Pressure Dynamic Analysis of Vertical Well Flow with Partial Penetration Fractures

Abstract

Abstract: An actual physical model which shows partial penetration of heterogeneous reservoir formations was built and a three-dimensional mathematical model for instability of anisotropic rectangular reservoirs was built. The mathematical model takes impermeable top, combination of boundary conditions of constant pressure and top border and bottom border into consideration. By using dimensionless transformation, Laplace transformation, Fourier cosine transformation and variable separation methods analytical solution of Laplace domain was obtained. By using Stephenson numerical methods numerical solution pressure of real domain was obtained.Dynamic pressures were plotted and sensitivity analysis was carried out.Pressures obtained are basically consistent with numerical simulation, which shows reliability of the method. Sensitivity analysis shows that:Dynamic pressure curve can be divided into early linear flow, mid-radial flow, late spherical flow and boundary control flow.Fracture length mainly affects early linear flow. Permeability anisotropy mainly affects mid-radial flow.Degree of penetration in reservoir and fracture orientation mainly affect late spherical flow.Boundary conditions and reservoir border width mainly affect boundary control flow.Optimal degree of open shot, vertical permeability and other parameters can be obtained easily.It provides theoretical guidance for reservoir engineering analysis and fracturing process design.

Key words: partially penetrating, dynamic analysis, pressure, seepage, sensitivity analysis

CLC Number:

TE319

LIU Hailong. Pressure Dynamic Analysis of Vertical Well Flow with Partial Penetration Fractures[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(3): 322-332.

References

[1] WARREN J E, ROT P J.The behavior of naturally fractured reservoirs[J].SPE 1842,1963.
[2] MILLS M,CLEGG M W.A Study of behavior of partially penetrating wells[R].SPE, 2054,1969.
[3] RAMEY H J,GRINGARTEN A C.The use of source and Green's function in solving unsteady-flow problem in reservoir[J].SPE, 3818,1973.
[4] RAMEY H J, GRINGARTEN A C.Unsteady pressure distribution created by a single horizontal fracture,and partial penetration,or restricted entry[R].SPE, 3819,1974.
[5] BUHIDMAL M, RAGHAVEN R.Transient pressure of partially penetrating wells subject to bottom-water drive[R].SPE, 8143,1980.
[6] KUCHUK F J, KIRWAN P A.New skin and well bore storage type curves for partially penetrated wells[R].SPE l676,1987.
[7] HEGEMAN P, ABBASZAQDEH M.Pressure-transient analysis for a slanted well in a reservoir with vertical pressure support[J].SPEFE,1990:84-277.
[8] RAGHAVAN R, OZKAN E.New solutions for well-test:Analysis problems:Part 1 Analytical considerations[J].SPEFE,1991:76-359.
[9] ONUR M, SATMAN A.New type curve for analyzing the transition time data from naturally fractured reservoirs[R].SPE 25873,1993.
[10] BUI T D, MAMORA D D, LEE W J.Transient pressure analysis for partially penetrating wells in naturally fractured reservoirs[R].SPE 60289,2000.
[11] 冯文光,葛家理.单一介质、双重介质中非定常非达西低速渗流问题[J].石油勘探与开发,1985,12(1):56-62.
[12] 冯文光,葛家理.单一介质、双重介质非达西低速渗流的压力曲线动态特征[J].石油勘探与开发,1986,13(5):52-57.
[13] 同登科,葛家理.分形油藏非达西低速渗流模型及其解[J]. 大庆石油地质与开发,1996,23(3):18-23.
[14] 李凡华,刘慈群.含启动压力梯度的不定常渗流的压力动态分析[J].油气井测试,1997,6(1):1-4.
[15] 程时清,李功权,卢涛,等.双重介质油气藏低速非达西渗流试井有效井径数学模型及典型曲线[J].天然气工业,1997,17(2):35-37.
[16] 宋付权,刘慈群.变形介质油藏压力产量分析方法[J].石油勘探与开发,2000,27(1):57-59.
[17] 刘启国,李晓平,吴晓庆.用边界元法分析复杂形状油藏不稳定压力动态[J].西南石油学院学报,2001,23(2):40-43.
[18] 刘青山,段永刚,陈伟,等.用边界元法分析油藏不稳定渗流问题[J].大庆石油地质与开发,2004,23(2):36-37.
[19] 王建平,王晓冬,马世东.各向异性部分射开直井不稳定渗流理论研究[J].大庆石油地质与开发,2007,26(3):65-71.
[20] 程时清,徐论勋,张德超.低速非达达西渗流试井典型曲线拟合法[J].石油勘探与开发,1996,23(4):50-53.
[21] 冯曦,钟孚勋,低速非达西渗流试井模型的一种新的求解方法[J].油气井测试,1997,6(3):16-21.
[22] 王晓冬.渗流力学基础[M].北京:中国地质大学出版社,2006:65-67.
[23] STEHFEST H.Numerical inversion of Laplace transform[R].ACM,1970,20(1):47-48.