Scale effect on porosity and permeability: Kinetics, model, and correlation
TL;DR: In this paper, the porosity and permeability by scale dissolution and precipitation in porous media is described based on fractal attributes of the pores, realization of flow channels as a bundle of uniformly distributed mean-size cylindrical and tortuous hydraulic flow tubes, a permeability-porosity relationship conforming to Civan's power law flow units equation, and the pore surface scale precipitation and dissolution kinetics.
Abstract: Variation of porosity and permeability by scale dissolution and precipitation in porous media is described based on fractal attributes of the pores, realization of flow channels as a bundle of uniformly distributed mean-size cylindrical and tortuous hydraulic flow tubes, a permeability-porosity relationship conforming to Civan's power law flow units equation, and the pore surface scale precipitation and dissolution kinetics. Practical analytical solutions, considering the conditions of typical laboratory core tests and relating the lumped and phenomenological parameters, were derived and verified by experimental data. Deviations of the empirically determined exponents of the pore-to-matrix volume ratio compared to the Kozeny-Carman equation were due to the relative fractal dimensions of pore attributes of random porous media. The formulations provide useful insights into the mechanism of porosity and permeability variation by surface processes and accurate representation of the effect of scale on porosity and permeability by simpler lumped-parameter models.
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TL;DR: In this article, the authors derived an analytical expression for the permeability in homogeneous porous media based on the fractal characters of porous media and capillary model, which is expressed as a function of fractal dimensions, porosity and maximum pore size.
577 citations
Cites background or methods from "Scale effect on porosity and permea..."
...In addition, the effective porosity [13] and percolation [14] were taken into account for the modification of the KC equation; the fractal geometry [15–18] and the Archie law [17,18] were also used in derivation of permeability....
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...The fractal geometry theory has been proven to be powerful means for analysis of porous media with complex and random microstructures [15–18,28–43], and several fractal geometry models were presented for the hydraulic conductivity of porous media [16– 18,35,36,38,39,43,44]....
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...Civan [17] ffiffiffi K / q 1⁄4 Cð / a / Þ n...
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TL;DR: In this paper, the authors test the ability of a Darcy-scale model to describe the different dissolution regimes and to characterize the influence of the flow parameters on the wormhole development.
Abstract: Dissolution of a porous medium creates, under certain conditions, some highly conductive channels called wormholes. The mechanism of propagation is an unstable phenomenon depending on the microscopic properties at the pore scale and is controlled by the injection rate. The aim of this work is to test the ability of a Darcy-scale model to describe the different dissolution regimes and to characterize the influence of the flow parameters on the wormhole development. The numerical approach is validated by model experiments reflecting dissolution processes occurring during acid injection in limestone. Flow and transport macroscopic equations are written under the assumption of local mass non-equilibrium. The coupled system of equations is solved numerically in two dimensions using a finite volume method. Results are discussed in terms of wormhole propagation rate and pore volume injected.
364 citations
Cites background from "Scale effect on porosity and permea..."
...Two parameters have a strong influence on the breakthrough time: (i) α-correlation and (ii) the permeability–porosity correlation (Civan 2001)....
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TL;DR: Fractal geometry and technique have the potentials in analysis of flow and transport properties in fractal porous media as mentioned in this paper, and they have been used extensively in the past few decades.
Abstract: The flow in porous media has received a great deal of attention due to its importance and many unresolved problems in science and engineering such as geophysics, soil science, underground water resources, petroleum engineering, fibrous composite manufacturing, biophysics (tissues and organs), etc. It has been shown that natural and some synthetic porous media are fractals, and these media may be called fractal porous media. The flow and transport properties such as flow resistance and permeability for fractal porous media have steadily attracted much attention in the past decades. This review article intends to summarize the theories, methods, mathematical models, achievements, and open questions in the area of flow in fractal porous media by applying the fractal geometry theory and technique. The emphases are placed on the theoretical analysis based on the fractal geometry applied to fractal porous media. This review article shows that fractal geometry and technique have the potentials in analysis of flow and transport properties in fractal porous media. A few remarks are made with respect to the theoretical studies that should further be made in this area in the future. This article contains 220 references.
