Kozeny-Carman Equation Research Articles

Experimental and simulation study of calcium carbonate non-uniform distribution characteristics of bio-cemented sand

The innovative technology of microbially induced calcium carbonate precipitation (MICP) soil modification is widely used in soil reinforcement, soil remediation, environmental remediation and other fields, and has gradually become a hot research direction. Recent research is more focused on the overall physical and mechanical characteristics of the uniform reinforced specimen. There is limited research on the distribution characteristics of calcium carbonate along the seepage path during the reinforcement process. However, the distribution characteristics of calcium carbonate play a significant role in the physical and mechanical characteristics of the solid, especially in the large-scale MICP reinforcement process. In this study, based on the microbial mineralization reaction tests of different concentrations of cement solution at the laboratory sample scale, the calcium carbonate distribution on the surface of the sample at the microscale SEM observation and the CT scanning reconstruction of the micro pore structure characteristics of the microbial reinforced soil, we discussed the characteristics of the non-uniform reduction of calcium carbonate distribution and porosity in the process of microbial consolidation. Based on the Kozeny-Carman equation, the conceptual model of effective porosity was introduced, and the time relationship between porosity and calcium carbonate precipitation was considered to establish a bio-chemical-seepage multi-physics field coupling model. The precipitation of calcium carbonate in the axial direction of the model sample exhibits an uneven feature of more at the top and less at the bottom, and the distribution characteristics of porosity also show an uneven feature of more at the top and less at the bottom.

Effects of particle density and fluid properties on mono-dispersed granular flows in a rotating drum

Due to their simple geometric configuration and involved rich physics, rotating drums have been widely used to elaborate granular flow dynamics, which is of significant importance in many scientific and engineering applications. This study both numerically and experimentally investigates dry and wet mono-dispersed granular flows in a rotating drum, concentrating on the effects of relative densities, ρs−ρf, and rotating speeds, ω. In our numerical model, a continuum approach based on the two-phase flow and μI theory is adopted, with all material parameters calibrated from experimental measurements. It is found that, in the rolling and cascading regimes, the dynamic angle of repose and the flow region depth are linearly correlated with the modified Froude number, Fr*, introducing the relative density. At the pore scale, flow mobility can be characterized by the excess pore pressure, pf. To quantify the variance of the local pf, it is specifically nondimensionalized as a pore pressure number, K, and then manifested as a function of porosity, 1−ϕs. We find K(ϕs) approximately follow the same manner as the Kozeny–Carman equation, K∝ ϕs2/1−ϕs3. Furthermore, we present the applicability of the length-scale-based rheology model developed by Ge et al. [“Unifying length-scale-based rheology of dense suspensions,” Phys. Rev. Fluids 9, L012302 (2024)], which combines all the related time scales in one dimensionless number G, and a power law between G and 1−ϕs/ϕc is confirmed. This work sheds new lights not only on the rigidity of implementing continuum simulations for two-phase granular flows, but also on optimizing rotating drums related engineering applications and understanding their underlying mechanisms.

Layout optimization of pore microstructure in fluid-saturated porous media using Galerkin decoupling technology and independent continuous mapping method (GDT-ICM)

A layout optimal design method combining Galerkin decoupling technology and independent continuous mapping method (GDT-ICM) is proposed to rearrange the layout of pore microstructure. Firstly, the Galerkin decoupling technology (GDT) is employed to solve the Brinkman equation for fluid flow in fluid-saturated porous media, which integrates the Stokes equation and Darcy's law. Within this framework a self-programmable element balance equation is developed. Secondly, a permeability interpolation function is defined for each element, incorporating the permeability of the fluid and pore microstructure. This function distinguishes strictly between the fluid domain and the pore domain. Pore microstructures with arbitrary shape including permeability information are established in an Euler mesh by introducing the Carman-Kozeny equation, shape functions, the Joukowski mapping and filter functions (the modified arctan mapping function and the ‘inpolygon’ function) based on the ICM method. Thirdly, a layout optimization model aiming at minimizing energy dissipation is established to accomplish the optimal distribution of pore microstructures. A sensitivity analysis is calculated with respect to design variables and the optimal model is solved by a genetic algorithm. Numerical results demonstrate that the proposed method is effective and feasible in 2D-space. The maximum velocity within the fluid field is reduced by 45%, and the issue of localized high pressure occurring around the pore is solved. This paper provides guidance for solving the Brinkman coupled equation and the layout optimization of the microstructure in porous media.

