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.