343 citations
TL;DR: In this article, the authors examined and assessed predictive methods for the saturated hydraulic conductivity of soils and found that most predictive methods were calibrated using laboratory permeability tests performed on either disturbed or intact specimens for which the test conditions were either measured or supposed to be known.
Abstract: This paper examines and assesses predictive methods for the saturated hydraulic conductivity of soils. The soil definition is that of engineering. It is not that of soil science and agriculture, which corresponds to “top soil” in engineering. Most predictive methods were calibrated using laboratory permeability tests performed on either disturbed or intact specimens for which the test conditions were either measured or supposed to be known. The quality of predictive equations depends highly on the test quality. Without examining all the quality issues, the paper explains the 14 most important mistakes for tests in rigid-wall or flexible-wall permeameters. Then, it briefly presents 45 predictive methods, and in detail, those with some potential, such as the Kozeny-Carman equation. Afterwards, the data of hundreds of excellent quality tests, with none of the 14 mistakes, are used to assess the predictive methods with a potential. The relative performance of those methods is evaluated and presented in graphs. Three methods are found to work fairly well for non-plastic soils, two for plastic soils without fissures, and one for compacted plastic soils used for liners and covers. The paper discusses the effects of temperature and intrinsic anisotropy within the specimen, but not larger scale anisotropy within aquifers and aquitards.
270 citations
Cites background from "Scale effect on porosity and permea..."
...For wide ranges, and either artificial or remoulded clays, they proposed logðKÞ ¼ A logðeÞ þ B: ð49Þ Equation 49 may be rewritten as a power law, with a constant dimensionless power b, such as K ¼ K e0ð Þ e e 0 b : ð50Þ Other relationships were proposed to link K and total porosity n for rock cores, such as logðKÞ ¼ C1 þ C2n or logðKÞ ¼ C1 þ C2 logðnÞ: ð51Þ The power law and other specific laws are used for rocks such as shale, sandstone, and mudstone (e.g., Walder and Nur 1984; Cao et al. 1986; Dutta 1987; Rajani 1988; Lerche 1991; Rice 1992; Neuzil 1994; Panda and Lake 1994; Nelson 1994, 2005; David et al. 1994; Dewhurst et al. 1999; Pape et al. 2000; Civan 2001; Yang and Aplin...
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...In the case of intact and remoulded London Clay, consolidated at very high pressures, to become mudstone (data from Dewhurst et al. 1999), the fit with a KozenyCarman equation is not very good for the direct and indirect Ksat values; however, it gives the general trend (Fig....
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...…laws are used for rocks such as shale, sandstone, and mudstone (e.g., Walder and Nur 1984; Cao et al. 1986; Dutta 1987; Rajani 1988; Lerche 1991; Rice 1992; Neuzil 1994; Panda and Lake 1994; Nelson 1994, 2005; David et al. 1994; Dewhurst et al. 1999; Pape et al. 2000; Civan 2001; Yang and Aplin...
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...The power law and other specific laws are used for rocks such as shale, sandstone, and mudstone (e.g., Walder and Nur 1984; Cao et al. 1986; Dutta 1987; Rajani 1988; Lerche 1991; Rice 1992; Neuzil 1994; Panda and Lake 1994; Nelson 1994, 2005; David et al. 1994; Dewhurst et al. 1999; Pape et al. 2000; Civan 2001; Yang and Aplin 1998, 2007, 2010)....
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TL;DR: In this paper, a 3D simulator for methane hydrate formation and dissociation in porous media is developed for designing and interpreting laboratory and field hydrate experiments, which is used to study the formation and the dissociation of hydrates in laboratory-scale core samples.
