A well test analysis model of generalized tube flow and seepage coupling

LIN Jia’en,HE Hui,WANG Yihua

PDF(628 KB)
Petroleum Exploration and Development ›› 2021, Vol. 48 ›› Issue (4) : 923-934. DOI: 10.1016/S1876-3804(21)60077-0
RESEARCH PAPER

A well test analysis model of generalized tube flow and seepage coupling

  • LIN Jia’en1,2,*(),HE Hui2,3,WANG Yihua2,3
Author information +
History +

Abstract

"Generalized mobility" is used to realize the unification of tube flow and seepage in form and the unification of commonly used linear and nonlinear flow laws in form, which makes it possible to use the same form of motion equations to construct unified governing equations for reservoirs of different scales in different regions. Firstly, by defining the generalized mobility under different flow conditions, the basic equation governing fluid flow in reservoir coupling generalized tube flow and seepage is established. Secondly, two typical well test analysis models for coupling tube flow and seepage flow are given, namely, pipe-shaped composite reservoir model and partially open cylindrical reservoir model. The log-log pressure draw-down type-curve of composite pipe-shaped reservoir model can show characteristics of two sets of linear flow. The log-log pressure drawdown plot of partially opened cylindrical reservoir model can show the characteristics of spherical flow and linear flow, as well as spherical flow and radial flow. The pressure build-up derivative curves of the two models basically coincide with their respective pressure drawdown derivative curves in the early stage, pulling down features in the late stage, and the shorter the production time is, the earlier the pulling down feature appears. Finally, the practicability and reliability of the models presented in this paper are verified by three application examples.

Key words

generalized mobility / complex reservoir / multiphase flow / coupled tube flow and seepage / well test analysis

Cite this article

Download Citations
LIN Jia’en,HE Hui,WANG Yihua. A well test analysis model of generalized tube flow and seepage coupling. Petroleum Exploration and Development. 2021, 48(4): 923-934 https://doi.org/10.1016/S1876-3804(21)60077-0

