Seepage Boundary Research Articles

Two Nitsche-based mixed finite element discretizations for the seepage problem in Richards’ equation

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards’ equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

Consolidation and seepage solutions in enclosure space based on non-zero-constant values boundary.

Research is ongoing to find solutions to the problem of Consolidation and seepage in saturated clay in enclosure space. Firstly, the boundary of non-zero-constant values is established, considering the seepage boundary of the clay is affected by pumping water or lowering boundary pressure on the site. Secondly, the differential equation is established to reflect the spatial and temporal variations of excess pore water pressure dissipation in the clay in enclosure space, and the solution is derived using variable separation methods. Finally, based on results of the solution derived, contour maps of the water pressure are drawn corresponding with the different inhomogeneous boundary conditions.

Analytical solution for suction-induced seepage flow during suction bucket installation in multilayered soil with anisotropic permeability

Suction-induced seepage flow can significantly reduce the soil resistance during the installation of suction buckets, thereby ensuring their intended penetration depths and the designed in-service capacities. However, the lack of analytical models describing seepage flow behavior in the literature poses a significant challenge, primarily due to the complexity of seepage boundary conditions and the anisotropy and spatial variation of soil permeability. This paper addresses this gap by presenting a novel analytical solution for analyzing suction-induced seepage flow around buckets, with a particular focus on the general multilayered soil profile featuring anisotropic permeability. The method of separation of variables is used initially to derive general solutions, and the final solutions are subsequently obtained by combining continuous conditions with the orthogonality of Bessel functions. The accuracy of the solutions is confirmed through comparisons with the results obtained from finite element analysis. Furthermore, this study discusses the seepage flow behavior in several typical scenarios, including permeability anisotropy, increased permeability within the bucket, and the presence of an overlying low-permeability layer. The analytical solutions presented in this paper provide a rapid and accurate method for the analysis of suction-induced seepage flow during suction-assisted installations across a wide range of complex soil permeability conditions.

Interpretation of Sand Body Architecture in Complex Fault Block Area of Craton Basin: Case Study of TIII in Sangtamu Area, Tarim Basin

The complex fault block oilfields in the craton basin contain vast reserves of oil and gas resources. During the development of an oilfield, the flow of oil, gas, and water, is controlled by faults and configuration boundaries. The distribution of remaining oil and gas depends on the interpretation of the reservoir’s architecture. However, recognizing the faults and the architecture boundary remains a challenge, hindering the efficient development of these resources. This study proposes a new idea for interpreting the configuration of thick sand bodies. This study was conducted in order to interpret the fine architecture of thick sand bodies in the Sangtamu area, using core samples, well logging, and production data, guided by sedimentation patterns from ancient to modern times. Results indicate that the Sangtamu area is a braided river delta front sedimentary system, dominated by the backbone underwater distributary channel and branch-type underwater distributary channels. The backbone channel is larger in scale, with a relatively large rock grain size and a box-shaped logging curve, whereas the smaller-scale branch channels have a bell-shaped logging curve resulting from the gradual weakening of water energy. Sandstone bodies from different types of underwater distributary channels are spatially overlapped, forming thick plate-like sandstones. The architecture interface between channels can be used as the fluid seepage boundary and can help prevent bottom water intrusion to a certain extent. The remaining oil is primarily concentrated in the architecture boundary area, which presents the next potential tapping area.

Discrepancy between Forward and Reverse Seepage Characteristics in a Single Rough Fracture

Under the uniform seepage boundary condition, the forward and reverse seepage flow rates will vary widely. In response to this phenomenon, this paper studies the mechanism of the difference in seepage characteristics between the forward and reverse directions from the fracture profile’s roughness, Darcy and non‐Darcy seepage, and distribution of eddy currents. First of all, wavelet transform was used to decompose and reconstruct the single rough fracture for 8 times, and then 9 fracture models with various roughness degrees were constructed. Then, Finite Volume Method was used to simulate the seepage in the original and approximate models of the Reynolds number varying from 0.001 to 1000. The results show that the nonlinear seepage is necessary for the difference between the forward and reverse seepage characteristics of the single rough fracture. The mechanism of the discrepancy between forward and reverse nonlinear seepages is the diverse shapes and distribution of the eddy current generated by the forward and reverse seepage. The secondary roughness provides space for the existence and development of the eddy current. The secondary roughness is the geometric basis of the discrepancy between the forward and reverse seepage characteristics.

