Tortuosity Fractal Dimension Research Articles

A physically based model for the electrical conductivity of partially saturated porous media

SUMMARY In reservoir and environmental studies, the geological material characterization is often done by measuring its electrical conductivity. Its main interest is due to its sensitivity to physical properties of porous media (i.e. structure, water content, or fluid composition). Its quantitative use therefore depends on the efficiency of the theoretical models to link them. In this study, we develop a new physically based model that takes into account the surface conductivity for estimating electrical conductivity of porous media under partially saturated conditions. The proposed model is expressed in terms of electrical conductivity of the pore fluid, water saturation, critical water saturation and microstructural parameters such as the minimum and maximum pore/capillary radii, the pore fractal dimension, the tortuosity fractal dimension and the porosity. Factors influencing the electrical conductivity in porous media are also analysed. From the proposed model, we obtain an expression for the relative electrical conductivity that is consistent with other models in literature. The model predictions are successfully compared with published experimental data for different types of porous media. The new physically based model for electrical conductivity opens up new possibilities to characterize porous media under partially saturated conditions with geoelectrical and electromagnetic techniques.

Effect of tortuosity on the stress-dependent permeability of tight sandstones: Analytical modelling and experimentation

Accurately modelling stress-dependent permeability is of great significance to predicting the oil/gas production of unconventional tight sandstone reservoirs with time-dependent pressure depletion. The classic theory indicates that the porosity exponents of the capillary tube model and the fracture model are 2 and 3, respectively. However, experimental results demonstrate that the value of the porosity exponent usually varies greatly. The effect of the nonuniform distribution of tortuosity on stress-dependent permeability is rarely studied. Assuming that tight sandstones with natural microfractures can be represented by a bundle of tortuous capillary tubes and parallel plate fractures, a new stress-dependent permeability model of tight sandstones is proposed based on fractal theory considering the tortuosity effect. The research results show that the porosity exponents of the tortuous capillary tube model and the tortuous plate fracture model are (3+DT)/2 and 2+DT, respectively (here, DT is the tortuosity fractal dimension). For the capillary tube model and the plate fracture model without tortuosity (DT=1), their porosity exponents can be simplified to 2 and 3, respectively. The tortuosity fractal dimension is one of the reasons causing the porosity exponent to deviate from the classic theoretical value. The newly developed stress-dependent permeability model is verified with experimental data determined using tight sandstone core samples from the Yanchang Formation in the Ordos Basin, China. The average error of the permeability prediction under different effective stresses is only 3.78%; thus, the newly developed model can accurately predict the stress-dependent permeability of tight sandstones.

Evaluation of Relative Permeability From Resistivity Data for Fractal Porous Media

The characteristics of multiphase flow in porous media are of great significance to various applications, such as reservoir evaluation and engineering geology. The analogy between fluid flow and electric flow provides a new idea for studying multiphase flow properties from geophysical resistivity data. However, a theoretical relationship between relative permeability and resistivity index, which is the key to the successful joint interpretation of multiphase flow and rock electric characteristics in porous media, is poorly understood. Based on fractal theory, a relative permeability-resistivity index model is developed to accurately describe the link between the rock electric and multiphase flow characteristics. The relative permeability is found not only to be related to fluid saturation and resistivity index, but also to be affected by structural parameters, such as the tortuosity fractal dimension, pore fractal dimension, water-phase fractal dimension, and tortuosity ratio. The proposed model reveals the significant effect of structural parameters on the resistivity index and relative permeability, on the other hand, the study provides an effective method to calculate the relative permeability from the resistivity data. By applying the relative permeability-resistivity index model to real cases, it shows that the predicted relative permeability results calculated by our model are in good agreement with experimental data.

Size and spatial fractal distributions of coal fracture networks under different mining-induced stress conditions

