Implicit finite difference schemes for a linear model of well-reservoir coupling |
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Authors: | Cazenave T; Dickstein F |
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Institution: |
Y Analyse Numerique, URA CNRS 189, Universite Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05, France Email: cazenave@ccr.jussieu.fr W Instituto de Matematica, Universidade Federal do Rio de Janeiro, Caixo Postal 68530, 21944-970, Rio de Janeiro, R.J., Brazil Email: flavio@labma.ufrj.br
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Abstract: | Standard reservoir models usually consider wells as Dirac measuresover an interval length. Moreover, the well-reservoir couplingis taken into account under quite simplified assumptions. Mostrecently, however, attention has been drawn to the fact thatin some situations, such as those related to non-vertical wells,these simplifications do not allow us to model some relevantmechanisms of the coupled flow. Therefore, more complex alternativemodels have been proposed recently in the oil reservoir simulationliterature. A linearized version for the well-reservoir couplingcan be written, in an appropriate functional setting, in theform U'(t) + AU(t) = F(t). In this work we discuss implicitin time discretizations of this equation, of the form { Un+1h - Unh÷ +AhUn+1h = Fn=1h, U0h=U0.h We propose two different approximations, corresponding to first-and second-order spatial truncation errors, and we establishthe convergence of both approximations. |
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