Seepage Model Research Articles

A Modified Model of Micro-Scale Gas Seepage in Rock Porous Media

It is of significance to study the micro-scale gas seepage mechanism in rock porous media due to shale gas exploitation and prevention of tunnel gas explosion. However, current microscale seepage models have problems, such as poor accuracy or small computational domain. In this work, a representative volume element scale microscopic seepage model with high precision and large computational domain is established using the lattice Boltzamnn method. In the representative volume element scale model, micro-scale effect is considered by the Beskok-Karniadakis correction relationship. Then the accuracy of the representative volume element scale model is improved by proposing an equivalent resistance correction coefficient. The correction coefficient value is obtained by comparing the calculated result for the flow rate at a representative volume element scale and more precise pore scale. For example, when the porosity is 0.9 and the dimensionless specific surface area is 30, the corrected model can reduce the average deviation from 34.38 to 0.14%. Finally, to expand the applicability of the proposed model, a correlation for the correction coefficient is introduced as a function of the Knudsen number, porosity of porous media, and dimensionless specific surface area. The mean absolute percentage deviation of the correction coefficient correlation is 9.25%.

“This Is Our Revolution Too”: LGBTQ Rights Activism and the National Question in Northern Ireland

Existing research frames ethnonationalism as homophobic, in which the queer is positioned outside of the boundaries of the ethnic nation. Less well understood is how LGBTQ activism engages with ethnonationalism, particularly in relation to questions of national self-determination. The limited research on this issue frames LGBTQ activist movements as groups that reject divisive ethnonationalisms by forging alternative cosmopolitan and transnational expressions of sexual identity. By exploring a single case-study, Northern Ireland, this article draws attention to how LGBTQ movements can be sites of conflict over questions of national self-determination, particularly when sexual liberation is wedded to anti-imperialist struggles. The paper concludes by reaffirming Horowitz’s model of ethnic seepage, in which the dominant ethnonational cleavages infuse all issues in divided societies. The article uses a wide range of primary data, including interviews and archival documents, to analyze LGBTQ activism in Northern Ireland during the period of ethnonationalist conflict in the 1970s and 1980s.

Numerical Simulation of Rainfall-Induced Erosion on Infiltration and Slope Stability

In slopes where a mixture of coarse and fine particles is present, the infiltration of rainfall can cause the migration of fine particles. This migration alters the hydraulic properties of the soil and has implications for slope stability. In this study, the slope under investigation is a tailings dam composed of loosely consolidated soil with a wide particle size distribution. Due to rainfall infiltration, fine particles tend to migrate within the voids of the coarse particle framework, leading to changes in hydraulic properties and inducing slope instability. The classical internal erosion constitutive model, known as the Cividini and Gioda erosion criterion, is commonly used to predict the behavior and effects of fine particle erosion in geotechnical engineering. However, certain parameters in this erosion criterion equation, such as long-term density, are challenging to obtain through experiments. To investigate the coupled evolution of seepage and erosion within landfill slopes under the influence of rainfall infiltration and to understand the mechanisms of slope instability, this research assumes the erosion of fine particle suspension and adopts the Worman and Olafsdottir erosion criterion to establish a coupled model of unsaturated seepage and internal erosion. The developed model simulates the coupled response of seepage and erosion in unsaturated landfill slopes under three different rainfall intensities. It is then combined with the infinite slope model to quantitatively analyze the impact of fine particle migration on soil permeability and slope stability. The numerical simulations provide the following findings: The Worman and Olafsdottir erosion criterion, unlike the Cividini and Gioda erosion criterion, only requires the determination of the soil’s gradation curve to estimate the erosion rate. Internal erosion primarily occurs within the leading edge of moisture penetration, accelerating the advancement of the wetting front and reducing slope stability. When the rainfall intensity is lower than the saturated permeability coefficient, the influence of internal erosion can be disregarded. However, under rainfall intensities equal to or greater than the saturated permeability coefficient, considering internal erosion results in a difference in the depth of the wetting front of up to 34.2 cm after 6 h in the R2 scenario. The safety factor without considering internal erosion is 1.12, whereas considering internal erosion yields safety factors between 1.08 and 1.09. In the R3 scenario, the difference in the depth of the wetting front reaches 53.8 cm after 6 h, with a safety factor of 1.12 without considering internal erosion and safety factors between 1.06 and 1.07 when considering internal erosion.