Coal permeability is a key issue in CO2 injection and enhanced coalbed methane (CBM) recovery, and it is determined by the fracture network, which is strongly influenced by mining-induced stress evolutions. For a comprehensive understanding of the size and spatial distribution characteristics of coal fracture networks under different mining-induced stress conditions, a series of laboratory experiments, computed tomography (CT) scans and image analyses focusing on 3D coal fracture systems have been conducted considering the stress conditions induced by three typical mining layouts, i.e., top-coal caving mining (TCM), non-pillar mining (NM) and protective coal-seam mining (PCM). The size and spatial distributions of mining-induced coal microfractures and the anisotropic tortuosity characteristics of coal fracture networks have been quantitatively determined based on fractal theory. The results show that the size distributions of microfracture geometries, the fractal dimensions of fracture size distribution and the tortuosity of the mining-induced coal fracture networks vary according to the mining-induced stress conditions, resulting in differences in the seepage capacity of coal masses. The coal samples subjected to PCM conditions have the highest percentage of large microfractures, and those exposed to NM conditions have the lowest percentage. The fractal dimensions (Da and Dd) of the microfracture size distributions of the typical coal specimens decrease in the order of PCM, NM and TCM conditions, and the Da and Dd of coal specimens without pre-mining unloading-expansion simulation (PUES) are much lower than those of specimens with PUES. The tortuosity fractal dimensions (δ) of the mining-induced fracture network are spatially anisotropic. The ranges of δ for the coal masses exposed to PCM, NM and TCM conditions are 1.0–1.2, 1.2–1.3 and 1.25–1.4, respectively. Using fractal theory and the measured fracture network data, the anisotropic spatial distribution of coal permeability can be theoretically estimated.

Electrical resistivity and capillary absorption in mortar with styrene-acrylic emulsion and air-entrained agent: improvement and correlation with pore structure

In realistic situation, the uptake of water through capillary absorption process substantially decrease the bulk electrical resistivity. Pore structure is vital to both the bulk electrical resistivity and the capillary absorption process. In this study, to improve the bulk electrical resistivity and mitigate the capillary absorption, styrene-acrylic emulsion (SAE) and air-entrained agent (AE) were incorporated into the mortar sample to modify the pore structure. The evolution of bulk electrical resistivity during the capillary absorption process was investigated. Results showed that the evolution of bulk electrical resistivity exhibits a periodic change along with the water absorption process. The addition of 6% SAE executes a significant improvement on both bulk electrical resistivity and sorptivity coefficient. To reveal the underlying mechanism, the evolution of electrical resistivity of pore solution and porosity was estimated and measured by a theoretical method and mercury intrusion porosimetry (MIP). Characteristic values of pore structure including tortuosity and connectivity were deduced from models. These obtained values indicated that the tortuosity or connectivity exerts a greater influence on the bulk electrical resistivity compared to porosity. No evident relationship between pore structure and sorptivity coefficient was observed via the conventional Lucas-Washburn model. To integrate the effect of the characteristic parameters of pore structure on the capillary absorption, a fractal model was established. The alternations of SAE and AE on the pore structure were manifested into the change of tortuosity fractal dimension and pore fractal dimension. The sorptivity coefficient calculated from this proposed model is in good agreement with the experimental value.

Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs.

Pore Fractal Characteristics of Hydrate‐Bearing Sands and Implications to the Saturated Water Permeability

AbstractPermeability mainly governs fluid flow through hydrate‐bearing sediments, and its theoretical models play a primary role in the efficiency prediction of gas recovery from hydrate reservoirs by using numerical simulators. Most of these numerical simulators rely on empirical or semiempirical permeability models largely due to the lack of suitable parameters that well quantify the evolution of pore structures. In this study, X‐ray computed tomography scans are conducted on methane hydrate‐bearing sands, followed by extractions of the maximal diameter and fractal dimensions for the pore space occupied by fluids. These extracted parameters, including area and volume pore‐size fractal dimensions, tortuosity fractal dimension, and the area maximal pore diameter, are further extended to develop fractal theory‐based models for predictions of the hydraulic tortuosity and the saturated water permeability in hydrate‐bearing sands. Results show that the pore space occupied by fluids within hydrate‐bearing sands is inherently fractal. The area pore‐size fractal dimension decreases but the tortuosity fractal dimension changes little with increasing hydrate saturation, and the sum of these two fractal dimensions can be used to predict the volume pore‐size fractal dimension. In addition, the area maximal pore diameter decreases with increasing hydrate saturation, and a semiempirical model is proposed. The fractal theory‐based permeability reduction model agrees well with available experimental data, and it can capture the essential physics of saturated water permeability reduction in hydrate‐bearing sediments during hydrate formation.

