Seepage Model Research Articles

Quantitative characterization of drying-induced cracks and permeability of granite residual soil using micron-sized X-ray computed tomography

Drying-induced cracks negatively impacts the performance of soils in the context of global warming. Traditional testing approaches used for the cracking characterization of soils are mainly based on surface observation and qualitative inspections. In this study, a temporal investigation of micron-sized X-ray computed tomography (Micro-CT) tests was performed on the granite residual soil (GRS) during desiccation for the first time. Through three-dimensional (3D) reconstructions and seepage simulations, the dynamic evolution of drying-induced cracks and permeability that evolved (0 to 120 h) was visually characterized and intensively quantified. Experimental results show that the averaged area-porosity ratio varies as an increasing trend, appearing fast at first and slowly thereafter during desiccation.. Observed by 3D reconstruction models, connected cracks rapidly propagated through the samples while isolated cracks occupied small volumes and remained almost unchanged. The pore-diameter distribution of GRS reveals that the propagation of connected cracks is essential in influencing soil cracking. The simulated permeability is generally comparable with measuring ones with an acceptable error margin, demonstrating the accuracy of seepage models. The increasing permeability from both experiments and numerical simulations indicates the desiccation process severely impacts the hydraulic properties of soils. This study provides an adamant evidence that the Micro-CT is an effective and feasible tool for the elucidation of drying-induced crack evolutions and in building numerical models for permeability validation.

Study on the Mechanical Properties of Flexible Prefabricated Highway Structural Systems considering the Effect of Two-Way Fluid-Structure Interaction

The rainfall often causes changes in the physical performance of the embankment, which leads to disasters such as embankment collapse and road surface settlement and cracking. Past research has tended to be limited to traditional embankment seepage models and is mostly based on the assumption that surface precipitation is uniform and rainfall intensity is constant. To adapt to the changes and development of the times, based on the water leakage mode of the flexibly assembled highway embankment, a new rainfall calculation model of the reinforced soil embankment is constructed and combined with the solid-fluid coupling physics theory, the sedimentation amount and slope stability of the embankment are analyzed at multiple levels, the mechanical properties of the new embankment under rainfall conditions are summarized, the factors affecting the settlement of the embankment and the stability of the slope are explored, and the reference model is provided for the construction of the new embankment, and the existing construction process is improved through multilevel cause analysis. We improve and develop the existing theoretical system to reduce the probability of road diseases, improve the efficiency of road construction, and reduce the cost of road maintenance.

Parameter Optimization of Constant Pressure Grouting Technology for Borehole Sealing with Inorganic Noncondensable Material in Tectonic Coalbed of South China

To solve the problem of a rapid attenuation of gas concentration along with drainage borehole collapse in the tectonic coalbeds of South China, a constant pressure grouting technology with inorganic, noncondensable material was proposed. Firstly, the slurry fluidity, water separation rate, and sealing performance of the inorganic sealing materials were tested under different water-cement ratios. The seepage model of slurry in a layer-through borehole was built with COMSOL Multiphysics simulation software, to explore the scopes of loose circles around drainage roadway and borehole, and to analyze the seepage capacity of the slurry under different grouting pressures. Eventually, the sealing performance of the slurry was investigated in the field. The results showed that the inorganic, noncondensable material with the water-cement ratio of 5 : 1 has a strong fluidity, low water retention, high permeability, and good sealing performance. After the excavations of No.2164 drainage roadway and layer-through borehole, there are obvious stress concentrations both at the shoulder corners of the roadway and at the borehole bottom, and the scope of the loose circle around the roadway is about 6.2 m. The effective seepage radius of the inorganic slurry gradually increases with a rising grouting pressure, and the slurry seepage range in the sandstone section is broader than that in the mudstone section. Adopting the constant pressure grouting technology with the slurry, the average drainage concentration of boreholes in Puxi coal mine is 51.5%, and the average gas flow rate is 0.005 m3/min, which are 1.35 times and 1.67 times than those with the cement grouting method.

