩短求解时间 提高收敛速率, 包括应用全局优化算法, 计算 CRMP 目标函数的解析梯度向量及 Hessian 矩阵并应用于解算器中, 进行参数缩放等, 使 CRMP 可以应用于大型油田 通过逐步历史拟合可提高 CRMP 模拟结果的可靠性 实例分析结果表明, 采用该方法得到的连通性分析结果与生产实际相符, 验证了该方法的可靠性 根据 CRMP 模拟结果, 可以有效分析注入井与其周围生产井的连通性, 并进行相关分析, 例如判断哪些注水井可以改注二氧化碳以及某二氧化碳注入井是否适宜注二氧化碳等 图 6 表 3 参 12 关键词 : 电容电阻模型 ; 成熟油田 ; 井间连通性 ; 提高采收率中图分类号 :TE357.6 文献标识码 :A Application of capacitance resistance models to interwell connectivity of large-scale mature oil fields JAMALI Ali, ETTEHADTAVAKKOL Amin (Texas Tech University, Lubbock, TX 79409, USA) Abstract: In view of the problems existing in the application of Capacitance Resistance Models (CRMs) to large-scale mature oil fields, Capacitance Resistance Model for Producers (CRMP) was selected for analysis, a simplified procedure for applying CRMP to large-scale mature oil fields was proposed, and some examples analyzed. A simplified derivation for CRMP was presented with consideration of characteristics of large-scale mature oil fields. Several strategies were presented to optimize the solution method, in order to shorten the solution time and speed up convergence rate. These include the implementation of a global optimization algorithm, parameter scaling, analytical development of gradient vector and Hessian matrix of the CRMP obective function and so on. These improvements enable the application of CRMP to large-scale problems. Stepwise history matching was shown to be an effective technique to improve reliability of the analysis. Example analysis results show that, the connectivity got by the presented method agrees with the practical production, which proves the reliability of the presented method. The connectivity of an inector to the nearby producers can be analyzed based on the CRMP simulation results, and the analysis results can be used for related study, such as determining current water inectors suited for CO2 inection, or current CO2 inectors not suited for CO2 inection. Key words: capacitance resistance model; mature oil field; interwell connectivity; enhanced oil recovery 引用 :JAMALI A, ETTEHADTAVAKKOL A. [J]., 2017, 44(1): 130-136. JAMALI A, ETTEHADTAVAKKOL A. Application of capacitance resistance models to interwell connectivity of large-scale mature oil fields[j]. Petroleum Exploration and Development, 2017, 44(1): 130-136. 0 - [1-3] Yousef [4] CRMsSayarpour [5] 3
2017 2 JAMALI Ali 131-60 Weber [6] Nguyen [7] ICR CRMP Slaughter 1 1 图 1 基本电容电阻模型和生产井电容电阻模型示意图 / c t 2 1 dvp 1 dvp dt ct 1 vp dp vp dt dp 3 0.04~0.12 km 2 10~30 acre dvp dp I Q cv t p dt dt 2 CRMP [4-5] 1a Q p pwf J 3 32 cv t p dq dpwf cv t p J dt dt I Q 4 τ cv t p J 5
132 Vol. 44 No.1 e t/τ =e (1/τ)dt 4 n1 nk 1 N Ni t t t 1e e Q 1 e n Q fi I ik 1 e t k2 10 i1 Q t Qt1 e e I d t1 10 I ik t tt 1 Q e t 1 τ J pwf t1 e pwf t e pwf d 6 t1 f i 2.1 离散化 CRMP 2.2 CRMP 未知参数估算 N p N i i 1b f i i CRMP τ Q 1 f i 6 p wf r i CRMP CRMP 90% Np N 2 min fcrmp Qn Qn,obs 11 [8-9] Ettehadtavakkol [10] CRMP 0 Q1 0 fi 0 Np 12 fi 1 i 1,2,, Ni 1 r i r i f i f 0 k 6 Q 1 τ f i Q n Q n,obs tk tk t k1 N i e tk Q tkq tk1 e e fiii d t k 1 i 1 7 k I ik 7 2.3 全局最小值和局部最小值 t k t k 1 t 1 i k t N k CRMP Q tk Q tk 1 e fii ik 1e 8 i1 CRMP n tnt1 tntk tk tk1 N Ni Q tn Q t1 e e 1e fi I ik k2 i1 CRMP CRMP 9 Hessian 9 [11] 6 8 10 CRMP 1 n1
2017 2 JAMALI Ali 133 64 70 1 min 1 000 2 10 6 CRMP CRMP 图 2 全局优化解算器所用初始点分布 2.4 求解时间和收敛速率 3 CRMP Hessian Hessian 90%~99% Mallet Hessian 17 000 Hessian CRMP fcrmp fcrmp f 3 h CRMP fcrmp,, 13 Q1 f i CRMP Hessian Hessian Hessian Hessian CRMP Hessian 2 2 2 fcrmp fcrmp f CRMP Q1Ql1 Q1 fiq1 2 2 2 2 fcrmp fcrmp fcrmp H CRMP fcrmp Q1 l fi 图 3 利用本文方法对不同规模区块目标函数进行求解 2 2 2 所需收敛时间 fcrmp fcrmp fcrmp fiq1 fi fif m Hessian l 1, 2,, Np; m1, 2,, Ni 14 Hessian CRMP 500 r i Slaughter 4 Hessian