EFFECTIVE THERMAL CONDUCTIVITY OF POROUS MEDIA WITH ROUGHENED SURFACES BY FRACTAL-MONTE CARLO SIMULATIONS

In this paper, the Fractal-Monte Carlo has been employed to simulate the effective thermal conductivity of porous media with roughened surfaces. The proposed probability model for the effective thermal conductivity of porous media with roughened surfaces can be expressed as a function of the relative roughness, porosity, minimum and maximum diameter of pores, fractal dimensions, and random number. The proposed model is validated by a satisfying agreement of our Fractal-Monte Carlo simulations and the experimental data. In our Fractal-Monte Carlo model, there is no extra empirical constant and each parameter has clear physical meaning. Then, the effects of micro-structural parameters of porous media on the effective thermal conductivity of porous media with roughened surfaces have been analyzed in detail. It can be found that the effective thermal conductivity of porous media with roughened surfaces decreases with the increase of relative roughness and tortuosity fractal dimension. Our results demonstrate that the proposed Fractal-Monte Carlo model can be used to characterize other transport properties such as mass transfer of porous media.

A generalized thermal conductivity model for unsaturated porous media with fractal geometry

Evaluation of effective thermal conductivity (ETC) of unsaturated porous media is significant for many engineering applications and thus has received growing attention in multi-disciplinary fields. However, the existing models for ETC cannot realistically account for the complex pore structures and generally contain empirical parameters. In this study, fractal dimensions for pore size distribution and capillary tortuosity are introduced to characterize the pore-scale structure. A generalized model for ETC of unsaturated porous media is developed based on thermal-electrical analogy. The proposed fractal model has been validated by comparing with available experimental data. The results show that ETC of unsaturated porous media increases with the increase of liquid saturation as the thermal conductivity of solid and liquid phases are larger than that of gas phase. However, ETC is inversely proportional to liquid saturation as the thermal conductivity of solid and liquid phases are smaller than that of gas phase. The pore structures indicate significant effect on ETC of unsaturated porous media. ETC gradually decreases with the increment of porosity and pore fractal dimension as well as tortuosity fractal dimension. All the parameters in the proposed ETC model have specific physical meanings, and it may capture the microstructure characteristics and help understanding the heat transfer mechanisms of unsaturated porous media.

A FRACTAL PERMEABILITY MODEL FOR REAL GAS IN SHALE RESERVOIRS COUPLED WITH KNUDSEN DIFFUSION AND SURFACE DIFFUSION EFFECTS

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

Study on the seepage characteristics of coal based on the Kozeny-Carman equation and nuclear magnetic resonance experiment

It is of great significance to quantitatively describe the change in the permeability of the water-injected coal to improve the effect of the coal seam water injection technology. However, the current permeability model often assumes the pores of the porous medium are smooth, which is a large difference from the coarse coal matrix-pore interface. Therefore, a rough capillary bundle is used as the physical model to characterize the coal structure in this paper. Combined with fractal theory, a permeability model including the tortuosity fractal dimension and the specific surface area of the pores is established based on the traditional Kozeny-Carman equation, and the degree of influence of each factor on the permeability was obtained. Then, liquid permeability and structural parameters of the coal samples from the Daliuta Coal Mine and the Qincheng Coal Mine in China were obtained by nuclear magnetic resonance experiments, which verified the accuracy of the model. The research show that the tortuosity fractal dimension has the greatest influence on the theoretical permeability, and the theoretical permeability decreases rapidly when the tortuosity fractal dimension is between 1.05 and 1.20. Increasing the specific surface area of the pores will lead to an increase in the tortuosity fractal dimension and a decrease in the theoretical permeability. Under the different nuclear magnetic resonance experimental conditions, the theoretical permeability of the coal samples is consistent with the change in the liquid permeability and is closer to the measured value compared with the permeability models of Xu and Liu.

A Novel Porous Media Permeability Model Based on Fractal Theory and Ideal Particle Pore-Space Geometry Assumption

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of our model are closer to the experimental data. The results show that the tortuosity fractal dimension is negatively correlated with porosity, while the pore area fractal dimension is positively correlated with porosity; The permeability is negatively correlated with the tortuosity fractal dimension and positively correlated with the integral fractal dimension of pore surface and particle radius. When the tortuosity fractal dimension is close to 1 and the pore area fractal dimension is close to 2, the faster the permeability changes, the greater the impact. Different particle arrangement has great influence on porous media permeability. When the porosity is close to 0 and close to 1, the greater the difference coefficient is, the more the permeability of different arrangement is affected. In addition, the larger the particle radius is, the greater the permeability difference coefficient will be, and the greater the permeability difference will be for different particle arrangements. With the increase of fractal dimension, the permeability difference coefficient first decreases and then increases. When the pore area fractal dimension approaches 2, the permeability difference coefficient changes faster and reaches the minimum value, and when the tortuosity fractal dimension approaches 1, the permeability difference coefficient changes faster and reaches the minimum value. Our research is helpful to further understand the connotation of medium transmission in porous media.

