Real Porous Media Research Articles

Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise

This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than the autonomous equations when modelling real world phenomena. Such equations find applications in many fields such as transport in porous media, quantum fields theory, electromagnetism and nuclear physics. Numerical approximations of autonomous SPDEs are thoroughly investigated in the literature, while the non-autonomous case are not yet well understood. Here, a non-autonomous SPDE is discretized in space by the finite element method and in time by the linear implicit Euler method. We break the complexity in the analysis of the time depending, not necessarily self-adjoint linear operators with the corresponding semi group and provide the strong convergence result of the fully discrete scheme toward the mild solution. The results indicate how the converge orders depend on the regularity of the initial solution and the noise. Additionally, for additive noise we achieve convergence order in time approximately 1 under less regularity assumptions on the nonlinear drift term than required in the current literature, even in the autonomous case. Numerical simulations motivated from realistic porous media flow are provided to illustrate our theoretical finding.

An improved simulated annealing algorithm for reconstructing 3D large-scale porous media

Based on the morphological information obtained from 2D slice images of real porous media, an improved simulated annealing algorithm (SAA) was proposed to reconstruct 3D large-scale porous media, which are intractable to handle for conventional SAA. Three different statistical functions were introduced to characterize the morphological information of real sandstone, including the one-point probability function, the two-point probability function and the lineal-path function. By changing the update method of the two-point probability function and the lineal-path function, i.e., using incremental calculation instead of conventional global calculation, the efficiency of reconstructing 3D large-scale porous media was greatly improved. Besides, in the later stage of reconstruction that the basic structure of porous media had been formed, the pixel selection algorithm was performed to speed up the reconstruction process. To evaluate the accuracy of the improved SAA, the similarity between the 3D reconstructed volume and the reference image of prototype sandstone was examined. The results showed good agreement between the reconstructed model and the references. The efficiency of the improved SAA was verified by comparison with the conventional SAA, the results of which indicated that the improved SAA can significantly shorten the reconstruction time of 3D large-scale porous media.

Pore-Scale Simulations of Single- and Two-Phase Flow in Porous Media: Approaches and Applications

We present a review of pore-scale simulations of immiscible fluid transport with focus on two of the most popular approaches: lattice Boltzmann modeling for direct simulations on digital models of the pore space and simulations on network models extracted from the pore space. This review focuses on covering basic theory and implementation strategies and gives the readers input and motivation to start their own pore-scale simulations and relate them to realistic porous media. We present a review of recent and relevant applications and how a digital workflow that combines advanced pore-scale imaging and simulations can give very useful input to different fields of science and industry, including reservoir characterization. Given the large span in methods and applications, this review does not aim to cover all methods or applications. However, it covers popular methods and describes to some extent their applicability to different types of transport problems.

Impact of Synthetic Porous Medium Geometric Properties on Solute Transport Using Direct 3D Pore-Scale Simulations

Transport processes in porous media have been traditionally studied through the parameterization of macroscale properties, by means of volume-averaging or upscaling methods over a representative elementary volume. The possibility of upscaling results from pore-scale simulations, to obtain volume-averaging properties useful for practical purpose, can enhance the understanding of transport effects that manifest at larger scales. Several studies have been carried out to investigate the impact of the geometric properties of porous media on transport processes for solute species. However, the range of pore-scale geometric properties, which can be investigated, is usually limited to the number of samples acquired from microcomputed tomography images of real porous media. The present study takes advantage of synthetic porous medium generation to propose a systematic analysis of the relationships between geometric features of the porous media and transport processes through direct simulations of fluid flow and advection-diffusion of a non-reactive solute. Numerical simulations are performed with the lattice Boltzmann method on synthetic media generated with a geostatistically based approach. Our findings suggest that the advective transport is primarily affected by the specific surface area and the mean curvature of the porous medium, while the effective diffusion coefficient scales as the inverse of the tortuosity squared. Finally, the possibility of estimating the hydrodynamic dispersion coefficient knowing only the geometric properties of porous media and the applied pressure gradient has been tested, within the range of tested porous media, against advection-diffusion simulations at low Reynolds (<10-1) and Peclet numbers ranging from 101 to 10-2.

