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Int. J. Numer. Anal. Mod., 6 (2009), pp. 375-388. |
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Well flow models for various numerical methods Zhangxin Chen 1, Youqian Zhang 2 1 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. Abstract
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 [17]. 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, 76T05Key words: Well models, petroleum reservoirs, aquifer remediation, finite difference, finite element, control volume finite element, mixed finite element, fluid flow, numerical experiments. Email: zhachen@ucalgary.ca, yzhang@smu.edu |