Analytical spatiotemporal distribution equations of viscous slurry grouting pressure during the grouting process in rock fissures

To give a simpler theoretical solving approach for modeling the grouting process of viscous slurry in porous/broken rocks, this work derives two theoretical spatiotemporal distribution equations of viscous slurry penetration in rock fissures based on the Darcy seepage model (DM) and the Bingham fluid model (BM) through a hypothetical micro-element model. Through a two-dimensional (2D) conceptual grouting hole model with porous media, the applicability of the two proposed theoretical spatiotemporal distribution equations of viscous slurry pressure is validated by comparing the analytical results with the numerical results obtained from the two-phase flow simulation. The results indicate that the analysis results obtained from two proposed theoretical spatiotemporal distribution equations are well consistent with the simulation results at different times and under different grouting velocities. That means the time-consuming numerical simulation of the porous/broken rocks grouting process can be replaced by two proposed theoretical spatiotemporal distribution equations, which will greatly reduce the difficulty of real-time evaluation of the grouting effects in engineering practice and shorten the assessment time.

Fracture propagation and pore pressure evolution characteristics induced by hydraulic and pneumatic fracturing of coal.

A two-dimensional unsteady seepage model for coal using a finite element program is developed, and the temporal variations of key factors such as water pressure and hydraulic gradient are analyzed in this paper. Additionally, the triaxial rock mechanical experiment and utilized pneumatic fracturing equipment on raw coal samples to investigate both hydraulic and pneumatic fracturing processes are conducted. Through these experiments, the relationship between pressure and crack formation and expansion are examined. The analysis reveals that the pore pressure gradient at the coal inlet reaches its peak during rapid surges in water pressure but diminishes over time. Conversely, the pore pressure gradient at the outlet side exhibits a gradual increase. Hydraulic fracturing is most likely to occur at the water inlet during sudden increases in water pressure. Besides, as the permeability of coal decreases, the duration for seepage stabilization prolongs due to the intensified pore pressure gradient resulting from sudden increases in water pressure. Moreover, an extended period of high hydraulic gradient further increases the risk of hydraulic fracturing. The experimental findings indicate that coal samples initially experience tensile failure influenced by water and air pressure. Subsequently, mode I cracks form under pressure, propagating along the fracture surface and becoming visible. The main types of failure observed in hydraulic and pneumatic fracturing are diametrical tensile failure, and the development of fractures can be categorized into three distinct stages, which contains the initial stage characterized by slight volume changes while water pressure increases, the expansion stage when pressure reaches the failure strength, and the crack closure stage marked by little or even decreasing volume changes during pressure unloading. The acoustic emission signal accurately corresponds to these three stages.

A discrete approach for modelling the permeability evolution of granite under triaxial and true-triaxial stress conditions

In deep underground engineering, modelling the seepage characteristics of rock masses under complex stress conditions is crucial for the safe construction and stable operation of a project. The permeability of the rock mass is not only controlled by its internal pore structure but is also closely related to the deformation and fracturing of the rock. Although discrete methods offer advantages in describing the formation and development of fractures, these methods still face challenges due to the difficulties in establishing microscopic seepage models. This paper introduces a new hydro-mechanical coupled numerical model. In this model, a simple method is proposed to couple the Rigid-Body-Spring Method (RBSM) for rock deformation and fracturing simulation and the Equivalent Matrix-Fracture Network (EMFN) for seepage simulation. Subsequently, the model is employed to simulate the permeability of granite under three-dimensional stress conditions. The simulation results show that under hydrostatic stress conditions, the model accurately captures the decrease in permeability due to pore compression and collapse. Additionally, under deviatoric stress conditions, it reveals the stage-wise increase in permeability caused by granite fracturing. Finally, the model is applied to study the permeability evolution behaviour of rocks under true triaxial stress conditions. The results unveiled the significant impact of the intermediate principal stress on permeability evolution and revealing the microscopic mechanisms underpinning these effects. This paper paves a way for enhancing the application of discrete methods in forecasting the permeability evolution behaviour of intricate rock masses.

Slope stability analysis based on rate-dependent soil-water characteristic curve

Rainfall-induced landslides are a common geological hazard. Analyzing this problem necessitates the use of the unsaturated soil theory, with the soil-water characteristic curve (SWCC) being a crucial component. Most existing unsaturated soil seepage models are established based on the static soil-water characteristic curve model. However, the dynamic capillary pressure has been observed in experiments conducted in previous studies. In this study, experiments were performed to explore the dynamic impact of the SWCC. The influence of different infiltration rates was studied, and a rate-dependent SWCC model under dynamic conditions was established. The model was validated through experiments. The behavior of an unsaturated soil slope under different rainfall intensities was analyzed based on the equivalent model. The equation for the slope safety factor was then derived using the Bishop method. The slope safety factors based on both the rate-independent and rate-dependent SWCC models were compared. The results indicated that the safety factor continuously decreased with increasing rainfall intensity. The dynamic effect reduced the safety factor, making the slope more susceptible to instability.

