低频振动对低渗油藏径向渗流影响的变参量Biot固结分析
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摘要
基于波动采油对低渗储层物性改善的动态过程,利用变参量的岩土固结模型分析弹性波对饱和渗流流体径向模型流固位移、孔隙压力等的影响规律。通过Laplace变换与迭代消去,得到拉氏变换下低渗开发油藏波动控制方程为变系数高阶微分方程;利用变系数向量拆分与矩阵求法,推导了波动采油作用下饱和单相流体径向(定流量或定压)开发储层的流固位移近似解。通过Matlab编程,算例分析了饱和水相介质和不同振动频率下饱和油相介质的渗流、物性变化。结果表明,低频波动采油技术可增加低渗开发储层孔压和渗流速度,文中基础参数下,存在最佳振动频率5~30 Hz使得增幅最大,作用范围可达60 m,径向模型Laplace变换–Durbin离散近似求解适用于波传播时间较小的情况。
The low-frequency vibration stimulation technology can improve the seepage of fluid in low-permeability reservoir, which is rather deeper than that of the regular geotechnical formation. Few researches on the mechanisms of low-frequency vibration on seepage in developing reservoir are available through Biot's consolidation analysis. Changes in the seepage rate, pore pressure and porosity in radial model under low-frequency vibration are thereby investigated. Through the Laplace transformation and iterative elimination, a four-order differential equation with non-linear coefficients is obtained. Then, vector splitting and matrix solution for the non-linear coefficients are done successively. Utilizing the boundary and initial conditions in actual developed reservoirs, the approximate displacements of fluid are derived. The displacements in two cases, constant boundary pressure or constant flow, are given. Based on the formula for rock properties in Yanchang oilfield, numerical analysis is carried out with Durbin inverse transform and Matlab programming. Two examples, as in the medium saturated with oil phase under different vibration frequencies and in the medium saturated with water phase, are given. The results show that the physical properties are improved obviously by the low-frequency vibration stimulation technology. There is an optimal frequency, 5~30 Hz under basic parameters, making the largest increase in porosity, permeability, pore pressure and seepage velocity. The action radius is up to sixty meters, which far exceeds that of high-frequency vibration treatment. The approximate calculation of Laplace-transform and Durbin-discrete in two-dimensional model is applicable to the wave propagation with short duration.
The low-frequency vibration stimulation technology can improve the seepage of fluid in low-permeability reservoir, which is rather deeper than that of the regular geotechnical formation. Few researches on the mechanisms of low-frequency vibration on seepage in developing reservoir are available through Biot's consolidation analysis. Changes in the seepage rate, pore pressure and porosity in radial model under low-frequency vibration are thereby investigated. Through the Laplace transformation and iterative elimination, a four-order differential equation with non-linear coefficients is obtained. Then, vector splitting and matrix solution for the non-linear coefficients are done successively. Utilizing the boundary and initial conditions in actual developed reservoirs, the approximate displacements of fluid are derived. The displacements in two cases, constant boundary pressure or constant flow, are given. Based on the formula for rock properties in Yanchang oilfield, numerical analysis is carried out with Durbin inverse transform and Matlab programming. Two examples, as in the medium saturated with oil phase under different vibration frequencies and in the medium saturated with water phase, are given. The results show that the physical properties are improved obviously by the low-frequency vibration stimulation technology. There is an optimal frequency, 5~30 Hz under basic parameters, making the largest increase in porosity, permeability, pore pressure and seepage velocity. The action radius is up to sixty meters, which far exceeds that of high-frequency vibration treatment. The approximate calculation of Laplace-transform and Durbin-discrete in two-dimensional model is applicable to the wave propagation with short duration.
引文
[1]HUH C.Improved oil recovery by seismic vibration:a preliminary assessment of possible mechanisms[C]//International Oil Conference and Exhibition in Mexico.Cancun:Society of Petroleum Engineers,2006:1–16.
[2]LIU J,PU C S,LIN C Y,et al.Adsorption of surfactant on sandstone under vibro-engery[J].Asian Journal of chemistry,2014,26(17):5383–5386.
[3]KOSTROV S A,WOODEN W O.Possible mechanisms and case studies for enhancement of oil recovery and production using in-situ seismic stimulation[C]//SPE Symposium on Improved Oil Recovery.Tulsa:Society of Petroleum Engineers,2008.
[4]VUONG A T,YOSHIHARA L,WALL W A.A general approach for modeling interacting flow through porous media under finite deformations[J].Computer Methods in Applied Mechanics&Engineering,2015,283:1240–1259.