A coarse-grained approach to modeling gas transport in swelling porous media

In many engineering applications, understanding gas adsorption and its induced swelling in nanoporous materials is crucial. In this study, we propose a novel coarse-grained molecular dynamics (CGMD) model with gas-gas, solid-solid, and gas-solid interactions explicitly controlled to achieve the coupling between gas transport and solid deformation at the microscale. The CGMD model has the capability to recover solid and gas properties, including density, Young's modulus of the solid, and viscosity of the gas to generate a broad range of swelling ratios relevant to nanostructures by using the innovative bead-spring chain networks. A comparison is made between gas transport through deformable and non-deformable nanochannels of varying sizes (35.4–123.9 nm), which is also compared with the macroscopic Hagen-Poiseuille equation. The proposed model has been further tested in a simplified nanoporous medium composed of four randomly distributed spherical solids. The Kozeny-Carman equation can generally describe the relationship between permeability and porosity, but small deviations are observed in the case of swelling porous media. Our results justify the effect of swelling on reducing gas permeability and provide a new approach to modeling gas transport in swelling porous media at the microscale within the framework of CGMD, with potential applications spanning nanofluidics, energy storage technologies, and environmental nanotechnology.

Applying machine learning for hydraulic flow unit classification and permeability prediction: case study from carbonate reservoir in the Southern part, Song Hong basin

Machine learning (ML) is an artificial intelligence (AI) that enables computer systems to classify, cluster, identify, and analyze vast and complex sets of data while eliminating the need for explicit instructions and programming. For decades, machine learning has become helpful for complex reservoir characterization such as carbonate reservoirs. Permeability prediction from well logs is a significant challenge, especially when the core data is rarely available due to its high cost. In this study, we aimed to bridge this gap by demonstrating the practical application of integrating Hydraulic Flow Units (HFU) and machine learning methods. Our goal was to provide a reliable estimation of permeability using core and wireline logging data in the complex Middle Miocene carbonate reservoir of the CX gas field in the southern part of the Song Hong basin. In the first step, due to the reservoir’s heterogeneity, the core plug dataset was classified into 5 HFUs based on the flow zone indicators (FZI) concept from the modified Kozeny-Carman equation using unsupervised machine learning - K-means method. The porosity - permeability for each HFU was defined after HFU clustering. In the second step, we designed three different workflows to predict permeability and HFU using supervised machine learning from a combination of core and log data. These workflows were rigorously test and compared with the core data. The most accurate result was chosen as the base, providing a high confidence level in our predictions’ reliability.

A new fractal pore-throat chain model for non-Darcy flow through porous media

Non-Darcy flow through porous media is of great significance in hydraulics, oil and gas engineering, biomedical science, chemical and civil engineering etc. However, it is difficult to fully grasp the nature of fluid flow through porous media from macroscopic scale alone. Based on the statistically fractal scaling laws of pore structures, a new fractal pore-throat chain model (FPTCM) for non-Darcy flow through the isotropic porous media is developed. The analytical expressions for the Darcy and non-Darcy permeability as well as non-Darcy coefficient are derived accordingly. In order to explore the local flow field of high-speed non-Darcy flow through porous media, the finite element method is also carried out on an equivalent pore-throat unit. The predicted permeability by FPTCM shows better agreement with present numerical results and available experimental data, compared with commonly used semi-empirical formulas including Kozeny-Carman and Ergun equations. It has been found that both Darcy and non-Darcy permeability as well as non-Darcy coefficient strongly relate to the pore structures of porous media. The non-Darcy permeability is positively correlated to porosity, pore fractal dimension and Darcy permeability, while it is negatively related to tortuosity fractal dimension and pore size range. The non-Darcy coefficient shows opposite correlation with these parameters. The present work can provide theoretical basis for oil and gas development, nuclear waste treatment, carbon dioxide geological sequestration etc.

