水平井筒与煤层气藏耦合的理论研究
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摘要
通过对煤层气藏赋存运移机理的深入研究,结合油藏中水平井筒与储层耦合的理论,建立了煤层气藏羽状水平井井筒与储层耦合的数学模型,并开发了相应的数值模拟软件。取得的主要成果如下:
(1)针对煤层气开采经历的解吸、扩散以及渗流等复杂流动过程,建立了双重介质煤层气藏三维、非平衡吸附、拟稳态条件下气—水两相耦合流动数学模型,利用IMPES方法进行数值求解,并将模拟结果与数值模拟软件CMG的结果进行对比,验证了模拟结果的可靠性;
(2)在考虑煤层气解吸吸附特性的基础上,结合油藏中水平井筒与储层耦合的理论,建立了煤层气藏水平井、羽状水平井井筒与储层耦合的数学模型,利用数值差分的方法进行求解,将直井、水平井和羽状水平井的模拟结果进行了对比,着重研究了羽状水平井中分支数与分支角度对产气量的影响;
(3)基于低渗透煤层气藏的特点,建立了考虑启动压力梯度项的双重介质煤层气储层水平井开采的数学模型,利用数值差分的方法进行求解,并着重研究了气相启动压力梯度对产气量的影响。
A pinnate horizontal well mathematics model was given in coalbed methane reservoir, considered the coupling of well bore and reservoir. The model based on the coupling theory of horizontal well in oil reservoir and the storage migration mechanisms of coalbed methane. Besides, a corresponding reservoir simulator was developed. The major study of this paper includes:
(1) A three-dimensional, dual-porosity, pseudo-steady, non-equilibrium sorption, two-phase mathematical model was built, included complex processes of desorption, diffusion and seepage during the exploiting procedure of coalbed methane. The model was numerical solved with IMPES method. And the result was compared with CMG software’s.
(2) Both horizontal well and pinnate horizontal well mathematics models were built in coalbed methane reservoir, considered the coupling of well bore and reservoir. The models were solved by numerical difference method. And the effect of simulation parameters to gas production was studied, with the emphasis on the branch number and angle.
(3) Based on the character of low permeability coalbed methane reservoir, a two-phase, 3-D flow model considering the starting pressure gradient of dual-porosity media was established. The model was solved by numerical difference method. And the effect of gas phase’s starting pressure gradient to gas and water production was studied.
(1)针对煤层气开采经历的解吸、扩散以及渗流等复杂流动过程,建立了双重介质煤层气藏三维、非平衡吸附、拟稳态条件下气—水两相耦合流动数学模型,利用IMPES方法进行数值求解,并将模拟结果与数值模拟软件CMG的结果进行对比,验证了模拟结果的可靠性;
(2)在考虑煤层气解吸吸附特性的基础上,结合油藏中水平井筒与储层耦合的理论,建立了煤层气藏水平井、羽状水平井井筒与储层耦合的数学模型,利用数值差分的方法进行求解,将直井、水平井和羽状水平井的模拟结果进行了对比,着重研究了羽状水平井中分支数与分支角度对产气量的影响;
(3)基于低渗透煤层气藏的特点,建立了考虑启动压力梯度项的双重介质煤层气储层水平井开采的数学模型,利用数值差分的方法进行求解,并着重研究了气相启动压力梯度对产气量的影响。
A pinnate horizontal well mathematics model was given in coalbed methane reservoir, considered the coupling of well bore and reservoir. The model based on the coupling theory of horizontal well in oil reservoir and the storage migration mechanisms of coalbed methane. Besides, a corresponding reservoir simulator was developed. The major study of this paper includes:
(1) A three-dimensional, dual-porosity, pseudo-steady, non-equilibrium sorption, two-phase mathematical model was built, included complex processes of desorption, diffusion and seepage during the exploiting procedure of coalbed methane. The model was numerical solved with IMPES method. And the result was compared with CMG software’s.