[5]余俊,尚守平,黄娟,等.Biot动力固结方程简化模型在桩水平动力响应中适用性研究[J].岩土工程学报,2014,36(8):1558–1563.(YU Jun,SHANG Shou-ping,HUANG Juan,et al.Applicability of simplified model of Biot's dynamic consolidation equation to response of horizontal vibration of piles[J].Chinese Journal of Geotechnical Engineering,2014,36(8):1558–1563.(in Chinese))
[6]丁伯阳,童晓刚,陈军,等.排水状态下饱和土中基桩动力特性分析[J].岩土工程学报,2013,35(1):85–95.(DING Bo-yang,TONG Xiao-gang,CHEN Jun,et al.Dynamic properties of a single pile in saturated soil under drainage[J].Chinese Journal of Geotechnical Engineering,2013,35(1):85–95.(in Chinese))
[7]XIONG W,LEI Q,GAO S S,et al.Pseudo threshold pressure gradient to flow for low permeability reservoirs[J].Petroleum Exploration and Development,2009,36(2):232–236.
[8]贝君平.低渗透油藏大功率人工简谐波强化采油技术研究与应用[D].青岛:中国石油大学(华东),2009.(BEI Jun-ping.Research and application of enhanced oil recovery technology of artificial high-power monochromatic wave in low permeability reservoir[D].Qingdao:China University of petroleum(East China),2009.(in Chinese))
[9]周志军.低渗透储层流固耦合渗流理论及应用研究[D].大庆:大庆石油学院,2003.(ZHOU Zhi-jun.The theory and application research of fluid-solid coupling seepage flow in low permeability reservoir[D].Daqing:Northeast Petroleum University,2003.(in Chinese))
[10]刘静,蒲春生,郑黎明,等.低频振动对原油黏度影响的实验研究[J].科学技术与工程,2012,27:7061–7063,7067.(LIU Jing,PU Chun-sheng,ZHENG Li-ming,et al.Experiment research on effects of low frequency vibration wave for crude oil viscosity[J].Science Technology and Engineering,2012,27:7061–7063,7067.(in Chinese))
[11]马中高,周枫,赵群.鄂尔多斯盆地下石盒子组致密砂岩的弹性特征[J].石油学报,2011,32(6):1001–1006.(MA Zhong-gao,ZHOU Feng,ZHAO Qun.Elastic properties of tight sands in the lower Shihezi formation of Ordos basin[J].Acta Petrolei Sinica,2011,32(6):1001–1006.(in Chinese))
[12]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅰ.low-frequency range[J].Journal of the Acoustical Society of America,1956,28(2):168–178.
[13]ZIENKIEWICZ O C,CHANG C T,BETTESS P.Drained,undrained,consolidating and dynamic behaviour assumptions in soils[J].Géotechnique,1980,30(4):385–395.
[14]张学元.高阶变系数线性齐次微分方程内xveλx型解的探求[J].上海第二工业大学学报,2004,21(2):1–5.(ZHANG Xue-yuan.A research on the xveλx type solution of linear homogeneous differential equation of higher order with variable coefficients[J].Journal of Shanghai Second Polytechnic University,2004,21(2):1–5.(in Chinese))
[15]戴中林.一类非齐次微分方程特解的矩阵求法[J].高等数学研究,2013,16(3):25–26.(DAI Zhong-lin.Matrix method for special solutions of a class of nonhomogeneous differential equations[J].Studies in College Mathematics,2013,16(3):25–26.(in Chinese))
[16]秦爱芳,孙德安,谈永卫.非饱和土一维固结的半解析解[J].应用数学和力学,2010,31(2):199–209.(QIN Ai-fang,SUN De-an,TAN Yong-wei.Semi-analytical solution to one-dimensional consolidation in unsaturated soil[J].Applied Mathematics and Mechanics,2010,31(2):199–209.(in Chinese))
[17]郑忠文,秦文龙,肖曾利,等.低渗油藏渗流规律及水驱油特征实验研究[J].西安石油大学学报(自然科学版),2007,22(增刊1):77–79.(ZHENG Zhong-wen,QIN Wen-long,XIAO Zeng-li,et al.Experiment research on the seepage flow and water drive characteristics in low permeability reservoir[J].Journal of Xi'an Shiyou University(Natural Science Edition),2007,22(S1):77–79.(in Chinese))
[2]LIU J,PU C S,LIN C Y,et al.Adsorption of surfactant on sandstone under vibro-engery[J].Asian Journal of chemistry,2014,26(17):5383–5386.
[3]KOSTROV S A,WOODEN W O.Possible mechanisms and case studies for enhancement of oil recovery and production using in-situ seismic stimulation[C]//SPE Symposium on Improved Oil Recovery.Tulsa:Society of Petroleum Engineers,2008.