Evaluation and development of pedotransfer functions of saturated hydraulic conductivity for subtropical soils

The determination of soil saturated hydraulic conductivity (Ks) is crucial in environmental and engineering fields. However, the current direct measurement methods of Ks are time-consuming and labor-intensive. As an alternative method, many researchers have developed a series of pedotransfer functions (PTFs) that estimate Ks based on easily accessible soil properties. Unfortunately, most existing PTFs of Ks focus on temperate and tropical regions in the United States and Europe. There is a lack of research discussing the applicability of Ks models in subtropical areas. To resolve this issue, we conduct a study using 515 subtropical soil samples to test the performance of existing PTFs of Ks. The Ks values of investigated soils range from 1.4 × 10-4 to 290 cm h−1. Among the affecting factors, soil bulk density (ρb) and effective porosity (φe) are found to be the most important variables. Current PTFs considering soil pore structural property (i.e., φe) or soil texture solely are not effective in assessing Ks of subtropical soils. To address this limitation, we integrate soil pore structural and textural properties and develop a new PTF based on the Kozeny-Carman equation. The performance and reliability of the new PTF are evaluated using independent Ks datasets from various regions. The results show a significant positive correlation between the measured Ks and the predicted Ks from the new PTF for subtropical soils with an R2 of 0.69, an average RMSE in log10Ks (cm h−1) of 0.496, and a mean bias value of 0.070. Besides, the new PTF is found to perform as well as widely used machine learning tools.

Model for fracture conductivity considering particle size redistribution caused by proppant crushing

Clarifying the dynamic evolution and control mechanisms of fracture conductivity is crucial for optimizing hydraulic fracturing design. Previous studies on fracture conductivity mechanisms in deep shale reservoirs have been insufficient, particularly when considering proppant crushing, rendering existing models inapplicable. Therefore, in this study, the coupled effects of particle size redistribution caused by proppant crushing were considered. A particle crushing model based on fractal theory was introduced. It was combined with the Kozeny–Carman equation, and equations were derived for the evolution of the equivalent diameter of the proppant pile gradation curve and permeability, establishing a new model for predicting the fracture conductivity considering the particle size redistribution caused by proppant crushing. Furthermore, it provides an optimized chart of conductivity that matches the supply conductivity of the reservoir. The results of the study reveal that the fracture conductivity decreases owing to proppant rearrangement, compaction, and crushing, with a more significant decline in the initial compression stage, where the rate of conductivity reduction is 2.5 times that of the compaction stage. Proppant crushing shifts the gradation curve leftward, reducing the equivalent particle diameter and, consequently, the fracture conductivity. By adjusting the crushing ratio, apparent Young's modulus, looseness factor, and proportion of large-particle components of the proppant, the fracture conductivity can be controlled. This provides a theoretical basis for the development of proppant properties and fracturing optimization in deep shale reservoirs.

Assessing the impact of pore‐fracture structures on permeability sensitivity in tectonic coal using computerized tomography scanning

AbstractThe heterogeneity in permeability of coal reservoirs is primarily attributed to the considerable variation in the morphologies and structures of microscopic pore‐fractures, shaped by complex geological processes. This study emphasizes the necessity of understanding the impact and governance of these morphological and structural variations in pore‐fractures across different types of coal bodies on their permeability. Utilizing computerized tomography scanning and three‐dimensional imaging, we examined coal samples from the Datong coalfield in the southeastern Qinshui Basin, Shanxi Province, to characterize the pore‐fracture morphologies and structures distinct to various coal‐body types based on tomographic data. This introduces a methodology for assessing the influence of microscopic pore‐fracture parameters, such as porosity, specific surface area, tortuosity and fractal dimension, on permeability sensitivity. This is achieved through the application of the modified Kozeny–Carman equation and a fractal permeability model. Findings indicate a predominance of slab fractures in raw coal, whereas fragmented coal under weak brittle deformation exhibits small, isolated pore‐fractures with minimal diameter and volume and poor connectivity. In contrast, granular coal subjected to strong brittle deformation features extensive clusters of large pore‐fractures with significant diameter and volume, enhancing connectivity. Moreover, permeability predictions are refined by integrating the modified Kozeny–Carman equation with tomographic data, offering a more precise understanding of the permeability across different coal bodies.

A practical equation for predicting saturated hydraulic conductivity of fine-grained soils

The saturated hydraulic conductivity (ks) of soils plays a crucial role in various agricultural and environmental engineering applications, particularly in relation to pollution prevention and water migration. Firstly, the traditional Kozeny-Carman (KC) equation, which are commonly used to estimate ks, has limitations in predicting ks for different types of fine-grained soils based on the analyses of permeability test data in the literature. Secondly, to tackle this issue, a modified KC equation was proposed by introducing an expression for the shape parameter and establishing a relationship between the tortuosity equation and the plastic limit. Additionally, the validation of the proposed equation was conducted using ks values of 25 fine-grained soils obtained from other sources. Finally, a comparison was made with the four commonly used ks models to evaluate its performance. The results indicate that the proposed equation demonstrates a relatively high coefficient of determination and a low root mean square error. This suggests that the proposed equation has the potential to accurately assess ks for fine-grained soils. The predictions for ks using the modified equation showed good agreement with the experimental data mentioned in the literature.

