Compositional Modeling of Discrete-Fractured Media Without Transfer Functions by the Discontinuous Galerkin and Mixed Methods

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 341-352 ◽  
Author(s):  
Hussein Hoteit ◽  
Abbas Firoozabadi

Summary In a recent work, we introduced a numerical approach that combines the mixed-finite-element (MFE) and the discontinuous Galerkin (DG) methods for compositional modeling in homogeneous and heterogeneous porous media. In this work, we extend our numerical approach to 2D fractured media. We use the discrete-fracture model (crossflow equilibrium) to approximate the two-phase flow with mass transfer in fractured media. The discrete-fracture model is numerically superior to the single-porosity model and overcomes limitations of the dual-porosity model including the use of a shape factor. The MFE method is used to solve the pressure equation where the concept of total velocity is invoked. The DG method associated with a slope limiter is used to approximate the species-balance equations. The cell-based finite-volume schemes that are adapted to a discrete-fracture model have deficiency in computing the fracture/fracture fluxes across three and higher intersecting-fracture branches. In our work, the problem is solved definitively because of the MFE formulation. Several numerical examples in fractured media are presented to demonstrate the superiority of our approach to the classical finite-difference method. Introduction Compositional modeling in fractured media has broad applications in CO2, nitrogen, and hydrocarbon-gas injection, and recycling in gas condensate reservoirs. In addition to species transfer, the compressibility effects should be also considered for such applications. Heterogeneities and fractures add complexity to the fluid-flow modeling. Several conceptually different models have been proposed in the literature for the simulation of flow and transport in fractured porous media. The single-porosity approach uses an explicit computational representation for fractures (Ghorayeb and Firoozabadi 2000; Rivière et al. 2000). It allows the geological parameters to vary sharply between the matrix and the fractures. However, the high contrast and different length scales in the matrix and fractures make the approach unpractical because of the ill conditionality of the matrix appearing in the numerical computations (Ghorayeb and Firoozabadi 2000).The small control volumes in the fracture grids also add a severe restriction on the timestep size because of the Courant-Freidricks-Levy (CFL) condition if an explicit temporal scheme is used.

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 536-543
Author(s):  
Yueying Wang ◽  
Jun Yao ◽  
Shuaishi Fu ◽  
Aimin Lv ◽  
Zhixue Sun ◽  
...  

AbstractIsolated fractures usually exist in fractured media systems, where the capillary pressure in the fracture is lower than that of the matrix, causing the discrepancy in oil recoveries between fractured and non-fractured porous media. Experiments, analytical solutions and conventional simulation methods based on the continuum model approach are incompetent or insufficient in describing media containing isolated fractures. In this paper, the simulation of the counter-current imbibition in fractured media is based on the discrete-fracture model (DFM). The interlocking or arrangement of matrix and fracture system within the model resembles the traditional discrete fracture network model and the hybrid-mixed-finite-element method is employed to solve the associated equations. The Behbahani experimental data validates our simulation solution for consistency. The simulation results of the fractured media show that the isolated-fractures affect the imbibition in the matrix block. Moreover, the isolated fracture parameters such as fracture length and fracture location influence the trend of the recovery curves. Thus, the counter-current imbibition behavior of media with isolated fractures can be predicted using this method based on the discrete-fracture model.


Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3070
Author(s):  
Renjie Shao ◽  
Yuan Di ◽  
Dawei Wu ◽  
Yu-Shu Wu

The embedded discrete fracture model (EDFM), among different flow simulation models, achieves a good balance between efficiency and accuracy. In the EDFM, micro-scale fractures that cannot be characterized individually need to be homogenized into the matrix, which may bring anisotropy into the matrix. However, the simplified matrix–fracture fluid exchange assumption makes it difficult for EDFM to address the anisotropic flow. In this paper, an integrally embedded discrete fracture model (iEDFM) suitable for anisotropic formations is proposed. Structured mesh is employed for the anisotropic matrix, and the fracture element, which consists of a group of connected fractures, is integrally embedded in the matrix grid. An analytic pressure distribution is derived for the point source in anisotropic formation expressed by permeability tensor, and applied to the matrix–fracture transmissibility calculation. Two case studies were conducted and compared with the analytic solution or fine grid result to demonstrate the advantage and applicability of iEDFM to address anisotropic formation. In addition, a two-phase flow example with a reported dataset was studied to analyze the effect of the matrix anisotropy on the simulation result, which also showed the feasibility of iEDFM to address anisotropic formation with complex fracture networks.


2020 ◽  
Vol 140 ◽  
pp. 103602 ◽  
Author(s):  
Behshad Koohbor ◽  
Marwan Fahs ◽  
Hussein Hoteit ◽  
Joanna Doummar ◽  
Anis Younes ◽  
...  

2014 ◽  
Vol 668-669 ◽  
pp. 1488-1492
Author(s):  
Fang Qi Zhou

Considering the discontinuities of the phase saturations and pressure gradients at the matrix-fracture interface, a modified algorithm for the embedded discrete fracture model is proposed. In this algorithm, the exchange rate between fracture and matrix on two sides of the interface are calculated separately. To avoid the problem for defining the physical variables on the matrix grid blocks overlaid by fracture, the Neumann boundary conditions are instead in the calculations of other matrix grid blocks. The numerical examples show that the simulation results of the proposed algorithm agree very well with those of the discrete fracture model. In reservoir with high matrix capillary pressure, the grids must be enough refined in the neighborhood of the matrix-fracture interface to achieve high numerical accuracy.


2017 ◽  
Vol 107 ◽  
pp. 180-190 ◽  
Author(s):  
Qingfu Zhang ◽  
Zhaoqin Huang ◽  
Jun Yao ◽  
Yueying Wang ◽  
Yang Li

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