[4]VUONG A T,YOSHIHARA L,WALL W A.A general approach for modeling interacting flow through porous media under finite deformations[J].Computer Methods in Applied Mechanics&Engineering,2015,283:1240–1259.
[5]余俊,尚守平,黄娟,等.Biot动力固结方程简化模型在桩水平动力响应中适用性研究[J].岩土工程学报,2014,36(8):1558–1563.(YU Jun,SHANG Shou-ping,HUANG Juan,et al.Applicability of simplified model of Biot's dynamic consolidation equation to response of horizontal vibration of piles[J].Chinese Journal of Geotechnical Engineering,2014,36(8):1558–1563.(in Chinese))
[6]丁伯阳,童晓刚,陈军,等.排水状态下饱和土中基桩动力特性分析[J].岩土工程学报,2013,35(1):85–95.(DING Bo-yang,TONG Xiao-gang,CHEN Jun,et al.Dynamic properties of a single pile in saturated soil under drainage[J].Chinese Journal of Geotechnical Engineering,2013,35(1):85–95.(in Chinese))
[7]XIONG W,LEI Q,GAO S S,et al.Pseudo threshold pressure gradient to flow for low permeability reservoirs[J].Petroleum Exploration and Development,2009,36(2):232–236.
[8]贝君平.低渗透油藏大功率人工简谐波强化采油技术研究与应用[D].青岛:中国石油大学(华东),2009.(BEI Jun-ping.Research and application of enhanced oil recovery technology of artificial high-power monochromatic wave in low permeability reservoir[D].Qingdao:China University of petroleum(East China),2009.(in Chinese))
[9]周志军.低渗透储层流固耦合渗流理论及应用研究[D].大庆:大庆石油学院,2003.(ZHOU Zhi-jun.The theory and application research of fluid-solid coupling seepage flow in low permeability reservoir[D].Daqing:Northeast Petroleum University,2003.(in Chinese))
[10]刘静,蒲春生,郑黎明,等.低频振动对原油黏度影响的实验研究[J].科学技术与工程,2012,27:7061–7063,7067.(LIU Jing,PU Chun-sheng,ZHENG Li-ming,et al.Experiment research on effects of low frequency vibration wave for crude oil viscosity[J].Science Technology and Engineering,2012,27:7061–7063,7067.(in Chinese))
[11]马中高,周枫,赵群.鄂尔多斯盆地下石盒子组致密砂岩的弹性特征[J].石油学报,2011,32(6):1001–1006.(MA Zhong-gao,ZHOU Feng,ZHAO Qun.Elastic properties of tight sands in the lower Shihezi formation of Ordos basin[J].Acta Petrolei Sinica,2011,32(6):1001–1006.(in Chinese))
[12]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅰ.low-frequency range[J].Journal of the Acoustical Society of America,1956,28(2):168–178.
[13]ZIENKIEWICZ O C,CHANG C T,BETTESS P.Drained,undrained,consolidating and dynamic behaviour assumptions in soils[J].Géotechnique,1980,30(4):385–395.
[14]张学元.高阶变系数线性齐次微分方程内xveλx型解的探求[J].上海第二工业大学学报,2004,21(2):1–5.(ZHANG Xue-yuan.A research on the xveλx type solution of linear homogeneous differential equation of higher order with variable coefficients[J].Journal of Shanghai Second Polytechnic University,2004,21(2):1–5.(in Chinese))
[15]戴中林.一类非齐次微分方程特解的矩阵求法[J].高等数学研究,2013,16(3):25–26.(DAI Zhong-lin.Matrix method for special solutions of a class of nonhomogeneous differential equations[J].Studies in College Mathematics,2013,16(3):25–26.(in Chinese))
[16]秦爱芳,孙德安,谈永卫.非饱和土一维固结的半解析解[J].应用数学和力学,2010,31(2):199–209.(QIN Ai-fang,SUN De-an,TAN Yong-wei.Semi-analytical solution to one-dimensional consolidation in unsaturated soil[J].Applied Mathematics and Mechanics,2010,31(2):199–209.(in Chinese))
[17]郑忠文,秦文龙,肖曾利,等.低渗油藏渗流规律及水驱油特征实验研究[J].西安石油大学学报(自然科学版),2007,22(增刊1):77–79.(ZHENG Zhong-wen,QIN Wen-long,XIAO Zeng-li,et al.Experiment research on the seepage flow and water drive characteristics in low permeability reservoir[J].Journal of Xi'an Shiyou University(Natural Science Edition),2007,22(S1):77–79.(in Chinese))