The Dual-Reciprocity Boundary Element Method Solution for Gas Recovery from Unconventional Reservoirs with Discrete Fracture Networks

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 2898-2914
Author(s):  
Miao Zhang ◽  
Luis F. Ayala
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Nonlinear Partial Differential Equations ◽  
Boundary Integral ◽  
Element Formulation ◽  
Gas Reservoirs ◽  
Gas Recovery ◽  
Infinite Conductivity ◽  
Fractured Horizontal Wells ◽  
Element Method

Summary In this paper, we present a novel application of the dual-reciprocity boundary-element formulation (DRBEM) to model compressible (gas) fluid flow in tight and shale-gas reservoirs containing arbitrary distributed finite- or infinite-conductivity discrete fractures. Compared with the standard boundary-element method (BEM), the DRBEM transforms the nonlinear domain integrals at the righthand side (RHS) of BEM formulations for nonlinear partial differential equations into equivalent boundary integrals. This transformation allows retention of the domain-integral-free, boundary-integral-only character of standard BEM approaches. The proposed approach is based on coupling DRBEM with the finite-volume method (FVM) in which a multidimensional system is solved by integrating over a line with random fractures. The resulting system of equations is solved simultaneously for fracture and matrix boundary conditions by combining DRBEM and FVM without invoking any approximation for pressure-dependent nonlinear terms such as gas viscosity and compressibility. Numerical examples and field cases are presented to test the validity and showcase the capabilities of the proposed approach. The proposed model provides a general framework that can be applied to a variety of well and fracture geometries and operating schedules, and it is used to analyze production behavior for these complex systems. To the best of the authors’ knowledge, this is the first successful application of the dual-reciprocity principle to the BEM analysis of massively fractured horizontal wells (MFHWs) performance in natural-gas formations in which nonlinear, pressure-dependent gas properties are captured without approximation.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Large Scale ◽  
Boundary Integral ◽  
Practical Significance ◽  
Fast Multipole ◽  
Tree Structures ◽  
Wave Problems ◽  
Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

A Boundary Element Method for Multi-Body Contact Problems and its Application to the Analysis of a Huge Excavator

1995 ◽  
Author(s):  
Chong-De Liu ◽  
Jiyuan Yu ◽  
Xiaoming Wang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Contact Problems ◽  
Fortran Program ◽  
Boundary Integral ◽  
Element Formulation ◽  
Body Contact ◽  
Boundary Integral Formulation ◽  
Discretization Technique ◽  
Multi Body

Abstract The derivation of a boundary integral formulation and discretization technique in terms of boundary elements for the solution of multi-body contact problems has been carried out. A FORTRAN program has been developed based on this boundary element formulation and has been applied to the stress analysis of a huge caterpillar excavator woth 16 m3 bucket capacity.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

scholarly journals Thermal Stress Analysis of 3D Anisotropic Materials Involving Domain Heat Source by the Boundary Element Method

2019 ◽  
Vol 35 (6) ◽  
pp. 839-850
Author(s):  
Y. C. Shiah ◽  
Nguyen Anh Tuan ◽  
M.R. Hematiyan
Keyword(s):  
Boundary Element Method ◽  
Heat Source ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Quadratic Function ◽  
Boundary Integral ◽  
Volume Integral ◽  
Direct Evaluation ◽  
Volume Heat ◽  
Element Method

ABSTRACTIn engineering applications, it is pretty often to have domain heat source involved inside. This article proposes an approach using the boundary element method to study thermal stresses in 3D anisotropic solids when internal domain heat source is involved. As has been well noticed, thermal effect will give rise to a volume integral, where its direct evaluation will need domain discretization. This shall definitely destroy the most distinctive notion of the boundary element method that only boundary discretization is required. The present work presents an analytical transformation of the volume integral in the boundary integral equation due to the presence of internal volume heat source. For simplicity, distribution of the heat source is modeled by a quadratic function. When needed, the formulations can be further extended to treat higher-ordered volume heat sources. Indeed, the present work has completely restored the boundary discretization feature of the boundary element method for treating 3D anisotropic thermoelasticity involving volume heat source.

Boundary Element Method Analysis of Three-Dimensional Thermoelastic Fracture Problems Using the Energy Domain Integral

2005 ◽  
Vol 73 (6) ◽  
pp. 959-969 ◽  
Author(s):  
R. Balderrama ◽  
A. P. Cisilino ◽  
M. Martinez
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Auxiliary Function ◽  
Boundary Integral ◽  
Crack Advance ◽  
Domain Integral ◽  
Energy Domain ◽  
Element Method

A boundary element method (BEM) implementation of the energy domain integral (EDI) methodology for the numerical analysis of three-dimensional fracture problems considering thermal effects is presented in this paper. The EDI is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains, temperatures, and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations. Special emphasis is put on the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of the crack front with free surfaces. Several examples are analyzed to demonstrate the efficiency and accuracy of the implementation.

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