134 Vol. 44 No.1 2.5 逐步历史拟合 3 Slaughter 5aSlaughter 20 30 60 19851995 3~4 8~12 2 2.6 注入井影响半径计算 CRMP r i f 0 r i r i CRMP 4 Slaughter 图 4 归一化历史拟合误差 - 影响半径关系 4 r i 457.2 m1 500 ft r i 457.2~762.0 m1 500~2 500 ft 4 图 5 西德克萨斯 Slaughter 油田位置及 East Mallet 区块井位 400 CRMP
2017 2 JAMALI Ali 135 300 500 3.1 本文方法验证 5b Slaughter East Mallet CTI01 1 CTI01 3 CRMP 1 19851991 2 19922004 3 20052013 1992 2005 2004 P12 P11 P11/P12 表 1 CTI01 井与其周围生产井的连通性 1 2 3 P03 0.16 0.11 P04 0.26 0.05 P05 0.30 0.27 0.48 P06 P09 0.02 P10 0.24 P11/P12 0.04 0.32 P13 0.07 0.15 0.20 0.10 1 CTI01 P03P04P05 P11/P12 6a CTI01 P04 P05 P74 P80/P82 P88 P90 0.04 0.10 0.14 0.07 0.42 0.10 0.05 0.06 P93 0.13 0.07 1992 P96 0.11 0.26 P04 P05 P98 0.16 0.17 0.19 6~12 0.34 0.10 0.25 P04 P05 6b CTI01 CRMP 3.2 转注二氧化碳井优选 5b East Mallet I38 2 I38 CRMP P82 P80 P80/P82 2 I38 East Mallet I38 1 3.3 二氧化碳无效注入井判断 5b East Mallet I23 3 I23 CRMP 图 6 P04 井和 P05 井对 CTI01 井二氧化碳注入信号的产出量响应 表 2 I38 井与其周围生产井的连通性 1 2 3 P69 0.07
136 Vol. 44 No.1 表 3 I23 井与其周围生产井的连通性 k l m n 1 2 3 P36 0.54 参考文献 : [1] HEFFER K J, FOX R J, MCGILL C A, et al. Novel techniques show P44 0.05 0.24 links between reservoir flow directionality, earth stress, fault P47 0.13 structure and geomechanical changes in mature waterfloods[j]. SPE P51 0.22 Journal, 1997, 2(2): 91-98. P57 0.07 0.09 [2] PANDA M N, CHOPRA A K. An integrated approach to estimate P63 0.14 0.07 well interactions[r]. SPE 39563-MS, 1998. 0.15 0.25 0.30 [3] ALBERTONI A, LAKE L W. Inferring interwell connectivity only from well-rate fluctuations in waterfloods[j]. SPE Reservoir I23 Evaluation & Engineering, 2003, 6(1): 6-16. [4] YOUSEF A A, GENTIL P H, JENSEN J L, et al. A capacitance model to infer interwell connectivity from production and inection 1991 rate fluctuations[j]. SPE Reservoir Evaluation & Engineering, 2006, 1.13 10 8 m 3 40 10 8 ft 3 9(6): 630-646. [5] SAYARPOUR M, ZULUAGA E, KABIR C S, et al. The use of capacitance-resistance models for rapid estimation of waterflood performance and optimization[j]. Journal of Petroleum Science and Engineering, 2009, 69(3/4): 227-238. 4 [6] WEBER D, EDGAR T F, LAKE L W, et al. Improvements in capacitance-resistive modeling and optimization of large scale reservoirs[r]. SPE 121299, 2009. CRMP [7] NGUYEN A P, KIM J S, LAKE L W, et al. Integrated capacitance resistive model for reservoir characterization in primary and secondary recovery[r]. SPE 147344, 2011. CRMP CRMP [8] ATHICHANAGORN S, HORNE R N, KIKANI J. Processing and interpretation of long-term data from permanent downhole pressure gauges[r]. SPE 56419-MS, 1999. Hessian CRMP [9] CUTLER R P, MANSURE A J. Fluid dynamics in sucker rod pumps[r]. SAND99-0093C, 1999. [10] ETTEHADTAVAKKOL A, LAKE L W, BRYANT S L. CO 2 -EOR and storage design optimization[j]. International Journal of Greenhouse Gas Control, 2014, 25(6): 79-92. [11] LASDON L S, WAREN A D. Large scale nonlinear programming[j]. Computers & Chemical Engineering, 1983, 7(5): 595-604. [12] SAYARPOUR M, KABIR C S, LAKE L W. Field applications of 符号注释 : ct Pa 1 capacitance-resistive models in waterfloods[j]. SPE Reservoir f0 Engineering, 2009, 12(6): 853-864. fi i I m 3 /sii i 第一作者简介 :JAMALI Ali(1989-), 男, 伊朗人, 德州理工大学在 m 3 /sj m 3 读博士研究生, 主要从事老油田增产方法研究 地址 :2500 Broadway, /PasN Lubbock, TX 79409, USA E-mail:ali.amali@ttu.edu Ni Np pwf 联系作者 :ETTEHADTAVAKKOL Amin(1984-), 男, 伊朗人, 博士, Pa p PaQ m 3 /s Q m 3 /sri mri mt st1 德州理工大学助理教授, 主要从事提高采收率 油藏工程等方面的研究 地址 :2500 Broadway, Lubbock, TX 79409, USA E-mail:amin.ettehadtavakkol@ ttu.edu svp m 3 ξ τ 收稿日期 :2016-06-22 修回日期 :2016-11-28 si 胡苇玮