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

Abstract

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.

Hierarchical simultaneous upscaling of porosity and permeability features using the bandwidth of kernel function and wavelet transformation in two dimensions: Application to the SPE-10 model

“…Because the basis of the upscaling is bandwidth, and the cells are merged together when the bandwidth allows, therefore, determining optimal bandwidth is crucial. In order to determine the optimal bandwidth, we have introduced various methods in previous studies [18][19][20]. One of these methods uses a defined number of cells for the final upscaled model before starting the upscaling process; this is an important distinguishing feature of this method compared to conventional upscaling methods in which the number of cells in the final upscaled model before starting the upscaling process is unknown.…”

“…Once the option is chosen, the standard procedure of upscaling is performed. Therefore, the main challenge in the upscaling process is how to upgrid the cells, otherwise the essence of any upscaling method is averaging [20]. If the upgridding done is based on cell variability, the coarse scale model will have the least difference with the fine scale model.…”

Accelerating multiscale simulation of complex geomodels by use of dynamically adapted basis functions

“…These partitions could be constructed by increasing the coarse-grid resolution near features of interest such as fractures and well paths, and/or by ensuring that block interfaces follow geological layers, fault surfaces, boundaries between different rock types, flow units, and depositional environments, etc. One effective way to generate such partitions is to agglomerate cells into blocks according to user-defined cell/face indicators and partitioning rules [13,12,24,23]. Several partition examples are shown in [25].…”

The use of flow diagnostics to rank model ensembles

“…Although using a simplified model means results are not quantitatively correct, the relative heterogeneity between models can still be estimated. Various types of flow diagnostics computed with finite-volume methods have been utilized to develop proxies that differentiate between macroscopic and microscopic sweep improvements resulting from polymer injection [13], to optimize waterflood performance [5,19,20], to validate rapid prototyping of reservoir models [9], in production data integration [23], to rank downscaled models in chemical EOR [35] or validate upscaling methods [16,22], and to cluster [36] or initialize [3] data-driven models, to mention a few applications.…”