Hui, Mun-Hong (Chevron Energy Technology Company) | Dufour, Gaelle (Chevron Energy Technology Company) | Vitel, Sarah (Chevron Energy Technology Company) | Muron, Pierre (Chevron Energy Technology Company) | Tavakoli, Reza (Chevron Energy Technology Company) | Rousset, Matthieu (Chevron Energy Technology Company) | Rey, Alvaro (Chevron Energy Technology Company) | Mallison, Bradley (Chevron Energy Technology Company)
Traditionally, fractured reservoir simulations use Dual-Porosity, Dual-Permeability (DPDK) models that can idealize fractures and misrepresent connectivity. The Embedded Discrete Fracture Modeling (EDFM) approach improves flow predictions by integrating a realistic fracture network grid within a structured matrix grid. However, small fracture cells with high conductivity that pose a challenge for simulators can arise and ad hoc strategies to remove them can alter connectivity or fail for field-scale cases. We present a new gridding algorithm that controls the geometry and topology of the fracture network while enforcing a lower bound on the fracture cell sizes. It honors connectivity and systematically removes cells below a chosen fidelity factor. Furthermore, we implemented a flexible grid coarsening framework based on aggregation and flow-based transmissibility upscaling to convert EDFMs to various coarse representations for simulation speedup. Here, we consider pseudo-DPDK (pDPDK) models to evaluate potential DPDK inaccuracies and the impact of strictly honoring EDFM connectivity via Connected Component within Matrix (CCM) models. We combine these components into a practical workflow that can efficiently generate upscaled EDFMs from stochastic realizations of thousands of geologically realistic natural fractures for ensemble applications.
We first consider a simple waterflood example to illustrate our fracture upscaling to obtain coarse (pDPDK and CCM) models. The coarse simulation results show biases consistent with the underlying assumptions (e.g., pDPDK can over-connect fractures). The preservation of fracture connectivity via the CCM aggregation strategy provides better accuracy relative to the fine EDFM forecast while maintaining computational speedup. We then demonstrate the robustness of the proposed EDFM workflow for practical studies through application to an improved oil recovery (IOR) study for a fractured carbonate reservoir. Our automatable workflow enables quick screening of many possibilities since the generation of full-field grids (comprising almost a million cells) and their preprocessing for simulation completes in a few minutes per model. The EDFM simulations, which account for complicated multiphase physics, can be generally performed within hours while coarse simulations are about a few times faster. The comparison of ensemble fine and coarse simulation results shows that on average, a DPDK representation can lead to high upscaling errors in well oil and water production as well as breakthrough time while the use of a more advanced strategy like CCM provides greater accuracy. Finally, we illustrate the use of the Ensemble Smoother with Multiple Data Assimilation (ESMDA) approach to account for field measured data and provide an ensemble of history-matched models with calibrated properties.
Most existing upscaling methods attempt to evaluate effective permeabilities of coarse-scale gridblocks, so that the upscaled model locally reproduces the behavior of the fine-scale grid, under a set of boundary conditions. When applied to fractured reservoirs, this approach shows several drawbacks. First, it assumes the existence of a representative elementary volume (REV), which size is constrained by the practical needs for an efficient simulation. Yet, no REV exists for fractured systems which are characterized by a wide variety of fracture sizes. Second, the dynamic behavior of the model is unknown far from the applied boundary conditions. Third, this approach tends to underestimate the impact of steep pressure gradients that may occur between fracture and matrix media.
The presented method overcomes all three limitations by upscaling transmissibilities, so that the coarse-scale model preserves the same pressure response as the detailed geological model at a set of arbitrarily chosen observation points. A discrete fracture network and a corner-point grid are first jointly discretized using a dual approach (pipe network). Nodes of the pipe network represent either discrete fractures or matrix blocks. Pipes stand for matrix-to-matrix, fracture-to-fracture and matrix-to-fracture connections. Then, upgridding and upscaling are simultaneously performed, without imposing any boundary conditions: nodes are iteratively removed by applying electric simplifications (series, parallel, star-mesh transformations) until only the selected observation points remain. This process introduces new connections that may link nodes that were initially not connected, thus better modeling features such as super-K or large-scale fractures. This tends to convert a large sparse system into a smaller but fuller one; therefore parts of the network need to be lopped off before informing a flow simulator. Pipes holding the lowest transmissibilities are decimated and the remaining transmissibilities are updated accordingly in an optimization procedure. Flow simulation results obtained for several data sets on upscaled models are in good accordance with those obtained before upscaling, and show appreciable improvements compared to conventional structured local approaches.
Upscaling and flow prediction in fractured reservoirs are still challenging despite most of the developments carried out over the past few decades. Because fractures introduce very high heterogeneities in reservoirs, they must be represented in detail in geological models. Discrete Fracture Network (DFN) models have thus been developed to represent fractures as discrete objects (e.g. Koudina et al. , Karimi-Fard et al. , Macé ). However, due to variations in fracture size (from decimeters to hundreds of meters in length and millimeters to centimeter in aperture) and number (up to several millions), those discrete models cannot be used for direct reservoir flow simulation and therefore need to be upscaled.
The two conventional approaches for upscaling fractured reservoirs are single- or dual-continuum models (Berkowitz , Gilman ). Whereas single-continuum models represent effect of both matrix and fracture through one equivalent parameter, dual-continuum models (dual-porosity, dual-porosity/dual-permeability) consist in separating the flow occurring in fractures from the flow in matrix, with exchanges between both media modeled through the term called shape factor. This formulation, first proposed by Barenblatt and Zheltov , was then applied in petroleum industry by Warren and Root . It is an idealization of the fractured medium, where fractures are represented as regularly spaced parallel and orthogonal planes that separate matrix blocks. In the dual-porosity formulation, matrix acts as a source for fluid and flow occurs only in fractures. This limitation is remedied with dual-porosity/dual-permeability models. Today, the dual-medium model is the most widely used representation and has been extensively applied for large-scale simulations.