Modeling Hydraulically Fractured Shale Wells Using the Fast Marching Method with Local Grid Refinements LGRs and Embedded Discrete Fracture Model EDFM

2019 ◽  
Author(s):  
Xu Xue ◽  
Changdong Yang ◽  
Tsubasa Onishi ◽  
Michael J. King ◽  
Akhil Datta-Gupta
Keyword(s):  
Fracture Model ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Discrete Fracture Model ◽  
Discrete Fracture ◽  
Local Grid ◽  
Marching Method

Modeling Hydraulically Fractured Shale Wells Using the Fast-Marching Method With Local Grid Refinements and an Embedded Discrete Fracture Model

SPE Journal ◽  
2019 ◽  
Vol 24 (06) ◽  
pp. 2590-2608 ◽  
Author(s):  
Xu Xue ◽  
Changdong Yang ◽  
Tsubasa Onishi ◽  
Michael J. King ◽  
Akhil Datta–Gupta
Keyword(s):  
Computational Efficiency ◽  
Flow Simulation ◽  
Fracture Model ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Discrete Fracture Model ◽  
Discretization Schemes ◽  
Discrete Fracture ◽  
Local Grid ◽  
Marching Method

Summary Recently, fast–marching–method (FMM) –based flow simulation has shown great promise for rapid modeling of unconventional oil and gas reservoirs. Currently, the application of FMM–based simulation has been limited to using tartan grids to model the hydraulic fractures (HFs). The use of tartan grids adversely impacts the computational efficiency, particularly for field–scale applications with hundreds of HFs. Our purpose in this paper is to extend FMM–based simulation to incorporate local grid refinements (LGRs) and an embedded discrete fracture model (EDFM) to simulate HFs with natural fractures, and to validate the accuracy and efficiency of the methodologies. The FMM–based simulation is extended to LGRs and EDFM. This requires novel gridding through the introduction of triangles (2D) and tetrahedrons (2.5D) to link the local and global domain and solution of the Eikonal equation in unstructured grids to compute the diffusive time of flight (DTOF). The FMM–based flow simulation reduces a 3D simulation to an equivalent 1D simulation using the DTOF as a spatial coordinate. The 1D simulation can be carried out using a standard finite–difference method, thus leading to orders of magnitude of savings in computation time compared with full 3D simulation for high–resolution models. First, we validate the accuracy and computational efficiency of the FMM–based simulation with LGRs by comparing them with tartan grids. The results show good agreement and the FMM–based simulation with LGRs shows significant improvement in computational efficiency. Then, we apply the FMM–based simulation with LGRs to the case of a multistage–hydraulic–fractured horizontal well with multiphase flow, to demonstrate the practical feasibility of our proposed approach. After that, we investigate various discretization schemes for the transition between the local and global domain in the FMM–based flow simulation. The results are used to identify optimal gridding schemes to maintain accuracy while improving computational efficiency. Finally, we demonstrate the workflow of the FMM–based simulation with EDFM, including grid generation; comparison with FMM with unstructured grid; and validation of the results. The FMM with EDFM can simulate arbitrary fracture patterns without simplification and shows good accuracy and efficiency. This is the first study to apply the FMM–based flow simulation with LGRs and EDFM. The three main contributions of the proposed methodology are (i) unique mesh–generation schemes to link fracture and matrix flow domains, (ii) DTOF calculations in locally refined grids, and (iii) sensitivity studies to identify optimal discretization schemes for the FMM–based simulation.

Multiple reflection and transmission phases in complex layered media using a multistage fast marching method

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1338-1350 ◽  
Author(s):  
N. Rawlinson ◽  
M. Sambridge
Keyword(s):  
Layered Media ◽  
Computational Domain ◽  
Grid Refinement ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Reflection And Transmission ◽  
Local Grid Refinement ◽  
Local Grid ◽  
Marching Method ◽  
Grid Based

Traditional grid‐based eikonal schemes for computing traveltimes are usually confined to obtaining first arrivals only. However, later arrivals can be numerous and of greater amplitude, making them a potentially valuable resource for practical applications such as seismic imaging. The aim of this paper is to introduce a grid‐based method for tracking multivalued wavefronts composed of any number of reflection and refraction branches in layered media. A finite‐difference eikonal solver known as the fast marching method (FMM) is used to propagate wavefronts from one interface to the next. By treating each layer that the wavefront enters as a separate computational domain, one obtains a refracted branch by reinitializing FMM in the adjacent layer and a reflected branch by reinitializing FMM in the incident layer. To improve accuracy, a local grid refinement scheme is used in the vicinity of the source where wavefront curvature is high. Several examples are presented which demonstrate the viability of the new method in highly complex layered media. Even in the presence of velocity variations as large as 8:1 and interfaces of high curvature, wavefronts composed of many reflection and transmission events are tracked rapidly and accurately. This is because the scheme retains the two desirable properties of a single‐stage FMM: computational speed and stability. Local grid refinement about the source also can increase accuracy by an order of magnitude with little increase in computational cost.

A Generalized Fast Marching Method on Unstructured Triangular Meshes

2013 ◽  
Vol 51 (6) ◽  
pp. 2999-3035 ◽  
Author(s):  
E. Carlini ◽  
M. Falcone ◽  
Ph. Hoch
Keyword(s):  
Fast Marching Method ◽  
Triangular Meshes ◽  
Fast Marching ◽  
Marching Method
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