Research on the helium seepage mechanism in the strata surrounding bedded salt cavern helium storage and its tightness evaluation

To improve the safety and scale of helium storage, large-scale or strategic helium storage in underground salt caverns can be implemented. Salt caverns leached from bedded salt formations have been considered as potential underground storage sites for helium in China. However, the salt formations are typical lacustrine sedimentary rocks with an interbedded structure, thus the sealing feasibility of such salt caverns must be evaluated before they can be used. To this end, the helium seepage equation in deep strata and permeability evolution function are derived with the help of experimental results and theoretical analysis. Based on these, a helium seepage model considering slippage effect and threshold pressure gradient is proposed to evaluate the sealing properties of salt caverns for helium storage. The analysis results indicate that it is feasible to use bedded salt mine formations for helium storage when the formations permeability parameters and reservoir design parameters meet the long-term tightness evaluation criteria, including permeability, porosity, salt pillar width, salt roof thickness and operating pressure and duration. More importantly, specific recommendations are provided for the operation parameters, design parameters and formation permeability thresholds of salt caverns for ensuring helium storage safety while maintaining stable cavern operations. The threshold permeability of the target salt formations should be approximately 1 × 10−18 m2 to ensure tightness. The minimum and maximum operating pressure are recommended to be 10 MPa and 18 MPa respectively for 50 years of this helium storage. The salt pillar width should be 300 m, and the salt roof thickness should be 40 m.

A gas-mechanical-damage coupling model based on the TLF-SPH method and its application to gas seepage in fractured coal

The coupled calculation of gas seepage in fractured coal is a challenge in computational mechanics. In this paper, a gas seepage model of fractured coal is developed based on smoothed particle hydrodynamics (SPH). Then, the accuracy of the seepage model based on the partial differential equation (PDE) with a constant coefficient is verified by a reference example. Moreover, the seepage characteristics of gas in homogeneous coal based on a PDE with constant and variable coefficients are analyzed, and their numerical errors are compared. Then, based on the gas seepage model of fractured coal, the effects of heterogeneity, defect opening and inclination on gas seepage in coal are studied. In addition, considering the influence of coal deformation and preexisting defects on gas seepage, a gas-mechanical-damage coupling model for gas seepage simulation is proposed by using the SPH method with the total Lagrangian formula (TLF-SPH). Subsequently, the permeability evolution and gas seepage characteristics of borehole surrounding rock under different conditions (such as overburden load, extraction pressure, borehole radius and initial gas pressure) are investigated, revealing the seepage-mechanical coupling mechanism of fractured coal during gas extraction. This work provides important theoretical support for mine gas extraction and gas outburst disaster prevention technology.

Data-driven hydraulic property analysis and prediction of two-dimensional random fracture networks

The large parameter space and uncertainty of the discrete fracture networks (DFNs) make the hydraulic characteristics have multiple possibilities. Statistical analysis of hydraulic characteristics based on a large amount of data is a standard practice and central to DFN methodology. The present study developed a two-dimensional (2D) DFN numerical seepage model based on Matlab and Comsol from modeling and parameter calculation to simulation to investigate the influence of parameters involved fracture network on seepage characteristics of DFNs. In total, 1728 2D DFN models were generated with increasing fracture density, fracture length, power-law exponent, fracture orientations, and fracture included angles, and 1728 × 3 = 5184 numerical simulations of fluid flow along the x-axis, y-axis, and center through the DFN models are conducted using a self-developed numerical code. The influence of fracture geometric features on connectivity and permeability are estimated, respectively. And to realize the prediction of permeability tensor by known geological data, a theoretical model based on the Snow model and a data mining model based on the back-propagation model are discussed. The analysis helps researchers and engineers can make informed decisions and develop effective strategies for addressing the challenges posed by uncertainty hydraulic property of the fractured rock masses.

