基于幂函数形式物质平衡方法的高压、超高压气藏储量评价
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摘要
高压、超高压气藏的储层岩石有效压缩系数、含水层体积及水侵量难以确定,常规视储层压力与累计产气量曲线外推法或其改进方法计算的该类气藏储量的准确度较低。为了提高储量评估的准确性和可靠性,在Gonzalez方法的基础上,建立幂函数形式的高压、超高压气藏物质平衡方程,并结合20个国外已开发高压、超高压气藏实例,确定幂指数经验值,分析了视储层压力衰竭程度和采出程度对储量计算可靠性的影响,确定影响储量评价可靠性的关键参数(视储层压力衰竭程度)的临界值,并与两段式临界值进行了对比和实例计算。研究结果表明:①幂函数形式物质平衡方法的幂指数经验值为1.028 47,其上限值为1.115 67;②经典二段式拐点对应的视储层压力衰竭程度介于0.14~0.38,平均值为0.23,第二直线段外推点对应的视储层压力衰竭程度介于0.23~0.50,平均值为0.33,对应的采出程度介于33%~65%,平均值为45%;③采用上述方法计算了高压、超高压气藏的储量,当视储层压力衰竭程度大于0.33时,计算结果误差小于10%。结论认为,针对高压、超高压及裂缝性应力敏感气藏,所提出的幂函数形式物质平衡方法避开了储层岩石有效压缩系数、含水层体积及水侵量等不确定性参数,具有计算过程简单、实用性较好、误差较小的优点。
It is difficult to determine the effective reservoir rock compressibility, aquifer volume and water influx of high pressure and ultra high pressure gas reservoirs, so when the traditional apparent reservoir pressure and cumulative gas production curve extrapolation method and its modified version are used to calculate the initial gas in-place of such gas reservoirs, the calculation accuracy is lower. The material balance equation in the form of power function for such gas reservoirs was established based on Gonzalez method in order to improve the accuracy and reliability of reserve evaluation. Then, based on 20 high pressure and ultra high pressure reservoirs that had been developed abroad, the empirical value of the power exponent was defined, and the influences of the depletion degree of apparent reservoir pressure and the degree of reserve recovery on the reliability of reserve calculation were analyzed. Besides, the critical value of the key parameter affecting the reliability of reserve evaluation(depletion degree of apparent reservoir pressure) was determined and compared with the critical value of the two-linear trends. Finally, an example calculation was carried out. And the following research results were obtained. First, the empirical value of the power exponent calculated using the material balance method in the form of power function is 1.028 47, with an upper limit of 1.115 67. Second, the depletion degree of apparent reservoir pressure corresponding to the inflection point of the classical two-linear trends ranges from 0.14 to 0.38 with an average of 0.23 while that corresponding to the extrapolation point of the second straight line is between 0.23 and 0.50 with an average of 0.33 and the corresponding degree of reserve recovery is in the range of 33%-65% with an average of 45%. Third, the reserves of such high pressure gas reservoirs calculated with this new method has an error rate less than 10% if the depletion degree of apparent reservoir pressure is greater than 0.33. In conclusion, for such high pressure gas reservoirs and the stress-sensitive fractured gas reservoirs, the material balance method in the form of power function proposed in this paper can avoid the uncertainty parameters(e.g. effective reservoir rock compressibility, aquifer volume and water influx)and it is advantageous with simple calculation process, better practicability and small error.
