Partitioning Thresholds in Hybrid Implicit-Explicit Representations of Naturally Fractured Reservoirs

Fractures can have variable effects on fluid flow in a porous rock. Moderately conductive fractures may enhance the rock's overall effective permeability, while highly conductive fractures may completely dominate fluid transport. Fluid flow modeling is important to quantify the impact of fractures on the performance of a reservoir. However, simulating fluid flow is computationally intensive due to the heterogeneities introduced by the fracture network. In this work, complex fracture patterns are simplified using hybrid implicit-explicit representations to yield a computationally tractable model. Hybrid modeling requires the selection of a partitioning size to group fractures by size. Small fractures are upscaled with the rock matrix; large fractures are explicitly represented. Our study shows that, given a naturally fractured reservoir, an upper limit exists for the partitioning size and that this threshold partitioning size can be determined without trial and error. Using artificial and realistic fracture patterns, we created hybrid models using different partitioning sizes and subjected them to pressure drawdowns. Simulated production rates were compared against reference results obtained from simulations on the original fracture patterns. Beyond a threshold partitioning size unique to each fracture pattern, hybrid model results deviate significantly from reference solutions. The threshold is identified from the relationship between upscaled permeabilities and partitioning sizes and corresponds to the point where the effective permeability of small fractures begins to increase rapidly. The permeability-size relationship is obtained using numerical flow-based upscaling. For uniformly distributed fractures with no abutment relationships, the effective medium theory is shown to generate accurate permeability-size relationships.