Fractures are often implicitly represented in models used to simulate flow in fractured porous media. This simplification results in smaller models that are computationally tractable. As computational power continues to increase, there has been growing interest in simulation methods that explicitly represent fractures. The embedded discrete fracture model (EDFM) is one such method. In EDFM, fracture and matrix grids are constructed independently. The grids are then coupled to each other via source/sink relations. This modeling approach makes EDFM versatile and easy to use. EDFM has been shown to be able to handle complex fracture networks. The grid construction process is also straightforward and requires minimal fine-tuning. Within academia and industry, EDFM has been used to study geothermal energy production, unconventional gas production, multiphase flow in fractured reservoirs, and enhanced oil recovery processes. In this chapter, the mathematical formulation of EDFM is introduced. We then demonstrate the usage of EDFM via three examples. The first example involves a simple fracture network containing only three fractures. The second involves upscaling a stochastically generated fracture network. Finally, a well test will be simulated in a publicly available data set sourced from the Jandaira carbonate formation in Brazil.@en

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.

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Flow modelling challenges in fractured reservoirs have led to the development of many simulation methods. It is often unclear which method should be employed. High-resolution discrete fracture and matrix (DFM) studies on small-scale representative models allow us to identify dominant physical processes influencing flow. We propose a workflow that utilizes DFM studies to characterize subsurface flow dynamics. The improved understanding facilitates the selection of an appropriate method for large-scale simulations. Validation of the workflow was performed via application on a gas reservoir represented using an embedded discrete fracture model, followed by the comparison of results obtained from hybrid and dual-porosity representations against fully explicit simulations. The comparisons ascertain that the high-resolution small-scale DFM studies lead to a more accurate upscaled model for full field simulations. Additionally, we find that hybrid implicit–explicit representations of fractures generally outperform pure continuum-based models.

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Naturally fractured reservoirs hold significant reserves but are highly heterogeneous and are challenging to simulate flow in. Dual Porosity (DP) methods, although widely used, require fine tuning using production data and thus lack predictive capability in green field applications. The Embedded Discrete Fracture Model (EDFM), which explicitly represents complex fracture network geometries at the cost of computational efficiency, is an excellent tool that can complement the DP method. Using EDFM, we study water coning phenomena in a green fractured Latin American gas field. We do this by simulating gas flow in a stochastically generated sector model representative of the field. EDFM simulations performed using different well rates revealed three possible flow regimes that the field may experience: stable flooding at low flow rates, coning with matrix production at moderate flow rates, and coning without matrix production at high flow rates. These results have implications in field development plans and can also be used for validating any DP models that may be used for full field simulations in the future. Through this study, we demonstrated how EDFM can be used, before any field production, to gain insights into the flow behaviour in a green field.

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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