Seepage Equation Research Articles

Cnoidal water wave induced seepage in a permeable seabed with a defined thickness

Extreme waves can induce seepage in a seabed and cause problems to marine structures in coastal regions. In this study, the seepage under cnoidal waves was studied using the transient seepage equation. An analytical solution is presented for the pore pressure in a seabed of defined thickness. Parametric studies were carried out to examine the influence of air content in the pore water, and of the soil hydraulic conductivity on the seepage. It has been shown that the air content and the soil hydraulic conductivity can affect the pore pressure response significantly. An increase in the air content or a decrease in the soil hydraulic conductivity will increase the magnitude of the pore pressure gradient and results in the pore pressure varying sharply. The liquefaction potential of a seabed under cnoidal waves is discussed. Consequently, comparative studies are carried out to show that the soil shear modulus and Poisson constant can influence the difference between the transient seepage equation and Biot's equation, and the transient seepage equation is a limit of Biot's equation.

A new microseismic location method accounting for the influence of the hydraulic fracturing process

In the hydraulic fracturing process, the velocity model of traditional inversion is usually constructed by well logs, seismic data or calibration shots. The variation of pore pressure and fractures in this process has a major influence on the velocity. However, this influence is usually ignored in the velocity estimation model. In this paper, we propose a new microseismic location method that accounts for the influence of hydraulic fracturing on velocity. Firstly, we simulate the 3D hydraulic fracturing process based on mass conservation, the seepage equation and fracture mechanics. Then the equivalent velocity model is constructed using the Coates–Schoenberg method and fracture compliances. The 3D ray-tracing method is applied to forward-model the microseismic data and traditional inversion methods are applied to locate events and analyse the inversion error. Finally, we introduce a new method, called the equivalent velocity inversion method (EVIM), taking into account the influence of the fracturing process. The simulation results show that the hydraulic fracturing process affects the velocity and thus makes the inversion accuracy of the same receiver array vary considerably with the sources in the traditional methods. The new EVIM can effectively reduce the inversion error.

Permeability and sedimentation characteristics of pleistocene fluvio-glacial deposits in the Dadu river valley, Southwest China

There exist many fluvio-glacial deposits in the valley of Dadu River, Southwest China, which dates back to the Pleistocene. As some of the deposits are located within the seasonal water fluctuation zone of reservoirs, the seepage of groundwater acts as one of the key factors influencing their stability. Investigation into the sediment properties and permeability is, therefore, crucial for evaluating the sediment stability. In this study, in-situ permeability and sieving tests have been carried out to determine grain size distribution, correlations of permeability and hydraulic gradients, and relations between permeability and sedimentation properties. Test results indicate that the deposits are composed mostly of sands, gravels, cobbles and boulders, and the percentage of fines is less than 5%. The sediments have high densities, low porosities and natural moisture contents. At low hydraulic gradients, the seepage velocity obeys the Darcy’s law, while a non-Darcy permeability is observed with hydraulic gradient exceeding a certain value (about 0.5 - 0.7). The linear permeability coefficient ranges from 0.003 to 0.009 cm/s. Seepage failure occurs above a threshold between 1.1 and 1.5. The test data fit well with the non-linear permeability equations suggested by Forchheimer and Izbash. The non-Darcy permeability proves to be in accordance with the seepage equation suggested by Izbash with the power ' m ' of about 0.6 - 0.7. The characteristic grain sizes of the studied deposits are found in a narrow range between 0.024 and 0.031 mm, which is much lower than the effective grain size ( d 10 ).

Research on Transient Flow Regulation With the Effect of Quadratic Pressure Gradient

During the course of reservoir engineering calculations and derivation of fluid equations, the nonlinear term of fluid state equation are often ignored under the assume of slightly compressible fluid. But this would cause great error in the long-lasting well testing and then it would lead to the incorrect understanding to the actual reservoir. The authors studied the transient seepage flow regulation with the effect of quadratic pressure gradient, induced the seepage equation by remaining the quadratic pressure gradient, meanwhile considering the well bore storage and the effect of skin factor, obtained Laplace space analytic solution with dimensionlessness and Laplace transformation, and then the type curves were established by use of numerical inversion. At last, relative error curves intuitively show that the quadratic pressure gradient and skin factor are of great impact to transient flow regulation and great errors would occur if they were ignored. In conclusion, the quadratic pressure gradient and skin factor must be taken into consideration in both transient flow and well-testing analysis.