(2) Both horizontal well and pinnate horizontal well mathematics models were built in coalbed methane reservoir, considered the coupling of well bore and reservoir. The models were solved by numerical difference method. And the effect of simulation parameters to gas production was studied, with the emphasis on the branch number and angle.
(3) Based on the character of low permeability coalbed methane reservoir, a two-phase, 3-D flow model considering the starting pressure gradient of dual-porosity media was established. The model was solved by numerical difference method. And the effect of gas phase’s starting pressure gradient to gas and water production was studied.
引文
[1]周世宁.瓦斯在煤层中的流动机理[J].煤炭学报,1990,15(1):15-24
[2]郭勇义.煤层瓦斯一维流场流动规律的完全解[J].中国矿业大学学报,1984(2)
[3]谭学术等.矿井煤层真实瓦斯渗流方程的研究[J].重庆建筑工程学院学报.1986,(1):106-112
[4]余楚新,鲜学福等,煤层瓦斯流动理论及渗流控制方程的研究[J].重庆大学学报,1989(5)
[5]孙培德.瓦斯动力学模型的研究[J ].煤田地质与勘探,1993,21(1):32-40
[6] Sevenster P.G. Diffusion of Gas Through Coal[J]. Fuel. 1959,38:409-413
[7]杨其銮,王佑安.煤屑瓦斯扩散理论及其应用[J].煤炭学报,1986,11[3]
[8]杨其銮,王佑安.瓦斯球向流动的数学模拟[J].中国矿业学院学报,1987,3
[9] Saghafi, A. et al.煤层瓦斯流动的计算机模拟及其在预测瓦斯涌出和抽放瓦斯中的应用.第22届国际采矿安全会议论文集.北京:煤炭工业出版社,1987
[10] King G.R., Ertekin T., Schwerer F.C. Numerical Simulation of the Transient Behavior of Coal-Seam Degasification Wells[J].SPE Formation Evaluation(Apr,1986):165-183
[11] Spencer S.J., Somers M.L. et al. Numerical Simulation of Gas Drainage From Coal Seams[J].SPE Paper 16857
[12] Sawyer W.K. Paul G.M. et al. Development and Application of a 3D Coalbed Simulator[J].CIM/SPE Paper 90119
[13] Kohler T.E. Ertekin T. Modeling of Undersaturated Coal Seam Gas Reservoirs[J].SPE 29578
[14]李斌.煤层气非平衡吸附的数学模型和数值模拟[J].石油学报,1996,17(4):42-49
[15]冯文光,梅世昕,侯鸿斌等.煤层气藏三维数值模拟[J].矿物岩石,1999,19 (1):43-48
[16]彼特罗祥.煤矿沼气涌出[M] .宋世钊译.北京:煤炭工业出版社, 1983.
[17] Harpalani S. Gas flow through stressed coal[D]. Univ of California Berkeley Ph.D. thesis,1985
[18] Gawuga J. Flow of Gas Through Stressed Carboniferous Strata [D]. Univ. of Nottingham,Ph.D. Thesis, 1979
[19]赵阳升.煤体─瓦斯耦合数学模型及数值解法[J].岩石力学与工程学报,1994,13(3):229-239.
[20]梁冰,章梦涛,王泳嘉.煤层瓦斯渗流与煤体变形的耦合数学模型及数值解法[J].岩石力学与工程学报,1996 ,15(2):135-142
[21]赵庆波等.世界煤层气发展现状[M].北京:地质出版社,1998
[22] Airey E.M. Gas emission from broken coal: an experimental and theoretical investigation[J]. International Journal of Rock Mechanics and Mining sciences, 1968, 5:475-494.
