基于数值模型的气井现代产量递减分析及动态预测
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摘要
传统的气井生产动态预测方法常采用拟稳态产能方程结合物质平衡方程来进行,由于低渗、致密储层流动很难达到拟稳态,预测结果可能存在较大误差。现代产量递减分析技术已成为单井动态预测的新技术,但还停留在解析模型阶段,通常采用叠加原理进行全程历史拟合。由于气井生产阶段产量波动大、流动阶段多,历史拟合计算周期长,解析法难以满足现场需求。针对上述问题,以垂直压裂井为例,建立了不稳定渗流数学模型,采用混合有限元方法获得了定产降压、定压降产和变产变压等3种生产模式的数值解。并根据定产降压解绘制了现代产量递减分析曲线,变产变压解进行全程历史拟合以及先定产降压、后定压降产的组合进行气井生产动态预测。模型结果与Topaze商用软件的计算结果一致,且数值模型的全程历史拟合速度具有明显优势,与传统生产动态预测方法的结果对比以及现场实例分析结果表明,新模型结果准确且方法实用、可靠。
The pseudo-steady state productivity equation in combination with material balance equation is always used as the traditional performance forecasting method of gas-well production.Due to low permeability,the flow of tight reservoirs is difficult to reach a pseudo-steady state,so that big errors may exist in the forecasting results.The advanced production decline analysis has been a new technology for single-well performance forecasting,but still at the analytical model stage,and thus the superposition principle is commonly used for whole-course history matching.Because of the large yield fluctuation at gas-well production stage and the multiple flow stages,history matching shows a long computation period,so the analytical method is difficult to meet the onsite demand.In view of above questions,a type of unstable porous flow mathematical model was established by taking the vertical fractured well as an example,and the numerical solutions to three kinds of production patterns including producing at a constant rate,producing at a constant bottom hole flowing pressure and variable pressure and variable rate were obtained using the mixed finite element method.The advanced production decline analysis curve was drawn based on the solution of constant rate production,the whole-course history matching was conducted by variable pressure and variable rate solutions,and the production performance forecasting of gas wells was carried out according to the combination of the constant rate production and the later constant pressure production.By comparison,the model results and the calculation results of Topaze commercial software are consistent,and the whole-course history matching rate of numerical model has significant advantages.The comparison with the results of traditional production performance forecasting method and the field-case analysis results show that the model results of this study are accurate and the used methods are practical and reliable.
The pseudo-steady state productivity equation in combination with material balance equation is always used as the traditional performance forecasting method of gas-well production.Due to low permeability,the flow of tight reservoirs is difficult to reach a pseudo-steady state,so that big errors may exist in the forecasting results.The advanced production decline analysis has been a new technology for single-well performance forecasting,but still at the analytical model stage,and thus the superposition principle is commonly used for whole-course history matching.Because of the large yield fluctuation at gas-well production stage and the multiple flow stages,history matching shows a long computation period,so the analytical method is difficult to meet the onsite demand.In view of above questions,a type of unstable porous flow mathematical model was established by taking the vertical fractured well as an example,and the numerical solutions to three kinds of production patterns including producing at a constant rate,producing at a constant bottom hole flowing pressure and variable pressure and variable rate were obtained using the mixed finite element method.The advanced production decline analysis curve was drawn based on the solution of constant rate production,the whole-course history matching was conducted by variable pressure and variable rate solutions,and the production performance forecasting of gas wells was carried out according to the combination of the constant rate production and the later constant pressure production.By comparison,the model results and the calculation results of Topaze commercial software are consistent,and the whole-course history matching rate of numerical model has significant advantages.The comparison with the results of traditional production performance forecasting method and the field-case analysis results show that the model results of this study are accurate and the used methods are practical and reliable.
引文
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[17]陈元千,唐玮.广义递减模型的建立及应用[J].石油学报,2016,37(11):1410-1413.CHEN Yuanqian,TANG Wei.Establishment and application of generalized decline model[J].Acta Petrolei Sinica,2016,37(11):1410-1413.
[18]王永祥,段晓文,徐小林,等.SEC准则油气证实储量判别标准与评估方法[J].石油学报,2016,37(9):1137-1144.WANG Yongxiang,DUAN Xiaowen,XU Xiaolin,et al.Determination criterion and the estimation methods for the proved reserves under the US.SEC regulation[J].Acta Petrolei Sinica,2016,37(9):1137-1144.
[19]NEWMAN G H.Pore-volume compressibility of consolidated,friable and unconsolidated reservoir rocks under hydrostatic loading[J].Journal of Petroleum Technology,1973,25(2):129-134.
[20]DRANCHUK P M,PURVIS R A,ROBINSON D B.Computer calculation of natural gas compressibility factors using the Standing and Katz correlation[R].Edmonton:Petroleum Society of Canada,1973.
[21]LEE A L,GONZALEZ M H,EAKIN B E.The viscosity of natural gases[J].Journal of Petroleum Technology,1966,18(8):997-1000.
[22]欧阳伟平,刘曰武.射孔完井参数对试井理论曲线的影响[J].石油学报,2013,34(3):528-534.OUYANG Weiping,LIU Yuewu.Effects of perforated completion parameters on well test type curves[J].Acta Petrolei Sinica,2013,34(3):528-534.
[23]WAN Yizhao,LIU Yuewu,OUYANG Weiping,et al.Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model[J].Applied Mathematics and Mechanics,2016,37(5):611-626.
[24]WAN Yizhao,LIU Yuewu,LIU Wenchao,et al.A numerical approach for pressure transient analysis of a vertical well with complex fractures[J].Acta Mechanica Sinica,2016,32(4):640-648.