Seepage analysis in multi-domain general anisotropic media by three-dimensional boundary elements

Abstract A three-dimensional boundary element solution for the seepage analysis in multi-domain general anisotropic media has been developed based on the transformation approach. Using analytical eigenvalues and eigenvectors of the hydraulic conductivity tensor, a closed-form coordinate transformation matrix has been provided to transform the quadratic form of governing equation of seepage for the general anisotropic media to the Laplace equation. This transformation allows the analysis to be carried out using any standard BEM codes for the potential theory on the transformed space by adding small pre- and post-processing routines. With this transformation, any physical quantity like the total head remains unchanged at corresponding nodes on the physical and transformed space, and the normal gradient across the domain boundaries should also be transformed. In multi-domain problems, compatibility equations (equality of the potential on corresponding nodes on the interface) and equilibrium equations (conservation of the flux across the interface boundaries of adjacent domains) on the corresponding nodes of interface between two neighbor domains are needed for boundary element method. In the transformed space, the compatibility equation remains unchanged. However, due to the distortion of boundaries in the mapped space and therefore misalignment of the unit outward normal vectors along the inter-domain boundaries, the equilibrium of the normal fluxes have to be transformed accordingly. Based on the proposed transformation, the normal to boundary flux boundary conditions in the mapped space and the transformed equilibrium equation for interface of adjacent zones have been given in this paper. Examples have been solved with the proposed scheme and the results were verified with the finite element method. Excellent agreement of the results shows the veracity of the proposed transformation and the formulas given for transformation of equilibrium equation for multi-domain general anisotropic media.

Effect of Coal Dust on Coalbed Methane Wells Productivity

CBM has the largest reserve except for conventional natural gas and is the cleanest energy. However, neither coal seam permeability nor CBM vertical well productivity has been determined when the immigration of coal dust are considered, which restricts the economic CBM exploitation. Based on coal seam characteristics, use permeability parallel path model and CBM seepage equation. The results show that with different ratio of non-clogging path and the total path, coal seam permeability and CBM vertical well productivity may either increase or decrease.

Fractured Reservoir Blocking Dosage Calculation Method

Fractured reservoir development process are often faced with the angle wells flooded serious and side wells don’t get the effect of water injection. In order to increase the water flooding sweep efficiency. Profile control plugging is a measure that is frequently used. Traditional plugging program design does not take into account the fluid loss, Program design of the blocking agent dosage is always small, the result is not satisfactory. In this paper, the classic percolation theory is used, seepage equation of the fracture system and matrix system is established, the blocking agent Filtrate analytical solution that considers the different reservoir properties and different blocking agent performance is obtained, that can be used to guide the design of profile control water plugging program and can calculate the best blocking agent dosage. Through the actual implementation of the effect, the proposed method can be more substantial increase in the effect of plugging.

Stabality Analysis of Deep Roadway Based on Coupled Thermo-Hydro-Mechanical Behaviors

In order to research the stability of excavation in deep mines under high ground stress, high rock temperature and high karst hydraulic, the interaction of stress field, seepage field and temperature field are discussed through basic constitutive relation, seepage equation, thermometer equation and coupled thermo-hydro-mechanical equation. A numerical model was built to simulate the excavation of deep roadway. The result shows that the simulated ground stress based on three fields coupled is much closer to the field measured value and the change of stress and displacement caused by the excavation are limited which is about same as the later monitoring.

Research on Solid-Gas Coupling Dynamic Model for Loaded Coal Containing Gas

Considering the variation of the porosity and permeability of coal containing gas at differential deformation stages, a dynamic model for porosity and permeability is developed based on the previous researches. Furthermore, taking coal containing gas as a kind of isotropic elastoplastic material and taking into account the effect of gas adsorption, the stress and seepage equations are derived and, the solid gas coupling model for coal containing gas is constructed, which is appropriate to describe the skeleton deformability of coal containing gas and the compressibility of gas under the solid-gas interaction condition. In addition, the numerical simulation model is built by using the finite element method, and the numerical calculation solution of the model for a special loading case is given in term of the constraint conditions and corresponding parameters. The research results may have significance for further enriching and improving solid-gas coupling theories for coal containing gas.