It is difficult to determine the effective reservoir rock compressibility, aquifer volume and water influx of high pressure and ultra high pressure gas reservoirs, so when the traditional apparent reservoir pressure and cumulative gas production curve extrapolation method and its modified version are used to calculate the initial gas in-place of such gas reservoirs, the calculation accuracy is lower. The material balance equation in the form of power function for such gas reservoirs was established based on Gonzalez method in order to improve the accuracy and reliability of reserve evaluation. Then, based on 20 high pressure and ultra high pressure reservoirs that had been developed abroad, the empirical value of the power exponent was defined, and the influences of the depletion degree of apparent reservoir pressure and the degree of reserve recovery on the reliability of reserve calculation were analyzed. Besides, the critical value of the key parameter affecting the reliability of reserve evaluation(depletion degree of apparent reservoir pressure) was determined and compared with the critical value of the two-linear trends. Finally, an example calculation was carried out. And the following research results were obtained. First, the empirical value of the power exponent calculated using the material balance method in the form of power function is 1.028 47, with an upper limit of 1.115 67. Second, the depletion degree of apparent reservoir pressure corresponding to the inflection point of the classical two-linear trends ranges from 0.14 to 0.38 with an average of 0.23 while that corresponding to the extrapolation point of the second straight line is between 0.23 and 0.50 with an average of 0.33 and the corresponding degree of reserve recovery is in the range of 33%-65% with an average of 45%. Third, the reserves of such high pressure gas reservoirs calculated with this new method has an error rate less than 10% if the depletion degree of apparent reservoir pressure is greater than 0.33. In conclusion, for such high pressure gas reservoirs and the stress-sensitive fractured gas reservoirs, the material balance method in the form of power function proposed in this paper can avoid the uncertainty parameters(e.g. effective reservoir rock compressibility, aquifer volume and water influx)and it is advantageous with simple calculation process, better practicability and small error.
引文
[1]江同文,孙雄伟.库车前陆盆地克深气田超深超高压气藏开发认识与技术对策[J].天然气工业,2018,38(6):1-9.Jiang Tongwen&Sun Xiongwei.Development of Keshen ultra-deep and ultra-high pressure gas reservoirs in the Kuqa foreland basin,Tarim Basin:Understanding points and technical countermeasures[J].Natural Gas Industry,2018,38(6):1-9.
[2]李熙喆,郭振华,胡勇,罗瑞兰,苏云河,孙贺东,等.中国超深层构造型大气田高效开发策略[J].石油勘探与开发,2018,45(1):111-118.Li Xizhe,Guo Zhenhua,Hu Yong,Luo Ruilan,Su Yunhe,Sun Hedong,et al.Efficient development strategies for large ultra-deep structural gas fields in China[J].Petroleum Exploration and Development,2018,45(1):111-118.
[3]Hammerlindl DJ.Predicting gas reserves in abnormally pressured reservoirs[C]//paper 3479-MS presented at the Fall Meeting of the Society of Petroleum Engineers of AIME,3-6 October 1971,New Orleans,Louisiana,USA.
[4]Havlena D&Odeh AS.The material balance as an equation of a straight line[J].Journal of Petroleum Technology,1963,15(8):896-900.
[5]Duggan JO.The Anderson"L"-An abnormally pressured gas reservoir in South Texas[J].Journal of Petroleum Technology,1972,24(2):132-138.
[6]陈元千,胡建国.确定异常高压气藏地质储量和有效压缩系数的新方法[J].天然气工业,1993,13(1):53-58.Chen Yuanqian&Hu Jianguo.A new method for determining gas in place and effective compressibility in abnormal high pressure reservoir[J].Natural Gas Industry,1993,13(1):53-58.
[7]李大昌,林平一.异常高压气藏的动态模型、压降特征及储量计算方法[J].石油勘探与开发,1985,12(2):56-64.Li Dachang&Lin Pingyi.Dynamic models of abnormally pressured gas reservoirs with pressure drop and a new method of predicting reserve[J].Petroleum Exploration and Development,1985,12(2):56-64.
[8]Ramagost BP&Farshad FF.p/Z abnormally pressured gas reservoirs[C]//paper 10125-MS presented at the SPE Annual Technical Conference and Exhibition,4-7 October 1981,San Antonio,Texas,USA.https://doi.org/10.2118/10125-MS.
[9]Bourgoyne Jr AT.Shale water as a pressure support mechanism in gas reservoirs having abnormal formation pressure[J].Journal of Petroleum Science&Engineering,1990,3(4):305-319.
[10]Fetkovich MJ,Reese DE&Whitson CH.Application of a general material balance for high-pressure gas reservoirs(includes associated paper 51360)[J].SPE Journal,1998,3(1):3-13.
[11]Roach RH.Analyzing geopressured reservoirs-A material balance technique[C].Society of Petroleum Engineers,1981.