A Novel Inversion Method for Permeability Coefficients of Concrete Face Rockfill Dam Based on Sobol-IDBO-SVR Fusion Surrogate Model

The accurate and efficient inversion of permeability coefficients is significant for the scientific assessment of seepage safety in concrete face rockfill dams. In addressing the optimization challenge of permeability coefficients with few samples, multiple parameters, and strong nonlinearity, this paper proposes a novel intelligent inversion method based on the Sobol-IDBO-SVR fusion surrogate model. Firstly, the Sobol sequence sampling method is introduced to extract high-quality combined samples of permeability coefficients, and the equivalent continuum seepage model is utilized for the forward simulation to obtain the theoretical hydraulic heads at the seepage monitoring points. Subsequently, the support vector regression surrogate model is used to establish the complex mapping relationship between the permeability coefficients and hydraulic heads, and the convergence performance of the dung beetle optimization algorithm is effectively enhanced by fusing multiple strategies. On this basis, we successfully achieve the precise inversion of permeability coefficients driven by multi-intelligence technologies. The engineering application results show that the permeability coefficients determined based on the inversion of the Sobol-IDBO-SVR model can reasonably reflect the seepage characteristics of the concrete face rockfill dam. The maximum relative error between the measured and the inversion values of the hydraulic heads at each monitoring point is only 0.63%, indicating that the inversion accuracy meets the engineering requirements. The method proposed in this study may also provide a beneficial reference for similar parameter inversion problems in engineering projects such as bridges, embankments, and pumping stations.

Experimental and numerical investigation on effects of gas adsorption pressures on damage behaviors, failure characteristics, and energy evolution of coals

Coal and gas outbursts are anthropogenic hazards that can be divided into four stages: preparation, occurrence, development, and termination. Studying the influence of gas on coal damage and energy changes during the formation of outbursts is highly important for investigating the entire hazard. In this paper, laboratory experiments were performed on samples. The energy changes and failure mechanism of coal under different gas pressures were revealed, and a seepage model was established based on compressibility and adsorption to investigate gas-induced coal damage. The results demonstrated that gas pressure caused initial damage within the coal, resulting in nonlinear deformation and strength deterioration of the coal. Gas-induced damage affected the energy evolution mechanism of coal under loading, as pressure caused the premature release of energy at the tips of internal microcracks and reduced the ability to accumulate energy. These changes increased the proportion of dissipative energy under unstable conditions. The combined acoustic emission (AE) parameters—rising angle (RA) and average frequency (AF)—were used to study the fracture mode of gas-containing coal. As the gas pressure increased from 0 to 4 MPa, the RA–AF distribution pattern changed from tensile failure to tensile–shear composite failure, with the proportion of shear cracks increasing from 0.30% to 25.44%. As the complexity of the crack network increased, the randomness of crack propagation increased, and the fracture surface roughness parameters, arithmetic mean height Sa, root mean square height Sq, and maximum height Sz increased by 90.33%, 94.02%, and 81.70%, respectively. These findings could contribute to a comprehensive understanding of the underlying mechanism of coal and gas outbursts and guide for predicting and preventing these hazards.

Fractal study on the nonlinear seepage mechanism during low-permeability coal water injection

In the initial stage of coal seam water injection, due to the high density and low permeability of coal bodies, an obvious startup pressure gradient is observed in relation to water seepage; this phenomenon leads to low-velocity nonlinear seepage. In this paper, we study the nonlinear seepage law and the main influencing parameters of the water injection process. First, based on the startup pressure gradient, the nonlinear seepage equation, and the fractal theory, we formulated a nonlinear seepage model of coal seam water injection that considered the fractal characteristics of a complex coal structure. Subsequently, we carried out coal seam water injection and gas radial seepage experiments under a high overburden pressure, obtaining the startup pressure gradient according to the seepage characteristics and the changes of dynamic parameters. Then, the dynamic parameters of water injection, the structural parameters of the coal samples, the physical parameters, and the fractal dimension were substituted into the theoretical model to obtain the theoretically calculated value. Finally, through comparative analysis of theoretical and experimental startup pressure gradient calculation results, it is found that with the increase in the overburden pressure, the permeability of coal and the connectivity effect are reduced, while the fracture tortuosity and the startup pressure gradient increase. Moreover, coal seam permeability does not seem to be the single decisive factor for the nonlinear startup pressure gradient.

