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Mathematical Model of Spontaneous Potential Well-Logging and Its Numerical Solutions

  • Tatsien Li
  • Yongji Tan
  • Zhijie Cai
  • Wei Chen
  • Jingnong Wang

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Tatsien Li, Yongji Tan, Zhijie Cai, Wei Chen, Jingnong Wang
    Pages 1-5
  3. Tatsien Li, Yongji Tan, Zhijie Cai, Wei Chen, Jingnong Wang
    Pages 7-17
  4. Tatsien Li, Yongji Tan, Zhijie Cai, Wei Chen, Jingnong Wang
    Pages 19-31
  5. Tatsien Li, Yongji Tan, Zhijie Cai, Wei Chen, Jingnong Wang
    Pages 33-46
  6. Tatsien Li, Yongji Tan, Zhijie Cai, Wei Chen, Jingnong Wang
    Pages 47-67

About this book

Introduction

Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axi-symmetric situation the well-posedness of the corresponding mathematical model is proved and three efficient schemes of numerical solution are proposed, supported by a number of numerical examples to meet practical computation needs.

Keywords

Elliptic partial differential equations Numerical solution Sobolev space with fractional power Spontaneous potential well-logging

Authors and affiliations

  • Tatsien Li
    • 1
  • Yongji Tan
    • 2
  • Zhijie Cai
    • 3
  • Wei Chen
    • 4
  • Jingnong Wang
    • 5
  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople's Republic of China
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiPeople's Republic of China
  3. 3.School of Mathematical SciencesFudan UniversityShanghaiPeople's Republic of China
  4. 4.Shanghai Lixin University of CommerceShanghaiPeople's Republic of China
  5. 5.Technical CenterChina Petroleum Logging Co. LtdXi'anPeople's Republic of China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-41425-1
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-41424-4
  • Online ISBN 978-3-642-41425-1
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site