Coarse Grid Generation Research Articles

Multiscale simulation of highly heterogeneous subsurface flow with physically adaptive 3D unstructured grids

The multiscale finite volume framework is extended with physical-based grid adaptation (MSFV-GA) for three-dimensional fully unstructured grids. The MSFV method produces large errors for highly heterogeneous and anisotropic problems on standard coarse grids generated based on geometrical features. Adding constraints based on the fine-scale physical properties to construct coarse grids can increase the accuracy and robustness of the MSFV solutions. A novel and automated coarse grid generation strategy adaptable to the reservoir heterogeneity for 3D unstructured grids is presented. Adaptive coarse grids are generated based on local variations of fine scale permeability field. The proposed procedure is very flexible respect to the local physical and geometrical limitations in coarse blocks. Multiscale coarse grid adaptation notably improves the basis functions calculations. The performance of the MSFV-GA in handling challenging problems involving high media contrasts or impermeable shale layers is assessed. The results are very promising and show that the MSFV-GA can accurately approximate complex physics problems. The presented 3D unstructured procedure can notably improve the applicability of the multiscale finite volume method and provide a promising framework for the next generation of reservoir flow simulators.

An algebraic multiscale solver for the simulation of two-phase flow in heterogeneous and anisotropic porous media using general unstructured grids (AMS-U)

We introduce a new multiscale finite volume framework for the simulation of multi-phase flow in heterogenous and anisotropic porous media on quite general unstructured grids that enable geophysical grid defined properties to be used directly on a high definition grid.A novel background grid strategy is presented, where an auxiliary mesh aids the creation of multiscale primal and dual coarse grids. Due to the unstructured grid connectivity, the dual grids do not retain the natural structured grid decomposition. This may induce errors in the computed basis functions, and contribute to loss of mass conservation. A generalization of the Algebraic Multiscale Solver (AMS) is proposed to prevent the basis function induced leakage outside the support region enabling coupling with a Control Volume Distributed MultiPoint Flux Approximation (CVD-MPFA), ensuring consistency on non k-orthogonal unstructured grids.We present three different problems in which the accuracy of the framework is validated by comparing the multiscale solver with the direct simulation on the fine-scale. The results obtained show that the method can produce well resolved solutions for two-phase flow in highly heterogeneous and anisotropic porous media using general unstructured grids on all scales. As a consequence, the method captures the most important flow features that result on high-resolution geophysical models while providing suitable discretization for complex geological formations found in current petroleum reservoir problems.The novelty of this scheme involves three components which are combined to enable consistent multiscale simulation on unstructured grids: i) a new approach to primal and dual coarse grid generation, ii) a novel technique to prevent basis function induced leakage and iii) the coupling of the Algebraic Multiscale Solver (AMS) with a Multipoint Flux approximation with a Diamond Stencil (MPFA-D).

Development of adaptive coarse grid generation methods for fast fluid dynamics in simulating indoor airflow

The control of indoor air quality and thermal comfort requires faster-than-real-time simulations of air distribution. One approach to achieve such simulations is to use coarse grid. This study developed two adaptive coarse grid generation methods by analysing the grid-related truncation errors in the solution of the Navier–Stokes equations by fast fluid dynamics (FFD). Method 1 generates a grid that is coarser than that for a grid-independent solution but can still provide accurate FFD predictions. Method 2 generates a very coarse grid that provides acceptable FFD predictions. This study assessed the performance of the developed methods by using them to simulate three typical indoor airflows. The assessment showed that the coarse grid generated by Method 1 accelerated the FFD simulation by at least two to five times, with similar computational accuracy. The coarse grid generated by Method 2 provided faster-than-real-time FFD simulations for the cases tested in this study.

Generation of Voronoi Grid Based on Vorticity for Coarse-Scale Modeling of Flow in Heterogeneous Formations

We present a novel unstructured coarse grid generation technique based on vorticity for upscaling two-phase flow in permeable media. In the technique, the fineness of the gridblocks throughout the domain is determined by vorticity distribution such that where the larger is the vorticity at a region, the finer are the gridblocks at that region. Vorticity is obtained from single-phase flow on original fine grid, and is utilized to generate a background grid which stores spacing parameter, and is used to steer generation of triangular and finally Voronoi grids. This technique is applied to two channelized and heterogeneous models and two-phase flow simulations are performed on the generated coarse grids and, the results are compared with the ones of fine scale grid and uniformly gridded coarse models. The results show a close match of unstructured coarse grid flow results with those of fine grid, and substantial accuracy compared to uniformly gridded coarse grid model.

Performance of combined vorticity-based gridding and dual mesh method for gravity dominated reservoir flows

This paper presents a new combined method for accurate upscaling of two-phase displacements in highly heterogeneous reservoirs. The method has the capability to retain its high performance for various flow regimes, from viscous to gravity dominant displacements, without the need for further modifications and computational steps. Two different grids are incorporated for simulation. The grid on fine scale is used to recognize the complicated physics of flow which depends on dominated driving forces and their interaction with heterogeneity. However, to achieve a fast simulation, the global flow calculation is performed on the coarse scale grid using upscaled equivalent properties. The communication between two different scale grids is achieved by the dual mesh method (DMM) procedure. A simple geometric mean upscaling technique is used to assign effective permeability for coarse grid blocks which introduces a significant error due to homogenization. As a result, DMM is incorporated in conjunction with the vorticity-based coarse grid generation technique to limit the homogenization error. The distribution of the coarse grid is optimized by the vorticity preservation concept which attempts to preserve single-phase vorticity between fine and coarse grid models. To demonstrate accuracy and efficiency, the combined DDM–vorticity method is applied to highly heterogeneous systems in two dimensions with and without gravity. The results reveal that the flow regime has only a minor impact on the performance (accuracy and speed up) of the method.

