Flow-based Grid Coarsening for Transport Simulations

Hauge, Vera Louise; Lie, Knut–Andreas; Natvig, Jostein R.

doi:10.3997/2214-4609.20145016

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…The objective of our work is to develop and test the accuracy and efficiency of a novel multiscale method to bridge the gap in gridblock sizes between typical geological models (fine scale  centimeters to decimeters in the vertical direction and meters to tens of meters in horizontal directions) and dynamic models (coarse scale  meters to tens of meters in the vertical direction and tens of meters to hundreds of meters in horizontal directions). Recently, several authors proposed multiscale methods for the subgrid transport (Aarnes and Efendiev 2008;Zhou et al 2009;Hauge et al 2010). Conventional approaches to solve such multiscale problems have limitations with respect to spatial and temporal resolution.…”

Section: Introductionmentioning

confidence: 99%

A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs

Alpak

Pal

Lie

2011

SPE Reservoir Simulation Symposium

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A robust and efficient simulation technique is developed based on the extension of the mimetic finite volume method to multiscale hierarchical hexahedral (corner-point) grids via use of the multiscale mixed finite element method. The implementation of the mimetic subgrid discretization method is compact and generic for a large class of grids, and thereby, suitable for discretizations of reservoir models with complex geologic architecture. Flow equations are solved on a coarse grid where basis functions with subgrid resolution accurately account for subscale variations from an underlying fine-scale geomodel. The method relies on the construction of approximate velocity spaces that are adaptive to the local properties of the differential operator. A variant of the method for computing velocity basis functions is developed that utilizes an adaptive local-global algorithm to compute multiscale velocity basis functions by capturing the principal characteristics of global flow. Both local and local-global methods generate subgrid-scale velocity fields that reproduce the impact of fine-scale stratigraphic architecture. By using multiscale basis functions to discretize the flow equations on a coarse grid, one can retain the efficiency of an upscaling method, while at the same time produce detailed and conservative velocity fields on the underlying fine grid. The accuracy and efficacy of the multiscale method is compared to that of fine-scale models and of coarse-scale models with no subgrid treatment for several two-phase flow scenarios. Numerical experiments involving two-phase incompressible flow and transport phenomena are carried out on high-resolution corner-point grids that explicitly represent example stratigraphic architectures found in real-life shallow marine and turbidite reservoirs. The multiscale method is several times faster than the direct solution of the fine-scale problem and yields more accurate solutions than coarse-scale modeling techniques that resort to explicit effective properties. The accuracy of the multiscale simulation method with adaptive local-global velocity basis functions are compared to that of the local velocity basis functions. The multiscale simulation results are consistently more accurate when the local-global method is employed for computing the velocity basis functions.

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Section: Introductionmentioning

confidence: 99%

A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs

Alpak

Pal

Lie

2011

SPE Reservoir Simulation Symposium

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A Mass-Conservative Sequential Implicit Multiscale Method for Isothermal Equation-of-State Compositional Problems

Møyner

2018

SPE Journal

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Summary Compositional simulation is necessary for a wide variety of reservoir-simulation applications, and it is especially valuable for accurate modeling of near-miscible gas injection for enhanced oil recovery. Because the nonlinear behavior of gas injection is sensitive to the resolution of the simulation grid used, it is important to use a fine grid to accurately resolve the compositional and saturation gradients. Compositional simulation of highly detailed reservoir models entails the use of small timesteps and large, poorly conditioned linear systems. The high computational cost of solving such systems renders field-scale simulations practically unfeasible. The coupling of the flow and transport to the phase-equilibrium calculations adds to the challenge. This is especially the case for near-miscible gas injection, in which the phase state and the phase compositions are very strong functions of space and time. We present a multiscale solver for compositional displacements with three-phase fluid flow. The thermodynamic phase behavior is described by general nonlinear cubic equations of state (EOS). The fully implicit (FI) natural-variables formulation is used as the basis to derive a sequential implicit (SI) solution strategy, whereby the pressure field is decoupled from the multicomponent transport. The SI scheme is mass conservative without the need to iterate between the pressure and transport equations during the timestep. This conservation property allows the errors caused by fixing the total-velocity field between the pressure- and transport-updating steps to be represented as a volume error. The method computes approximate pressure solutions—within a prescribed residual tolerance—that yield conservative fluxes on the computational grid of interest (fine, coarse, or intermediate). We use basis functions computed using restricted smoothing to allow for generally unstructured grids. The new method is verified against existing research and commercial compositional simulators using a simple conceptual test case and also using more-complex cases represented on both unstructured and corner-point grids with strong heterogeneity, faults, and pinched-out and eroded cells. The SI method and the implementation described here represent the first demonstrated multiscale method applicable to general compositional problems with complexity relevant for industrial-reservoir simulation.

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A General Non-Uniform Coarsening and Upscaling Framework for Reduced-Order Modeling

Lie

Kedia

Skaflestad

et al. 2017

Day 1 Mon, February 20, 2017

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This paper presents a general framework for constructing effective reduced-order models from an existing high-fidelity reservoir model, irrespective of grid topology. We employ a flexible hierarchical grid coarsening strategy that is designed to preserve geologic features and structures in the underlying model such as environments of deposition and faults. The strategy supports selecting and combining coarsening methods that are targeted to the flow patterns in different parts of the reservoir. This includes, but is not limited to, explicit user-imposed boundaries, using efficient field-wide flow indicators, topological and geometric partitioning and methods for amalgamating and splitting clusters of cells. Collectively, these schemes enable an automatic strategy that separates a model into flow-dependent compartments that are respectively close to, far away from, or in between regions of sharp flow transients such as wells. These compartments may then be coarsened using different tailored techniques and target grid resolutions providing much more flexibility compared to traditional coarsening methods. We demonstrate that various techniques for flow-based transmissibility upscaling can be deployed on the resulting coarsened model to compute effective model properties. The hierarchical construction strategy allows efficient exploration of the geologic features of a reservoir that most impact flow patterns and well communication. The coarsened models are shown to be rank and trend accurate, enabling a more exhaustive sensitivity analysis if needed. We study the accuracy of the reduced-order model with a particular emphasis on the upscaled model's ability to capture effects of multiple phases in simulation runs compared to the full high-fidelity model.

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Flow-based Grid Coarsening for Transport Simulations

Cited by 3 publications

References 21 publications

A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs

A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs

A Mass-Conservative Sequential Implicit Multiscale Method for Isothermal Equation-of-State Compositional Problems

A General Non-Uniform Coarsening and Upscaling Framework for Reduced-Order Modeling

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