Kozeny–Carman and empirical formula for the permeability of computer rock models

Latief, Fourier Dzar Eljabbar; Fauzi, Umar

doi:10.1016/j.ijrmms.2011.12.005

Cited by 51 publications

(24 citation statements)

References 28 publications

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“…However, this is in agreement with analysis presented in [12] and [13]. In [12] Kameda presented an analysis of relation between porosity vs. permeability for two reservoir sandstone, that is the Fontainebleau and Ottawa Sandstone.…”

Section: Resultssupporting

confidence: 89%

“…For both sandstone, in the porosity range of 20%-25%, the permeability is approximately larger than 10 4 mD. Latief in [13] also proposed a modified Kozeny-Carman equation which predicts the permeability for three models that are the Continuum Geometrical Model, the Ellipsoid Model and the 3D Pigeon Hole Model which produced results that are in agreement with [12]. This however does not represent the majority condition of most sandstone reservoir.…”

Section: Resultsmentioning

confidence: 76%

See 1 more Smart Citation

Digital characterization and preliminary computer modeling of hydrocarbon bearing sandstone

Latief¹,

Haq²

2014

AIP Conference Proceedings

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With the advancement of three dimensional imaging technologies, especially the μCT scanning systems, we have been able to obtain three-dimensional digital representation of porous rocks in the scale of micrometers. Characterization was then also possible to conduct using computational approach. Hydrocarbon bearing sandstone has become one of interesting objects to analyze in the last decade. In this research, we performed digital characterization of hydrocarbon bearing sandstone reservoir from Sumatra. The sample was digitized using a μCT scanner (Skyscan 1173) which produced series of reconstructed images with the spatial resolution of 15 μm. Using computational approaches, i.e., image processing, image analysis, and simulation of fluid flow inside the rock using Lattice Boltzmann Method, we have been able to obtain the porosity of the sandstone, which is 23.89%, and the permeability, which is 9382 mD. Based on visual inspection, the porosity value, along with the calculated specific surface area, we produce a preliminary computer model of the rock using grain based method. This method employs a reconstruction of grains using the nonspherical model, and a purely random deposition of the grains in a virtual three dimensional cube with the size of 300 x 300 x 300. The model has porosity of 23.96%, and the permeability is 7215 mD. While the error of the porosity is very small (which is only 0.3%), the permeability has error of around 23% from the real sample which is considered very significant. This suggests that the modeling based on porosity and specific surface area is not satisfactory to produce a representative model. However, this work has been a good example of how characterization and modeling of porous rock can be conducted using a non-destructive computational approach.

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Section: Resultssupporting

confidence: 89%

Section: Resultsmentioning

confidence: 76%

Digital characterization and preliminary computer modeling of hydrocarbon bearing sandstone

Latief¹,

Haq²

2014

AIP Conference Proceedings

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“…The most well‐known empirical relation for permeability prediction is K‐C equation, which can be written as:

K = \frac{ϕ^{3}}{c ς^{2} S^{2}}

where

ϕ

is the porosity of porous media (dimensionless); S represents the specific surface area which is defined as the ratio of surface area of whole pores to total volume of specimen (m −1 ); c is the Kozeny constant which depends on the geometry of porous media, for example, for cylindrical capillaries, c = 2,

ς

is the tortuosity of porous media (dimensionless). For tortuosity, the empirical relation proposed by Saxena et al can be used and written as:

ς = 1 - 3 e^{- 5 ϕ} \log false(ϕ false)

…”

Section: Methodology and Theoriesmentioning

confidence: 99%

Comparative analysis on pore‐scale permeability prediction on micro‐CT images of rock using numerical and empirical approaches

Song

Wang

Liu

et al. 2019

Energy Science & Engineering

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Varieties of pore‐scale numerical and empirical approaches have been proposed to predict the rock permeability when the pore structure is known, for example, microscopic computerized tomography (micro‐CT) technology. A comparative study on these approaches is conducted in this paper. A reference dataset of nine micro‐CT images of porous rocks is generated and processed including artificial sandpacks, tight sandstone, and carbonate. Multiple numerical and empirical approaches are used to compute the absolute permeability of micro‐CT images including the image voxel‐based solver (VBS), pore network model (PNM), Lattice Boltzmann method (LBM), Kozeny‐Carman (K‐C) equation, and Thomeer relation. Computational accuracy and efficiency of different numerical approaches are investigated. The results indicate that good agreements among numerical solvers are achieved for the sample with a homogeneous structure, while the disagreement increases with an increase in heterogeneity and complexity of pore structure. The LBM and VBS solver both have a relative higher computation accuracy, whereas the PNM solver is less accurate due to simplification on the topological structure. The computation efficiency of the different solver is generally computation resources dependent, and the PNM solver is the fastest, followed by VBS and LBM solver. As expected, empirical relation can over‐estimate permeability by a magnification of 50 or more, particularly for those strong heterogeneous structures reported in this study. Nevertheless, empirical relation is still applicable for artificial rocks.

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“…Permeability is one of the most important parameters for reservoir characterization and productivity prediction. There are many well established theoretical and empirical methods to predict the permeability combining conventional MICP parameters and the fractal dimension [ Swanson , ; Katz and Thompson , ; Hunt , ; Hunt and Gee , ; Yu and Liu , ; Glover et al ., ; Yang and Aplin , ; Xu and Yu , ; Abojafer , ; Othman et al ., ; Zinovik and Poulikakos , ; Latief and Fauzi , ; Rezaee et al ., ; Gao and Hu , ; Buiting and Clerke , ; Nooruddin et al ., ; Lala , ; Cai et al ., ; Miao et al ., ].…”

Section: Algorithm and Applicationmentioning

confidence: 99%

An improvement of the fractal theory and its application in pore structure evaluation and permeability estimation

Fan

Deng

et al. 2016

JGR Solid Earth

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We present an improved fractal model for pore structure evaluation and permeability estimation based on the high pressure mercury porosimetry data. An accumulative fractal equation is introduced to characterize the piecewise nature of the capillary pressure and the mercury saturation. The iterative truncated singular value decomposition algorithm is developed to solve the accumulative fractal equation and obtain the fractal dimension distributions. Furthermore, the fractal dimension distributions and relevant parameters are used to characterize the pore structure and permeability. The results demonstrate that the proposed model provides better characterization of the mercury injection capillary pressure than conventional monofractal theory. In addition, there is a direct relationship between the pore structure types and the fractal dimension spectrums. What is more, the permeability is strongly correlated with the geometric and the arithmetic mean values of fractal dimensions, and the permeability estimated using these new fractal dimension parameters achieve excellent result. The improved model and solution give a fresh perspective of the conventional monofractal theory, which may be applied in many geological and geophysical fields.

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Kozeny–Carman and empirical formula for the permeability of computer rock models

Cited by 51 publications

References 28 publications

Digital characterization and preliminary computer modeling of hydrocarbon bearing sandstone

Digital characterization and preliminary computer modeling of hydrocarbon bearing sandstone

Comparative analysis on pore‐scale permeability prediction on micro‐CT images of rock using numerical and empirical approaches

An improvement of the fractal theory and its application in pore structure evaluation and permeability estimation

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