Abstract
A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed. The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
CLONTS M. D., RAMEY H. J. Pressure transient analysis for wells with horizontal drainholes[C]. SPE 15116. Oakland, California, USA, 1986, 215–230.
OZKAN E. Analysis of horizontal-well responses: Contemporary vs. conventional[J]. SPE Reservoir Evaluation and Engineering, 2001, 4(4): 260–269.
OGUNSANYA B. O. A physically consistent solution for describing the transient response of hydraulically fractured and horizontal wells[D]. Ph. D. Thesis, Lubbock, Texas, USA: Texas Tech University, 2005.
OGUNSANYA B. O., OETAMA T. P. and LEA J. F. et al. A coupled model for analyzing transient pressure behavior of horizontal drainholes[C]. SPE 94331. Oklahoma City, Oklahoma, USA, 2005, 1–14.
OZKAN E. Comparison of fractured horizontal-well performance in conventional and unconventional reservoirs[C]. SPE 121290. San Jose, California, USA, 2009, 1–16.
OZKAN E., BROWN M. and RAGHAVAN R. et al. Comparison of fractured-horizontal-well performance in tight sand and shale reservoirs[J]. SPE Reservoir Evaluation and Engineering, 2011, 14(2): 248–259.
BROWN M., OZKAN E. and RAGHAVAN R. et al. Practical solutions for pressure transient responses of fractured horizontal wells in unconventional reservoirs[J]. SPE Reservoir Evaluation and Engineering, 2011, 14(6): 663–676.
LIANG Bin, LI Min and ZENG Fanhua et al. Study on the analytical solution of mathematical model for the tight gas reservoir about start-up gradient[J]. Fault-Block Oil and Gas Field, 2004, 11(6): 31–34 (in Chinese).
LIU Qi-guo, YANG Xu-ming and WEI Hong-mei et al. Study of well-test model of low permeability’s dual-pore media with flowing boundary in oil and gas[J]. Journal of Southwest Petroleum Institute, 2004, 26(5): 30–33 (in Chinese).
ZHANG Yun, WANG Zi-sheng and YAO Jun et al. Study and application of pressure transient of naturally fractured reservoirs with stree-sensitive and start pressure grade[J]. Journal of Hydrodynamics, Ser. A, 2007, 22(3): 332–337 (in Chinese).
FENG Guo-qing, LIU Qi-guo and SHI Guang-zhi et al. An unsteady seepage flow model considering kickoff pressure gradient for low-permeability gas reservoirs[J]. Petroleum Exploration and Development, 2008, 35(4): 457–461 (in Chinese).
CHENG Lin-song, REN Sheng-li and LIAN Pei-qing. Well test analysis on low velocity and non-Darcy flow in dual-porosity reservoir with dynamic boundary[J]. Chinese Journal of Computational Mechanics, 2011, 28(6): 879–883 (in Chinese).
ZHANG Xue-yuan. The resolvent method of solving second order variable coefficient linear non-homogeneous differential equation[J]. Journal of Shanghai Second Polytechnic University, 2004, (1): 1–7 (in Chinese).
ZHANG Llie-hui, GUO Jing-jing and LIU Qi-guo. A new well test model for a two-zone linear composite reservoir with varied thicknesses[J]. Journal of Hydrodynamics, 2010, 22(6): 804–809.
GUO J., ZHANG L. and WANG H. et al. Pressure transient analysis for multi-stage fractured horizontal wells in shale gas reservoirs[J]. Transport in Porous Media, 2012, 93(3): 635–653.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Science Fund for Distinguished Young Scholars of China (Grant No. 51125019), the National Key Basic Research and Development Program of China (973 Program, Grant No. 2011CB201005).
Biograophy: GUO Jing-jing (1986-), Female, Ph. D. Candidate
Rights and permissions
About this article
Cite this article
Guo, Jj., Zhang, S., Zhang, Lh. et al. Well Testing Analysis for Horizontal Well With Consideration of Threshold Pressure Gradient in Tight Gas Reservoirs. J Hydrodyn 24, 561–568 (2012). https://doi.org/10.1016/S1001-6058(11)60278-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1001-6058(11)60278-3