[23] King G.R. and Ertekin T. M. A survey of mathematical models related to methane production from coal seams, Part I: Empirical & equilibrium sorption models[C]. Proceedings of the 1989 Coalbed Methane Symposium, the University of Alabama/ Tuscaloosa, April 17-20,1989: 125-138
[24] Price H.S., McCulloch R.C. et al. A computer model study of methane migration in coalbeds[C]. The Canadian Mining and Metallurgical Bulletin, 1973,66(737): 103-112
[25] Bumb A.C, McKee C.R. Gas-well testing in the presence of desorption for coalbed methane and Devonian shale[R].SPE15227,l986
[26] Pavone A.M. and Schwerer F.C. Development of coal gas production simulators and mathematical models for well test strategies[R]. Final Report under GRI Contract Number 5081-321-0457,April,1984
[27] Ertekin T. and King G.R. Development of coal gas production simulators and mathematical models for well test strategies. Topical report under GRI contract number 5081-321-0457, July, 1983
[28] King GR. And Ertekin T. M. A Survey of Mathematical Models Related to Methane Production from Coal Seams, Part II: Non-Equilibrium Sorption Models, proceedings of the 1989 Coal bed Methane Symposium, the University of Alabama/Puscaloosa, April 17-20, 1989:139-153
[29] King G R, Ertekin T M. State-of-the-art modeling for unconventional gas recovery, Part II: Recent developments (1989—1994).Paper SPE29575
[30] Seidle J.P.,Arri L.E. Use of Conventional Reservoir Models for Coalbed Methane Simulation. CIM/SPE Paper 90118
[31] Gas Research Institute. A guide to coalbed methane reservoir engineering[R]. GRI一94/0397
[32] Scott Reeves. Advanced Reservoir Modeling In Desorption-Controlled Reservoirs. SPE Paper 71090
[33] ICF Lewin Energy. Coalbed methane reservoir modeling [R].Short Course for GRI, 1987
[34] Paul G.W, Sawyer W.K, Dean R H. Validation of 3D coalbed simulators[C].Paper SPE20733
[35] COMETPC 3D User’s Guide. Advanced Resources International, Inc. January 1994
[36] User’s guide for SABRETM and COALGASTM petroleum reservoir simulators. S. A. Holditch & Associates, Inc. Oct, 1993
[37] Advanced Resources International COMET http://www.adv-res.com/ comet.htm
[38] Thakur, P.C. Poundstone, W.N. Horizontal Drilling technology for Advance Degasification [J]. Mining Engineering, June, 1980, 676-80
[39] Ertekin, Sung Schwerer. Production Performance Analysis of Horizontal Drainage Wells for Degasification of Coal-Seams. SPE paper 15453
[40] Sarkar, P.S. Rajtar, J.M. Horizontal Well Transient Pressure Testing in Coalbed Reservoirs. Paper SPE26995
[41] Sarkar, P.S. Rajtar, J.M. Transient Well Testing Of Coalbed Methane Reservoirs with Horizontal Wells. Paper SPE27681
[42]何应付等.煤层气藏水平井渗流规律与压力动态分析[J].煤田地质与勘探. 2007, 35(1):41-45
[43] Dikken, B.J. Pressure Prop in Horizontal Well and Its Effect on Production Performance. JPT, Nov, 1990
[44] Penmatcha, V.R. Modeling of Horizontal with Pressure Drop in The Well, PhD thesis
[45] Ozkan. Performance of Horizontal Wells. PhD dissertation, U. of Tulsa. Tulsa, OK(1988)
[46] Ozkan et al. Effect of Conductivity on Horizontal Well Pressure Behavior. SPE24683,1992
[47] Ozkan et al. New Solution for Well-Test-Analysis Problem: Part1-Analytical Considerations. SPE Formation Evaluation, Sept 1991
[48] Ozkan et al. New Solution for Well-Test-Analysis Problem: Part2- ComputationalConsiderations and Applications. SPE Formation Evaluation, Sept 1991
[49]刘想平等.油层中渗流与水平井筒内流动的耦合模型[J].石油学报. 1999, 20(3):82-87
[50]刘想平等.水平井筒内与渗流耦合的流动压降计算模型[J].西南石油学院学报. 2000, 22(2):36-40
[51]段永刚等.井筒与油藏耦合条件下的水平井非稳态产能预测(I)-数学模型.西南石油学院学报. 2004,26(1):23-26
[52]王先彬.开发能源资源的思考与选择[J].科学通报,1999,5
[53] Langmuir I. The Adsorption of Gases on Plane Surfaces of Glass, Mica and Platinum[J].Journal of American Chemical Society., 40, 1361, 1918
[54] Ertekin T. and King G.R. Development of coal gas production simulators and mathematical models for well test strategies. Topical report under GRI contract number 5081-321-0457, July, 1983.
