Analytical and Numerical Methods for Nonlinear Fluid Flow Problems in Porous Media

This book investigates in detail the mathematical methods and computation methods in efficient solution of some open nonlinear seepage flow problems involved in engineering problems. Developed engineering technologies and some relevant practical field applications are also provided. The introduced open nonlinear problems include nonlinear quadratic pressure gradient term problem, compressible gas seepage flow problem and low-velocity non-Darcy seepage flow problem. Studies on these nonlinear seepage flow problems have attracted engineers and scientists from various disciplines, such as geo-energy engineering, civil and environmental engineering, fluid mechanics, applied mathematics and computation. In particular, the book systematically establishes a fundamental theory for a strongly nonlinear problem of low-velocity non-Darcy seepage flow from a new perspective of moving boundary, while emphasizing the usage of mathematical linearization transformation methods and computational methods into the analytical and numerical solution of the strongly nonlinear partial differential equations. Sufficient knowledge of mathematics is always introduced ahead of model solution to assist readers. And the procedure of strict formula deduction in the model solution process is provided in detail. High-solution figures and tables from model solution are rich in the book. Therefore, it is very helpful for the readers to master the nonlinear model solution methods and engineering technologies. The book is intended for upper undergraduate students and graduate students who are interested in engineering technology, fluid mechanics and applied mathematics, researchers and engineers working on geo-energy science and engineering and field applications.

Dr. Wenchao Liu is an associate professor at University of Science and Technology Beijing (USTB) in China. In 2007, Dr. Wenchao Liu received a Bachelor’s degree in Information and Computing Science from China University of Petroleum (East China). In 2010, he received a Master’s degree in Mathematics from China University of Petroleum (East China). In 2013, Dr. Liu received a Doctorate in Petroleum Engineering from China University of Petroleum (East China). From 2012 to 2013, he studied at the University of Calgary in Canada with the support of the China National Study Abroad Fund. From 2014 to 2017, he worked as a post-doctor at Institute of Mechanics, Chinese Academy of Sciences. Since 2017, he has been engaged in teaching and scientific research at School of Civil and Resource Engineering at University of Science and Technology Beijing.

Dr. Yao Jun, born in March 1964, holds a Ph.D. and is a full professor at China University of Petroleum (East China). He is a member of the 6th and 7th Petroleum and Natural Gas Engineering Discipline Evaluation Groups of the Academic Degree Committee of the State Council of China, a member of the Department of Geology of Resources and Environment of the Science and Technology Advisory Committee of the China Ministry of Education, a co-initiator and an academic advisor of the International Carbonate Reservoir Research Center (ICCR), an academic member of the International Porous Media Association (Interpore) and also a founder/leader of the China region of Interpore. Dr. Yao has published 8 monographs (2 monographs in English), published over 500 papers, cited over 7527 times and authorized 38 invention patents and 12 software copyrights.

Dr. Weiyao Zhu is a full professor at University of Science and Technology Beijing (USTB) in China. He is a doctoral supervisor, head of the discipline of mechanics and director of the Institute of Applied Mechanics at USTB. He graduated from Daqing Petroleum Institute with a bachelor’s degree in oilfield development in 1983, a master’s degree in Lanzhou Seepage flow Mechanics Laboratory of Chinese Academy of Sciences in 1986 and a doctor’s degree in Chinese Academy of Sciences Seepage Fluid Mechanics Institute in 1990. He has successively worked in the Chinese Academy of Sciences, the Ministry of Petroleum of China and University of Science and Technology Beijing and has 35 years of experience in seepage flow mechanics theory and engineering technology research and development, and development scheme design.