214 citations
References
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TL;DR: In this article, a new, practical and theoretically correct methodology is proposed for identi$cation and characterization of hydraulic units based on a modified Kozeny-Carmen equation and the concept of mean hydraulic raditis.
Abstract: Understanding complex variations in pare geomet~ within different Iithofacies is the key to improved reservoir description and exploitation. Core data provide in~ornration on various depositional and diagenetic controls on pore geometry. Variations in pore geometrical attributes in rum, de$ne the existenceof distinct zones(hydraulic units) with similar f?uid-jlow characteristics. Classic discrimination of mck types has been based on subjective geological observations and on empirical relationships between the log of permeability versus porosity. Howevec for any porosity within a given mck type,permeability can vary by several orders of nragnitnde, which indicates the existenceof severalflow units. In this papec a new, practical and theoretically correct methodology is proposedfor identi$cation and characterization of hydraulic units widtin mappable geological units (facies). The technique is based on a modified Kozeny-Carmen equation and the conceptof mean hydraulic raditis. The equation indicatesIhat for any hydraulic unit, a log-log p!ot of a “Reservoir Quality index,” (RQI), which is equal to 0.0314 ~. versus a “Normalized PorosityIndex” (+=) which is equal to WI-W should yield a straight line with a unit slope. 7he intercept of the unit slope line with +Z = 1, designated as the “FIow Zme Indicator” (M), is a unique parameter for each hydraulic unit. RQI, 4, and FZI are based on stressed potvsity and permeability data measuredon core samples.
878 citations
TL;DR: In this paper, the important geologic parameters that can be described and mapped to allow accurate petrophysical quantification of carbonate geologic models are defined and mapped, and the pore space is divided into interparticle (intergrain and intercrystal) and vuggy pores.
Abstract: This paper defines the important geologic parameters that can be described and mapped to allow accurate petrophysical quantification of carbonate geologic models. All pore space is divided into interparticle (intergrain and intercrystal) and vuggy pores. In nonvuggy carbonate rocks, permeability and capillary properties can be described in terms of particle size, sorting, and interparticle porosity (total porosity minus vuggy porosity). Particle size and sorting in limestones can be described using a modified Dunham approach, classifying packstone as grain dominated or mud dominated, depending on the presence or absence of intergrain pore space. To describe particle size and sorting in dolostones, dolomite crystal size must be added to the modified Dunham terminology. Lar er dolomite crystal size improves petrophysical properties in mud-dominated fabrics, whereas variations in dolomite crystal size have little effect on the petrophysical properties of grain-dominated fabrics. A description of vuggy pore space that relates to petrophysical properties must be added to the description of interparticle pore space to complete the petrophysical characterization. Vuggy pore space is divided into separate vugs and touching vugs on the basis of vug interconnection. Separate vugs are fabric selective and are connected only through the interparticle pore network. Separate-vug porosity contributes little to permeability and should be subtracted from total porosity to obtain interparticle porosity for permeability estimation. Separate-vug pore space is generally considered to be hydrocarbon filled in reservoirs; however, intragranular microporosity is composed of small pore sizes and may contain capillary-held connate water within the reservoir. Touching vugs are nonfa ric selective and form an interconnected pore system independent of the interparticle system.
659 citations
460 citations
TL;DR: In this article, the authors developed a model for the permeability of a clay-free sand as a function of the grain diameter, the porosity, and the electrical cementation exponent.