A fractal permeability model for 2D complex tortuous fractured porous media

The complex fracture networks are of significance to petroleum production in unconventional reservoirs, but effectively predicting its permeability is challenging due to the complex distribution and geometry of fracture networks. This paper proposes a new permeability model for 2D complex tortuous fractured porous media based on fractal theory, and two important characteristics of fractures, i.e. branching and tortuosity are considered in the developed permeability model. In this paper, the fractured porous media is assumed to be made up of a bundle of tortuous fractal-like tree fracture networks. First, the modified cubic law for describing flow rate in a fracture with fractal distribution of tortuosity is derived. Secondly, the fractal-like tree fracture network is used to represent the distribution of complex fracture networks, and then flow rate in a tortuous fractal-like tree fracture network is derived. After that, with the assumption of the fractal scaling law between fracture number and fracture apertures, the total flow rate in a bundle of tortuous fractal-like tree fracture networks is given and then the analytical expression for permeability of 2D complex tortuous fractured porous media is derived. Finally, the model reliability is verified with a case study and the key parameters influencing permeability of 2D fracture porous media are investigated with sensitivity study. The research results show that the fractal dimension of aperture distribution Df, tortuosity fractal dimension DT, branch level m and fracture length ratio γ have significant influence on fracture network permeability; the effects of branch angle θ and the straight length of the zero-level fracture l0 on fracture network permeability are insignificant.

Fractal analysis of shape factor for matrix-fracture transfer function in fractured reservoirs

As the core function of dual-porosity model in fluids flow simulation of fractured reservoirs, matrix-fracture transfer function is affected by several key parameters, such as shape factor. However, modeling the shape factor based on Euclidean geometry theory is hard to characterize the complexity of pore structures. Microscopic pore structures could be well characterized by fractal geometry theory. In this study, the separation variable method and Bessel function are applied to solve the single-phase fractal pressure diffusion equation, and then the obtained analytical solution is used to deduce one-dimensional, two-dimensional and three-dimensional fractal shape factors. The proposed fractal shape factor can be used to explain the influence of microstructure of matrix on the fluid exchange rate between matrix and fracture, and is verified by numerical simulation. Results of sensitivity analysis indicate that shape factor decreases with tortuosity fractal dimension and characteristic length of matrix, increases with maximum pore diameter of matrix. Furthermore, the proposed fractal shape factor is effective in the condition that tortuosity fractal dimension of matrix is roughly between 1 and 1.25. This study shows that microscopic pore structures have an important effect on fluid transfer between matrix and fracture, which further improves the study on flow characteristics in fractured systems.

An Improved Relative Permeability Model for Gas-Water Displacement in Fractal Porous Media

Many researchers have revealed that relative permeability depends on the gas-water-rock interactions and ultimately affects the fluid flow regime. However, the way that relative permeability changes with fractal porous media has been unclear so far. In this paper, an improved gas-water relative permeability model was proposed to investigate the mechanism of gas-water displacement in fractal porous media. First, this model took the complexity of pore structure, geometric correction factor, water film, and the real gas effect into account. Then, this model was compared with two classical models and verified against available experimental data. Finally, the effects of structural parameters (pore-size distribution fractal dimension and tortuosity fractal dimension) on gas-water relative permeability were investigated. It was found that the sticking water film on the surface of fracture has a negative effect on water relative permeability. The increase of geometric correction factor and the ignorance of real gas effect cause a decrease of gas relative permeability.

EVOLUTION OF FRACTAL DIMENSIONS AND GAS TRANSPORT MODELS DURING THE GAS RECOVERY PROCESS FROM A FRACTURED SHALE RESERVOIR

Previous studies ignore the evolutions of pore microstructure parameters (pore diameter fractal dimension [Formula: see text] and tortuosity fractal dimension [Formula: see text]) but these evolutions may significantly impact the gas transport during gas extraction. In order to investigate these evolutions of fractal dimension properties during gas extraction, following four aspects are studied. Firstly, surface diffusion in adsorbed multilayer is modeled for fractal shale matrix. Our new matrix permeability model considers the slip flow, Knudsen diffusion and surface diffusion. This model is verified by experimental data. Secondly, a new fracture permeability model is proposed based on fractal theory and the coupling of viscous flow and Knudsen diffusion. Thirdly, the multilayer adsorption and these permeability models are introduced into the equations of gas flow and reservoir deformation. Finally, sensitivity analysis is performed to determine the key factors on fractal dimension evolution. The results show that the multilayer adsorption can accurately describe the adsorption properties of real shale reservoir. Shale reservoir deformation and gas desorption govern the evolutions of fractal dimensions. The multilayer adsorption and adsorbed gas porosity [Formula: see text] play an important role in the evolutions of fractal dimensions during gas extraction. The monolayer saturated adsorption volume [Formula: see text] is the most sensitive parameter affecting the evolution of fractal dimensions. Therefore, the effects of gas adsorption on the evolution of fractal dimensions cannot be neglected in shale reservoirs.