Vorticity as a measure of heterogeneity for improving coarse grid generation

ABSTRACT This paper presents a novel coarse grid generation technique based on using vorticity as a measure of the impact of heterogeneity on flow. Vorticity is a maximum when the total flow is high and perpendicular to a large permeability gradient. Maps of vorticity were generated from single-phase flow simulations and used to generate coarse simulation grids from finely gridded geological models. The resulting grid was more refined in areas of high vorticity and coarser in areas of low vorticity. The method is first demonstrated on a simple five-layered model before being applied to three, 2D models of geologically realistic heterogeneity. The homogenized model generated from vorticity maps shows an improved match to the finely gridded simulation in all cases compared to simulation results using a regularly gridded homogenization.

Coarsening of three-dimensional structured and unstructured grids for subsurface flow

We present a generic, semi-automated algorithm for generating non-uniform coarse grids for modeling subsurface flow. The method is applicable to arbitrary grids and does not impose smoothness constraints on the coarse grid. One therefore avoids conventional smoothing procedures that are commonly used to ensure that the grids obtained with standard coarsening procedures are not too rough. The coarsening algorithm is very simple and essentially involves only two parameters that specify the level of coarsening. Consequently the algorithm allows the user to specify the simulation grid dynamically to fit available computer resources, and, e.g., use the original geomodel as input for flow simulations. This is of great importance since coarse grid-generation is normally the most time-consuming part of an upscaling phase, and therefore the main obstacle that has prevented simulation workflows with user-defined resolution. We apply the coarsening algorithm to a series of two-phase flow problems on both structured (Cartesian) and unstructured grids. The numerical results demonstrate that one consistently obtains significantly more accurate results using the proposed non-uniform coarsening strategy than with corresponding uniform coarse grids with roughly the same number of cells.

Vorticity-based coarse grid generation for upscaling two-phase displacements in porous media

Coarse grid generation from finely gridded geological model is a main step in reservoir simulation. Coarse grid generation algorithms aim at optimizing size, number and location of the grid blocks by identifying the important geological and flow features which control flow in porous media. By optimizing coarse grid structure we can improve accuracy of the coarse scale simulation results to reproduce fine grid behavior. A number of techniques have been proposed in the literature. We present a novel coarse grid generation procedure based on vorticity preservation between fine and coarse grids. In the procedure, the coarse grid mesh tries to capture variations in both permeability and fluid velocity using a single physical quantity — “vorticity” which is extracted from single-phase flow simulation. One essential element in the procedure is that the improved coarse grid (ICG) has minimum single-phase vorticity error with respect to the fine grid vorticity. Our numerical investigations on modeling two-phase flow demonstrate that the ICG represents fine grid flow behavior very closely. In addition, our analyses show that the use of single-phase vorticity has only a minor impact on the ICG generation, and its performance is not affected by two-phase flow parameters such as mobility ratio.

Overview: Reservoir Simulation and Visualization (June 2006)

In last year's overview of Reservoir Simulation and Visualization, the focus was on technology designed to handle the ever-increasing volumes of data that are readily available for use by reservoir engineers. This trend has continued and has resulted in some extremely innovative adaptations of technology toward reservoir management. Large volumes of data produce large models, which in turn produce large amounts of simulation results. This large volume of simulation results is difficult to analyze by conventional means. Significant improvements have been made by extending the methods of analysis of reservoir-simulation results to use the senses of hearing and touch, in addition to sight, to better understand the mechanisms at work in large full-field models. Research has been done with methods of artificial intelligence to predict reservoir performance, such as the training of neural networks. It is essential that research continues in these innovative areas as the industry strives to maximize production to meet market demands. On the traditional front, important research has continued in the area of grid coarsening and scaleup to reduce model sizes to more-manageable levels. Significant contributions have been made by both industry and academia, with improved methods for selecting layers for grouping and with new algorithms for including additional reservoir flow characteristics in the scaleup calculations. As computing power continues to increase, the inclusion of compositional fluids and geomechanical effects in full-field reservoir models is becoming more feasible. Workflows continue to be invaluable to reservoir management. With the ambitious goal of simulating the geological model, significant work remains to enable seamless transition of geological models through to numerical simulation. As the industry continues to move closer to this goal, we will also move closer to the ultimate goal of managing risk and uncertainty better. Ongoing work to provide the tools to understand both the input and the output of these large models will largely determine the success of this endeavor. Reservoir Simulation and Visualization additional reading available at the SPE eLibrary: www.spe.org SPE 96410 "Reservoir Simulation and Reserves Classifications—Guidelines for Reviewing Model History Matches To Help Bridge the Gap Between Evaluators and Simulation Specialists," by D. Rietz, SPE, Ryder Scott Co., et al. SPE 94319 "Improved Coarse-Grid Generation Using Vorticity," by H. Mahani, SPE, Imperial College London, et al. SPE 97155 "How To Approximate Effects of Geomechanics in Conventional Reservoir Simulation," by A.T. Settari, SPE, U. of Calgary, et al. SPE 96416 "Tuning an Equation of State—The Critical Importance of Correctly Grouping Composition Into Pseudocomponents," by A.A. Al-Meshari, SPE, Saudi Aramco, et al.

On Multigrid for Overlapping Grids

The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Other important features include optimizations for Cartesian component grids, the use of over-relaxed red-black smoothers, and the generation of coarse grid operators through Galerkin averaging. Numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for Dirichlet, Neumann, and mixed boundary conditions. A comparison to Krylov-based solvers shows that the multigrid solver can be much faster and require significantly less memory.