Abstract: The permeability of a sand shale mixture is analyzed as a function of shale fraction and the permeability of the two end-members, i.e., the permeability of a clay-free sand and the permeability of a pure shale. First, we develop a model for the permeability of a clay-free sand as a function of the grain diameter, the porosity, and the electrical cementation exponent. We show that the Kozeny-Carman-type relation can be improved by using electrical parameters which separate pore throat from total porosity and effective from total hydraulic radius. The permeability of a pure shale is derived in a similar way but is strongly dependent on clay mineralogy. For the same porosity, there are 5 orders of magnitude of difference between the permeability of pure kaolinite and the permeability of pure smectite. The separate end-members' permeability models are combined by filling the sand pores progressively with shale and then dispersing the sand grains in shale. The permeability of sand shale mixtures is shown to have a minimum at the critical shale content at which shale just fills the sand pores. Pure shale has a slightly higher permeability. Permeability decreases sharply with shale content as the pores of a sand are filled. The permeability of sand shale mixtures thus has a very strong dependence on shale fraction, and available data confirm this distinctive shale-fraction dependence. In addition, there is agreement (within 1 order of magnitude) between the permeabilities predicted from our model and those measured over 11 orders of magnitude from literature sources. Finally, we apply our model to predict the permeabilities of shaly sand formations in the Gulf Coast. The predictions are compared to a data set of permeability determination made on side-wall cores. The agreement between the theoretical predictions and the experimental data is very good.
412 citations
Book•
28 Feb 2007
TL;DR: In this article, the authors present a characterization of the Porous Media Processes for Formation Damage in Reservoir Rock and demonstrate that these processes can be used to diagnose and mitigate the effects of Formation Damage.
Abstract: Preface Chapter 1-Overview of Formation Damage PART I Characterization of Reservoir Rock for Formation Damage- Mineralogy, Texture, Petrographics, Petrophysics, and Instrumental Techniques Chapter 2- Mineralogy and Mineral Sensitivity of Petroleum-Bearing Formations Chapter 3- Petrographical Characteristics of Petroleum-Bearing Formations Chapter 4- Petrophysics-Flow Functions and Parameters Chapter 5- Porosity and Permeability Relationships of Geological Formations Chapter 6- Instrumental and Laboratory Techniques for Characterization of Reservoir Rock PART II Characterization of the Porous Media Processes for Formation Damage-Accountability of Phases and Species, Rock-Fluid-Particle Interactions, and Rate Processes Chapter 7- Multi-Phase and Multi-Species Transport in Porous Media Chapter 8-Particulate Processes in Porous Media Chapter 9-Crystal Growth and Scale Formation in Porous Media PART III Formation Damage by Particulate Processes Chapter 10-Single-Phase Formation Damage by Fines Migration and Clay Swelling Chapter 11- Multi-Phase Formation Damage by Fines Migration Chapter 12-Cake Filtration: Mechanism, Parameters and Modeling PART IV Formation Damage by Inorganic and Organic Processes-Chemical Reactions, Saturation Phenomena, Deposition, and Dissolution Chapter 13-Inorganic Scaling and Geochemical Formation Damage Chapter 14-Formation Damage by Organic Deposition PART V Assessment of the Formation Damage Potential-Testing, Simulation, Analysis, and Interpretation Chapter 15-Laboratory Evaluation of Formation Damage Chapter 16- Formation Damage Simulator Development Chapter 17- Model Assisted Analysis and Interpretation of Laboratory and Field Tests PART VI Formation Damage Models for Fields Applications- Drilling Mud Invasion, Injectivity of Wells, Sanding and Gravel-Pack Damage, and Inorganic and Organic Deposition Chapter 18- Drilling Mud Filtrate and Solids Invasion and Mudcake Formation Chapter 19-Injectivity of the Waterflooding Wells Chapter 20- Reservoir Sand Migration and Gravel-Pack Damage: Stress-Induced Formation Damage, Sanding Tendency, and Prediction Chapter 21- Near-Wellbore Formation Damage by Inorganic and Organic Precipitates Deposition PART VII Diagnosis and Mitigation of Formation Damage-Measurement, Assessment, Control, and Remediation Chapter 22- Field Diagnosis and Measurement of Formation Damage Chapter 23-Determination of Formation- and Pseudo-Damage from Well Performance- Identification, Characterization, and Evaluation Chapter 24-Formation Damage Control and Remediation- Fundamentals Chapter 25-Reservoir Formation Damage Abatement- Guidelines, Methodology, Preventive Maintenance, and Remediation Treatments Index
385 citations