Parallel simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer framework

Wu, Yuanqing; Salama, Amgad; Sun, Shuyu

doi:10.1016/j.compgeo.2015.06.021

Cited by 59 publications

(45 citation statements)

References 49 publications

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“…Apparently, the porosity may become very large (but less than one) in the wormhole channels, and thus, the fluid velocity may be fast and close to the velocity of the clear fluid flow. Since the Brinkman model accounts for transitional flows between boundaries of porous media and clear fluids [3], and the Forchheimer model considers the inertial effect of high velocity, the Darcy-Brinkman-Forchheimer model that accounts for higher velocity and nonuni-form porosity is strongly suggested to describe matrix acidization for the purpose of retrieving more reasonable results [24].…”

Section: Mathematical Model Of the Wormhole Problemmentioning

confidence: 99%

“…Apparently, there are situations in which the porosity becomes close to unity, and as a result, there may exist an area of clear fluid within the porous medium. It is worth accounting for both the porous media and clear fluid area, and the Darcy-Brinkman-Forchheimer framework exactly deals with the problems [11,24]. In [13], the Darcy-Forchheimer model is used to model the flow of high velocity in nonuniform porosity instead of the conventional Darcy framework.…”

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confidence: 99%

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A semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy–Brinkman–Forchheimer model

Kou

Sun

2019

Journal of Computational and Applied Mathematics

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In this paper, we consider numerical simulation of wormhole propagation with the Darcy-Brinkman-Forchheimer model. Matrix acidization in carbonate reservoirs is a widely practiced technique in the product enhancement of the oil and gas reservoir. A wormhole, i.e. a flow channel with high porosity, is generated during reactive dissolution of carbonates by the action of the injected acid. In the wormhole forming process, the porosity changes non-uniformly in space, and it even becomes close to unity in the central regions of a wormhole. The Darcy-Brinkman-Forchheimer model accounts for both the porous media and clear fluid area, so it can be used to model wormhole propagation perfectly. This model, however, strongly depends on porosity. Therefore, the time schemes for solving the evolutionary equation of porosity have a significant effect on accuracy and stability of the numerical simulation for wormhole propagation. We propose a semi-analytic time scheme, which solves the porosity equation analytically at each time step for given acid concentration. The proposed numerical method can improve the accuracy and stability of numerical simulation significantly. For theoretical analysis of the proposed time scheme for the wormhole simulation, we first reconstruct the analytical functions of porosity to analyze the time error of the porosity, and on the basis of error estimates of porosity, we employ a coupled analysis approach to achieve the estimates of pressure, velocity and solute concentration. The time error estimates for velocity, pressure, concentration and porosity are obtained in different norms. Finally, numerical results are provided to verify the effectiveness of the proposed scheme.

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Section: Mathematical Model Of the Wormhole Problemmentioning

confidence: 99%

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confidence: 99%

A semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy–Brinkman–Forchheimer model

Kou

Sun

2019

Journal of Computational and Applied Mathematics

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“…Salama et al [145,146] also developed what they called the experimenting field algorithm in which the matrix of coefficients of a linear system is constructed automatically, rather than being inputted manually. This technique has been tested in various cases and shows to be very effective (Salama et al [147][148][149], Wu et al [150], Negara et al [151,152], and El-Amin et al [153]). Furthermore, Salama et al [154] and Salama [155] developed a technique that numerically solves the problem of flow towards a well in an efficient manner.…”

Section: Numerical Methods For Solving the Governing Lawsmentioning

confidence: 99%

Flow and Transport in Tight and Shale Formations: A Review

et al. 2017

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A review on the recent advances of the flow and transport phenomena in tight and shale formations is presented in this work. Exploration of oil and gas in resources that were once considered inaccessible opened the door to highlight interesting phenomena that require attention and understanding. The length scales associated with transport phenomena in tight and shale formations are rich. From nanoscale phenomena to field-scale applications, a unified frame that is able to encounter the varieties of phenomena associated with each scale may not be possible. Each scale has its own tools and limitations that may not, probably, be suitable at other scales. Multiscale algorithms that effectively couple simulations among various scales of porous media are therefore important. In this article, a review of the different length scales and the tools associated with each scale is introduced. Highlights on the different phenomena pertinent to each scale are summarized. Furthermore, the governing equations describing flow and transport phenomena at different scales are investigated. In addition, methods to solve these equations using numerical techniques are introduced. Cross-scale analysis and derivation of linear and nonlinear Darcy's scale laws from pore-scale governing equations are described. Phenomena occurring at molecular scales and their thermodynamics are discussed. Flow slippage at the nanosize pores and its upscaling to Darcy's scale are highlighted. Pore network models are discussed as a viable tool to estimate macroscopic parameters that are otherwise difficult to measure. Then, the environmental aspects associated with the different technologies used in stimulating the gas stored in tight and shale formations are briefly discussed.

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“…hancing oil production rate when muds and fines deposit at the perforated well pore pipe [4,5,7,9,15,20,26,29,30]. In the technique, acid is injected into matrix to dissolve the rocks and deposits around the well bore and a channel with high porosities is formed.…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

“…Because of its importance in enhancing production rate, matrix acidization in carbonate reservoirs has been extensively studied in [4,5,7,9,15,20,26,29,30], but the numerical methods are restricted to finite difference and finite volume methods. In [31], the combination of the finite element method and the finite difference method has been used to simulate the wormhole generation and propagation in carbonate rocks.…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

Mixed finite element-based fully conservative methods for simulating wormhole propagation

Kou

Sun

2016

Computer Methods in Applied Mechanics and Engineering

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. MIXED FINITE ELEMENT-BASED FULLY CONSERVATIVE METHODS FOR SIMULATING WORMHOLE PROPAGATION *JISHENG KOU † , SHUYU SUN ‡ , AND YUANQING WU § Abstract. Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy-Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy-Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.

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Parallel simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer framework

Cited by 59 publications

References 49 publications

A semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy–Brinkman–Forchheimer model

A semi-analytic porosity evolution scheme for simulating wormhole propagation with the Darcy–Brinkman–Forchheimer model

Flow and Transport in Tight and Shale Formations: A Review

Mixed finite element-based fully conservative methods for simulating wormhole propagation

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