Application of State Equation Method for Coupled Hydro-Mechanical Analysis in Dual-Porosity Media

Seepage is one of the major influence factors for engineering stability. In this study, the equations of hydro-mechanical coupling in dual-porosity media including the governing equations of deformation and seepage are employed. The fluid gravity in whole system is considered in the seepage governing equation. The solid displacement, pore fluid pressure and fissure fluid pressure are the unknown qualities. The finite element formulation of the governing equations are acquired after using the Galerkin discretization technique. The physical parameters are discussed here. Finally, the state equation method is applied to solve the finite element equations.

The Coupled Thermo-Hydro-Mechanical Behavior of Saturated Fractured Solids

The stress equilibrium equation of anisotropic solids, coupled to the hydrodynamic seepage equation and heat transfer equation of saturated fractured rocks, are studied here based on the standard space of physical presentation, in which an new thermo-hydro-elastic model is induced. A set of uncoupled equation of heat and hydraulic propagations in anisotropic saturated fractured rocks is deduced. From them, two new phenomena of heat and hydraulic propagation are obtained, which are affected by both anisotropic subspaces of solids and thermo-mechanical and hydro-mechanical coupling coefficients. Based on these laws, we discuss the heat and hydraulic wave behaviour for isotropic solids.

Optimization of Analytical Equations of Groundwater Seepage into Tunnels: A Case Study of Amirkabir Tunnel

Abstract In this study, with investigation of validity limits of analytical equations in computing groundwater seepage discharge into tunnels in different values of r/h (tunnel radius/water table height above tunnel), using optimization by regression analysis, we have tried to converge the results of analytical equations for any value of r/h. There are various experimental, analytical and numerical methods by which it is possible to calculate the amount of groundwater seepage into tunnels. Due to their simplicity and practical base theory, analytical methods have been applied more frequently. Studies imply that amount of real seepage into tunnel is significantly less than what is anticipated from analytical equations; on the other hand, the results of seepage calculations using these equations are depended on tunnel geometry and medium conditions. Previous investigations confirmed that in a tunnel for which, r/h is more than 0.4; these results are highly different both from one another and from the real seepage inflow. In this paper, optimization has been successfully performed on analytical equations so that the results of these methods are converged to each other for any value of r/h.

Coupling Numerical Analysis of Seepage and Stress Fields after Excavation of Slope

This paper, based on the mechanism analysis of coupling of seepage and stress fields, builds a mathematical model of coupling on equivalent continuous medium, combined with equations of seepage and stress fields and empirical formula of stress and permeate rate. It also obtains the variation of seepage and stress fields after excavation of slope by the numerical simulation analysis of example. The results show that: (1) The permeability coefficient redistributes with the stress fields, and it increases on the excavation surface. (2) The spill points of free surface rise; the free surface under excavation platform and water head decreases. (3) The body force of seepage near overflow surface doesn’t change significantly. In general, it is disadvantageous to the slope stability.

A representation of the equations of multicomponent multiphase seepage

A mathematical model of non-isothermal multicomponent flows in a porous medium is investigated. A general case is considered when the model can be used to describe processes with an arbitrary number of components and phases. A general form of the system of mixed-type equations describing the flow, which is similar to the Godunov form for hyperbolic systems is proposed. The equations obtained are applicable to flows with gas, liquid and solid phases. The thermodynamic properties of the medium are determined solely by a single multivalued function, by changing which one can obtain models of different flows in a porous medium. A clear geometrical interpretation of the solutions of the equations is proposed. An equation for the entropy is obtained, and it is shown that in order that the model should not contradict the second law of thermodynamics, it is necessary to take into account, in the energy equation, the work of the gravity force, which is often neglected when investigating seepage.

Integrable seepage equations

Well-known results of the classification of parabolic-type differential equations, possessing an infinite Lie–Bäcklund algebra, are used to describe seepage models, which, using (in general) differential substitutions, can be reduced to the heat conduction equation. Relations between the functional parameters, characterizing the properties of the liquid and gas phases and the porous medium, are obtained that ensure the existence of such substitutions.

