Constrained clustering approaches to identify hydraulic flow units in petroleum reservoirs

Hydraulic flow units (HFUs) are recognized as volumetric regions that favor the flow of reservoir fluids. Their determination is made possible through correlations between data that are transferred from miscroscale to reservoir scale by upscaling. However, the strong dependence on microscale parameters inherited by commonplace analytical methods based on flow indicators is still less tractable to achieve models having uniform continuity of HFUs at reservoir scale. This paper is intended to propose a class of partitioning algorithms to deal with the problem of identifying hydraulic flow units in petroleum reservoirs. As a result, a novel viewpoint inspired on constrained clusterwise linear regression is presented to describe the identification problem. We have studied the micro-to-macroscale correspondence through a mathematical isomorphism that maps the sample domain onto the reservoir domain by using the so called flow zone indicator (FZI) as underlying parameter. Each HFU is theoretically identified by a partition of FZI points that must lie on a straight line of unitary slope in a log-log plot of two quantities: porosity and reservoir quality index (RQI). By setting up constrained clustering approaches with different must-link hard constraints, we have found multiple HFUs directly from the dataset without resorting to usual conversion formulae. Pros and cons of each approach are discussed from analyses performed over the UNISIM-I-D dataset (a reservoir model for the Namorado oilfield, Campos Basin, Brazil), as with their feasibility to devise new data-driven workflows turned to reservoir modeling and characterization, especially at the interest of exploration and production oil industry upstream. Besides, a short overall comparison by taking a correlative flow zone indicator (namely, FZI*) as underlying parameter is appended to the text. We point out that an existent tradeoff between analytical and physical requirements is a limiting factor to properly identify hydraulic flow units at reservoir scale regardless the flow indicator. In particular, it turns out that algorithms that find highly correlated partitions indicate HFUs that lack of uniform continuity and are less physically meaningful. Oppositely, algorithms that produce less correlated partitions determine HFUs with satisfactory local continuity and compactness, being more physically acceptable. Additionally, we show that a inter-clustering process is recommended when selecting data points associated to representative volumes and local spots characterizing HFUs.