[12]Ambastha AK.A type-curve matching procedure for material balance analysis of production data from geopressured gas reservoirs[J].Journal of Canadian Petroleum Technology,1991,30(5):61-65.
[13]Gan RG&Blasingame TA.A semianalytical p/Z technique for the analysis of reservoir performance from abnormally pressured gas reservoirs[C]//paper 71514-MS presented at the SPEAnnual Technical Conference and Exhibition,30 September-3October 2001,New Orleans,Louisiana,USA.https://doi.org/10.2118/71514-MS.
[14]Gonzalez FE,Ilk D&Blasingame TA.A quadratic cumulative production model for the material balance of an abnormally pressured gas reservoir[C]//paper 114044-MS presented at the SPEWestern Regional and Pacific Section AAPG Joint Meeting,29March-4 April 2008,Bakersfield,California,USA.https://doi.org/10.2118/114044-MS.
[15]卞小强,杜志敏,陈静.二项式物质平衡方程预测异常高压气藏储量[J].西南石油大学学报(自然科学版),2010,32(3):75-79.Bian Xiaoqiang,Du Zhimin&Chen Jing.A quadratic material balance equation of calculation of initial gas in place for abnormal geo-pressured gas reservoirs[J].Journal of Southwest Petroleum University(Science&Technology Edition),2010,32(3):75-79.
[16]张迎春,赵春明,童凯军,郑旭.拟抛物线方程在异常高压气藏地质储量计算中的应用[J].中国海上油气,2010,22(2):99-103.Zhang Yingchun,Zhao Chunming,Tong Kaijun&Zheng Xu.An application of a pseudo-parabolic equation in calculating gas in place for abnormally high pressure reservoirs[J].China Offshore Oil and Gas,2010,22(2):99-103.
[17]侯振,黄炳光,王怒涛,宋洋.异常高压气藏储量计算新方法[J].重庆科技学院学报(自然科学版),2010,12(3):62-63.Hou Zhen,Huang Bingguang,Wang Nutao&Song Yang.New calculation method for gas reserves under abnormal high pressure[J].Journal of Chongqing University of Science and Technology(Natural Sciences Edition),2010,12(3):62-63.
[18]丁显峰,刘志斌,潘大志.异常高压气藏地质储量和累积有效压缩系数计算新方法[J].石油学报,2010,31(4):626-628.Ding Xianfeng,Liu Zhibin&Pan Dazhi.A new method for estimating gas in place and cumulative effective compressibility of abnormal high-pressure gas reservoirs[J].Acta Petrolei Sinica,2010,31(4):626-628.
[19]郑琴,刘志斌.含累积产量三次方项的异常高压气藏物质平衡新模型及计算[J].北京大学学报(自然科学版),2011,47(1):115-119.Zheng Qin&Liu Zhibin.A new material balance model of an abnormally pressured gas reservoirs which contains cubic term of cumulative production and its calculation[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2011,47(1):115-119.
[20]朱义东,黄炳光,章彤,王怒涛.异常高压气藏地质储量计算新方法[J].大庆石油地质与开发,2005,24(1):10-12.Zhu Yidong,Huang Bingguang,Zhang Tong&Wang Nutao.Anew method for the reserves calculation in abnormal high pressure gas reservoir[J].Petroleum Geology&Oilfield Development in Daqing,2005,24(1):10-12.
[21]Jiao Yuwei,Xia Jing,Liu Pengcheng,Zhang Jing,Li Baozhu,Tian Qing,et al.New material balance analysis method for abnormally high-pressured gas-hydrocarbon reservoir with water influx[J].International Journal of Hydrogen Energy,2017,42(29):18718-18727.
[22]Ronald Gunawan G.A new p/Z technique for the analysis of abnormally pressured gas reservoirs[D].Texas:Texas A&M University,2001.
[23]Prasad RK&Rogers LA.Superpressured gas reservoirs:Case studies and a generalized tank model[C]//paper 16861-MS presented at the SPE Annual Technical Conference and Exhibition,27-30 September 1987,Dallas,Texas,USA.https://doi.org/10.2118/16861-MS.