[2]卢晓敏,何晓东.气藏动态预测物质平衡法研究[J].天然气勘探与开发,1999,22(3):29-39.LU Xiaomin,HE Xiaodong.Study on material balance method for gas reservoir dynamic prediction[J].Natural Gas Exploration and Development,1999,22(3):29-39.
[3]疏壮志,杜志敏,刘建仪,等.气井生产动态预测方法研究[J].天然气工业,2004,24(8):78-81.SHU Zhuangzhi,DU Zhimin,LIU Jianyi,et al.Prediction method of production performance of gas wells[J].Natural Gas Industry,2004,24(8):78-81.
[4]史海东,王晖,郭春秋,等.异常高压气藏采气速度与稳产期定量关系——以阿姆河右岸B-P气田为例[J].石油学报,2015,36(5):600-605.SHI Haidong,WANG Hui,GUO Chunqiu,et al.Quantitative relationship between gas recovery rate and stable production period of abnormally high pressure gas reservoirs:a case study of B-P gas field on the right bank of the Amu Darya[J].Acta Petrolei Sinica,2015,36(5):600-605.
[5]孙贺东.具有补给的气藏物质平衡方程及动态预测[J].石油学报,2011,32(4):683-686.SUN Hedong.A balance equation of gas materials with recharge capacity and their performance prediction[J].Acta Petrolei Sinica,2011,32(4):683-686.
[6]孙贺东.油气井现代产量递减分析方法及应用[M].北京:石油工业出版社,2013.SUN Hedong.Advanced production decline analysis and application[M].Beijing:Petroleum Industry Press,2013.
[7]BLASINGAME T A,JOHNSTON J L,LEE W J.Type curve analysis using the pressure integral method[R].SPE 18799,1989.
[8]PRATIKNO H,RUSHING J A,BLASINGAME T A.Decline curve analysis using type curves-fractured wells[R].SPE84287,2003.
[9]韩永新.低渗致密气藏气井动态分析研究[D].北京:中国地质大学,2006.HAN Yongxin.Study on gas well dynamic performance analysis in low permeability tight gas reservoirs[D].Beijing:China University of Geosciences,2006.
[10]MARHAENDRAJANA T,BLASINGAME T A.Decline curve analysis using type curves-evaluation of well performance behav-ior in a multi-well reservoir system[R].SPE71517,2001.
[11]SHIH M Y,BLASINGAME T A.Decline curve analysis using type curves:horizontal wells[R].SPE29572,1995.
[12]CLARKSON C R,JORDAN C L,ILK D,et al.Production data analysis of fractured and horizontal CBM wells[R].SPE125929,2009.
[13]ZAREENEJAD M H,GHANAVATI M,ASL A K.Production data analysis of horizontal wells using vertical well decline models,a field case study of an oil field[J].Petroleum Science and Technology,2014,32(4):418-425.
[14]NOBAKHT M,CLARKSON C R,KAVIANI D.New type curves for analyzing horizontal well with multiple fractures in shale gas reservoirs[J].Journal of Natural Gas Science and Engineering,2016,10:99-112.
[15]魏明强,段永刚,方全堂,等.基于物质平衡修正的页岩气藏压裂水平井产量递减分析方法[J].石油学报,2016,37(4):508-515.WEI Mingqiang,DUAN Yonggang,FANG Quantang,et al.Production decline analysis method of fractured horizontal well in shale gas reservoirs based on modifying material balance[J].Acta Petrolei Sinica,2016,37(4):508-515.
[16]孙贺东,朱忠谦,施英,等.现代产量递减分析Blasingame图版制作之纠错[J].天然气工业,2015,35(10):71-77.SUN Hedong,ZHU Zhongqian,SHI Ying,et al.A note on the Blasingame type curve plotting of production decline analysis[J].Natural Gas Industry,2015,35(10):71-77.
[17]陈元千,唐玮.广义递减模型的建立及应用[J].石油学报,2016,37(11):1410-1413.CHEN Yuanqian,TANG Wei.Establishment and application of generalized decline model[J].Acta Petrolei Sinica,2016,37(11):1410-1413.
[18]王永祥,段晓文,徐小林,等.SEC准则油气证实储量判别标准与评估方法[J].石油学报,2016,37(9):1137-1144.WANG Yongxiang,DUAN Xiaowen,XU Xiaolin,et al.Determination criterion and the estimation methods for the proved reserves under the US.SEC regulation[J].Acta Petrolei Sinica,2016,37(9):1137-1144.
[19]NEWMAN G H.Pore-volume compressibility of consolidated,friable and unconsolidated reservoir rocks under hydrostatic loading[J].Journal of Petroleum Technology,1973,25(2):129-134.
[20]DRANCHUK P M,PURVIS R A,ROBINSON D B.Computer calculation of natural gas compressibility factors using the Standing and Katz correlation[R].Edmonton:Petroleum Society of Canada,1973.
[21]LEE A L,GONZALEZ M H,EAKIN B E.The viscosity of natural gases[J].Journal of Petroleum Technology,1966,18(8):997-1000.
[22]欧阳伟平,刘曰武.射孔完井参数对试井理论曲线的影响[J].石油学报,2013,34(3):528-534.OUYANG Weiping,LIU Yuewu.Effects of perforated completion parameters on well test type curves[J].Acta Petrolei Sinica,2013,34(3):528-534.
[23]WAN Yizhao,LIU Yuewu,OUYANG Weiping,et al.Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model[J].Applied Mathematics and Mechanics,2016,37(5):611-626.
[24]WAN Yizhao,LIU Yuewu,LIU Wenchao,et al.A numerical approach for pressure transient analysis of a vertical well with complex fractures[J].Acta Mechanica Sinica,2016,32(4):640-648.