Simulating water and salt transport in subsurface pipe drainage systems with HYDRUS-2D

Subsurface pipe drainage (SPD) has been widely applied in arid and semiarid regions to control soil salinization. To increase the accuracy of HYDRUS-2D simulations in SPD, three effective strategies, including the resistance layer (RL), actual infiltration surface (AIS), and equivalent radius (ER) treatments, were proposed to replace the standard seepage boundary (SSB) for subsurface pipes in HYDRUS-2D. First, the accuracy of the three strategies was calibrated using laboratory experiments with the multi-objective calibration method of the PEST program. Second, additional laboratory experiments were conducted to validate the three strategies. The RL, AIS, and ER strategies obtained a relatively high simulation accuracy in terms of the soil salt content (SSC), soil water content (SWC), and drainage and salt discharge processes that was significantly higher than that obtained with the standard seepage boundary (SSB) strategy. Moreover, compared with the AIS, ER, and SSB strategies, the RL strategy attained the highest simulation accuracy regarding the water drainage (root mean square error (RMSE) = 3.42 L; mean absolute error (MAE) = 2.91 L) and salt discharge (RMSE = 0.12 kg; MAE = 0.11 kg) in SPD. The relative position of the subsurface pipe has an important effect on the desalting rate of the clay layer (CL). Based on the SPD simulation by HYDRUS-2D with the RL strategy, we recommend placing the subsurface pipe below the clay layer to obtain the best water drainage and salt discharge effects in regions containing CLs. Furthermore, a positive logarithmic relationship between the drainage rate of the subsurface pipe and the CL saturated hydraulic conductivity was found (R2 = 0.99). Future research should focus on the upper and lower boundary conditions of HYDRUS-2D to further increase the SPD simulation accuracy.

Seepage Characteristics of a Single Ascending Relief Well Dewatering an Overlying Aquifer

The application of groundwater relief, i.e., dewatering, ascending wells, drilled upward from the mining tunnel into the overlying aquifer, is common in underground mining engineering. In this study, the seepage characteristics of single ascending partially and fully penetrating relief wells are investigated using a series of laboratory sand-tank experiments and numerical simulations. The seepage characteristics of ascending wells dewatering an overlying aquifer are different from those of conventional pumping wells descending from the ground surface into the underlying aquifer, because of the pronounced influence of the seepage face boundary condition along the seepage boundary of the ascending dewatering well. The seepage face of the ascending well is formed as the well casing remains open and water is discharged under the action of gravity through the well casing. The results of laboratory sand-tank experiments and modeling show that when the degree of penetration of an ascending relief well does not exceed a critical value, the effect of the seepage face cannot be ignored. In particular, the seepage flux increases as the degree of penetration increases following an exponential function, and the relationship between the seepage flux and the well radius can be described using a power law function. The results of numerical simulations are used to develop a series of type curves to evaluate the effects of the critical degree of penetration for different well radii and different aquifer water levels. Modified versions of the Dupuit and Dupuit–Thiem formulae for a single ascending partially well for the degree of penetration less than the critical one for the unconfined, confined, and confined-unconfined aquifers are developed.

A thermal-hydraulic-mechanical coupling model for freezing process simulation of cementitious materials with entrained air voids

Frost resistance of cementitious materials is enhanced with introduction of a series of randomly-dispersed air-entrained voids. While it is understood that the improvement of frost resistance is due to the functions of cryo-suction and water reservoir of the voids, their heterogeneous, random distribution has not been considered in the modeling framework to investigate the material responses during freezing process. In this paper, a thermal-hydraulic-mechanical coupling model is proposed to study the responses of temperature, pore pressure and deformation of cementitious materials with randomly-distributed air voids. The entire freezing process is simulated with consideration of thermal, mechanical, and seepage boundary conditions of cementitious materials. The predictions achieve satisfactory consistency with previous experimental results from the overall freezing deformation of mortar. The filling effect of entrained air voids by expelled water is also assessed. Finally, the proposed model is used to analyze the influence of cooling rate on the freezing of mortar.

