A Cut-Cell Polyhedral Finite Element Model for Coupled Fluid Flow and Mechanics in Fractured Reservoirs

2021 ◽  
Author(s):  
Igor Shovkun ◽  
Hamdi A. Tchelepi
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Fractured Reservoirs ◽  
Computational Cost ◽  
Mechanical Deformation ◽  
Naturally Fractured Reservoirs ◽  
Fracture Model ◽  
Single Fracture ◽  
Cut Cell ◽  
Flux Approximation

Abstract Mechanical deformation induced by injection and withdrawal of fluids from the subsurface can significantly alter the flow paths in naturally fractured reservoirs. Modeling coupled fluid-flow and mechanical deformation in fractured reservoirs relies on either sophisticated gridding techniques, or enhancing the variables (degrees-of-freedom) that represent the physics in order to describe the behavior of fractured formation accurately. The objective of this study is to develop a spatial discretization scheme that cuts the "matrix" grid with fracture planes and utilizes traditional formulations for fluid flow and geomechanics. The flow model uses the standard low-order finite-volume method with the Compartmental Embedded fracture Model (cEDFM). Due to the presence of non-standard polyhedra in the grid after cutting/splitting, we utilize numerical harmonic shape functions within a Polyhedral finite-element (PFE) formulation for mechanical deformation. In order to enforce fracture-contact constraints, we use a penalty approach. We provide a series of comparisons between the approach that uses conforming Unstructured grids and a Discrete Fracture Model (Unstructured DFM) with the new cut-cell PFE formulation. The manuscript analyzes the convergence of both methods for linear elastic, single-fracture slip, and Mandel’s problems with tetrahedral, Cartesian, and PEBI-grids. Finally, the paper presents a fully-coupled 3D simulation with multiple inclined intersecting faults activated in shear by fluid injection, which caused an increase in effective reservoir permeability. Our approach allows for great reduction in the complexity of the (gridded) model construction while retaining the solution accuracy together with great saving in the computational cost compared with UDFM. The flexibility of our model with respect to the types of grid polyhedra allows us to eliminate mesh artifacts in the solution of the transport equations typically observed when using tetrahedral grids and two-point flux approximation.

A Cut-Cell Polyhedral Finite Element Model for Coupled Fluid Flow and Mechanics in Fractured Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-24
Author(s):  
I Shovkun ◽  
H. A. Tchelepi
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Fractured Reservoirs ◽  
Mechanical Deformation ◽  
Fracture Model ◽  
Single Fracture ◽  
Discrete Fracture Model ◽  
Cut Cell ◽  
Flux Approximation ◽  
Discrete Fracture

Summary Mechanical deformation induced by injection and withdrawal of fluids from the subsurface can significantly alter the flow paths in naturally fractured reservoirs. Modeling coupled fluid flow and mechanical deformation in fractured reservoirs relies on either sophisticated gridding techniques or enhancing the variables (degrees of freedom) that represent the physics to describe the behavior of fractured formation accurately. The objective of this study is to develop a spatial discretization scheme that cuts the “matrix” grid with fracture planes and utilizes traditional formulations for fluid flow and geomechanics. The flow model uses the standard low-order finite volume method with the compartmental embedded discrete fracture model (cEDFM). Due to the presence of nonstandard polyhedra in the grid after cutting/splitting, we use numerical harmonic shape functions within a polyhedral finite element (PFE) formulation for mechanical deformation. To enforce fracture-contact constraints, we use a penalty approach. We provide a series of comparisons between the approach that uses conforming unstructured grids and an unstructured discrete fracture model (uDFM) with the new cut-cell PFE formulation. The manuscript validates and compares both methods for linear elastic, single-fracture slip, and Mandel’s problems with tetrahedral, Cartesian, and perpendicular-bisectional (PBI) grids. Finally, the paper presents a fully coupled 3D simulation with multiple inclined intersecting faults activated in shear by fluid injection, which caused an increase in effective reservoir permeability. Our approach allows for great reduction in the complexity of the (gridded) model construction while retaining the solution accuracy together with great savings in the computational cost compared with uDFM. The flexibility of our model with respect to the types of grid polyhedra allows us to eliminate mesh artifacts in the solution of the transport equations typically observed when using tetrahedral grids and two-point flux approximation.

scholarly journals Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

SPE Journal ◽  
2013 ◽  
Vol 19 (02) ◽  
pp. 289-303 ◽  
Author(s):  
Ali Moinfar ◽  
Abdoljalil Varavei ◽  
Kamy Sepehrnoori ◽  
Russell T. Johns
Keyword(s):  
Fluid Flow ◽  
Oil Recovery ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Fracture Model ◽  
Continuum Models ◽  
Fine Grid ◽  
Discrete Fracture Model ◽  
Discrete Fracture ◽  
Naturally Fractured

Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

A Sensitivity Analysis for Effective Parameters on 2D Fracture-Network Permeability

2009 ◽  
Vol 12 (03) ◽  
pp. 455-469 ◽  
Author(s):  
Alireza Jafari ◽  
Tayfun Babadagli
Keyword(s):  
Sensitivity Analysis ◽  
Experimental Design ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Static Model ◽  
Naturally Fractured Reservoirs ◽  
Single Fracture ◽  
Data Sets ◽  
Fracture Networks ◽  
Fractal Characteristics

Summary Fracture-network mapping and estimation of its permeability constitute two major steps in static-model preparation of naturally fractured reservoirs. Although several different analytical methods were proposed in the past for calculating fracture-network permeability (FNP), different approaches are still needed for practical use. We propose a new and practical approach to estimate FNP using statistical and fractal characteristics of fracture networks. We also provide a detailed sensitivity analysis to determine the relative importance of fracture-network parameters on the FNP in comparison to single-fracture conductivity using an experimental-design approach. The FNP is controlled by many different fracture-network parameters such as fracture length, density, orientation, aperture, and single-fracture connectivity. Five different 2D fracture data sets were generated for random and systematic orientations. In each data set, 20 different combinations of fracture density and length for different orientations were tested. For each combination, 10 different realizations were generated. The length was considered as constant and variable. This yielded a total of 1,000 trials. The FNPs were computed through a commercial discrete-fracture-network (DFN) modeling simulator for all cases. Then, we correlated different statistical and fractal characteristics of the networks to the measured FNPs using multivariable-regression analysis. Twelve fractal (sandbox, box counting, and scanline fractal dimensions) and statistical (average length, density, orientation, and connectivity index) parameters were tested against the measured FNP for synthetically generated fracture networks for a wide range of fracture properties. All cases were above the percolation threshold to obtain a percolating network, and the matrix effect was neglected. The correlation obtained through this analysis using four data sets was tested on the fifth one with known permeability for verification. High-quality match was obtained. Finally, we adopted an experimental-design approach to identify the most-critical parameters on the FNP for different fracture-network types. The results are presented as Pareto charts. It is believed that the new method and results presented in this paper will be useful for practitioners in static-model development of naturally fractured reservoirs and will shed light on further studies on modeling and understanding the transmissibility characteristics of fracture networks. It should be emphasized that this study was conducted on 2D fracture networks and could be extended to 3D models. This, however, requires further algorithm development to use 2D fractal characteristics for 3D systems and/or development of fractal measurement techniques for a 3D system. This study will provide a guideline for this type of research.

Usage of Geomechanically Consistent Fracture Model for Drilling Deviated Wells

2021 ◽  
Author(s):  
Nikita Vladislavovich Dubinya ◽  
Sergey Andreevich Tikhotskiy ◽  
Sergey Vladimirovich Fomichev ◽  
Sergey Vladimirovich Golovin
Keyword(s):  
Optimal Trajectory ◽  
Fractured Reservoirs ◽  
Fluid Pressure ◽  
Naturally Fractured Reservoirs ◽  
Natural Fracture ◽  
Fracture Model ◽  
Drilling Process ◽  
Natural Fractures ◽  
Drilling Parameters ◽  
Deviated Wells

Abstract The paper presents an algorithm for the search of the optimal frilling trajectory for a deviated well which is applicable for development of naturally fractured reservoirs. Criterion for identifying the optimal trajectory is the feature of the current study – optimal trajectory is chosen from the perspective of maximizing the positive effect related to activation of natural fractures in well surrounding rock masses caused by changes of the rocks stress-strain state due to drilling process. Drilling of a deviated well is shown to lead to the process of natural fractures in the vicinity of the well becoming hydraulically conductive due to drilling. The paper investigates the main natural factors – tectonic stresses and fluid pressure – and drilling parameters – drilling trajectory and mud pressure – influencing the number and variety of natural fractures being activated due to drilling process. An algorithm of finding the optimal drilling parameters from the perspective of natural fractures activation is proposed as well. Different theoretical scenarios are considered to formulate the general recommendations on drilling trajectory choice according to estimations of stress state of the reservoir. These estimations can be provided based on results of three- and four-dimensional geomechanical modeling. Such modeling may be completed as well for constructing geomechanically consistent natural fracture model which can be used to optimize drilling trajectories during exploration and development of certain objects. The paper presents a detailed algorithm of constructing such fracture models and deviated wells trajectories optimization. The results presented in the paper and given recommendations may be used to enhance drilling efficiency for reservoirs characterized by considerable contribution of natural fractures into filtration processes.

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