Computing Pressure Front Propagation Using the Diffusive Time of Flight in Structured and Unstructured Grid Systems Via the Fast Marching Method

2020 ◽  
Author(s):  
Chen Hongquan ◽  
Onishi Tsubasa ◽  
Park Jaeyoung ◽  
Datta-Gupta Akhil
Keyword(s):  
Unstructured Grid ◽  
Time Of Flight ◽  
Front Propagation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Grid Systems ◽  
Marching Method ◽  
Diffusive Time

Computing Pressure Front Propagation Using the Diffusive-Time-of-Flight in Structured and Unstructured Grid Systems via the Fast-Marching Method

SPE Journal ◽  
2021 ◽  
pp. 1-21
Author(s):  
Hongquan Chen ◽  
Tsubasa Onishi ◽  
Jaeyoung Park ◽  
Akhil Datta-Gupta
Keyword(s):  
Finite Difference ◽  
Analytical Solutions ◽  
Eikonal Equation ◽  
Front Propagation ◽  
Fast Marching Method ◽  
Fast Marching ◽  
Reservoir Properties ◽  
Grid Systems ◽  
Marching Method ◽  
Diffusive Time

Summary Diffusive-time-of-flight (DTOF), representing the travel time of pressure front propagation, has found many applications in unconventional reservoir performance analysis. The computation of DTOF typically involves upwind finite difference of the Eikonal equation and solution using the fast-marching method (FMM). However, the application of the finite difference-based FMM to irregular grid systems remains a challenge. In this paper, we present a novel and robust method for solving the Eikonal equation using finite volume discretization and the FMM. The implementation is first validated with analytical solutions using isotropic and anisotropic models with homogeneous reservoir properties. Consistent DTOF distributions are obtained between the proposed approach and the analytical solutions. Next, the implementation is applied to unconventional reservoirs with hydraulic and natural fractures. Our approach relies on cell volumes and connections (transmissibilities) rather than the grid geometry, and thus can be easily applied to complex grid systems. For illustrative purposes, we present applications of the proposed method to embedded discrete fracture models (EDFMs), dual-porositydual-permeability models (DPDK), and unstructured perpendicular-bisectional (PEBI) grids with heterogeneous reservoir properties. Visualization of the DTOF provides flow diagnostics, such as evolution of the drainage volume of the wells and well interactions. The novelty of the proposed approach is its broad applicability to arbitrary grid systems and ease of implementation in commercial reservoir simulators. This makes the approach well-suited for field applications with complex grid geometry and complex well architecture.

A Comprehensive Reservoir Simulator for Unconventional Reservoirs That Is Based on the Fast Marching Method and Diffusive Time of Flight

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2276-2288 ◽  
Author(s):  
Yusuke Fujita ◽  
Akhil Datta-Gupta ◽  
Michael J. King
Keyword(s):  
Time Of Flight ◽  
Unconventional Reservoirs ◽  
Hydraulic Fractures ◽  
Fast Marching Method ◽  
Simulation Approach ◽  
Fast Marching ◽  
Drainage Volume ◽  
Marching Method ◽  
Diffusive Time

Summary Modeling of fluid flow in unconventional reservoirs requires accurate characterization of complex flow mechanisms because of the interactions between reservoir rock, microfractures, and hydraulic fractures. The pore-size distribution in shale and tight sand reservoirs typically ranges from nanometers to micrometers, resulting in ultralow permeabilities. In such extremely low-permeability reservoirs, desorption and diffusive processes play important roles in addition to heterogeneity-driven convective flows. For modeling shale and tight oil and gas reservoirs, we can compute the well-drainage volume efficiently with a fast marching method (FMM) and by introducing the concept of “diffusive time of flight” (DTOF). Our proposed simulation approach consists of two decoupled steps—drainage-volume calculation and numerical simulation with DTOF as a spatial coordinate. We first calculate the reservoir drainage volume and the DTOF with the FMM, and then the numerical simulation is conducted along the 1D DTOF coordinate. The approach is analogous to streamline modeling whereby a multidimensional simulation is decoupled to a series of 1D simulations resulting in substantial savings in computation time for high-resolution simulation. However, instead of a “convective time of flight” (CTOF), a DTOF is introduced to model the pressure-front propagation. For modeling physical processes, we propose triple continua whereby the reservoir is divided into three different domains: microscale pores (hydraulic fractures and microfractures), nanoscale pores (nanoporous networks), and organic matter. The hydraulic fractures/microfractures primarily contribute to the well production, and are affected by rock compaction. The nanoporous networks contain adsorbed gas molecules, and gas flows into fractures by convection and Knudsen diffusion processes. The organic matter acts as the source of gas. Our simulation approach enables high-resolution flow characterization of unconventional reservoirs because of its efficiency and versatility. We demonstrate the power and utility of our approach with synthetic and field examples.

Development and Application of Fast Simulation Based on the PSS Pressure as a Spatial Coordinate

2021 ◽  
Author(s):  
Kenta Nakajima ◽  
Michael King
Keyword(s):  
Eikonal Equation ◽  
Time Of Flight ◽  
Fast Marching Method ◽  
Reservoir Model ◽  
Fast Marching ◽  
Flow Equations ◽  
Spatial Coordinate ◽  
Single Well ◽  
Marching Method ◽  
Diffusive Time

Abstract Recent studies have shown the utility of the Fast Marching Method and the Diffusive Time of Flight for the rapid simulation and analysis of Unconventional reservoirs, where the time scale for pressure transients are long and field developments are dominated by single well performance. We show that similar fast simulation and multi-well modeling approaches can be developed utilizing the PSS pressure as a spatial coordinate, providing an extension to both Conventional and Unconventional reservoir analysis. We reformulate the multi-dimensional multi-phase flow equations using the PSS pressure drop as a spatial coordinate. Properties are obtained by coarsening and upscaling a fine scale 3D reservoir model, and are then used to obtain fast single well simulation models. We also develop new 1D solutions to the Eikonal equation that are aligned with the PSS discretization, which better represent superposition and finite sized boundary effects than the original 3D Eikonal equation. These solutions allow the use of superposition to extend the single well results to multiple wells. The new solutions to the Eikonal equation more accurately represent multi-fracture interference for a horizontal MTFW well, the effects of strong heterogeneity, and finite reservoir extent than those obtained by the Fast Marching Method. The new methodologies are validated against a series of increasingly heterogeneous synthetic examples, with vertical and horizontal wells. We find that the results are systematically more accurate than those based upon the Diffusive Time of Flight, especially as the wells are placed closer to the reservoir boundary or as heterogeneity increases. The approach is applied to the Brugge benchmark study. We consider the history matching stage of the study and utilize the multi-well fast modeling approach to determine the rank quality of the 100+ static realizations provided in the benchmark dataset against historical data. The multi-well calculation uses superposition to obtain a direct calculation of the interaction of the rates and pressures of the wells without the need to explicitly solve flow equations within the reservoir model. The ranked realizations are then compared against full field simulation to demonstrate the significant reduction in simulation cost and the corresponding ability to explore the subsurface uncertainty more extensively. We demonstrate two completely new methods for rapid reservoir analysis, based upon the use of the PSS pressure as a spatial coordinate. The first approach demonstrates the utility of rapid single well flow simulation, with improved accuracy compared to the use of the Diffusive Time of Flight. We are also able to reformulate and solve the Eikonal equation in these coordinates, giving a rapid analytic method of transient flow analysis for both single and multi-well modeling.

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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