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Mathematical Modelling and Numerical Simulation of the Well-reservoir Coupling Flow
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery, Sep 2014, Volume 2014, p.1 - 14
Abstract
Normally, when reservoirs specialist solve the multiphase flow of oil, gas and water in petroleum reservoirs the existing wells are not treated with the required details. Well trajectories are poorly defined with respect to the reservoir grid and the well models for capturing the large gradients near the well are too simplified, among other simplifications. It is also true that when well specialists solve the flow in the well the reservoir is considered as a constant pressure body. However, the modern technologies for increasing oil production is focused on the design of the well completion, the so-called “smart wells”. These are complex devices installed along the column which are able to control and creating flow patterns from the reservoir to the well, increasing the production. The design of such completions required the knowledge of the flow characteristics near the well, what is only possible by solving the coupled flow between well and reservoir.
This paper presents a mathematical model for the oil, gas and water in the reservoir and in the well, following by the development of a numerical scheme for solving the coupled flow using a finite volume method. Full permeability tensor is considered, taking into account heterogeneities and anisotropies, with compressible fluids and rock. The unknowns are the mass fractions of the components, opposed to the saturation formulation, which has the numerical difficulty in dealing with the disappearance of the gas phase. For the well a drift flux method is employed solving a 1D flow along the horizontal well using a very stable approach for the pressure-velocity coupling in the well. A Newton-like method is used for both, reservoir and well variables, but using a segregated strategy for the well/reservoir coupling. This has proven to be suitable due to the large differences in the spatial and time scales of the problems. Several three-dimensional coupled multiphase flow were solved, including near well analysis with fractures, demonstrating the capabilities of the method.