Progress of Seepage Law and Development Technologies for Shale Condensate Gas Reservoirs

With the continuous development of conventional oil and gas resources, the strategic transformation of energy structure is imminent. Shale condensate gas reservoir has high development value because of its abundant reserves. However, due to the multi-scale flow of shale gas, adsorption and desorption, the strong stress sensitivity of matrix and fractures, the abnormal condensation phase transition mechanism, high-speed non-Darcy seepage in artificial fractures, and heterogeneity of reservoir and multiphase flows, the multi-scale nonlinear seepage mechanisms are extremely complicated in shale condensate gas reservoirs. A certain theoretical basis for the engineering development can be provided by mastering the percolation law of shale condensate gas reservoirs, such as improvement of productivity prediction and recovery efficiency. The productivity evaluation method of shale condensate gas wells based on empirical method is simple in calculation but poor in reliability. The characteristic curve analysis method has strong reliability but a great dependence on the selection of the seepage model. The artificial intelligence method can deal with complex data and has a high prediction accuracy. Establishing an efficient shale condensate gas reservoir development simulation technology and accurately predicting the production performance of production wells will help to rationally formulate a stable and high-yield mining scheme, so as to obtain better economic benefits.

Time-Dependent Effect of Seepage Force on Initiation of Hydraulic Fracture around a Vertical Wellbore

Fluid penetration into the rock during hydraulic fracturing has been an essential issue in studying the mechanism of fracture initiation, especially the seepage force caused by fluid penetration, which has an important effect on the fracture initiation mechanism around a wellbore. However, in previous studies, the effect of seepage force under unsteady seepage on the fracture initiation mechanism was not considered. In this study, a new seepage model that can predict the variations of pore pressure and seepage force with time around a vertical wellbore for hydraulic fracturing was established by using the method of separation of variables and the Bessel function theory. Then, based on the proposed seepage model, a new circumferential stress calculation model considering the time-dependent effect of seepage force was established. The accuracy and applicability of the seepage model and the mechanical model were verified by comparison with numerical, analytical and experimental results. The time-dependent effect of seepage force on fracture initiation under unsteady seepage was analyzed and discussed. The results show that when the wellbore pressure is constant, the circumferential stress induced by seepage force increases over time, and the possibility of fracture initiation also increases. The higher the hydraulic conductivity, the lower the fluid viscosity and the shorter the time required for tensile failure during hydraulic fracturing. In particular, when the tensile strength of rock is lower, the fracture initiation may occur within the rock mass rather than on the wellbore wall. This study is promising to provide a theoretical basis and practical guidance for further research on fracture initiation in the future.

Prediction of tunnel water inflow based on stochastic deterministic three-dimensional fracture network

With the rapid development of national infrastructure construction, the water inrush disaster of “strong burst, high water pressure and large flow” is more and more frequent in the construction process. To achieve high-precision prediction of tunnel water inflow, based on the Yue Longmen Tunnel, according to the structural plane detection data in the study area, combined with the Monte Carlo algorithm and using “parent-daughter” and “step–structure” correction mode, this paper constructs a random deterministic three-dimensional fracture network seepage model. Based on the three-dimensional fracture network seepage model and the principle of flow balance, the water inflow of each mileage section of the Yue Longmen Tunnel is solved by numerical calculation method, and good results are obtained through comparison and verification. The research results have important theoretical significance and engineering application value for tunnel water inflow prediction.

A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which was converted into a fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on the HAM are guaranteed to be more accurate than exact analytical solutions, with relative errors between 0.0089% and 2.64%. When λ = 0, the pressure drop of the Darcy seepage model could be instantaneously transmitted to infinity. When λ > 0, the pressure drop curve of the non-Darcy seepage model exhibited the characteristics of tight support, which was clearly different from the Darcy seepage model’s formation pressure distribution curve. According to the results of the HAM, a moving boundary is more influenced by threshold pressure gradients with a longer time. When the threshold pressure gradients were smaller, the moving boundaries move more quickly and are more sensitive to external influences. One-dimensional, low-permeability porous media with a non-Darcy flow with moving boundary conditions can be reduced to a Darcy seepage model if the threshold pressure gradient values tend to zero.