[24]Guehria FM.A new approach to p/Z analysis in abnormally pressured reservoirs[C]//paper 36703-MS presented at the SPEAnnual Technical Conference and Exhibition,6-9 October 1996,Denver,Colorado,USA.https://doi.org/10.2118/36703-MS.
[25]Becerra-Arteaga T.Analysis of abnormally pressured gas reservoirs[D].Texas:Texas A&M University,1993.
[26]Poston SW&Chen HY.Case history studies:Abnormal pressured gas reservoirs[C]//paper 18857-MS presented at the SPE Production Operations Symposium,13-14 March 1989,Oklahoma City,Oklahoma,USA.https://doi.org/10.2118/18857-MS.
[27]Wang SW,Stevenson VM,Ohaeri CU&Wotring DH.Analysis of overpressured reservoirs with a new material balance method[C]//paper 56690-MS presented at the SPE Annual Technical Conference and Exhibition,3-6 October 1999,Houston,Texas,USA.https://doi.org/10.2118/56690-MS.
[28]陈元千.异常高压气藏物质平衡方程式的推导及应用[J].石油学报,1983,4(1):45-53.Chen Yuanqian.Application and derivation of material balance equation for abnormally pressured gas reservoirs[J].Acta Petrolei Sinica,1983,4(1):45-53.
[29]Elsharkawy AM.MB solution for high pressure gas reservoirs[C]//paper 35589-MS presented at the SPE Gas Technology Symposium,28 April-1 May 1996,Calgary,Alberta,Canada.https://doi.org/10.2118/35589-MS.
[30]Yale DP,Nabor GW,Russell JA,Pham HD&Yousef M.Application of variable formation compressibility for improved reservoir analysis[C]//paper 26647-MS presented at the SPE Annual Technical Conference and Exhibition,3-6 October 1993,Houston,Texas,USA.https://doi.org/10.2118/26647-MS.
[31]Moran O O,Samaniego V F&Jorge A AV.Advances in the production mechanism diagnosis of gas reservoirs through material balance studies[C]//paper 91509-MS presented at the SPE Annual Technical Conference and Exhibition,26-29 September 2004,Houston,Texas,USA.https://doi.org/10.2118/91509-MS.
[32]Gonzalez FE.A quadratic cumulative production model for the material balance of an abnormally pressured gas reservoir[D].Texas:Texas A&M University,2003.
[33]夏静,谢兴礼,冀光,罗凯.异常高压有水气藏物质平衡方程推导及应用[J].石油学报,2007,28(3):96-99.Xia Jing,Xie Xingli,Ji Guang&Luo Kai.Derivation and application of material balance equation for over-pressured gas reservoir with aquifer[J].Acta Petrolei Sinica,2007,28(3):96-99.
[34]Aguilera R.Effect of fracture compressibility on gas-in-place calculations of stress-sensitive naturally fractured reservoirs[J]//SPEReservoir Evaluation&Engineering,2008,11(2):307-310.
[2]李熙喆,郭振华,胡勇,罗瑞兰,苏云河,孙贺东,等.中国超深层构造型大气田高效开发策略[J].石油勘探与开发,2018,45(1):111-118.Li Xizhe,Guo Zhenhua,Hu Yong,Luo Ruilan,Su Yunhe,Sun Hedong,et al.Efficient development strategies for large ultra-deep structural gas fields in China[J].Petroleum Exploration and Development,2018,45(1):111-118.
[3]Hammerlindl DJ.Predicting gas reserves in abnormally pressured reservoirs[C]//paper 3479-MS presented at the Fall Meeting of the Society of Petroleum Engineers of AIME,3-6 October 1971,New Orleans,Louisiana,USA.
[4]Havlena D&Odeh AS.The material balance as an equation of a straight line[J].Journal of Petroleum Technology,1963,15(8):896-900.
[5]Duggan JO.The Anderson"L"-An abnormally pressured gas reservoir in South Texas[J].Journal of Petroleum Technology,1972,24(2):132-138.
[6]陈元千,胡建国.确定异常高压气藏地质储量和有效压缩系数的新方法[J].天然气工业,1993,13(1):53-58.Chen Yuanqian&Hu Jianguo.A new method for determining gas in place and effective compressibility in abnormal high pressure reservoir[J].Natural Gas Industry,1993,13(1):53-58.