Boundary effect on the hydraulic characteristics of gravelly soil slopes in physical model tests

The stability of a residual gravelly soil slope during heavy rainfall is closely related to the seepage field, which is directly affected by the seepage boundaries of the slope. To examine the boundary effect, a novel model flume that can implement permeable and impermeable boundary conditions was designed. With this flume, hydraulic model tests of a gravelly soil slope considering those two seepage boundaries were carried out. The results show that distinct spatial morphology of seepage fields is reflected by the hydraulic characteristics of the slope models with different seepage boundaries. The slope with permeable boundaries generally exhibits a larger average infiltration rate as well as a relatively smaller moving speed of wetting front in the lower part compared to the slope with impermeable boundaries. The residual moisture content in the deep-lower part of the slope with permeable boundaries is 6.6% cm3/cm3 smaller than that of the slope with impermeable boundaries. Nevertheless, the maximum pore water pressure in the middle part of the slope with permeable boundaries is 1.2 kPa higher than that in the corresponding part of the slope with impermeable boundaries. It is noted that regional pore water pressures in the shallow-lower and shallow-middle parts of the slope with impermeable boundaries exhibit large fluctuations with an amplitude over 0.5 kPa. The seepage field in the slope with permeable boundaries presents a multi-dimensional development, which may lead to a local failure of the slope. The results are of great significance in studying the similarity of seepage boundary condition in the field of similarity theory on landslide model tests and provide an experimental basis for establishing rainfall-induced landslide theory.

Internal fluctuations in green roof substrate moisture content during storm events: Monitored data and model simulations

Understanding how the moisture content in a green roof substrate varies during a storm event is essential for accurately modelling runoff detention. In this paper, a green roof test bed installed with moisture probes at three depths was used to understand how moisture content varies during storms. Detailed studies were conducted on five selected storm events. Physical characterisation tests and field-data based calibrations were performed to acquire the model parameters. Two alternative detention models, based on Reservoir Routing and Richard’s Equation, were validated against the measured green roof runoff and temporary moisture storage data. Once the moisture content exceeds local field capacity, its response at different depths occurs simultaneously during storms, although the recorded data indicate a vertical gradient in the absolute values of local field capacity. Both Reservoir Routing and Richard’s Equation can provide reasonable estimations of the runoff and the vertical moisture content profiles, although Richard’s Equation exhibited stronger vertical water content gradients than were observed in practise. The vertical water content profile is not sensitive to the soil water release curve, although the hydraulic conductivity function influences both the vertical water content profile and runoff rate. The modelled results are highly sensitive to the bottom boundary condition, with a constant suction head boundary condition providing a more suitable option than a free drainage boundary condition or a seepage boundary condition.

Porewater salinity effect on flocculation and desiccation cracking behaviour of kaolin and bentonite considering working condition

Cracking behaviour of clays at a local working climate and soils' evolution under seepage boundary is very important for the geological engineering. In coastal regions, pore water salinity is incorporated into above processes. In this study, the properties of typical clays (kaolin and bentonite) in saline environments, including the consistency limits, particle sedimentation and crack pattern, were investigated. The consistency limits of kaolin remain constant regardless of the pore water salinity, while the liquid limits of bentonite noticeably decrease with increasing salinity. Flocculation of kaolin occurs in both distilled water and NaCl solution, whereas the fine particles in bentonite disperse in distilled water but aggregate in saline water. At the end of the evaporation process, the total crack area of bentonite is obviously decreased, and the total crack length increases with pore water salinity, whilst that of kaolin is not influenced. In the subsequent wetting process, the bentonite clods disperse easily in saline environment, but the collapse of kaolin clods is not significantly influenced by the water salinity. The above observations are explained by the initial aggregation of clay platelets for the interactive forces between particles.

