Well flow models for various numerical methods
Zhangxin Chen 1, Youqian Zhang 21 Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W. Calgary, Alberta T2N 1N4, Canada; and Faculty of Science, Xi'an Jiaotong University, Xi¡Šan 710049, P. R. China.
2 Department of Mathematics, Box 750156, Southern Methodist University, Dallas, TX 75275-0156, USA.
Received by the editors August 30, 2008.
Numerical simulation of fluid flow and transport processes in the subsurface must account for the presence of wells. The pressure at a gridblock that contains a well is different from the average pressure in that block and different from the flowing bottom hole pressure for the well . Various finite difference well models have been developed to account for the difference. This paper presents a systematical derivation of well models for other numerical methods such as standard finite element, control volume finite element, and mixed finite element methods. Numerical results for a simple well example illustrating local grid refinement effects are given to validate these well models. The well models have particular applications to groundwater hydrology and petroleum reservoirs.AMS subject classifications: 65N30, 65N10, 76S05, 76T05
Key words: Well models, petroleum reservoirs, aquifer remediation, finite difference, finite element, control volume finite element, mixed finite element, fluid flow, numerical experiments.
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