[55]孙茂远,黄盛初等.煤层气开发利用手册.北京:煤炭工业出版社,1998
[56] Gray I. Reservoir engineering in coal seams: Part 1-The physical process of gas storage and movement in coal seams. SPE Reservoir Engineering, Feb. 1987: 28-34.;
[57] Gray I. Reservoir engineering in coal seams: Part 2-Observations of gas movement in coal seams. SPE Reservoir Engineering, Feb. 1987: 28-34.;
[58] Edward D.T., Fred N.K. Diffusion of methane through coal. Fuel, Oct. 1973, 52:274-280.
[59]张力,何学秋等.煤吸附特性的研究[J].太原理工大学学报,2001,32 (4):449-451
[60] Smith D.M. and Williams F.L. Diffusional Effects in the Recovery of Methane from Coalbeds. SPE.J.(Oct.1984)
[61] Ancell K.L., Lambert S. Analysis of the coalbed degasification on process at a seventeen well pattern in the Warrior basin of Alabama. SPE Paper 8971
[62] Young G B. C., McElhiney J. E,Paul GW. An analysis of Fruitland coalbed methane production, Cedar Hill field, Northern San Juan basin. SPE Paper 22913
[63] Kolesar J.E., Ertekin T, Obut S.T. The unsteady stature of sorption and diffusion phenomena in the micropore structure of coal: Part 1-Theory and mathematical formulation[J]. SPE. Form.Eval.,1990
[64] Abou-Kassem J.H., Mattar L, Dranchuk P.M. Computer calculations of compressibility ofnatural gas[J]. The Journal of Canadian Petroleum Technology, No. 5, Vol 29, Sept-Oct. 1990, 105-108
[65]徐燕东,李春兰,魏惠琴等.考虑入流角的水平井筒混合损失模型[J].西南石油学院学报, 2005 (5)
[2]郭勇义.煤层瓦斯一维流场流动规律的完全解[J].中国矿业大学学报,1984(2)
[3]谭学术等.矿井煤层真实瓦斯渗流方程的研究[J].重庆建筑工程学院学报.1986,(1):106-112
[4]余楚新,鲜学福等,煤层瓦斯流动理论及渗流控制方程的研究[J].重庆大学学报,1989(5)
[5]孙培德.瓦斯动力学模型的研究[J ].煤田地质与勘探,1993,21(1):32-40
[6] Sevenster P.G. Diffusion of Gas Through Coal[J]. Fuel. 1959,38:409-413
[7]杨其銮,王佑安.煤屑瓦斯扩散理论及其应用[J].煤炭学报,1986,11[3]
[8]杨其銮,王佑安.瓦斯球向流动的数学模拟[J].中国矿业学院学报,1987,3
[9] Saghafi, A. et al.煤层瓦斯流动的计算机模拟及其在预测瓦斯涌出和抽放瓦斯中的应用.第22届国际采矿安全会议论文集.北京:煤炭工业出版社,1987
[10] King G.R., Ertekin T., Schwerer F.C. Numerical Simulation of the Transient Behavior of Coal-Seam Degasification Wells[J].SPE Formation Evaluation(Apr,1986):165-183
[11] Spencer S.J., Somers M.L. et al. Numerical Simulation of Gas Drainage From Coal Seams[J].SPE Paper 16857
[12] Sawyer W.K. Paul G.M. et al. Development and Application of a 3D Coalbed Simulator[J].CIM/SPE Paper 90119
[13] Kohler T.E. Ertekin T. Modeling of Undersaturated Coal Seam Gas Reservoirs[J].SPE 29578
[14]李斌.煤层气非平衡吸附的数学模型和数值模拟[J].石油学报,1996,17(4):42-49
[15]冯文光,梅世昕,侯鸿斌等.煤层气藏三维数值模拟[J].矿物岩石,1999,19 (1):43-48
[16]彼特罗祥.煤矿沼气涌出[M] .宋世钊译.北京:煤炭工业出版社, 1983.
