基于连续拟稳定法的页岩气体积压裂水平井产量计算
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摘要
水平井体积压裂是开发页岩气藏的关键技术。体积压裂后,未改造区域的流动为受微纳米孔隙介质控制的非线性渗流,而改造区域的流动则是由微米级裂缝网络控制的达西渗流。综合考虑页岩气藏体积压裂后的多尺度流动、页岩气解吸附、扩散等特点,建立了耦合未改造区域和改造区域流动的稳态产量计算模型;在此基础上,首次运用连续拟稳定法,考虑压力波不稳定扩散,结合物质平衡方程建立了页岩储层体积压裂水平井非稳态产量计算方法,并对页岩气体积压裂水平井非稳态产量的影响因素进行了分析。结果表明:基于连续拟稳定法建立的产量预测模型具有求解过程简单、计算速度快,与数值模拟结果吻合程度高的特点;页岩气的解吸效应主要影响生产中后期的产量;随着体积压裂区半径、压裂区渗透率、扩散系数、朗格缪尔体积的增大,页岩气井产能增大,且增加幅度逐渐减小;朗格缪尔压力对产量的影响较小。该方法为页岩气体积压裂水平井非稳态产量的计算提供了理论依据。
The volume fractured horizontal well is the key technology for developing shale gas reservoirs.After the stimulated reservoir volume is fractured,the gas flow in matrix is non-linear seepage controlled by the nano-scale pores,while the seepage in stimulated region is converted into Darcy flow controlled by the micro-scale fracture network.In this paper,the steady productivity model of volume fractured horizontal well was firstly established by comprehensively considering the multi-scale flowing states,shale gas desorption and diffusion,which coupled flows in matrix and stimulated region.On this basis,for the first time,a transient productivity calculation model combined with the material balance equation was obtained with the continuous succession pseudo-steady state method(SPSS),which considered the unstable propagation of pressure wave.And the horizontal well productivity prediction and factors analysis was carried out by using the SPSS.The results show that the model has the advantages of simple process,fast calculation speed and high agreement with numerical simulation results.Furthermore,it can be found that the seepage of shale gas is an unstable process.The pressure wave first reaches the boundary of the stimulated region,and then propagates to the reservoir boundary.During the production process,the desorption effect of shale gas is the key factor affecting the middle and late stage production of gas wells.With the increase of the radius and permeability of the stimulated region,the diffusion coefficient and Langmuir volume,the productivity of shale gas wells would increase,while the increasing rate would decrease.And the effect of Langmuir pressure on productivity is less.It is concluded that this method provides a theoretical basis for the calculation of transient productivity of shale gas fractured horizontal wells.
The volume fractured horizontal well is the key technology for developing shale gas reservoirs.After the stimulated reservoir volume is fractured,the gas flow in matrix is non-linear seepage controlled by the nano-scale pores,while the seepage in stimulated region is converted into Darcy flow controlled by the micro-scale fracture network.In this paper,the steady productivity model of volume fractured horizontal well was firstly established by comprehensively considering the multi-scale flowing states,shale gas desorption and diffusion,which coupled flows in matrix and stimulated region.On this basis,for the first time,a transient productivity calculation model combined with the material balance equation was obtained with the continuous succession pseudo-steady state method(SPSS),which considered the unstable propagation of pressure wave.And the horizontal well productivity prediction and factors analysis was carried out by using the SPSS.The results show that the model has the advantages of simple process,fast calculation speed and high agreement with numerical simulation results.Furthermore,it can be found that the seepage of shale gas is an unstable process.The pressure wave first reaches the boundary of the stimulated region,and then propagates to the reservoir boundary.During the production process,the desorption effect of shale gas is the key factor affecting the middle and late stage production of gas wells.With the increase of the radius and permeability of the stimulated region,the diffusion coefficient and Langmuir volume,the productivity of shale gas wells would increase,while the increasing rate would decrease.And the effect of Langmuir pressure on productivity is less.It is concluded that this method provides a theoretical basis for the calculation of transient productivity of shale gas fractured horizontal wells.