The effect of various lengths of pores and throats on the formation resistivity factor

Pore geometry, quantified by the length and size of the pore space, affects the electrical resistivity of the porous media. However, the length described by the geometrical tortuosity and pore topology effect on the resistivity of the model does not thoroughly consider the existing pore geometrical models, which only investigate the pore size, throat length and throat size of the models. A modified capillary model including a pore body and several throats derived the formation factor from the coordination number, the cross-sectional area ratio and geometrical tortuosity of the pores and throats in the model. The derived relationship between the formation factor and porosity of the capillary model compared with the formation factor versus porosity for the various rock types was shown in a plot. The geometrical tortuosity of each rock type almost followed the electrical tortuosity of the related rock type, and the electrical tortuosity was larger than the geometrical tortuosity caused by the variation in the size of the pore and throat. For low porosity, the resistivity of the real porous media was lower than the resistivity of the Archie equation due to the low values of the pore-to-throat cross-sectional area ratio and geometrical tortuosity. The sandstones and interparticle carbonates presented a porosity exponent close to 2.0 and an electrical tortuosity from 1.5 to 4.0 on the plot of the porosity exponent versus electrical tortuosity. The fractured carbonate showed a porosity exponent from 1.0 to 1.6 and an electrical tortuosity ranging from 1.0 to 3.0, while the vuggy carbonates were widely distributed, with a porosity exponent larger than 2.0 and an electrical tortuosity ranging from 2 to 8. This new model correlates the formation factor and porosity to the combination of the coordination number with the geometrical tortuosity and the throat and pore cross-sectional area ratios, thus enhancing the understanding of the pore geometry and topology effect on the electrical resistivity of a porous media with various pore types.

The Forecasting of Deformational and Strength Properties of Metals with Uniformly Scattered Defects in Form of Spherical Hollows at Single and Cyclic Loading

The technique of forecasting deformation and strength properties of metallic materials with uniformly distributed over the structure volume defects such as hollows under single and cyclic loading is considered. The proposed approach is based on the use of the corresponding characteristics of a defect-free material and the results of numerical experiments on samples models with different degrees of porosity of the medium. Analysis of the stress–strain state of objects was performed by the finite element method. The results of the study can be used both to normalize the permissible sizes of defects and their density, and to assign valid safety factors for stress and strain of a real porous medium.

A new model of emulsion flow in porous media for conformance control

Emulsion flow in porous media is of paramount importance to the use of emulsions in the conformance control and enhanced oil recovery processes. In this paper, a new theoretical model, incorporating physical properties of porous media, physicochemical properties of the emulsion system, injection strategy, and the interactions between porous media and emulsion, was developed to quantitatively describe flow behaviors of emulsions in porous media. The resistance factor of an emulsion when transported in porous media was first derived through a-two phase flow method. The strong interaction between emulsion droplets and porous media was characterized by the capillary resistance force in the model. A non-uniform capillary model which considers size differences of the pore-body and pore-throat in porous media was proposed to represent the complicated real porous media. By analyzing the adsorption and plugging properties of different emulsion droplets in the non-uniform capillary model, the capillary resistance force was finally determined. To describe emulsion flow in the subsequent water flooding process after emulsion injection, an emulsion dilution factor was introduced into the model. A set of experimental data of emulsion flow in sandpacks was used to validate the reliability of the newly proposed model. The validation results show that by appropriately choosing coefficients, the simulated results are in good agreement with experimental values, with a maximum average absolute error less than 10%, and the developed theoretical flow model can be used to describe emulsion flow behavior in porous media.

Pore-scale modeling of nanoparticle transport and retention in real porous materials

Modern pore-scale modeling has the ability to simulate flow and particle (i.e., colloids, nanoparticles) transport at the pore- and particle-scale in realistic porous media. The pore structure of a material can be obtained through x-ray micro tomography (XCT) or a similar three-dimensional imaging technique. From these data sets, fluid and particle transport can be simulated by direct numerical simulation of the fundamental equations of motion. In this paper, we employ the finite element method to simulate Stokes flow and, after the flow field is resolved, Lagrangian particle tracking to track the fate and transport of nanoparticles (NPs). The presented methodology for direct numerical modeling allowed the simulation of NP transport in real materials (i.e., natural or engineered samples that experiments can be performed on rather than a computer-generated porous medium) in larger domains or with more particles than previous works. XCT images of a micromodel and a Berea sandstone were used as the computational domains to analyze the effect of particle diameter, attractive and repulsive surface forces, flow rate, surface capacity, and XCT image-based mineralogy on particle transport. In the micromodel simulations, in the presence of attractive surface forces, NP effluent recovery increased as particle diameter increased and as flow rate increased – findings qualitatively consistent with published experimental data. The use of XCT image-based mineralogy to spatially distribute attachment sites (i.e., clay) in the Berea showed no difference in particle retention when compared to a random distribution of attachment sites. These results are being used to help understand ongoing micromodel experiments and to design continuum-scale models of NP transport.