[17] Harpalani S. Gas flow through stressed coal[D]. Univ of California Berkeley Ph.D. thesis,1985
[18] Gawuga J. Flow of Gas Through Stressed Carboniferous Strata [D]. Univ. of Nottingham,Ph.D. Thesis, 1979
[19]赵阳升.煤体─瓦斯耦合数学模型及数值解法[J].岩石力学与工程学报,1994,13(3):229-239.
[20]梁冰,章梦涛,王泳嘉.煤层瓦斯渗流与煤体变形的耦合数学模型及数值解法[J].岩石力学与工程学报,1996 ,15(2):135-142
[21]赵庆波等.世界煤层气发展现状[M].北京:地质出版社,1998
[22] Airey E.M. Gas emission from broken coal: an experimental and theoretical investigation[J]. International Journal of Rock Mechanics and Mining sciences, 1968, 5:475-494.
[23] King G.R. and Ertekin T. M. A survey of mathematical models related to methane production from coal seams, Part I: Empirical & equilibrium sorption models[C]. Proceedings of the 1989 Coalbed Methane Symposium, the University of Alabama/ Tuscaloosa, April 17-20,1989: 125-138
[24] Price H.S., McCulloch R.C. et al. A computer model study of methane migration in coalbeds[C]. The Canadian Mining and Metallurgical Bulletin, 1973,66(737): 103-112
[25] Bumb A.C, McKee C.R. Gas-well testing in the presence of desorption for coalbed methane and Devonian shale[R].SPE15227,l986
[26] Pavone A.M. and Schwerer F.C. Development of coal gas production simulators and mathematical models for well test strategies[R]. Final Report under GRI Contract Number 5081-321-0457,April,1984
[27] Ertekin T. and King G.R. Development of coal gas production simulators and mathematical models for well test strategies. Topical report under GRI contract number 5081-321-0457, July, 1983
[28] King GR. And Ertekin T. M. A Survey of Mathematical Models Related to Methane Production from Coal Seams, Part II: Non-Equilibrium Sorption Models, proceedings of the 1989 Coal bed Methane Symposium, the University of Alabama/Puscaloosa, April 17-20, 1989:139-153
[29] King G R, Ertekin T M. State-of-the-art modeling for unconventional gas recovery, Part II: Recent developments (1989—1994).Paper SPE29575
[30] Seidle J.P.,Arri L.E. Use of Conventional Reservoir Models for Coalbed Methane Simulation. CIM/SPE Paper 90118
[31] Gas Research Institute. A guide to coalbed methane reservoir engineering[R]. GRI一94/0397
[32] Scott Reeves. Advanced Reservoir Modeling In Desorption-Controlled Reservoirs. SPE Paper 71090
[33] ICF Lewin Energy. Coalbed methane reservoir modeling [R].Short Course for GRI, 1987
[34] Paul G.W, Sawyer W.K, Dean R H. Validation of 3D coalbed simulators[C].Paper SPE20733
[35] COMETPC 3D User’s Guide. Advanced Resources International, Inc. January 1994
[36] User’s guide for SABRETM and COALGASTM petroleum reservoir simulators. S. A. Holditch & Associates, Inc. Oct, 1993
[37] Advanced Resources International COMET http://www.adv-res.com/ comet.htm
[38] Thakur, P.C. Poundstone, W.N. Horizontal Drilling technology for Advance Degasification [J]. Mining Engineering, June, 1980, 676-80
[39] Ertekin, Sung Schwerer. Production Performance Analysis of Horizontal Drainage Wells for Degasification of Coal-Seams. SPE paper 15453