引文
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[20]Chapuis R P,Aubertin M.Predicting the coefficient of permeability of soils using the Kozeny-Carman equation[J].Canadian Geotechnical,2003,40(3):616-628.
[21]Zhu Weiyao,Deng Jia,Yang Baohua,et al.Seepagemodel of shale gas reservoir and productivity analysis of fractured vertical wells[J].Mechanics and Engineering,2014,36(2):156-160.朱维耀,邓佳,杨宝华,等.页岩气致密储层渗流模型及压裂直井产能分析[J].力学与实践,2014,36(2):156-160.
[22]Civan F,Rai C S,Sondergeld C H.Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms[J].Transport in Porous Media,2011,86(3):925-944.
[23]Kuchuk F J.Radius of investigation for reserve estimation from pressure transient well tests[C]∥SPE Middle East Oil and Gas Show and Conference.Manama,Bahrain:Society of Petroleum Engineers,2009:1-21.
[24]Zhang Liehui,Chen Guo,Zhao Yulong,et al.A modified material balance equation for shale gas reservoirs and acalculation method of shale gas reservoirs[J].Natural Gas Industry,2013,33(12):66-70.张烈辉,陈果,赵玉龙,等.改进的页岩气藏物质平衡方程及储量计算方法[J].天然气工业,2013,33(12):66-70.
[25]Sang Y,Chen H,Yang S,et al.A new mathematical model considering adsorption and desorption process for productivity prediction of volume fractured horizontal wells in shale gas reservoirs[J].Journal of Natural Gas Science&Engineering,2014,19(7):228-236.
[26]Cheng Y.Pressure transient characteristics of hydraulically fractured horizontal shale gas wells[C]∥SPE Eastern Regional Meeting.Columbus,Ohio:Society of Petroleum Engineers,2011:1-10.
[2]Chen Zuo,Xue Chengjin,Jiang Tingxue,et al.Proposals for the application of fracturing by stimulated reservoir volume(SRV)in shale gas wells in China[J].Natural Gas Industry,2010,30(10):30-32.陈作,薛承瑾,蒋廷学,等.页岩气井体积压裂技术在我国的应用建议[J].天然气工业,2010,30(10):30-32.
[3]Deng J,Zhu W,Ma Q.A new seepage model for shale gas reservoir and productivity analysis of fractured well[J].Fuel,2014,124(15):232-240.
[4]Clarkson C R.Production data analysis of unconventional gas wells:Review of theory and best practices[J].International Journal of Coal Geology,2013,109(4):101-146.
[5]Gao Shusheng,Liu Huaxun,Ye Liyou,et al.A coupling model for gas diffusion and seepage in SRV section of shale gas reservoirs[J].Natural Gas Industry,2017,37(1):97-104.高树生,刘华勋,叶礼友,等.页岩气藏SRV区域气体扩散与渗流耦合模型[J].天然气工业,2017,37(01):97-104.
[6]Duan Yonggang,Wei Mingqiang,Li Jianqiu,et al.Shale gas seepage mechanism and fractured wells’production evaluation[J].Journal of Chongqing University:Natural Science Edition,2011,34(4):62-66.段永刚,魏明强,李建秋,等.页岩气藏渗流机理及压裂井产能评价[J].重庆大学学报,2011,34(4):62-66.
[7]Zhu Weiyao,Qi Qian.Study on the multi-scale nonlinear flow mechanism and model of shale gas[J].Scientia Sinica Technologica,2016,46(2):111-119.朱维耀,亓倩.页岩气多尺度复杂流动机理与模型研究[J].中国科学:技术科学,2016,46(2):111-119.
[8]Ozkan E,Raghavan R S,Apaydin O G.Modeling of fluid transfer from shale matrix to fracture network[C]∥SPE Annual Technical Conference and Exhibition.Florence,Italy:Society of Petroleum Engineers,2010:1-18.
