Lanczos method for the solution of groundwater flow in discretely fractured porous media

Woodbury, Allan D.; Zhang, Keni

doi:10.1016/s0309-1708(00)00047-6

Cited by 18 publications

(17 citation statements)

References 18 publications

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“…Standard Galerkin method is applied to discretize the weak forms with appropriate boundary conditions (Zimmerman and Bodvarsson 1996;Woodbury and Zhang 2001).…”

Section: Finite Element Methods Formulationmentioning

confidence: 99%

Evaluation of water coning phenomenon in naturally fractured oil reservoirs

Azim

2015

J Petrol Explor Prod Technol

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Water coning is a complex phenomenon observed in conventional and unconventional reservoirs. This phenomenon takes place due to the imbalance between viscous and gravitational forces during simultaneous production of oil and water. In a fractured reservoir, controlling of water coning is challenging due to the complexity originates from large number of uncertain variables associated with such reservoirs system. This paper presents a fully coupled poroelastic multiphase fluidflow numerical model to provide a new insight and understanding of water coning phenomenon in naturally fractured reservoir under effect of various rock and fluid properties. These properties include anisotropy ratio, fracture permeability, mobility ratio, and production rate. The simulation workflow of the developed numerical model is based on upstream flux weighted finite element discretization method and a new hybrid methodology, which combines single-continuum and discrete fracture approach. Moreover, the capillary pressure effect is included during the discretization of the partial differential equations of multiphase fluid flow. The numerical system is decoupled using implicit pressure and explicit saturation (IMPES) approach. Discretization of water saturation equation using standard finite element method produces solution with spatial oscillations due to its hyperbolic nature. To overcome this, Galerkin's least square technique (GLS) is employed to stabilize the equation solutions. The developed numerical scheme is validated successfully against Eclipse-100 and then applied to a case study of fractured reservoir taken from Southern Vietnam. The results showed that the break through time is very sensitive to the distributions of fracture network, anisotropy ratio between fracture horizontal, vertical permeability, and mobility ratio. Furthermore, it has been concluded that aquifer strength has a little effect on coning behavior during oil production process.

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“…Standard Galerkin method is applied to discretize the weak forms with appropriate boundary conditions (Zimmerman and Bodvarsson 1996;Woodbury and Zhang 2001).…”

Section: Finite Element Methods Formulationmentioning

confidence: 99%

Evaluation of water coning phenomenon in naturally fractured oil reservoirs

Azim

2015

J Petrol Explor Prod Technol

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“…The continuum medium approach has proven to be inadequate in describing large scale regions since it has to oversimplify the fractured formation as a homogeneous zone [125]. The DFN approach cannot produce the detailed set of the geometrical parameters for individual fractures, while requiring extensive computational time for large scale simulations [126,127]. The third approach can be considered more efficient since it combines the advantages of both continuum and discrete methods.…”

Section: Direct Applications Of Hydraulic Fracturing Studiesmentioning

confidence: 99%

Recent Developments in Multiscale and Multiphase Modelling of the Hydraulic Fracturing Process

Sheng

Sousani

Ingham

et al. 2015

Mathematical Problems in Engineering

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Recently hydraulic fracturing of rocks has received much attention not only for its economic importance but also for its potential environmental impact. The hydraulically fracturing technique has been widely used in the oil (EOR) and gas (EGR) industries, especially in the USA, to extract more oil/gas through the deep rock formations. Also there have been increasing interests in utilising the hydraulic fracturing technique in geological storage of CO 2 in recent years. In all cases, the design and implementation of the hydraulic fracturing process play a central role, highlighting the significance of research and development of this technique. However, the uncertainty behind the fracking mechanism has triggered public debates regarding the possible effect of this technique on human health and the environment. This has presented new challenges in the study of the hydraulic fracturing process. This paper describes the hydraulic fracturing mechanism and provides an overview of past and recent developments of the research performed towards better understandings of the hydraulic fracturing and its potential impacts, with particular emphasis on the development of modelling techniques and their implementation on the hydraulic fracturing.

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“…Now let us return to the original case of model reduction for systems (1.1.4)-(1.1.8). From a control theory viewpoint we term it single input-complete outputconvection partial differential equation, then the Krylov subspace (1.1.31) with s o 0 is a very good choice for the lower dimensional subspace in Equation (1.1.6) [8,9,[37][38][39][40][41][42][43]. In this case, the model reduction step (1.1.8) can be viewed as an approximate solution of the original system (1.1.4), because it is possible to recover the solution for all of the original unknowns by means of Equation (1.1.6).…”

Section: Approximating a Transfer Function By Padé And Padé-type Apprmentioning

confidence: 99%

“…They mostly deal with the SICO case discussed above. Here, model reduction is at the beginning stage if we compare the number of papers in which model reduction is used to the total number of papers on the solution of advection-diffusion PDEs: advection dispersion equation for groundwater flow [37,38], mass transport in hydrogeological environments [39], photon diffusion (optical tomography) problem [40], radionuclide decay-chain transport in porous media [41], groundwater flow in dual-porosity media [42], radionuclide decay chain transport in dual-porosity media [43], groundwater flow in discretely fractured porous media [8] and diffusion and convection dominated flow [9].…”

Section: Approximating a Transfer Function By Padé And Padé-type Apprmentioning

confidence: 99%

“…[7]) and which will be referred to as automatic model reduction. There are some spectacular examples where the dimension of ODEs could be reduced by several orders of magnitude, almost without sacrificing precision (eg, see [8] and [9]). However, there still remains a certain gap between these ideas and common MEMS engineering practice and the aim of this chapter is to start to fill this gap.…”

Section: Introductionmentioning

confidence: 99%

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Review: Automatic Model Reduction for Transient Simulation of MEMS‐based Devices

Rudnyi

Korvink

2002

Sensors Update

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The rapid development of MEMS-based devices requires 3D time-dependent simulations for coupled physical domains (thermal, mechanical, electrical, etc.). This in turn requires the solution of high-dimensional ordinary differential equations (ODEs) that result from space discretization of the device. However, instead of a "brute force" approach to integrate a large system of ODEs, one can use modern mathematical methods to reduce the system's dimension. The goal of the present paper is to review them from an engineering perspective. It is shown that in many cases important for practice the order of ODEs can be reduced by several orders of magnitude almost without sacrificing precision.

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Lanczos method for the solution of groundwater flow in discretely fractured porous media

Cited by 18 publications

References 18 publications

Evaluation of water coning phenomenon in naturally fractured oil reservoirs

Evaluation of water coning phenomenon in naturally fractured oil reservoirs

Recent Developments in Multiscale and Multiphase Modelling of the Hydraulic Fracturing Process

Review: Automatic Model Reduction for Transient Simulation of MEMS‐based Devices

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