Advanced discretizations for general grids with full permeability tensors

    Student thesis: Master's Thesis

    Abstract

    Petroleum reservoir simulation plays a critical role in the modern management of valuable hydrocarbon resources. Complex permeability tensors together with general nonorthogonal and unstructured grids pose great challenges to reservoir simulation. A class of Multipoint Flux Approximation (MPFA) finite volume methods have been proposed to meet the challenges and hence, removing the O(1) error introduced by Two-Point Flux Approximation (TPFA) for non K-orthogonal grids. MPFA, however, suffers from monotonicity issues and nonphysical oscillations can be present in the pressure solution for highly anisotropic media or large grid aspect ratios. In this thesis, we first investigate the effect of quadrature parameterization on monotonicity properties of the most common MPFA-O(η) method. Three indicators are designed to quantify the strength of the unphysical oscillations in the pressure solution for different η values. The results suggest that there may be no optimal value of η to improve monotonicity. An optimization problem with two objective functions was setup to determine the best quadrature points within MPFA-O interaction regions. The results, again, showed no improvement in terms of monotonicity properties and optimization of both objective functions failed to reduce the unphysical oscillations. Our findings seem to suggest that monotonicity properties of MPFA-O(η) method cannot be improved significantly by simply changing the locations of continuity points within interaction regions as some have suggested. We then present three novel finite volume, advanced discretization methods: Enhanced MPFA (eMPFA for short), pseudo TPFA (pTPFA for short), and Globally Coupled Pressure (GCP for short) method. All three methods ensure flux continuity and can handle general grids with full permeability tensors as MPFA methods do. Extensive numerical experiments are conducted to test the monotonicity and convergence properties of the three methods. The results show that for highly anisotropic media, eMPFA and pTPFA reduce the strength of unphysical oscillations by almost one order of magnitude compared to MPFA-O method for both homogeneous and discontinuous permeability fields. The GCP method, on the other hand, performs equally well for less challenging problems compared to MPFA-O and is more robust as the problem becomes more difficult. Besides, all three methods reproduce linear and piece-wise liner flow fields and have comparable convergence properties to MPFA-O method. This thesis represents an important step towards the goal of conducting accurate reservoir simulation on arbitrary grids populated by complex permeability tensors.
    Date of Award2016
    Original languageAmerican English
    SupervisorMohammed Al Kobaisi (Supervisor)

    Keywords

    • Applied sciences
    • Monotonicity
    • Multi-point flux approximation
    • Permeability tensor
    • Reservoir simulation
    • Petroleum engineering
    • 0765:Petroleum engineering

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