Flow Simulation of Complex Fracture Systems With Unstructured Grids Using the Fast Marching Method

2017 ◽  
Author(s):  
Changdong Yang ◽  
Xu Xue ◽  
Michael J. King ◽  
Akhil Datta-Gupta
Keyword(s):  
Unstructured Grids ◽  
Flow Simulation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Complex Fracture ◽  
Fracture Systems ◽  
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.

Dynamic Ranking of Multiple Realizations by Use of the Fast-Marching Method

SPE Journal ◽  
2014 ◽  
Vol 19 (06) ◽  
pp. 1069-1082 ◽  
Author(s):  
Mohammad Sharifi ◽  
Mohan Kelkar ◽  
Asnul Bahar ◽  
Tormod Slettebo
Keyword(s):  
Flow Simulation ◽  
Finite Difference Approximation ◽  
Propagation Time ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Streamline Simulation ◽  
Dynamic Uncertainty ◽  
Geological Models ◽  
Marching Method ◽  
Dynamic Uncertainties

Summary One of the great challenges in reservoir modeling is to understand and quantify the dynamic uncertainties in geocellular models. Uncertainties in static parameters are easy to identify in geocellular models. Unfortunately, those models contain at least one to two orders of magnitude more gridblocks than typical simulation models. This means that, without significant upscaling, the dynamic uncertainties in these models cannot easily be assessed. Further, if we would like to select only a few geological models that can be carried forward for future performance predictions, we do not have an objective method of selecting the models that can properly capture the dynamic-uncertainty range. One possible solution is to use a faster simulation technique, such as streamline simulation. However, even streamline simulation requires solving a pressure equation at least once. For highly heterogeneous reservoir models with multimillion cells and in the presence of capillary effects or an expansion-dominated process, this can pose a challenge. If we use static permeability thresholds to determine the connected volume, it would not account for how tortuous the connection is between the connected gridblock and the well location. In this paper, we use the fast-marching method (FMM) as a computationally efficient method for calculating the pressure/front propagation time on the basis of reservoir properties. This method is based on solving the Eikonal equation by use of upwind finite-difference approximation. In this method, pressure/front location (radius of investigation) can be calculated as a function of time without running any flow simulation. We demonstrate that dynamically connected volume based on pressure-propagation time is a very good proxy for ultimate recovery from a well in the primary-depletion process. With a predetermined threshold propagation time, a large number of geocellular models can be ranked. FMM can be scaled almost linearly with the number of gridblocks in the model. Two main advantages of this ranking method compared with other methods are that this method determines dynamic connectivity in the reservoir and that it is computationally much more efficient. We demonstrate the validity of the method by comparing ranking of multiple geocellular realizations (on Cartesian grid with heterogeneous and anisotropic permeability) by use of FMM with ranking from flow simulation. This method will allow us to select the geological models that can truly capture the range of dynamic uncertainty very efficiently.

Mapping complex fracture systems as termite mounds—a fast-marching approach

2011 ◽  
Vol 30 (5) ◽  
pp. 496-501 ◽  
Author(s):  
Hao Guo ◽  
Kurt J. Marfurt ◽  
Jiang Shu
Keyword(s):  
Fast Marching ◽  
Termite Mounds ◽  
Complex Fracture ◽  
Fracture Systems

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

scholarly journals Tsunami wave propagation by voronoi diagram

2018 ◽  
Vol 7 (3) ◽  
pp. 1233
Author(s):  
V Yuvaraj ◽  
S Rajasekaran ◽  
D Nagarajan
Keyword(s):  
Wave Propagation ◽  
Voronoi Diagram ◽  
Tsunami Wave ◽  
Fast Marching Method ◽  
Coastal Regions ◽  
Fast Marching ◽  
Tsunami Waves ◽  
The Finite Difference Method ◽  
Run Up ◽  
Marching Method

Cellular automata is the model applied in very complicated situations and complex problems. It involves the Introduction of voronoi diagram in tsunami wave propagation with the help of a fast-marching method to find the spread of the tsunami waves in the coastal regions. In this study we have modelled and predicted the tsunami wave propagation using the finite difference method. This analytical method gives the horizontal and vertical layers of the wave run up and enables the calculation of reaching time.  

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