Peridynamic modeling of seepage in multiscale fractured rigid porous media

AbstractThe numerical simulation of seepage in fractured porous media holds significant relevance for subsurface energy development. The presence of fractures at various scales profoundly influences the hydraulic properties of porous media during seepage. A peridynamic (PD)‐based frame is proposed for the seepage problem analysis of multiscale fractured porous media, in which micro‐fractures are implicitly represented like the porous media, macro‐fractures are explicitly represented. For fluid flow modeling, the peridynamic bonds are divided into three types: pore seepage bond, fracture seepage bond, and fluid exchange bond. The micro‐permeabilities of different bonds are derived by Darcy's law, Poiseuille's law, and fluid exchange model, respectively. The proposed peridynamic model can naturally simulate the seepage problem of porous rock with multiscale fractures in a unified framework. Then, four cases of pore seepage and fracture seepage are analyzed using the proposed model, fractured porous media seepage with micro‐fractures and macro‐fractures are respectively considered. The predicted results are compared with the available theoretical solutions, the close agreement shows that the wide validity and applicability of the proposed model in multiscale seepage problems.

Seepage prediction model of the earth-rock dam based on TCN considering rainfall lag effect

Renewable energy has the highest conversion efficiency, is the most flexible in regulating peak power in the grid, and has the potential to significantly reduce emissions. Hydropower is one of the main ways to optimize power energy structure by building earth-rock dams that block water and generate electricity. Seepage is a physical quantity that characterizes the safety of earth-rock dams. Studying the intelligent prediction model of earth-rock dams is an effective means of understanding the evolution of seepage behavior, and it is also crucial for the safe operation and energy efficiency of earth-rock dams. To create a rainfall factor expression reflecting the hysteresis effect of rain, actual monitoring data of different piezoelectric tubes on the upstream and downstream sides of the soil core wall of an earth-rock dam is considered. Based on the key influencing factors of the seepage behavior of earth-rock dams, the novel temporal convolutional network (TCN) algorithm in deep learning is introduced into the seepage behavior prediction of earth-rock dams, constructing the intelligent prediction model of seepage of earth-rock dams based on TCN. The engineering example shows that the seepage prediction model of the earth-rock dam based on TCN has better prediction performance than the seepage prediction model of the earth-rock dam based on support vector regression (SVR), extreme learning machine, and long-short term memory. The determination coefficient is more significant than 0.9, and the relative error of prediction is less than 1‰. The model’s prediction accuracy is high, and the stability of the prediction performance is good. The model’s prediction performance also improves after considering the rainfall lag effect.

A dual-reciprocity boundary element method based transient seepage model with nonlinear distributed point source dual-porosity gas reservoir

As a result of advancements in gas reservoir development technologies and a deeper understanding of seepage theory, numerous nonlinear seepage problems have emerged. Consequently, conventional analytical solution models are no longer applicable. Moreover, existing semi-analytical and numerical solution models suffer from issues like high computational complexity and limited flexibility, significantly constraining their practical utility. For this purpose, a gas reservoir transient seepage model is established based on the dual-reciprocity boundary element method (DRBEM). This model couples the wellbore storage coefficients with skin factor and introduces a novel dual-porosity transient interporosity seepage algorithm, enabling the resolution of transient seepage problems in dual-porosity gas reservoirs with nonlinear point source distributions. Additionally, it investigates the dynamic behavior of bottomhole pressure during the early production stage of gas wells, while capturing the dynamic pressure distribution within the seepage field. This approach offers the advantages of semi-analyticity, meshless, and eliminates the need for Laplace transforms, resulting in a significant reduction in computational complexity. Ultimately, the application of our model to well-pattern production with the production system transition issues, in conjunction with the log-log type curves of bottomhole pressure, and the dynamics of gas reservoir pressure, enables the analysis of interference characteristics between injection-production wells. This showcases the practical advantages of the model's application. The findings of this study provide valuable assistance for modeling and solving transient seepage problems in dual-porosity oil and gas reservoirs production. The application of DRBEM in unsteady-state diffusion, heat conduction, stress fields, and other potential field problems is relevant for reference.