[7]李大昌,林平一.异常高压气藏的动态模型、压降特征及储量计算方法[J].石油勘探与开发,1985,12(2):56-64.Li Dachang&Lin Pingyi.Dynamic models of abnormally pressured gas reservoirs with pressure drop and a new method of predicting reserve[J].Petroleum Exploration and Development,1985,12(2):56-64.
[8]Ramagost BP&Farshad FF.p/Z abnormally pressured gas reservoirs[C]//paper 10125-MS presented at the SPE Annual Technical Conference and Exhibition,4-7 October 1981,San Antonio,Texas,USA.https://doi.org/10.2118/10125-MS.
[9]Bourgoyne Jr AT.Shale water as a pressure support mechanism in gas reservoirs having abnormal formation pressure[J].Journal of Petroleum Science&Engineering,1990,3(4):305-319.
[10]Fetkovich MJ,Reese DE&Whitson CH.Application of a general material balance for high-pressure gas reservoirs(includes associated paper 51360)[J].SPE Journal,1998,3(1):3-13.
[11]Roach RH.Analyzing geopressured reservoirs-A material balance technique[C].Society of Petroleum Engineers,1981.
[12]Ambastha AK.A type-curve matching procedure for material balance analysis of production data from geopressured gas reservoirs[J].Journal of Canadian Petroleum Technology,1991,30(5):61-65.
[13]Gan RG&Blasingame TA.A semianalytical p/Z technique for the analysis of reservoir performance from abnormally pressured gas reservoirs[C]//paper 71514-MS presented at the SPEAnnual Technical Conference and Exhibition,30 September-3October 2001,New Orleans,Louisiana,USA.https://doi.org/10.2118/71514-MS.
[14]Gonzalez FE,Ilk D&Blasingame TA.A quadratic cumulative production model for the material balance of an abnormally pressured gas reservoir[C]//paper 114044-MS presented at the SPEWestern Regional and Pacific Section AAPG Joint Meeting,29March-4 April 2008,Bakersfield,California,USA.https://doi.org/10.2118/114044-MS.
[15]卞小强,杜志敏,陈静.二项式物质平衡方程预测异常高压气藏储量[J].西南石油大学学报(自然科学版),2010,32(3):75-79.Bian Xiaoqiang,Du Zhimin&Chen Jing.A quadratic material balance equation of calculation of initial gas in place for abnormal geo-pressured gas reservoirs[J].Journal of Southwest Petroleum University(Science&Technology Edition),2010,32(3):75-79.
[16]张迎春,赵春明,童凯军,郑旭.拟抛物线方程在异常高压气藏地质储量计算中的应用[J].中国海上油气,2010,22(2):99-103.Zhang Yingchun,Zhao Chunming,Tong Kaijun&Zheng Xu.An application of a pseudo-parabolic equation in calculating gas in place for abnormally high pressure reservoirs[J].China Offshore Oil and Gas,2010,22(2):99-103.
[17]侯振,黄炳光,王怒涛,宋洋.异常高压气藏储量计算新方法[J].重庆科技学院学报(自然科学版),2010,12(3):62-63.Hou Zhen,Huang Bingguang,Wang Nutao&Song Yang.New calculation method for gas reserves under abnormal high pressure[J].Journal of Chongqing University of Science and Technology(Natural Sciences Edition),2010,12(3):62-63.
[18]丁显峰,刘志斌,潘大志.异常高压气藏地质储量和累积有效压缩系数计算新方法[J].石油学报,2010,31(4):626-628.Ding Xianfeng,Liu Zhibin&Pan Dazhi.A new method for estimating gas in place and cumulative effective compressibility of abnormal high-pressure gas reservoirs[J].Acta Petrolei Sinica,2010,31(4):626-628.
[19]郑琴,刘志斌.含累积产量三次方项的异常高压气藏物质平衡新模型及计算[J].北京大学学报(自然科学版),2011,47(1):115-119.Zheng Qin&Liu Zhibin.A new material balance model of an abnormally pressured gas reservoirs which contains cubic term of cumulative production and its calculation[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2011,47(1):115-119.