Pore scale modelling of DNAPL migration in a water–saturated porous medium

A numerical simulator based on the discrete network model approach has been developed to simulate drainage processes in a water-saturated porous medium. To verify the predictive potential of the approach to simulate the unstable migration of a dense nonaqueous phase liquid (DNAPL) at the pore scale, the numerical model was applied to laboratory experiments conducted on a sand-filled column. The parameters relative to pore body size and pore throat size used in the construction of the equivalent network were derived from discrete grain-size distribution of the real porous medium. The observed water retention curve (WRC) was first simulated by desaturation of the network model. The good agreement of the modelled WRC with the experimental one highlights that the applied approach reproduces the main characteristics of the real pore space. The numerical model was then applied to rate controlled experiments performed on a homogenous sand-filled column to study the gravity-driven fingering phenomenon of immiscible two-phase flow of water and a DNAPL. The numerical results match within 10% based on the standard deviation with the experiments. They correctly reproduce the effect of several system parameters, such as flow mode (upward flow and downward flow) and the flow rate, on the stability of the water/DNAPL front in a saturated porous medium.

Determination of Nanoparticle Macrotransport Coefficients from Pore Scale Processes

Nanoparticle transport in porous media is modeled using a hierarchical set of differential equations corresponding to pore scale and macroscale. At the pore scale, movement and interaction of a single particle with a solid matrix is modeled using the advection–dispersion–sorption equation. A single nanoparticle entering the space encounters viscous, diffusion and surface forces. Surface forces (electrostatic and van der Waals forces) between nanoparticles and mineral grains appear as sorption propensity on solid matrix boundary condition. These local events are then transformed into a macroscale continuum by imposing periodic boundary conditions for contiguous unit cells representing porous media and using a scheme of moment analysis. At the macroscale, propagation and retention of particles are characterized by three position-independent coefficients: mean nanoparticle velocity vector $${\bar{\mathbf{U}}}^*$$ , macroscopic dispersion coefficient $${\bar{\mathbf{D}}}^*$$ , and mean nanoparticle retention rate constant $${\bar{K}}^*$$ . The modeling results are validated with a set of nanoparticle transport tests in porous microchips. We also present simulations of realistic porous media, where an actual image of sandstone samples is processed into binary tones. The representative unit cells are constructed from the resulting binary image by searching for areas within the sample with maximum similarities to the whole sample in terms of porosity and specific surface area, which are found to show strong correlations with the resulting $${\bar{\mathbf{U}}}^*$$ and $${\bar{K}}^*$$ , respectively.

Bridging the scales in high-throughput dielectrophoretic (bio-)particle separation in porous media

Dielectrophoresis (DEP) is a versatile technique for the solution of difficult (bio-)particle separation tasks based on size and material. Particle motion by DEP requires a highly inhomogeneous electric field. Thus, the throughput of classical DEP devices is limited by restrictions on the channel size to achieve large enough gradients. Here, we investigate dielectrophoretic filtration, in which channel size and separation performance are decoupled because particles are trapped at induced field maxima in a porous separation matrix. By simulating microfluidic model porous media, we derive design rules for DEP filters and verify them using model particles (polystyrene) and biological cells (S. cerevisiae, yeast). Further, we bridge the throughput gap by separating yeast in an alumina sponge and show that the design rules are equally applicable in real porous media at high throughput. While maintaining almost 100% efficiency, we process up to 9 mL min−1, several orders of magnitude more than most state-of-the-art DEP applications. Our microfluidic approach provides new insight into trapping dynamics in porous media, which even can be applied in real sponges. These results pave the way toward high-throughput retention, which is capable of solving existing problems such as cell separation in liquid biopsy or precious metal recovery.