Study of inter-well interference in shale gas reservoirs by a robust production data analysis method based on deconvolution

In order to overcome the defects that the analysis of multi-well typical curves of shale gas reservoirs is rarely applied to engineering, this study proposes a robust production data analysis method based on deconvolution, which is used for multi-well inter-well interference research. In this study, a multi-well conceptual trilinear seepage model for multi-stage fractured horizontal wells was established, and its Laplace solutions under two different outer boundary conditions were obtained. Then, an improved pressure deconvolution algorithm was used to normalize the scattered production data. Furthermore, the typical curve fitting was carried out using the production data and the seepage model solution. Finally, some reservoir parameters and fracturing parameters were interpreted, and the intensity of inter-well interference was compared. The effectiveness of the method was verified by analyzing the production dynamic data of six shale gas wells in Duvernay area. The results showed that the fitting effect of typical curves was greatly improved due to the mutual restriction between deconvolution calculation parameter debugging and seepage model parameter debugging. Besides, by using the morphological characteristics of the log-log typical curves and the time corresponding to the intersection point of the log-log typical curves of two models under different outer boundary conditions, the strength of the interference between wells on the same well platform was well judged. This work can provide a reference for the optimization of well spacing and hydraulic fracturing measures for shale gas wells.

Study on microscale stress sensitivity of CO2 foam fracturing in tight reservoirs

With huge reserves and wide distribution, tight oil and gas resources are the focus and hotspot of unconventional oil and gas research in recent years. In this paper, firstly, the multi-scale model of CO2 fracturing gas is established by considering the phase evolution characteristics of CO2. Secondly, considering the hydrophilicity of the tight reservoir, a microscale seepage model of CO2 under the adsorption condition of fracturing fluid is proposed. Again, considering the shrinkage effect of dense reservoir matrix, a dynamic coupling model of gas-liquid-solid under CO2 fracturing conditions is established. The results show that: (a) When the volume of the adsorbed layer of CO2 fracturing fluid accounts for 10% of the pore volume and the CO2 concentration is 20%, the fluid transport in the tight reservoir shows significant separation characteristics. (b) More CO2 enters the crude oil after considering the diffusion effect of CO2 body. The influence of CO2 diffusion mechanism on oil recovery should not be neglected. (c) Enhancement of elastic energy is one of the main mechanisms by which CO2 improves oil driving efficiency in tight reservoirs.

Differences in stress sensitivity of natural-artificial fracture networks in tight sandstone gas reservoirs

Abstract The stress sensitivity of fractures has a significant impact on the production characteristics of tight sandstone gas reservoirs. However, there has been a lack of attention to and research on the differences between different types of fracture and their stress sensitivity. Based on the core samples of the Keshen gas reservoir in Xinjiang, China, this paper conducts a comprehensive comparison of the flow capacity, stress sensitivity, and the production characteristics of the structural fracture, diagenetic fracture, and artificial fracture. The findings reveal that the flow capacity of a single structural fracture is higher than that of a diagenetic fracture. Additionally, both structural and diagenetic fractures contribute to increasing the flow capacity of the porous system by 63 and 88%, respectively. The stress sensitivity of fractures varies from strong to weak, structural fractures exhibit a higher sensitivity compared to diagenetic fractures, and artificial fractures demonstrate the weakest stress sensitivity. Based on the fitting formulas of stress-sensitivity curves for different fractures, a new seepage model considering different stress sensitivities was established and numerical simulations were conducted. The numerical simulation results indicate that the gas well with a diagenetic-artificial fracture network yields a higher production, the 10-year production is 35.01% higher than that with a structural-artificial fracture network. This study is of great significance for understanding the production differences of fractured tight sandstone gas reservoirs and provides valuable insights for selecting optimal well locations.

Investigation of the chloride ion transport mechanism in unsaturated concrete considering the nonlinear seepage effect

In this paper, the mechanism of chloride ion transport in unsaturated concrete considering the nonlinear seepage effect is investigated by indoor experiments and analytical modelling. The concrete sheet imbibition test is used to reveal the nonlinear characters of seepage including water convection and moisture capillary within the unsaturated concrete in case of various water-binder ratios. For modelling purpose, an exponential function is introduced to mathematically depict the nonlinear relation between the specific discharge and hydraulic gradient during both water convection and moisture capillary processes. Based on such nonlinear seepage models, new mathematical models are proposed for the problem of chloride invasion within the reinforced concrete structure. The solution for the mathematical model of chloride transport is resolved by Laplace transform and finite difference method, of which acceptability is verified by the comparison with the results from chloride ion invasion test. The result indicates that, compared with linear seepage law, the use of the proposed nonlinear seepage solution is preferred to depict the saturation-relative humidity curves from concrete sheet imbibition test. The consideration of nonlinear seepage can result in a slower chloride transport rate, which further makes a later flow start-up time and a smaller free chloride iron concentration within the concrete. Such effect can be enhanced with the increase of nonlinear flow degree. The paper provides an effective solution to evaluate the chloride invasion within the unsaturated concrete.