References

[1] BRUCE G H, PEACEMAN D W, RACHFORD H H, et al. Calculation of unsteady-state gas flow through porous media. Journal of Petroleum Technology, 1953, 5(3):79-92.
[2] WARREN J E, ROOT P J. The behavior of naturally fractured reservoirs. SPE Journal, 1963, 3(3):245-255.
[3] CAMACHO V R, VÁSQUEZ C M, CASTREJÓN A R. Pressure-transient and decline-curve behavior in naturally fractured vuggy carbonate reservoirs. SPE 77689, 2005.
[4] GE Jiali, NING Zhengfu, LIU Yuetian, et al. Principles of modern reservoir percolation mechanics. Beijing: Petroleum Industry Press, 2001: 23- 35, 103-105.
[5] LIU Huapu, LIU Huiqing, WANG Jing. Nonlinear percolation law in low permeability fissure cave reservoir with fractal dimension. Chinese Journal of Computational Physics, 2018, 35(1):55-63.
[6] CHEN Li, WANG Yuan, CHEN Xiaojing. Study on high speed non-Darcy seepage characteristics of rough single fissure under tangential displacement. Water Resources and Power, 2019, 37(2):110-114.
[7] DAI Dexuan, WANG Shaowei. Linear stability analysis on thermo-bioconvection of gyrotactic microorganisms in a horizontal porous layer saturated by a power-law fluid. Applied Mathematics and Mechanics, 2019, 40(8):856-865.
[8] SONG Fuquan. Productivity analysis for low permeable reservoirs of media deformation. Special Oil and Gas Reservoirs, 2002, 9(4):33-35.
[9] KIYOUMARS R, SABA M A, DOMINIQUE M. Linear and non-linear approaches to predict the Darcy-Weisbach friction factor of overland flow using the extreme learning machine approach. International Journal of Sediment Research, 2018, 33(4):415-432.
[10] MU M, XU J. A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow. SIAM Journal on Numerical Analysis, 2007, 45(5):1801-1813.
[11] SUTERA S P, SKALAK R. The history of Poiseuille’s law. Annual Review of Fluid Mechanics, 1993, 25(1):1-20.
[12] DU Dianfa, LI Dongdong, SHI Dayou, et al. A study on heavy oil well test. Chinese Journal of Computational Physics, 2011, 28(3):385-396.
[13] ZHU Changyu, CHENG Shiqing, TANG Engao, et al. Well-test analyzing method with three-zone composite model for the polymer flooding. Petroleum Geology & Oilfield Development in Daqing, 2016, 35(3):106-110.
[14] YIN Hongjun, XING Cuiqiao, JI Bingyu, et al. Well test interpretation model for fracture-cavity reservoir with well developed large-scale caves. Special Oil & Gas Reservoirs, 2018, 25(5):84-88.
[15] POPOV P, QUIN G, BI L, et al. Multi scale methods for modeling fluid flow through naturally fractured carbonate karsts reservoirs. SPE 110778, 2007.
[16] LI Xiaoping, ZHAO Tianfeng. Inflow performance analysis on horizontal well bore with changing-quality-turbulence effection. Acta Petrolei Sinica, 2002, 23(6):63-67.
[17] YUAN Lin, LI Xiaoping, YUAN Gang. Law of gas-water horizontal wellbore pressure drop in low permeability gas reservoir. Chinese Journal of Hydrodynamics, 2015, 30(1):112-118.
[18] LI Yang, KANG Zhijiang, XUE Zhaojie, et al. Theories and practices of carbonate reservoirs development in China. Petroleum Exploration and Development, 2018, 45(4):669-678.
[19] COLLINS D, NGHIEM L, SHARMA R, et al. Field-scale simulation of horizontal wells. Journal of Canadian Petroleum Technology, 1992, 31(1):14-21.
[20] WU Shuhong, LIU Xiang’e, GUO Shangping, et al. A simplified model of flow in horizontal wellbore. Petroleum Exploration and Development, 1999, 26(4):64-65, 106.
[21] CHEN Chongxi, HU Litang. A review of the seepage-pipe coupling model and its application. Hydrogeology & Engineering Geology, 2008, 35(3):70-75.
[22] CHEN Chongxi. Groundwater flow model and simulation method in triple media of karstic tube-fissure-pore. Earth Science (Journal of China University of Geosciences), 1995, 20(4):361-366.
[23] ZHAO Yanlin, ZHANG Shengguo, WAN Wen, et al. Solid-fluid coupling-strength reduction method for karst cave water inrush before roadway based on flow state conversion theory. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(9):1852-1862.
[24] WAN Yizhao, LIU Yuewu. Three dimensional discrete-fracture-cavity numerical well test model for fractured-cavity reservoir. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6):1000-1008.
[25] DUAN Baojiang, CHANG Baohua, AN Weiguo, et al. Research on well test analysis of the dual cavity/fracture system in carbonate formations. Science Technology & Engineering, 2012, 12(25):6305-6309.
[26] WU Yonghui, CHENG Linsong, HUANG Shijun. Semi- analytical model for simulating fluid flow in naturally fractured reservoirs with non-homogeneous vugs and fractures. SPE 194023, 2018.
[27] POPOV P, EFENDIEV Y, QIN G. Multiscale modeling and simulations of flows in naturally fractured karst reservoirs. Communications in Computational Physics, 2009, 6(1):162-184.
[28] BRINKMAN H C. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research, 1949, 1(1):27-34.
[29] JIE H, JOHN E K, MOHAMED F. A unified finite difference model for the simulation of transient flow in naturally fractured carbonate karst reservoirs. SPE 173262, 2015.
[30] HUANG Zhaoqin, YAO Jun, LI Yajun, et al. Permeability analysis of fractured vuggy porous media based on homogenization theory. SCIENCE CHINA Technological Sciences, 2010, 53(3):839-847.
[31] LIN Jiaen, HE Hui, HAN Zhangying. Flow simulation and transient well analysis method based on generalized pipe flow seepage coupling: WO2020/224539( PCT/CN2020/088309). 2020 -11-12.
[32] RAGHAVAN R. Well-test analysis for multiphase flow. SPE 14098, 1989.
[33] MARHAENDRAJANA T, ARIADJI T, PERMADI A K. Performance prediction of a well under multiphase flow conditions. SPE 80534, 2003.
[34] ABATE J, WHITT W. A unified framework for numerically inverting Laplace transforms. INFORMS Journal on Computing, 2006, 18(4):408-421.
[35] GRINGARTEN A C, BOURDET D, LANDEL P A, et al. A comparison between different wellbore storage and skin type curves for early-time transient analysis. SPE 8205, 1979.
[36] KUCHUK F J. A new method for determination of reservoir pressure. SPE 56418, 1999.

Funding

Scientific Research Project of Key Laboratory of Shaanxi Provincial Department of Education(13JS090)
PDF(628 KB)

317

Accesses

0

Citation

Detail

Sections
Recommended

/