Laboratory investigation and prediction of permeability of fresh to five-year-old municipal solid wastes of low and high food contents

The permeability of municipal solid wastes (MSWs) is important for the design and operation of landfills. This study presented the experimental investigation of the permeability of low food content- (LF-) and high food content- (HF-) MSWs prepared in laboratory-scale bioreactors for up to 5 years. The permeability of MSWs with diverse degrees of decomposition (DOBs), void ratios, and permeation liquids was measured (288 tests). The measured permeability was compared to that predicted from the (modified) Kozeny-Carman (K-C) equations in four different forms. The results indicated that the permeability of both LF- and HF-MSWs decreased significantly (p < 0.05) with decomposition under a given void ratio. The predicted permeability using the original K-C equation fitted well with that of fresh MSWs. The permeability of decomposed MSWs was closer to the predicted results using the modified K-C equation with the effective void ratio. This can be attributed to the increase in the fine fractions due to degradation. The reduction in the effective voids was more significant with HF-MSWs. The parameters required in the (modified) K-C equations showed a good correlation with DOB and effective particle size (d10). The predicted permeability based on the relationship between DOB (or d10) and equation parameters was within 3 times the difference compared to the measured values. The above results indicated that the modified K-C equation can be adopted to predict the permeability of fresh and degraded MSWs while more field-scale experiments should be conducted to further evaluate its feasibility.

Developing and Assessing Performance of a Laboratory-Scale Fluidized Bed Dryer

A laboratory-scale batch fluidized bed dryer with 75 mm bed diameter was designed, fabricated and evaluated to study the hydrodynamics of river sand as well as the drying of cassava mash and bitter kola particulates. The hydrodynamics properties such as minimum fluidization velocity, effect of bed height and pressure drop across the bed, effect of particle size and density on minimum fluidization velocity and stability of the bed column of river sand were studied. Drying of cassava mash to edible garri was carried out at in fluidized bed dryer at controlled temperatures. Drying characteristics of the laboratory fluidized bed dryer was compared with the laboratory WiseVen oven (model number: WOF - 105) using bitter kola particulate material sample. The experimental results from laboratory-scale fluidized bed dryer showed that the minimum fluidization velocity increases as material density increases and the value of the minimum fluidization velocity obtained from the fluidized bed gave good agreement with other empirical correlation such as Kozeny-Carman Equation. The fluidized bed dryer showed high rates of moisture removal over the conventional oven with the ratio of 1:29 under the same operating conditions. Drying of cassava mash to edible garri was achieved at lower drying temperatures of 83 oC \(\pm\) 3 oC at 55 minutes when compared to conventional frying temperatures of cassava mash to edible at 180 – 200 oC thereby saving energy cost. Hence, this fluidized bed dryer is recommended for use in demonstrating hydrodynamics and drying of particulate materials in the laboratory.

Efficient estimation of crystal filterability using the discrete element method and the Kozeny-Carman equation

A new method is proposed for efficiently predicting filter cake resistance as a function of crystal size distribution. The method is useful for the preliminary design of processes where an economic tradeoff is encountered between a crystallization step and a filtration step. In that case it is necessary to estimate the filter cake resistance repeatedly as a function of crystal size distribution for the process design and optimization. The method is faster than CFD-DEM and more precise than the random packing assumption. The proposed method is validated using published experimental data. To demonstrate the proposed method, an integrated crystallization-filtration process of ammonium alum is simulated and analyzed. The results show that by increasing the residence time of ammonium alum crystals in the crystallizer from 15 min to 60 min, the crystal cake resistance can be reduced by 42% and the filter area can be reduced by 23%.

