A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization

doi:10.1016/j.petrol.2018.01.083

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	A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization
	Liu WC(刘文超); Liu YW(刘曰武); Zhu WY ; Sun HD
发表期刊	JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
	2018-05-01
卷号	164 页码:400-416
ISSN	0920-4105
摘要	Previous deconvolution algorithms based on B-splines are much easier to be understood and programmed for academic researchers and engineers. However, due to the use of a linear regularization, their stability is weaker than that of the commonly used von Schroeter et al.' s deconvolution algorithm in which a nonlinear regularization is used; the linear regularization can make the deconvolution algorithms less tolerant to data errors. Good stability for the deconvolution algorithms is very important in order to make deconvolution as a viable tool for well-test analysis. In the paper, in order to improve the stability of the deconvolution algorithms based on B-splines, a nonlinear regularization by minimizing the curvature of pressure derivative response, as used in von Schroeter et al.' s algorithm, is appended instead of the linear regularization. And the corresponding nonlinear regularization equations are appropriately deduced. In particular, the improved algorithm is based on the Duhamel principle directly, and the complex transformation by the nonlinear z function, as used in von Schroeter et al.' s algorithm, is avoided; it does simplify the whole deconvolution process; moreover, the sensitivity matrix of an involved basic linear system from the measured pressure and rate data can also be solved directly by the piecewise analytical integration method, which can largely improve the deconvolution computation speed. Ultimately, in combination with the nonlinear regularization equations, a nonlinear least-squares problem is formulated for the stability-improved deconvolution algorithm based on B-splines. Besides, a constraint condition for tuning the parameter values of the B-spline base and an involved smooth factor is presented for restricting the nonlinear regularization process. Through a simulated case study, it is found that the nonlinear least-squares problem can be solved stably by the advanced Powell's Dog Leg method due to its great convergence ability and numerical stability; and the solution accuracy is also verified. Then the effects of the two parameters on the type curves of the deconvolution results are analyzed. And the effect of the error in the initial formation pressure on the type curves of the deconvolution results is also analyzed. Then a statement on how to perform the nonlinear regularization is presented specifically. Furthermore, through the study on two simulated cases with added data errors and an actual case, it is demonstrated that when the nonlinear regularization is appended, the stability of the deconvolution algorithm based on B-splines can be largely improved for mitigating the effect of data errors; besides, the stability-improved algorithm based on B-splines even exhibits higher stability than von Schroeter et al.' s algorithm that takes the same nonlinear regularization method, and the reason can be attributed to the superior properties of the representation of the wellbore pressure derivative 9to be deconvolved) by B-spline functions in the numerical stability of computations and the inherent smoothness. Through the test of some simulated cases, it is also concluded that the stability-improved algorithm based on B-splines by appending the nonlinear regularization still has a high-level computation speed, which is nearly twenty times more than that of von Schroeter et al.' s algorithm. It can be attributed to the more undetermined coefficients and the computational complexity resulted from the zfunction transformation in the formulation of von Schroeter et al.' s algorithm.
关键词	Deconvolution Nonlinear least-squares problem Duhamel principle Stability improvement Second-order B-spline functions
DOI	10.1016/j.petrol.2018.01.083
URL	查看原文
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:000426941000037
关键词[WOS]	WELL-TEST DATA ; PRESSURE-RATE DECONVOLUTION
WOS研究方向	Energy & Fuels ; Engineering, Petroleum
WOS类目	Energy & Fuels ; Engineering
项目资助者	Natural Science Foundation of China (NSFC) [51404232] ; National Science and Technology Major Projects [2011ZX05038003, 2011ZX05046-03] ; China Postdoctoral Science Foundation [2014M561074]
论文分区	一类
力学所作者排名	1
引用统计	被引频次：3[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/77926
专题	流固耦合系统力学重点实验室
作者单位	1.Univ Sci & Technol Beijing, Sch Civil & Resource Engn, Beijing 100083, Peoples R China 2.Chinese Acad Sci, Inst Mech, Beijing 100190, Peoples R China 3.PetroChina Res Inst Petr Explorat & Dev, Dept Gas Field Dev, Langfang 065007, Hebei, Peoples R China
推荐引用方式 GB/T 7714	Liu WC,Liu YW,Zhu WY,et al. A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization[J]. JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING,2018,164:400-416.
APA	刘文超,刘曰武,Zhu WY,&Sun HD.(2018).A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization.JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING,164,400-416.
MLA	刘文超,et al."A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization".JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 164(2018):400-416.

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