[9]Swami V.Shale gas reservoir modeling:From nanopores to laboratory[C]∥SPE Annual Technical Conference and Exhibition.San Antonio,Texas:Society of Petroleum Engineers,2012:1-12.
[10]Zhang D,Zhang L,Zhao Y,et al.A composite model to analyze the decline performance of a multiple fractured horizontal well in shale reservoirs[J].Journal of Natural Gas Science&Engineering,2015,26:999-1010.
[11]Su Y,Zhang Q,Wang W,et al.Performance analysis of a composite dual-porosity model in multi-scale fractured shale reservoir[J].Journal of Natural Gas Science&Engineering,2015,26:1107-1118
[12]Zhao Y L,Zhang L H,Luo J X,et al.Performance of fractured horizontal well with stimulated reservoir volume in unconventional gas reservoir[J].Journal of Hydrology,2014,512(10):447-456.
[13]Shahamat M S,Mattar L,Aguilera R.A physics-based method for production data analysis of tight and shale petroleum reservoirs using succession of pseudo-steady states[J].SPE Reservoir Evaluation&Engineering,2015,18(4):508-522.
[14]Beskok A,Karniadakis G E.Report:A model for flows in channels,pipes,and ducts at micro and nanoscales[J].Microscale Thermophysical Engineering,1999,3(1):43-77.
[15]Soeder.Porosity and permeability of Eastern Devonian gas shale[J].SPE Formation Evaluation,1988,3(1):116-124.
[16]Javadpour F,Fisher D,Unsworth M.Nanoscale gas flow in shale gas ediments[J].Journal of Canadian Petroleum Technology,2007,46(10):55-61.
[17]Roy S,Raju R,Chuang H F,et al.Modeling gas flow through microchannels and nanopores[J].Journal of Applied Physics,2003,93(8):4870-4879.
[18]Nelson P H.Pore-throat sizes in sandstones,tight sandstones,and shales[J].AAPG Bulletin,2009,93(3):329-340.
[19]Faruk C.A triple-mechanism fractal model with hydraulic dispersion for gas permeation in tight reservoirs[C]∥SPE Petroleum Conference and Exhibition.Villahermosa,Mexico:Society of Petroleum Engineers,2002:1-6.
[20]Chapuis R P,Aubertin M.Predicting the coefficient of permeability of soils using the Kozeny-Carman equation[J].Canadian Geotechnical,2003,40(3):616-628.
[21]Zhu Weiyao,Deng Jia,Yang Baohua,et al.Seepagemodel of shale gas reservoir and productivity analysis of fractured vertical wells[J].Mechanics and Engineering,2014,36(2):156-160.朱维耀,邓佳,杨宝华,等.页岩气致密储层渗流模型及压裂直井产能分析[J].力学与实践,2014,36(2):156-160.
[22]Civan F,Rai C S,Sondergeld C H.Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms[J].Transport in Porous Media,2011,86(3):925-944.
[23]Kuchuk F J.Radius of investigation for reserve estimation from pressure transient well tests[C]∥SPE Middle East Oil and Gas Show and Conference.Manama,Bahrain:Society of Petroleum Engineers,2009:1-21.
[24]Zhang Liehui,Chen Guo,Zhao Yulong,et al.A modified material balance equation for shale gas reservoirs and acalculation method of shale gas reservoirs[J].Natural Gas Industry,2013,33(12):66-70.张烈辉,陈果,赵玉龙,等.改进的页岩气藏物质平衡方程及储量计算方法[J].天然气工业,2013,33(12):66-70.
[25]Sang Y,Chen H,Yang S,et al.A new mathematical model considering adsorption and desorption process for productivity prediction of volume fractured horizontal wells in shale gas reservoirs[J].Journal of Natural Gas Science&Engineering,2014,19(7):228-236.
[26]Cheng Y.Pressure transient characteristics of hydraulically fractured horizontal shale gas wells[C]∥SPE Eastern Regional Meeting.Columbus,Ohio:Society of Petroleum Engineers,2011:1-10.