The Role of Capillary Hysteresis and Pore‐Scale Heterogeneity in Limiting the Migration of Buoyant Immiscible Fluids in Porous Media

AbstractUnderstanding the main mechanisms affecting long‐term migration and redistribution of injected CO2 in geological carbon storage is needed for developing predictive models to assess environmental risks and designing monitoring schemes. Preparation of a postinjection site care plan is required for CO2 injection wells, including monitoring of pressure changes and injected CO2 plume. Knowledge gaps exist regarding assessment of postinjection monitoring timeframes for the CO2 plume because the processes driving long‐term CO2 plume migration and trapping are not fully understood. In the postinjection stage of geological carbon storage, redistribution of CO2 occurs mainly due to buoyancy and capillary forces. This work presents experimental and modeling studies to investigate processes contributing to postinjection plume distribution and stabilization. We conducted a flow cell experiments (0.5 m × 0.05 m × 0.01 m) with two immiscible fluid phases in a glass bead porous medium to study postinjection plume behavior. We employed a hysteretic macroscopic two‐phase flow model to interpret the experimental results and to understand main processes leading to plume stabilization. Our findings show that capillary pressure hysteresis explains the experimentally observed plume shape and redistribution at early postinjection stages; however, the long‐term plume migration and eventual plume stabilization can only be represented when in addition microscale heterogeneity is accounted for. Results also show that plume stabilization can be extremely slow and that the migration of the plume front can occur through multiple intermittent bursts over long times. Further studies are needed to understand implications of the results for more realistic porous media and large‐scale storage reservoirs.

Pore-scale modeling of rarefied gas flow in fractal micro-porous media, using lattice Boltzmann method (LBM)

Due to the widespread use of rarefied gas flow in micro-porous media in industrial and engineering problems, a pore-scale modeling of rarefied gas flow through two micro-porous media with fractal geometries is presented, using lattice Boltzmann method. For this purpose, square- and circular-based Sierpinski carpets with fractal geometries are selected due to their inherent behavior for real porous media. Diffusive reflection slip model is used and developed for these porous media through this study. With this respect, the planar Poiseuille flow is selected as a benchmark and validated with the literature. The effect of Knudsen number (Kn) on the permeability is investigated and compared in each geometry. It is shown that as Knudsen number increases, the permeability will increase due to the gas slippage effect on the solid blocks. In addition, it is observed that the permeability is more sensitive to the gaseous flow behavior at the slip and beginning of transition flow regimes. At last, the permeability relationship with Knudsen number is presented with a higher coefficient of determination for both fractal geometries, showing that this relation is logarithmic.

Microfluidic Model Porous Media: Fabrication and Applications.

Complex fluid flow in porous media is ubiquitous in many natural and industrial processes. Direct visualization of the fluid structure and flow dynamics is critical for understanding and eventually manipulating these processes. However, the opacity of realistic porous media makes such visualization very challenging. Micromodels, microfluidic model porous media systems, have been developed to address this challenge. They provide a transparent interconnected porous network that enables the optical visualization of the complex fluid flow occurring inside at the pore scale. In this Review, the materials and fabrication methods to make micromodels, the main research activities that are conducted with micromodels and their applications in petroleum, geologic, and environmental engineering, as well as in the food and wood industries, are discussed. The potential applications of micromodels in other areas are also discussed and the key issues that should be addressed in the near future are proposed.

Oil Fragmentation, Interfacial Surface Transport and Flow Structure Maps for Two-Phase Flow in Model Pore Networks. Predictions Based on Extensive, DeProF Model Simulations

In general, macroscopic two-phase flows in porous media form mixtures of connected- and disconnected-oil flows. The latter are classified as oil ganglion dynamics and drop traffic flow, depending on the characteristic size of the constituent fluidic elements of the non-wetting phase, namely, ganglia and droplets. These flow modes have been systematically observed during flow within model pore networks as well as real porous media. Depending on the flow conditions and on the physicochemical, size and network configuration of the system (fluids and porous medium), these flow modes occupy different volume fractions of the pore network. Extensive simulations implementing the DeProF mechanistic model for steady-state, one-dimensional, immiscible two-phase flow in typical 3D model pore networks have been carried out to derive maps describing the dependence of the flow structure on capillary number, Ca, and flow rate ratio, r. The model is based on the concept of decomposition into prototype flows. Implementation of the DeProF algorithm, predicts key bulk and interfacial physical quantities, fully describing the interstitial flow structure: ganglion size and ganglion velocity distributions, fractions of mobilized/stranded oil, specific surface area of oil/water interfaces, velocity and volume fractions of mobilized and stranded interfaces, oil fragmentation, etc. The simulations span 5 orders of magnitude in Ca and r. Systems with various viscosity ratios and intermediate wettability have been examined. Flow of the non-wetting phase in disconnected form is significant and in certain cases of flow conditions the dominant flow mode. Systematic flow structure mutations with changing flow conditions have been identified. Some of them surface-up on the macroscopic scale and can be measured e.g. the reduced pressure gradient. Other remain in latency within the interstitial flow structure e.g. the volume fractions of − or fractional flows of oil through − connected-disconnected flows. Deeper within the disconnected-oil flow, the mutations between ganglion dynamics and drop traffic flow prevail. Mutations shift and/or become pronounced with viscosity disparity. They are more evident over variables describing the interstitial transport properties of process than variables describing volume fractions. Τhis characteristic behavior is attributed to the interstitial balance between capillarity and bulk viscosity.