[40] Sarkar, P.S. Rajtar, J.M. Horizontal Well Transient Pressure Testing in Coalbed Reservoirs. Paper SPE26995
[41] Sarkar, P.S. Rajtar, J.M. Transient Well Testing Of Coalbed Methane Reservoirs with Horizontal Wells. Paper SPE27681
[42]何应付等.煤层气藏水平井渗流规律与压力动态分析[J].煤田地质与勘探. 2007, 35(1):41-45
[43] Dikken, B.J. Pressure Prop in Horizontal Well and Its Effect on Production Performance. JPT, Nov, 1990
[44] Penmatcha, V.R. Modeling of Horizontal with Pressure Drop in The Well, PhD thesis
[45] Ozkan. Performance of Horizontal Wells. PhD dissertation, U. of Tulsa. Tulsa, OK(1988)
[46] Ozkan et al. Effect of Conductivity on Horizontal Well Pressure Behavior. SPE24683,1992
[47] Ozkan et al. New Solution for Well-Test-Analysis Problem: Part1-Analytical Considerations. SPE Formation Evaluation, Sept 1991
[48] Ozkan et al. New Solution for Well-Test-Analysis Problem: Part2- ComputationalConsiderations and Applications. SPE Formation Evaluation, Sept 1991
[49]刘想平等.油层中渗流与水平井筒内流动的耦合模型[J].石油学报. 1999, 20(3):82-87
[50]刘想平等.水平井筒内与渗流耦合的流动压降计算模型[J].西南石油学院学报. 2000, 22(2):36-40
[51]段永刚等.井筒与油藏耦合条件下的水平井非稳态产能预测(I)-数学模型.西南石油学院学报. 2004,26(1):23-26
[52]王先彬.开发能源资源的思考与选择[J].科学通报,1999,5
[53] Langmuir I. The Adsorption of Gases on Plane Surfaces of Glass, Mica and Platinum[J].Journal of American Chemical Society., 40, 1361, 1918
[54] Ertekin T. and King G.R. Development of coal gas production simulators and mathematical models for well test strategies. Topical report under GRI contract number 5081-321-0457, July, 1983.
[55]孙茂远,黄盛初等.煤层气开发利用手册.北京:煤炭工业出版社,1998
[56] Gray I. Reservoir engineering in coal seams: Part 1-The physical process of gas storage and movement in coal seams. SPE Reservoir Engineering, Feb. 1987: 28-34.;
[57] Gray I. Reservoir engineering in coal seams: Part 2-Observations of gas movement in coal seams. SPE Reservoir Engineering, Feb. 1987: 28-34.;
[58] Edward D.T., Fred N.K. Diffusion of methane through coal. Fuel, Oct. 1973, 52:274-280.
[59]张力,何学秋等.煤吸附特性的研究[J].太原理工大学学报,2001,32 (4):449-451
[60] Smith D.M. and Williams F.L. Diffusional Effects in the Recovery of Methane from Coalbeds. SPE.J.(Oct.1984)
[61] Ancell K.L., Lambert S. Analysis of the coalbed degasification on process at a seventeen well pattern in the Warrior basin of Alabama. SPE Paper 8971
[62] Young G B. C., McElhiney J. E,Paul GW. An analysis of Fruitland coalbed methane production, Cedar Hill field, Northern San Juan basin. SPE Paper 22913
[63] Kolesar J.E., Ertekin T, Obut S.T. The unsteady stature of sorption and diffusion phenomena in the micropore structure of coal: Part 1-Theory and mathematical formulation[J]. SPE. Form.Eval.,1990
[64] Abou-Kassem J.H., Mattar L, Dranchuk P.M. Computer calculations of compressibility ofnatural gas[J]. The Journal of Canadian Petroleum Technology, No. 5, Vol 29, Sept-Oct. 1990, 105-108
[65]徐燕东,李春兰,魏惠琴等.考虑入流角的水平井筒混合损失模型[J].西南石油学院学报, 2005 (5)