Naturally Fractured Reservoirs usually exhibit power law length distributions which do not possess any characteristic length scale, rendering the use of continuum methods difficult. This necessitates the adoption of hybrid models that represent a subset of the fractures as continua and the remainder as discrete fractures. However, the appropriate partitioning of fractures into these two subsets is an unresolved issue. In this regard, we propose a workflow which utilizes the Effective Medium Theory (EMT) by Sævik et al. (2013) as both an upscaling tool and a partitioning guide for single porosity hybrid modelling. EMT is used to find the largest nonpercolating subset of small fractures which will be upscaled into a single porosity background. The remaining fractures will be represented explicitly. This workflow allows reservoir engineers to systematically design an appropriate partitioning strategy for hybrid modelling. The paper explores this workflow via a two-part study. Part one validates the accuracy of EMT. Part two compares simulation results generated from different partitioning choices. The results show that the output of EMT matches that of numerical upscaling and that the workflow proposed leads to a hybrid model that is fit-for-purpose with a reduction in computational costs.@en

Multi-scale fractured reservoirs can be modelled effectively using hybrid methods that partition fractures into two subsets: one where fractures are upscaled and another one where fractures are represented explicitly. Existing partitioning methods are qualitative or empirical. In this paper, we present a novel and quantitative partitioning approach based on a single-porosity hybrid modelling workflow that uses numerical (Embedded Discrete Fracture Methods - EDFM) and semi-analytical (Effective Medium Theory - EMT) methods for fracture subset upscaling. We demonstrate this workflow using synthetic fracture data and realistic data sourced from outcrops of the Jandaira Carbonate Formation in the Potiguar Basin, Brazil. Fracture subset upscaling with EDFM and EMT using three datasets (two real, one synthetic) shows that the smallest, most numerous fractures are poorly connected. The ability of fracture subset upscaling to identify these fractures is essential to the hybrid modelling workflow. EDFM and EMT methods give nearly identical results, but EMT enables us to greatly accelerate the calculations. To validate our workflow, hybrid models were created with different partitioning sizes and compared against EDFM simulations where all fractures are represented explicitly. A single-phase pressure drawdown was used a test problem. The simulation results show that once the upscaled fractures begin to connect, deviations in flow response start to grow because single-porosity representations are inadequate to capture the separation of timescales between flow in a well-connected fracture subset and flow in the matrix. In some cases, the flow regime in the model were observed to change entirely. Overall, the results justify the proposed workflow as a means for systematic and quantitative construction of hybrid models.@en

Fractured reservoirs often exhibit multiple length scales and are best modelled using hybrid methods that partition fractures into a subset to be upscaled and another to be represented explicitly. To address the open question of how partitioning can be done, we propose a single porosity hybrid modelling workflow that makes use of fracture subset upscaling to identify poorly connected small fractures for upscaling. Fracture subset upscaling was performed numerically on three datasets (two real, one synthetic); results showed that the smallest, most numerous fractures are the least connected. Semi-analytical fracture subset upscaling was also performed for the synthetic dataset, showing that this process can be accelerated with the aid of analytical upscaling tools. To test the proposed workflow, hybrid models were created with different partitioning sizes and compared against full Discrete Fracture Networks (DFN) using single phase pressure drawdown as a test problem. It is observed that as the upscaled small fractures begin to connect, deviations in flow response will start to grow. In some cases, the flow regime in the model will change entirely. Overall, the results justify the proposed workflow as a promising means for systematic construction of hybrid models with minimal guesswork.@en