Equivalent microstructure problem: Mathematical formulation and numerical solution

Analytical homogenization schemes, including the Mori–Tanaka (M–T) or Self-Consistent (S-C) schemes, are computationally attractive tools for estimating the homogenized properties of porous media. Utilizing these approaches, we evaluate the effective properties based on the solution of single inclusion problem and assuming a simplified morphology of microstructure (usually a finite number of inclusion families is postulated). The simplified microstructure is the main disadvantage of these methods since it does not conform in a geometrical sense to the microstructure of a real porous medium. In this work, we formulate the inverse problem of micromechanics in which we aim to identify a so-called equivalent microstructure for the real porous material. This microstructure has to preserve the overall response (thermal conductivity) that is analogous to that of real porous material, regardless of the conductivity of the fluid occupying the pore space. The equivalent microstructure (still simplified with respect to the real one) is a virtual one with morphology of oblate spheroids (pore space) embedded in a solid matrix (skeleton). The distribution of inclusions is described by the probability density function with a random variable being the semi-axis aspect ratio θ. The inverse problem is formulated as a linear Fredholm equation of the first kind supplemented with additional constraints. Stochastic optimization procedure is used to solve the inverse problem, i.e. identification of the probability density function. The methodology is verified against the theoretical results obtained via classical bounds on the effective thermal conductivity. Finally, the procedure is applied to real porous material, and an equivalent microstructure for sand, with respect to the overall thermal conductivity, is identified.

Simulation of membrane polarization of porous media with impedance networks

ABSTRACTThe spectral induced polarization method is supposed to have some potential to provide useful information on hydraulic properties of the subsurface. One difficulty for the practical implementation is the simulation of underlying physical processes at the pore scale and their upscaling to hydraulically relevant scales. We extend an existing semi‐analytical membrane polarization model to two‐ and three‐dimensional impedance networks, which are numerically solved to obtain a spectral induced polarization response that can be compared to measured data.The original model consists of two cylinders with different sizes. The model has been shown to be able to reproduce some basic features of spectral induced polarization spectra measured in the laboratory, but it is unable to meet the complexity of macroscopic porous media structures, which can be found within unconsolidated sediments or rocks. To approach realistic pore space geometry, we connect different combinations of cylinders to networks. We treat the smaller of the two cylinders as a pore throat. The pore throat distribution in the network is chosen by matching measured pore throat radii distributions obtained from the mercury injection method. The large cylinder is treated as the (large) pore body, and its radii are associated to the pore throats using existing relationships.We compare the behaviour of the networks with real porous media by using sandstone samples for which both the electrical and petrophysical properties have been measured. We adjust the geometrical parameters of the network, i.e., pore lengths, pore radii, and their relative occurrences, such that they match the measured parameters (specific internal surface area, pore throat distribution, and porosity) of the sandstone samples. The measured spectral induced polarization parameters, like the maximum phase shift and the characteristic relaxation time, are qualitatively consistent with our simulation results.