Tailings Pond Risk Prediction Using Long Short-Term Memory Networks

Tailings ponds are a major hazard, and are ranked 18th in the risk assessment of world accident hazards. The saturation line height is one of the most important factors that affects the safety of tailings ponds. Due to the extremely complicated seepage boundary conditions of tailings ponds, a precise calculation method is urgently needed for predicting the saturation lines. Therefore, the dynamic model should be investigated to evaluate the potential for dam breakage. In this paper, based on an analysis of tailings ponds in various regions, we use the long short-term memory (LSTM) algorithm to predict the time-series variation of the saturation line height. To evaluate and validate our model, we compare with traditional models. The results demonstrate that the deep learning method significantly outperforms the traditional methods, provides a new strategy and has significant potential for tailings ponds safety prediction.

Impact of water, nitrogen and CO2 fracturing fluids on fracturing initiation pressure and flow pattern in anisotropic shale reservoirs

Water-based fluids are currently main fracturing fluids but have some unavoidable limitation. Alternative options include nitrogen and CO2 in some new fracturing methods. However, the fracturing mechanism with water, CO2 and nitrogen has not been clear so far. This paper proposes a numerical model to investigate the impact of water, CO2 and nitrogen fluids on fracturing initiation pressure and seepage area of a shale reservoir. First, the governing equations for anisotropic deformation and anisotropic seepage are further extended for bedding shale. Second, a moving seepage boundary is used for fracturing fluid permeation. Third, a fracture initiation criterion is established based on the stress intensity factor of mode I crack. Fourth, a complex parameter is suggested to express the combined effect of shale permeability, fluid viscosity and pressurization rate. This numerical model is then verified with two sets of experimental data and numerical simulations available in literature. Finally, the impacts of the complex parameter, Biot's coefficient, confining pressure, and critical state on fracturing initiation pressure and seepage area are investigated. The permeability evolution during fracturing initiation process is discussed. It is found that this numerical model has the capability to simulate the hydraulic fracturing process with water, CO2 and nitrogen. Complex parameter, Biot's coefficient and confining pressure have significant impacts on fracturing initiation pressure and seepage area. The fracturing initiation pressure decreases with complex parameter and Biot's coefficient but increases with confining pressure regardless of fracturing fluid type. Water has the highest fracturing initiation pressure and the smallest seepage area. These differences are from the change of effective stress in seepage area, particularly nearby the permeation front. CO2 and nitrogen are good alternative fluids for hydraulic fracturing under the same condition of complex parameter, Biot's coefficient and confining pressure because they have lower fracturing initiation pressure and larger seepage area compared to water.

A seepage outlet boundary condition in hemodynamics modeling.

In computational fluid dynamics (CFD) models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. As an important part of the arterial circulation, microcirculation plays important roles in many aspects, such as substance exchange, interstitial fluid generation and inverse flow. It is necessary to consider microcirculation in hemodynamics modeling. This is a methodological paper to test and validate a new type of boundary condition never applied to microcirculation before. In order to address this issue, we introduce microcirculation as a seepage outlet boundary condition in computational hemodynamics. Microcirculation is treated as a porous medium in this paper. Numerical comparisons of the seepage and traditional boundary conditions are made. The results show that the seepage boundary condition has significant impacts on numerical simulation. Under the seepage boundary condition, the fluctuation range of the pressures progressively rises in the artery zone. The results obtained from the traditional boundary condition show that the pressure fluctuation range gradually falls. In addition, the wall shear stresses under the traditional outlet boundary condition are much higher than those under the seepage outlet boundary condition. The proposed boundary condition is more suitable in hemodynamics modeling.

Constrained optimization based F.E. mesh deforming algorithm for unconfined seepage problems

In this paper, a nonlinear programming technique is presented to calculate the location of the phreatic line in earth dams. Homogeneous and zoned earth dams with and without horizontal drain are considered in this study. A polynomial with unknown coefficients is assumed as equation of the phreatic line in the homogeneous dams. For zoned earth dams, phreatic line is considered as a multi-segment non smooth curve. Coefficients of the polynomials are calculated optimizing an objective function which is defined based on the physical conditions on the phreatic line. Seepage boundary conditions are introduced as constraints for the objective function. Linear finite elements method with adjustable mesh is used to calculate the distribution of the water pressure in the dam. An algorithm based on the location of the phreatic line is presented to construct the finite elements mesh. The result of the present method is verified by the results of the nonlinear finite elements and other mesh deforming methods.

