Two‐scale continuum model for simulation of wormholes in carbonate acidization

Panga, Mohan; Ziauddin, Murtaza; Balakotaiah, Vemuri

doi:10.1002/aic.10574

Cited by 379 publications

(293 citation statements)

References 35 publications

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“…The first three terms represent the accumulation, convection and dispersion of the acid respectively, and the fourth term represents the transfer of acid species from the fluid phase to the fluid-solid interface [20]. The advancement of chemical reaction front does not propagate uniformly along the injection direction.…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

“…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%

“…Oil and gas components in the reservoir can be pushed to the surface easily through the channel. In the procedure, the solute transport equation can be expressed as below [20] ∂(φc f ) ∂t + ∇ · (uc f ) − ∇ · (φD e ∇c f ) = k c a v (c s − c f ) + f P c f + f I c I ,…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

“…(1.2), (1.3), (1.4) and (1.5)). This model is mostly based on [20] except for the Darcy-Forchheimer equation.…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

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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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Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

“…(1.2), (1.3), (1.4) and (1.5)). This model is mostly based on [20] except for the Darcy-Forchheimer equation.…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

See 3 more Smart Citations

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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Long‐term observation of permeability in sedimentary rocks under high‐temperature and stress conditions and its interpretation mediated by microstructural investigations

Yasuhara

Kinoshita

Ohfuji

et al. 2015

Water Resources Research

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In this study, a series of long-term, intermittent permeability experiments utilizing Berea sandstone and Horonobe mudstone samples, with and without a single artificial fracture, is conducted for more than 1000 days to examine the evolution of rock permeability under relatively high-temperature and confining pressure conditions. Effluent element concentrations are also measured throughout the experiments. Before and after flow-through experiments, rock samples are prepared for X-ray diffraction, X-ray fluorescence, and scanning electron microscopy coupled with energy dispersive X-ray spectroscopy to examine the mineralogical changes between pre and postexperimental samples, and also for microfocus X-ray CT to evaluate the alteration of the microstructure. Although there are exceptions, the observed, qualitative evolution of permeability is found to be generally consistent in both the intact and the fractured rock samples-the permeability in the intact rock samples increases with time after experiencing no significant changes in permeability for the first several hundred days, while that in the fractured rock samples decreases with time. An evaluation of the Damkohler number and of the net dissolution, using the measured element concentrations, reveals that the increase in permeability can most likely be attributed to the relative dominance of the mineral dissolution in the pore spaces, while the decrease can most likely be attributed to the mineral dissolution/crushing at the propping asperities within the fracture. Taking supplemental observations by microfocus X-ray CT and using the intact sandstone samples, a slight increase in relatively large pore spaces is seen. This supports the increase in permeability observed in the flow-through experiments.

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Pore‐scale simulation of carbonate dissolution in micro‐CT images

2016

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We present a particle‐based method to simulate carbonate dissolution at the pore scale directly on the voxels of three‐dimensional micro‐CT images. The flow field is computed on the images by solving the incompressible Navier‐Stokes equations. Rock‐fluid interaction is modeled using a three‐step approach: solute advection, diffusion, and reaction. Advection is simulated with a semianalytical pore‐scale streamline tracing algorithm, diffusion by random walk is superimposed, while the reaction rate is defined by the flux of particles through the pore‐solid interface. We derive a relationship between the local particle flux and the independently measured batch calcite dissolution rate. We validate our method against a dynamic imaging experiment where a Ketton oolite is imaged during CO2‐saturated brine injection at reservoir conditions. The image‐calculated increases in porosity and permeability are predicted accurately, and the spatial distribution of the dissolution front is correctly replicated. The experiments and simulations are performed at a high flow rate, in the uniform dissolution regime – Pe ≫ 1 and PeDa ≪ 1—thus extending the reaction throughout the sample. Transport is advection dominated, and dissolution is limited to regions with significant inflow of solute. We show that the sample‐averaged reaction rate is 1 order of magnitude lower than that measured in batch reactors. This decrease is the result of restrictions imposed on the flux of solute to the solid surface by the heterogeneous flow field, at the millimeter scale.

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Two‐scale continuum model for simulation of wormholes in carbonate acidization

Cited by 379 publications

References 35 publications

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

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

Long‐term observation of permeability in sedimentary rocks under high‐temperature and stress conditions and its interpretation mediated by microstructural investigations

Pore‐scale simulation of carbonate dissolution in micro‐CT images

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