The Productivity Analysis in Tight Gas Reservoir by Using wire-line Logging and trial production Data

The limitation of long-time required to conduct deliverability test, which results in fewer testing, has brought ink-bottle effect on the productivity evaluation in tight gas reservoir. By means of transient seepage equation and optimum algorithm, trial production data is utilized to compute the accurate reservoir parameters, such as permeability etc, which can be substituted in pseudosteady-state flow equation to compute the open flow potential. Strict theory derivation and the result of this method from actual example on-site shows the credibility of this method, which can be reference for other low permeability gas reservoir.

Prediction of chloride penetration in unsaturated concrete using meshless BEM

Chloride penetration is one of the major problems that affect the durability of reinforced concrete structures, and it is of great importance to study the chloride penetration mechanisms, to develop proper models and complete related computation, to enhance the durability design of reinforced concrete structures, and to improve the system of service life prediction and assessments of concrete structures. In this paper, chloride penetration in unsaturated concrete was studied by considering the coupled effects of moisture seepage and chloride diffusion. With weighted residue method, the weak forms of seepage and diffusion control equations were established. Using radial integration method, function approximating with compacted support radial basis function, and central difference scheme, a meshless boundary element method was developed. System equations were solved, and a self-contained computing code was constructed with the developed meshless boundary element method. Numerical examples demonstrate that the effect of moisture seepage is significantly greater than that of chloride diffusion in unsaturated concrete, and its influence on diffusion process is lasted after concrete is saturated. The developed method could give some bases for studying chloride penetration in unsaturated concrete during dry-wet cycling process.

Numerical simulation study of spontaneous combustion in goaf based on non-Darcy seepage

In order to study the influence of non-Darcy seepage on spontaneous combustion in goaf, seepage tests were conducted in three groups of broken rocks which were different average particle sizes, and then the test data were processed by non-Darcy seepage equation. So that the equations of non-Darcy permeability coefficient K with porosity n and particle size d, non-Darcy flow factor β with the n and the d were achieved. On the basis of these equations, the paper analyzed the influential factors of the spontaneous combustion in goaf, and then established the spontaneous combustion mathematical model on the coupling of air flow field, oxygen concentration field and temperature field on moving coordinates. According to the model, the calculating software was programmed by VB6.0 to obtain the oxygen concentration distribution map and the residual coal temperature distribution map in goaf. The results are of theoretical and practical significance to prevent spontaneous combustion in goaf.

CFD simulation of spontaneous coal combustion in irregular patterns of goaf with multiple points of leaking air

Based on the non-linear air leakage seepage equation for an anisotropic porous medium, on the seepage diffusion equation of multicomponent gas and on the seepage synthetic heat transfer equation of a porous medium, the numerical model for field flow problems of irregular patterns of a goaf with multiple points of leaking air is established and simultaneously solved by the upwind mode finite element method (G3 computer program). According to the complexity of irregular patterns of a goaf with multiple points of leaking air, the flow pattern in a large area of such a goaf and the variation in gases of methane, oxygen and CO and in temperature are theoretically described. In the calculation, the goaf is regarded as a caving anisotropic medium and the coupling effect of methane effusion on spontaneous combustion is considered. The simulation results agree well with practical experience. In addition, the spontaneous combustion process is also simulated, indicating that 1) the spontaneous combustion often takes place near the area where fresh air leaks in and 2) the fire sources can be classified into static and dynamic zones. Therefore, in practical fire preventing and extinguishing, we should clearly distinguish the upstream air leaking points from the downstream ones in order to take proper measures for leakage stopping.

Gas seepage equation of deep mined coal seams and its application

In order to obtain a gas seepage law of deep mined coal seams, according to the properties of coalbed methane seepage in in-situ stress and geothermal temperature fields, the gas seepage equation of deep mined coal seams with the Klinkenberg effect was obtained by confirming the coalbed methane permeability in in-situ stress and geothermal temperature fields. Aimed at the condition in which the coal seams have or do not have an outcrop and outlet on the ground, the application of the gas seepage equation of deep mined coal seams in in-situ stress and geothermal temperature fields on the gas pressure calculation of deep mined coal seams was investigated. The comparison between calculated and measured results indicates that the calculation method of gas pressure, based on the gas seepage equation of deep mined coal seams in in-situ stress and geothermal temperature fields can accurately be identical with the measured values and theoretically perfect the calculation method of gas pressure of deep mined coal seams.