Transport mechanisms of contaminants released from fine sediment in rivers

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment ( 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

An evaluation of porosity and permeability based on an unsteady seepage model in a reservoir while underbalanced drilling

Abstract During underbalanced drilling, real-time monitoring of parameters such as the porosity and permeability of the gas reservoir is the fundamental basis for researching the formation properties and drilling risk prevention. As the drilled layer thickness increases, the exposed area of the gas reservoir also gradually increases, and the amount of gas that flows into the wellbore varies, which causes changes to the wellbore gas–liquid distribution and its control parameters. Such changes pose challenges to the precise interpretation of the gas reservoir in underbalanced drilling, and the difficulty of controlling the underbalanced well also increases. Therefore, a series of studies on computing formation gas output in underbalanced conditions was performed via real-time monitoring of the total hydrocarbon value using ground-monitoring equipment, and an unsteady seepage model of the reservoir gas was developed by considering the flow characteristics of the gas while drilling. We analyzed the time-varying gas output and seepage boundary characteristics of the gas reservoir that is opened gradually during the underbalanced drilling. Based on the superposition principle, a computational model of gas reservoir’s permeability was derived based on the computational results of the unsteady seepage flow model. Moreover, the porosity distribution in the working area was obtained according to the relationship between porosity and permeability, and a highly efficient and accurate evaluation of the gas reservoir while underbalanced drilling was achieved. Based on a field example it was demonstrated that these methods can meet the demands of engineering projects.

Limitations of Transient Seepage Analyses for Calculating Pore Pressures during External Water Level Changes

External water level variations, such as rapid drawdown or flood loading, change the internal pore pressures in an embankment as a result of changes in the boundary conditions. Three different effects result: (1) changes in water pressure on the slope change the seepage boundary conditions, (2) changes in the total stress applied by the weight of the water on the slope change the confining pressure on the soil, and (3) changes in the stabilizing load from the reservoir cause changes in shear stress. Uncoupled transient seepage analyses, which consider only the first effect, are increasingly being advocated as an appropriate means to calculate pore pressures for effective stress stability analyses following water level changes. This paper discusses the limitations of uncoupled transient seepage analyses for calculating pore pressures during drawdown, explains the requirements for more appropriate analyses, and gives examples that show the errors incumbent on the use of uncoupled analyses.

The New Methods for Non-Steady Productivity Prediction of Condensate Gas Reservoir and the Application Evaluation

In view of the existing shortcomings of the analysis methods for the production system of conventional condensate gas well, the new method that adopts the non-steady gas reservoir seepage and the wellbore coupling has been proposed in this paper, in other words, the gas nozzle control, the wellbore flow and the reservoir seepage have been considered as the coupling entirety; the traditional nodal analysis has been combined with the well test analysis of non-steady seepage; the new production system analysis methods have been employed to discuss the characteristics of gas reservoir seepage, wellbore flow and gas reservoir boundary; at the same time, the changing trends of indicators in the development process have been also analyzed. Afterwards, the coordination state and the changes of parameters of the production system can be predicted in different production methods and different times. And the better results can be obtained through the application evaluation of YK1.

Application of level set method for groundwater flow with moving boundary

A potential of level set methods for the numerical modeling of moving boundaries and interfaces in groundwater flow problems is shown by the application for a particular model of the flow with moving water table (the phreatic surface). The main ingredients of the level set methods like the advection of level set function, the computation of signed distance function and the extrapolation of missing data are explained for a class of possible applications. The numerical solution of the groundwater flow problem is proposed using the flux-based level set method and the immersed interface method that are based on a finite volume discretization on any fixed (unstructured) grid. Presented examples show good properties of the method concerning a small mass balance error and a good grid convergence even for an example with merging boundaries. An example with seepage boundary is computed using the locally adapted grids by refining and coarsening the mesh according to the position of moving water table.