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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
Source PublicationJOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
2018-05-01
Volume164Pages:400-416
ISSN0920-4105
AbstractPrevious 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.
KeywordDeconvolution Nonlinear least-squares problem Duhamel principle Stability improvement Second-order B-spline functions
DOI10.1016/j.petrol.2018.01.083
URL查看原文
Indexed BySCI ; EI
Language英语
WOS IDWOS:000426941000037
WOS KeywordWELL-TEST DATA ; PRESSURE-RATE DECONVOLUTION
WOS Research AreaEnergy & Fuels ; Engineering, Petroleum
WOS SubjectEnergy & Fuels ; Engineering
Funding OrganizationNatural Science Foundation of China (NSFC) [51404232] ; National Science and Technology Major Projects [2011ZX05038003, 2011ZX05046-03] ; China Postdoctoral Science Foundation [2014M561074]
Classification一类
Ranking1
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Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/77926
Collection流固耦合系统力学重点实验室
Affiliation1.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
Recommended Citation
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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