Data-driven calculation of porous geometry-dependent permeability and fluid-induced wall shear stress within tissue engineering scaffolds

It is commonly known that mechanical stimulation, for example, wall shear stress (WSS), can affect cellular behaviours. In vitro experiments have been performed by applying fluid-induced WSS to investigate the cell physiology and pathology. Porous scaffolds are used in these experiments for housing and facilitating the micro-physical/chemical environment on cells during 3-dimensional (3D) cell culturing. It is known that scaffold porous geometries influence scaffold permeability and internal WSS. Computational simulations are commonly employed to determine the WSS; however, these simulations can be computationally expensive and may not be readily accessible to everyone due to a knowledge gap. To address this limitation, this study proposes an empirical equation for calculating the scaffold permeability based on the Kozeny-Carman equation. The new equation considers the porous geometric features, providing an accurate estimation of the scaffold permeability. Furthermore, the study introduces a new correlation between WSS and permeability, aiming to establish an efficient and precise estimation of internal WSS. This correlation enables efficient estimation of the WSS within porous scaffolds without relying on computationally demanding simulations. Therefore, the output from this study can negate the issues of using computational simulation for determining scaffold permeability and internal WSS under perfusion flow by providing empirical equations.

Assessing heterogeneous groundwater systems: Geostatistical interpretation of well logging data for estimating essential hydrogeological parameters

This research presents an unsupervised learning approach for interpreting well-log data to characterize the hydrostratigraphical units within the Quaternary aquifer system in Debrecen area, Eastern Hungary. The study applied factor analysis (FA) to extract factor logs from spontaneous potential (SP), natural gamma ray (NGR), and resistivity (RS) logs and correlate it to the petrophysical and hydrogeological parameters of shale volume and hydraulic conductivity. This research indicated a significant exponential relationship between the shale volume and the scaled first factor derived through factor analysis. As a result, a universal FA-based equation for shale volume estimation is derived that shows a close agreement with the deterministic shale volume estimation. Furthermore, the first scaled factor is correlated to the decimal logarithm of hydraulic conductivity estimated with the Csókás method. Csókás method is modified from the Kozeny-Carman equation that continuously estimates the hydraulic conductivity. FA and Csókás method-based estimations showed high similarity with a correlation coefficient of 0.84. The use of factor analysis provided a new strategy for geophysical well-logs interpretation that bridges the gap between traditional and data-driven machine learning techniques. This approach is beneficial in characterizing heterogeneous aquifer systems for successful groundwater resource development.

A new index to measure the uniformity of remolded loess

The uniformity of remolded loess is crucial for engineering stability and in laboratory testing, as it affects physical and mechanical properties. It is important to have an index which can accurately and conveniently evaluate the uniformity of remolded loess. This study demonstrated and verified the feasibility of using hydraulic conductivity (K) as an indicator for evaluating the uniformity of remolded loess through laboratory experiments and theoretical analysis. In laboratory research, nine loess samples under different preparation conditions were meticulously prepared in duplicate, which were divided into three sets according to the whole dry density (WDD) of approximately 1.3 g/cm3, 1.4 g/cm3, and 1.5 g/cm3 respectively. For the nine duplicate samples, two procedures were performed for each of the sample. One is the uniformity analysis by cutting the soil column and weighing. The other is the hydraulic conductivity experiment. Results showed that sample uniformity is affected by sample preparation conditions, and there are differences in the uniformity of the same WDD samples. The values of K positively correlate with the degree of sample uniformity. In theoretical analysis, based on Darcy’s Law and Kozeny-Carman equation, it is found K is inversely proportional to the variance (σ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma^{2}$$\\end{document}) of the sample dry density. That is, K is positively proportional to the sample uniformity. Since K can be easily determined in the laboratory, the application of this new index in the field of geotechnical engineering makes it very convenient and simple to evaluate the uniformity of remolded loess.

The Effect of Porous Media Grain Size on non-Darcy Flow Behavior using Pore Scale Simulation

The impact of grain size of the porous media of the 3D images of a beadpack on the permeability values and non-Darcy flow behaviour is analyzed using pore-scale flow modelling utilizing the finite volume method. In this study, the sample used was a 3D image from random tight packing of spheres (beadpack) with a size of 250×250×250 voxels and a porosity of 0.36. Variation in grain size is carried out by upscaling the 3D image sample, so that this treatment affects the specific surface area value but does not change the porosity and tortuosity of the sample. Several variations of grain diameter include 100 μm, 125 μm, 150 μm, 175 μm, and 200 μm. In this study, we adopted PIMPLE algorithm, which combines SIMPLE and PISO algorithms to accomplish the Navier-Stokes equations of fluid dynamics in such porous media. The simulation results show that the permeability value exhibits an inverse relationship with the specific surface area. This correlation is in accordance with the Kozeny-Carman equation. In addition, the initiation of non-Darcy flow occurs at the reference length-based Reynolds number of 2.06 and the permeability-based Reynolds number of 0.049.

