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Modélisation numérique de modèles thermomécaniques polyphasiques, puits-milieux poreux

Abstract : With the increase of subsea wellheads and highly deviated wells, production log are less easy to be performed. By emerging new technologies such as optical fiber sensors, it is now possible to measure the temperature continuously in time and all along the well. We study here from a thermomechanical point of view two flow models, in order to interpret these temperature recordings.

We first couple a monophasic petroleum reservoir with a vertical wellbore, both written in a 2D axisymmetric form.
The reservoir model, assumed to be a multi-layered porous medium, is described by the Darcy-Forchheimer equation together with a non standard energy balance which includes viscous dissipation and compressibility effects. The wellbore model, which is a compressible fluid medium, is based on the Navier-Stokes equations coupled with an energy equation. Adequate transmission conditions are imposed at the interface and next dualized by Lagrange multipliers. This leads to a nonclassical mixed formulation for the coupled problem. Fluxes are discretized by means of conservative Raviart-Thomas elements. A technical analysis is carried out and the well-posedness of the time-discretized coupled problem, in both the continuous and the discrete cases, is established.

Then,we develop a multi-component multi-phase (oil, gas and water) flow for the reservoir. Taking into account the complexity of the model, we have chosen to extend an isothermal simulator GPRS (General Purpose Reservoir Simulator) by adding an energy equation and the corresponding thermodynamics. The governing equations are the mass conservation law for each hydrocarbon component coupled with extended Darcy's law for each phase, to which we add an exhaustive energy balance. The phase behavior is represented by an equation of state and by phase equilibrium relations. Finite volumes are employed for the space approximation and the nonlinear system is solved by Newton-Raphson's method.

Numerical tests including real cases validating the developed codes are presented.
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https://tel.archives-ouvertes.fr/tel-00361439
Contributor : Layal Lizaik <>
Submitted on : Monday, February 16, 2009 - 10:47:28 AM
Last modification on : Friday, January 15, 2021 - 9:24:19 AM
Long-term archiving on: : Wednesday, September 22, 2010 - 11:29:40 AM

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  • HAL Id : tel-00361439, version 2

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Layal Lizaik. Modélisation numérique de modèles thermomécaniques polyphasiques, puits-milieux poreux. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2008. Français. ⟨tel-00361439v2⟩

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