Gas Tracers: A Decade of Learning and Experience

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 183413, “A to Z for Gas Tracers: A Decade of Learning and Experience,” by M.N. Khan, H. Iwama, A. Al-Neaimi, and O. Al-Shehhi, Abu Dhabi Marine Operating Company, and M. Chatterjee, Tracerco, prepared for the 2016 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 7–10 November. The paper has not been peer reviewed. In interwell tracer studies, reservoir complexities often make tracer-breakthrough time difficult to assess. Although reservoir-simulation studies serve as an effective tool in predicting a breakthrough, the tracer behavior in the real porous media sometimes presents intriguing surprises. This paper discusses a crestal gas-injection project that was carried out in a supergiant heterogeneous-carbonate oil field. Introduction A tracer-survey study can provide a variety of information about the heterogeneity of a formation. While transient tests can provide information about reservoir continuity, thief zones are difficult, if not impossible, to detect. This is because pressure-transient tests provide an arithmetic average for reservoir total transmissibility over the tested formation thickness, while a tracer survey provides a direct evaluation of the flow field between the injection and production wells. Apart from heterogeneity, tracer studies also serve as an informative tool to yield fluid-flow paths inside the reservoir, popularly known as reservoir streamlines. A tracer survey not only can precisely identify these preferential paths that are detrimental to the sweep of the reservoir in the enhanced-oil-recovery stage but also can provide information about the time that fluid takes to move from one point (injection well) to another point in the reservoir. This time is termed the mean residence time. In addition, any flow barrier or directional thief zones such as faults can be identified by delayed tracer recovery. The mass-balance technique can be used to calculate the amount of tracer recovered to distinguish between the existence of a fault, a flow barrier, or a low-permeability zone. Tracer-Project Design Interwell tracer testing consists of injecting chemical tracers into injection wells at the beginning of a flood project or after the reservoir has reached its fill-up condition, depending on the objective of the project, and subsequent sampling of production wells for a prescribed period of time, which also depends on the objective of the project. Samples are analyzed for tracer content, which will delineate communication between the injection and production wells. The time during which samples are collected and analyzed depends greatly on the objective of the project. If the objective is to identify thief zones, deduce mean residence time, and determine other factors that could lead to full-field reservoir characterization that could be fed directly into a simulation model, sample collection and analysis must continue for a considerable period of time after tracer is first detected in order to establish a more-defined elution curve.

Cessation of Darcy regime in gas flow through porous media using LBM: Comparison of pressure gradient approaches

Natural Gas flow characterization in real porous media is one of the main challenging issues in oil and gas engineering projects such as gas production and natural gas storage. As of the predominant concern, more precise insight into investigating the Darcy regime cessation and Forchheimer flow parameter characterization have proved effective to make a sound quantitative reports in related projects.Using three-dimensional LBM fluid model, gas flow simulated through different real porous structures obtained from micro-CT technique, using conventional pressure gradient approach employed in many previous surveys, according to data available in the literature. The main medium parameters were determined and evaluated in comparison with previous researches. The results showed in conventional pressure gradient implementation procedure, the mass conservation law is not satisfied in inertial domination regime, leading estimated values inconsistent with physical basis. Therefore, the same procedure followed, using the modified pressure gradient approached, to prevail the intrinsic limitations of conventional approach. The Beta coefficient and different types of criteria, to detect the onset of Forchheimer regime, are then identified and compared with previous similar attempts. The onset of Forchheimer regime in natural gas flow, which imposes extra pressure drop especially around the wellbore and also far from it, is quantified as the ReK values. The determined velocity values of 0.1666 and 0.105 (m/s) for sandstone and carbonate respectively, showed the point of deviation in each cases. The results demonstrated precisely estimation of flow parameters employing the modified body force approach.

Evolution of the effective permeability for transient and pore-scale two-phase flow in real porous media

Permeability is one of the key parameters to model and predict the infiltration or transport process of fluid through a porous media. However, most models and approaches that have been developed experimentally, theoretically or numerically to determine the saturated permeability for steady flow are indirect or based on predefined or virtual porous media models. To the best of our knowledge, the variation behavior of the effective permeability with the infiltration length or time in unsaturated flow based on a real porous media has rarely been considered and is little understood. Herein, we propose a simple numerical method of modelling the infiltration processes of a liquid though a porous media preform based on a real porous media obtained from an experimental scanning electron microscopy (SEM) image and validate it by comparing the simulated results with experimental data. Then, we calculate the unsaturated permeability using Darcy’s law based on the results of numerical simulation without any structural parameters of porous media. The evolution of the effective permeability with the time or flow front is then presented, and the relationship between the saturation degree and permeability is also considered. The numerical results indicate that (i) the maximum infiltration length along the macroscopic flow direction globally characterizes the variations of the flow front better than the other parameters; (ii) the effective permeability of an unsaturated porous media decreases exponentially with time and the advancing of the flow front and decreases with the degree of saturation following a power-law trend; and (iii) the saturation evolution may have great effects on the effective permeability of a liquid through a porous media.