An Extended Hydro-Mechanical Coupling Model Based on Smoothed Particle Hydrodynamics for Simulating Crack Propagation in Rocks under Hydraulic and Compressive Loads

A seepage model based on smoothed particle hydrodynamics (SPH) was developed for the seepage simulation of pore water in porous rock mass media. Then, the effectiveness of the seepage model was proved by a two-dimensional seepage benchmark example. Under the framework of SPH based on the total Lagrangian formula, an extended hydro-mechanical coupling model (EHM-TLF-SPH) was proposed to simulate the crack propagation and coalescence process of rock samples with prefabricated flaws under hydraulic and compressive loads. In the SPH program, the Lagrangian kernel was used to approximate the equations of motion of particles. Then, the influence of flaw water pressure on crack propagation and coalescence models of rock samples with single or two parallel prefabricated flaws was studied by two numerical examples. The simulation results agreed well with the test results, verifying the validity and accuracy of the EHM-TLF-SPH model. The results showed that with the increase in flaw water pressure, the crack initiation angle and stress of the wing crack decreased gradually. The crack initiation location of the wing crack moved to the prefabricated flaw tip, while the crack initiation location of the shear crack was far away from the prefabricated flaw tip. In addition, the influence of the permeability coefficient and flaw water pressure on the osmotic pressure was also investigated, which revealed the fracturing mechanism of hydraulic cracking engineering.

Research on nonlinear spherical seepage model solution of fractal composite reservoir considering quadratic pressure gradient under elastic outer boundary

In order to break the limitation that only three ideal outer boundaries (infinity, constant pressure and closed) are considered in the traditional reservoir model, the paper introduces elasticity into the outer boundary condition, and establishes a nonlinear spherical seepage model for fractal composite reservoir that considers the quadratic pressure gradient, wellbore storage, skin factor and effective radius under the elastic outer boundary condition. The dimensionless bottom-hole pressure in real space is obtained by the process of variable substitution, similar construction method and numerical inversion, while the characteristic curves are plotted to analyze the influence laws of main parameters and elasticity. The results show that the ideal outer boundary conditions previously studied are only special cases of the elastic outer boundary conditions. Furthermore, the elastic outer boundary expands the scope of data interpretation, and makes the model more general. Meanwhile, it can be seen that the similar construction method is simpler and more effective than the traditional methods for solving nonlinear models. In addition, it is further demonstrated that neglecting the quadratic pressure gradient can cause large errors. This study not only provides a new idea for well testing analysis of reservoirs but also for solving more complex seepage models.

Computational modeling of seepage in a fractured rock mass during tunnel excavation: a case study from Liaoning Province, China

Computational modeling of seepage in a fractured rock mass during tunnel excavation: a case study from Liaoning Province, China

Study of the Influence of Dynamic and Static Capillary Forces on Production in Low-Permeability Reservoirs

Low-permeability reservoirs have strong heterogeneity, and the production prediction based on traditional seepage model is not accurate enough. The dynamic capillary-force seepage model can characterize the dynamic heterogeneity of seepage and more accurately describe the oil–water flow process. In this paper, the calculation formula of the dynamic capillary force is obtained through a real low-permeability core experiment, and the seepage model of dynamic capillary force is established. Based on the model, the authors quantitatively study the effects of formation pressure, heterogeneity and production speed on dynamic capillary force through numerical solutions. It is found that compared with the traditional static capillary-force seepage model, the dynamic capillary-force seepage model makes the predicted water cut increase and the recovery factor decrease. With the increase in development time, formation pressure and production rate will make the effect of dynamic capillary force more obvious. According to the comparison of heterogeneous reservoir models, results show that the horizontal heterogeneity will strengthen the dynamic capillary-force effect, while the vertical heterogeneity will weaken the dynamic capillary-force effect. In the range of research parameters, the recovery ratio predicted by the dynamic capillary-force seepage model can be reduced by 4.7%. A new oil–water seepage model is proposed, which can characterize the spatial difference and dynamic change of low-permeability reservoirs with time. It is of great significance for describing the remaining oil distribution of low-permeability reservoirs in detail and making decisions on efficient EOR measures.

Multiple seepage model and gas production simulation of shale with power law fracture distribution

Changes in the internal microstructure of shale reservoirs have a significant effect on gas production. In this research, based on the double power law model and the triple medium theory, a triple medium model of shale multi-scale power law fracture distribution is constructed. The accuracy of the model is verified by comparing with the actual test results. Then, the model is used to analyze the relationship between shale stress, permeability, and three kinds of pore media as well as the influence of power law parameters and external force on reservoir microstructure and macroscopic gas production. The findings indicate that (1) the microstructure of shale reservoirs is affected by power law parameters and external forces; (2) gas exchange can cause the evolution of reservoir structure; and (3) the stress change of a single system will cause stress rearrangement of the whole system. This model provides a basic and comprehensive understanding for considering the various transport mechanisms of shale matrix and the microstructure change law of gas production process and proposes a new method for optimizing shale permeability simulation.