A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

Three-dimensional modeling and analysis of macro-pore structure of coal using combined X-ray CT imaging and fractal theory

The porous structure of coal directly determines its gas transport property. The fluid flow behavior of coal is one of the key science questions that will influence the coal energy industry. In this study, the influence of real coal macropore structure on the fluid flow through coal was studied through 3-D coal structure reconstruction by the CT images. Based on the reconstructed coal structure, the micron-scale structure parameters were quantitatively analyzed. A newly programmed Matlab code was established to find the volume fractal dimension, obtain the relationship between porosity/permeability of coal and volume fractal dimension, and estimate the tortuosity fractal dimension by using the 3-D box dimension algorithm. The results show that the volume fractal dimensions of 6 coal samples range from 2.25 to 2.79 and the tortuosity fractal dimensions of capillaries range from 2.15 to 2.73. The 3-D coal structure cannot only quantitatively estimate the real porosity of the coal, but it can be used to characterize the complexity of coal's porous structure through mean deviation of surface porosity. It can be clearly seen from the reconstructed coal that coal specimen-C3 is highly heterogeneous because it has complex pore structure as well as wider pore size distribution and the highest mean deviation of the surface porosity. The volume fractal dimension can be used to quantitatively define the complexity of pores. The larger the porosity of coal, the greater the fractal dimension. The permeability and porosity of coal are negatively correlated with the volume fractal dimension. The tortuosity fractal dimension can effectively characterize coal permeability, but it weakly correlates with coal porosity. The outcome of this study helps to understand the structure-based flow characterization and gas transport behavior in heterogenous coal which will have the implication of the gas extraction from coalbed methane reservoirs and coal mine gas drainage.

Relative Permeability Model Taking the Roughness and Actual Fluid Distributions into Consideration for Water Flooding Reservoirs

Reservoir relative permeability is greatly important to the development of water flooding reservoirs. Currently, most researches on relative permeability have not taken the roughness of pore surface and actual fluid distributions into consideration. In this paper, a novel relative permeability model for water flooding reservoirs taking the roughness and actual fluid distributions into consideration has been proposed by using the fractal theory. The novel model contains some key parameters, all of which have clear physical meanings, such as the immobile liquid film thickness, relative roughness, tortuosity fractal dimension $$ D_{\text{T}} $$ and pore fractal dimension $$ D_{\text{f}} $$ . The predicted results of the novel fractal relative permeability model are consistent with published experimental data. That verifies the correctness of the novel fractal relative permeability model. Finally, sensitive factor analysis of novel relative permeability model is conducted. We can find that the wetting fluid relative permeability decreases as the immobile wetting fluid film thickness or relative roughness increases. When the tortuosity fractal dimension or pore fractal dimension increases, the wetting relative permeability and non-wetting relative permeability will both decrease. An increase in maximum pore diameter or the decreasing of minimum pore diameter results in the reduction in fractal dimension of flow channel and discontinuous saturation. The increasing of maximum pore diameter results in an increase in the relative permeability of wetting fluid. The minimum pore diameter has tiny effect on the relative permeability.

KOZENY–CARMAN CONSTANT FOR GAS FLOW THROUGH FIBROUS POROUS MEDIA BY FRACTAL-MONTE CARLO SIMULATIONS

In this paper, the Kozeny–Carman constant of fibrous porous media is simulated by the Fractal-Monte Carlo technique. The proposed probability model of the Kozeny–Carman constant is obtained based on the fractal distribution of pore size in fibrous porous media, and thus can be expressed as a function of structural parameters of fibrous porous media, including porosity, micro-pore size, fiber diameter, tortuosity fractal dimension and area fractal dimension of pores. Our results demonstrate that the Kozeny–Carman constant of fibrous porous media increases with increases in tortuosity fractal dimension and fiber diameter. Our results also illustrate a satisfying agreement of the Fractal Monte-Carlo simulations obtained by the proposed model and the existing experimental data. Therefore, the proposed Fractal-Monte Carlo technique can be used to characterize other transport properties of fluid in fibrous porous media.