[20]朱义东,黄炳光,章彤,王怒涛.异常高压气藏地质储量计算新方法[J].大庆石油地质与开发,2005,24(1):10-12.Zhu Yidong,Huang Bingguang,Zhang Tong&Wang Nutao.Anew method for the reserves calculation in abnormal high pressure gas reservoir[J].Petroleum Geology&Oilfield Development in Daqing,2005,24(1):10-12.
[21]Jiao Yuwei,Xia Jing,Liu Pengcheng,Zhang Jing,Li Baozhu,Tian Qing,et al.New material balance analysis method for abnormally high-pressured gas-hydrocarbon reservoir with water influx[J].International Journal of Hydrogen Energy,2017,42(29):18718-18727.
[22]Ronald Gunawan G.A new p/Z technique for the analysis of abnormally pressured gas reservoirs[D].Texas:Texas A&M University,2001.
[23]Prasad RK&Rogers LA.Superpressured gas reservoirs:Case studies and a generalized tank model[C]//paper 16861-MS presented at the SPE Annual Technical Conference and Exhibition,27-30 September 1987,Dallas,Texas,USA.https://doi.org/10.2118/16861-MS.
[24]Guehria FM.A new approach to p/Z analysis in abnormally pressured reservoirs[C]//paper 36703-MS presented at the SPEAnnual Technical Conference and Exhibition,6-9 October 1996,Denver,Colorado,USA.https://doi.org/10.2118/36703-MS.
[25]Becerra-Arteaga T.Analysis of abnormally pressured gas reservoirs[D].Texas:Texas A&M University,1993.
[26]Poston SW&Chen HY.Case history studies:Abnormal pressured gas reservoirs[C]//paper 18857-MS presented at the SPE Production Operations Symposium,13-14 March 1989,Oklahoma City,Oklahoma,USA.https://doi.org/10.2118/18857-MS.
[27]Wang SW,Stevenson VM,Ohaeri CU&Wotring DH.Analysis of overpressured reservoirs with a new material balance method[C]//paper 56690-MS presented at the SPE Annual Technical Conference and Exhibition,3-6 October 1999,Houston,Texas,USA.https://doi.org/10.2118/56690-MS.
[28]陈元千.异常高压气藏物质平衡方程式的推导及应用[J].石油学报,1983,4(1):45-53.Chen Yuanqian.Application and derivation of material balance equation for abnormally pressured gas reservoirs[J].Acta Petrolei Sinica,1983,4(1):45-53.
[29]Elsharkawy AM.MB solution for high pressure gas reservoirs[C]//paper 35589-MS presented at the SPE Gas Technology Symposium,28 April-1 May 1996,Calgary,Alberta,Canada.https://doi.org/10.2118/35589-MS.
[30]Yale DP,Nabor GW,Russell JA,Pham HD&Yousef M.Application of variable formation compressibility for improved reservoir analysis[C]//paper 26647-MS presented at the SPE Annual Technical Conference and Exhibition,3-6 October 1993,Houston,Texas,USA.https://doi.org/10.2118/26647-MS.
[31]Moran O O,Samaniego V F&Jorge A AV.Advances in the production mechanism diagnosis of gas reservoirs through material balance studies[C]//paper 91509-MS presented at the SPE Annual Technical Conference and Exhibition,26-29 September 2004,Houston,Texas,USA.https://doi.org/10.2118/91509-MS.
[32]Gonzalez FE.A quadratic cumulative production model for the material balance of an abnormally pressured gas reservoir[D].Texas:Texas A&M University,2003.
[33]夏静,谢兴礼,冀光,罗凯.异常高压有水气藏物质平衡方程推导及应用[J].石油学报,2007,28(3):96-99.Xia Jing,Xie Xingli,Ji Guang&Luo Kai.Derivation and application of material balance equation for over-pressured gas reservoir with aquifer[J].Acta Petrolei Sinica,2007,28(3):96-99.
[34]Aguilera R.Effect of fracture compressibility on gas-in-place calculations of stress-sensitive naturally fractured reservoirs[J]//SPEReservoir Evaluation&Engineering,2008,11(2):307-310.