Multi-source data-driven unsaturated seepage parameter inversion: Application to a high core rockfill dam

The inverse parameter’s estimation of unsaturated seepage models is important to ensure the safety of earth dams, while most existing studies determine the hydraulic characteristics only based on seepage pressure monitoring data, which may lead to inversion results deviating from the intrinsic properties of dam materials. This study proposed an advanced methodology for unsaturated seepage parameter inversion of earth dams driven by multi-source data. The transient unsaturated seepage behavior of earth dams is simulated using the Van Genuchten (VG) model, and the extreme learning machine (ELM) is adopted as the surrogate model to estimate the approximate simulation results. Then the multi-objective function for parameter inversion is constructed by combining the observed transient pressure data and ELM models, and the Pareto-optimal solutions are generated using the elitist non-dominated sorting genetic algorithm (NSGA-II). Multi-source information, including parameter design values, in-situ testing results, and monitoring data, are fused to construct a comprehensive index to drive the parameter decision. The proposed method is applied to the PB core rockfill dam, which has a well-established seepage pressure monitoring system. In addition, the design values and in-situ testing results of the hydraulic conductivity of the dam material are also available. The results showed that the inversion parameters of the proposed method are closer to the physical characteristics of materials and have advantages in prediction accuracy.

A three-dimensional thermal-hydro-mechanical coupling model for simulation of fracturing driven by multiphysics

Geothermal mining, nuclear waste disposal, and other projects involve rock fracturing under the multiphysics effect. There is an urgent need for a numerical analysis tool that can consider both thermal-hydro-mechanical coupling (THM) effects and rock fracturing to analyze such projects. This paper presents a three-dimensional thermal-hydro-mechanical coupling model that can consider rock fracturing, which incorporates the advantages of the combined finite discrete element method (FDEM) for simulating fracture and fragmentation. The 3D thermal-hydro-mechanical coupling model includes three parts: fracture-pore mixed seepage model, heat transfer model (including heat conduction in solid and fluid, heat advection, heat exchange between solid and fluid), and FDEM fracture mechanics calculation model. Some examples with the analytical solution for seepage, hydromechanical, thermal–mechanical, hydrothermal, and thermal-hydro-mechanical coupling problems are used to verify the correctness of the FDEM based 3D THM model in detail. In addition, an example of rock fracturing caused by the thermal-hydro-mechanical coupling effect is also given. The simulation results show that the FDEM based 3D thermal-hydro-mechanical coupling model can simulate the complex fractures initiation, propagation, and extension caused by multiphysics effects, such as heat, fluid, and mechanics.

A SEEPAGE MODEL FOR SOLID-PHASE PARTICLE INSTABILITY IN POROUS MEDIA-BASED FRACTAL THEORY

This paper presents a new fractal seepage model to study the decrease in seepage capacity caused by fluid erosion and pressure changes in porous media. The normalized permeability obtained by our model is in good agreement with the experiments and models in literature and has high accuracy and usability. The results demonstrate that: (1) the larger the instability coefficient, the higher the particle stability, the better the permeability of the porous medium, the later the normalized permeability decreases, and the slower it goes down, and (2) the fractal dimension of the solid skeleton set mainly affects the porosity and permeability of porous media, independent of the stability of solid particles. (3) The fractal dimension of movable particles is one of the main factors affecting the normalized permeability, it does not affect the instability conditions solid-phase particles in the porous media. The proposed model makes full use of the microstructure parameters of porous media, further reveals the mechanism of fluid flow in porous media with particle shedding, and provides a sound theoretical basis for various practical applications in petroleum engineering and other industries.