Multi-well clustering and inverse modeling-based approaches for exploring geometry, petrophysical, and hydrogeological parameters of the Quaternary aquifer system around Debrecen area, Hungary.

This research aims to explore the application of an unsupervised machine learning and inverse modeling-based methods to map the aquifers geometry and investigate the petrophysical and hydrogeological parameters of the Quaternary aquifer system around the Debrecen area, Eastern Hungary. The study utilized a limited well-logs, including spontaneous potential, natural gamma ray, and normal resistivity logs. The k-means clustering technique is applied to identify the distribution of lithological facies within the formerly identified basin-scale hydrostratigraphical units of coarsening upward, alluvial, valley incision, and Late Miocene deposits. Based on the mathematical and geological considerations, the analysis revealed three main clusters (C1, C2, and C3), representing different lithofacies of shale, shaly sand, and sand and gravel. The result of the cluster analysis is further validated with a surface geophysical survey using the vertical electrical sounding (VES) technique. Furthermore, an inverse-modeling-based approach using Csókás method is employed to detect the vertical and horizontal distribution of the hydraulic conductivity along these units. Csókás model is empirically modified from the Kozeny-Carman equation that suites the unconsolidated freshwater-bearing units. The results indicated that the petrophysical and hydrogeological parameters widely ranged with the hydraulic conductivity between almost zero in the shaly layers to more than 21.5 m/d in the sandy and gravely layers. However, the valley incision unit aquifers showed a more uniform distribution of hydraulic conductivity. Based on these results, the Quaternary aquifers in the Debrecen area are classified as moderate to highly productive and ideal for groundwater development. The applied methodology contributed to understanding the complexity of the hydrogeological conditions, providing a robust approach to characterize the heterogeneous groundwater systems.

Experimental and model analysis of the effect of pore and mineral characteristics on fluid transport in porous soil media

The fluid transport in porous media is a critical property for oil and gas exploitation, construction engineering, and environmental protection. It is profoundly influenced by pore geometry and mineral properties. Currently, the Kozeny–Carman equation serves as the permeability prediction equation for porous media, established on the circular pores model. However, it fails to fully account for the impact of pore shape and mineral properties of the soil, leading to significant deviations between predicted and measured soil permeability results. In this paper, based on scanning electron microscope image and mercury intrusion porosimetry, the pores were divided into circular pores and narrow slit pores according to the ratios of pore area and circumference. Then, the quantitative expression of the two types of pores and their connectivity and tortuosity were given, and the circular and narrow slit composite pore model was used to describe the soil pore. Subsequently, the electrostatic potential of pore water was calculated by the Poisson–Boltzmann equation to consider the adsorption effect of minerals on pore water. Combined with the Navier–Stokes equation, the permeability prediction equation considering pore geometry, pore connectivity, and tortuosity and mineral properties was established. Finally, the experimental results illustrated that the theoretical prediction results were in good agreement with the experimental results. The proposed permeability prediction equation proves valuable for assessing and predicting the fluid transport in porous media.

Experimental and Numerical Study of the Effect of Rock Dissolution on Absolute Permeability of Limestone Sub-Samples

Permeability is a key transport property of porous materials, and its accurate evaluation is relevant when studying applied tasks, such as CO2 injection into reservoirs and investigating groundwater quality. This study examines the dependence of permeability on total and connected porosity, hydraulic tortuosity, specific surface area, and mean pore radius based on the data of 408 cubic sub-volumes extracted from heterogeneous and naturally fractured cylindrical carbonate samples, before and after injection of HCl solutions. These parameters were computed using pore-scale modeling of fluid flow. Our results show that permeability correlates well with porosity and mean pore radius, with correlation coefficients of R2≈0.65−0.79 for heterogeneous samples. It was found that the presence of natural fractures significantly influenced the relationship between permeability and other parameters. The relationship between permeability k, tortuosity τ, and specific surface area S is described by the power laws k~τ−α and k~S−β, with coefficients α and β substantially exceeding those in the Kozeny–Carman equation. It was also found that there is a parabolic relationship between connected and total porosities, both before and after rock dissolution with R2≈0.96−0.99. This allowed for an estimation of percolation threshold porosity in accordance with the literature data.