A HYBRID NUMERICAL/ANALYTICAL MODEL OF TRANSIENT SEEPAGE FOR VERTICAL FRACTURED WELL IN TIGHT GAS RESERVOIR BY USE OF FRACTAL THEORY AND CONFORMAL MAPPING METHOD

Insufficient consideration of the complex morphology of hydraulic fractures (HF) and heterogeneous physical properties of fractured reservoirs in seepage models can result in unreliable well testing analyses. The fractal porosity and permeability (FPP) model provides an effective method for characterizing reservoir heterogeneity in the near-wellbore zone. However, its application to scenarios involving irregularly-shaped hydraulic fracture networks and multiple fracture clusters is challenging due to the lack of spatial symmetry. To address this issue, this paper proposes a combined approach of FPP and conformal mapping (FPP-CM) to transform the region of fractured formation into the exterior of the unit disk domain using numerical conformal mapping. The transient seepage flow model of the vertical fracture well (VFW) is then established by coupling it with the FPP model. The typical curve of pressure transient behavior with the division of flow stages was plotted, and the model verification and sensitivity analysis of parameters were conducted. The results indicate that the fractal dimension primarily affects the formation linear flow stage and its subsequent flow stages; with a decrease in fractal dimension resulting in an increase in the position of the typical curve. For VFW with multiple HF wings, a decrease in the included angle of fracture wings causes an increase in the heterogeneity distribution of microfracture physical properties, resulting in an increase in the position of the pseudo-pressure derivative curve during the late flow stage.

Implicit port-Hamiltonian systems: structure-preserving discretization for the nonlocal vibrations in a viscoelastic nanorod, and for a seepage model

A structure-preserving partitioned finite element method (PFEM), for the semi-discretization of infinite-dimensional explicit port-Hamiltonian systems (pHs), is extended to those pHs of implicit type, leading to port-Hamiltonian differential Algebraic Equations (pH-DAE). Two examples are dealt with: the nonlocal vibrations in a viscoelastic nanorod in 1D, and the dynamics of a fluid filtration model, the Dzektser seepage model in 2D, for which illustrative numerical simulations are provided.

Mathematical Modeling of Seepage–Temperature Field for Earth Dam Using Experimental Test

Monitoring the seepage field is essential to characterize the operation of the earth dam. However, conventional seepage monitoring typically involves the use of a piezometer tube or pressure sensor for point distribution. A mathematical model incorporating the feedback of the temperature field on the seepage field was proposed based on experimental test observations. First, a theoretical analysis of the mathematical model is conducted, which includes examining the relationship between the variation of temperature field and factors, such as hydraulic gradient, water and soil temperature difference, hydraulic conductivity, thermal conductivity, specific heat, and time. Second, a homogeneous earth dam model is constructed in the laboratory with a distributed temperature sensor system to obtain synchronous information of the seepage–temperature field. Finally, the parameters of the mathematical model are quantified using observations from experimental tests, demonstrating good agreement between calculated and measured values. The experimental results indicate the feasibility of inferring seepage field monitoring information from the temperature field and elucidation of the interaction mechanism of the coupled fields. The quantitative mathematical model of the temperature field feedback on the seepage field is validated for its applicability in earth dams.

Revolutionizing Tight Reservoir Production: A Novel Dual-Medium Unsteady Seepage Model for Optimizing Volumetrically Fractured Horizontal Wells

Revolutionizing Tight Reservoir Production: A Novel Dual-Medium Unsteady Seepage Model for Optimizing Volumetrically Fractured Horizontal Wells

A fractal power-law approach for investigating the interactions between reservoir microstructure and gas migration

As one of the most significant clean energy sources, the migration characteristics and extraction processes of coalbed methane (CBM) have been extensively studied. The structural distribution and evolutionary characteristics of reservoir fractures, as the main conduit for gas migration, significantly affect the permeability and gas production. However, few models have been able to quantitatively and accurately explore reservoir micro–macro interactions under coupled thermal-fluid–solid effects. This work develops a new highly coupled model based on the widely adopted power-law function to quantify reservoir thermal conduction effect, gas pressure evolution, reservoir deformation, in situ stress, the adsorption–desorption effect, and reservoir microstructure evolution. Three parameters are adopted to quantitatively characterize the reservoir structure: (1) fracture power index αf (to characterize the fracture density), (2) fracture length ratio rf (to characterize the fracture size), and (3) the maximum fracture length l. The results demonstrate that the fractal network is a special kind of network in the power-law length distribution. The proposed power-law seepage model is able to accurately characterize the evolution of reservoir microstructure and the impact of microevolution on extraction under multi-field coupling effects, compared to the traditional power-law model. The proposed model can provide a good theoretical and practical support for the study of CBM migration and extraction.