An Experimenting Field Approach for the Numerical Solution of Multiphase Flow in Porous Media

In this work, we apply the experimenting pressure field technique to the problem of the flow of two or more immiscible phases in porous media. In this technique, a set of predefined pressure fields are introduced to the governing partial differential equations. This implies that the velocity vector field and the divergence at each cell of the solution mesh can be determined. However, since none of these fields is the true pressure field entailed by the boundary conditions and/or the source terms, the divergence at each cell will not be the correct one. Rather the residue which is the difference between the true divergence and the calculated one is obtained. These fields are designed such that these residuals are used to construct the matrix of coefficients of the pressure equation and the right‐hand side. The experimenting pressure fields are generated in the solver routine and are fed to the different routines, which may be called physics routines, which return to the solver the elements of the matrix of coefficients. Therefore, this methodology separates the solver routines from the physics routines and therefore results in simpler, easy to construct, maintain, and update algorithms.     

TCAT Analysis of Capillary Pressure in Non-equilibrium, Two-fluid-phase, Porous Medium Systems

Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.     

两种不同势函数下半空间饱和多孔介质中Rayleigh波求解比较

分别对"考虑两种压缩波和幅值比例系数"和"考虑一种压缩波(P1或P2波)但不考虑幅值比例系数"两种不同势函数下的半空间饱和多孔介质中Rayleigh波求解进行详细推导,理论分析表明"考虑两种压缩波和幅值比例系数"下Rayleigh波求解推导更为严密,与饱和多孔介质中存在两种压缩波的事实相一致。在研究半空间饱和多孔介质中Rayleigh波时应采用"考虑两种压缩波和幅值比例系数"的势函数。     

Calculating Groundwater Response Times for Flow in Heterogeneous Porous Media

Predicting the amount of time required for a transient groundwater response to take place is a practical question that is of interest in many situations. This time scale is often called the response time. In the groundwater hydrology literature, there are two main methods used to calculate the response time: (1) both the transient and steady‐state groundwater flow equations are solved, and the response time is taken to be amount of time required for the transient solution to approach the steady solution within some tolerance; and (2) simple scaling arguments are adopted. Certain limitations restrict both of these approaches. In this study, we outline a third method, based on the theory of mean action time. We derive the governing boundary value problem for both the mean and variance of action time for confined flow in two‐dimensional heterogeneous porous media. Importantly, we show that these boundary value problems can be solved using widely available software. Applying these methods to a test case reveals the advantages of the theory of mean action time relative to standard methods.     

Three-Dimensional Numerical Investigation of Pore Water Pressure and Deformation of Pumped Aquifer Systems

Excessive groundwater withdrawal has caused severe land subsidence worldwide. The pore water pressure and the deformation of pumped hydrostratigraphic units are complex. A fully coupled three-dimensional numerical simulation was carried out for different pumping plans in this paper. When groundwater is pumped from a confined aquifer, the great compaction occurs in the pumped aquifer and its upper and lower adjacent aquitard units. Land subsidence is smaller and the area affected by land subsidence is greater when groundwater is pumped from the deeper confined aquifer. The pore water pressure in the pumped confined aquifer changes immediately with pumpage. In the adjacent aquitard units, however, the pore water pressure increases in the early pumping time and decreases in the early recharging time. The decrease in the pore water pressure vertically spreads from the interface between aquitard and pumped aquifer to the other surface of the aquitard. The pumped aquifer compacts and rebounds immediately with pumping and non-pumping or recharging actions, while the compaction and rebounding of the aquitard units clearly lag behind. The compaction of the adjacent aquitard unit first occurs near the interface between aquitard and pumped aquifer units, and the compaction zone spreads outward as the pumping goes on. The aquitards may expand vertically within some zones. Due to the inelastic deformation of soil skeleton, different pumping plans result in different land subsidence. For the same net pumpage, maximal land subsidence and horizontal displacement are the smallest for constant discharge and the greatest for recharge-discharge cycle.     

Experiment and Simulation of Non-Reactive Solute Transport in Porous Media

To more accurately predict the migration behavior of pollutants in porous media, we conduct laboratory scale experiments and model simulation. Aniline (AN) is used in one-dimensional soil column experiments designed under various media and hydrodynamic conditions. The advection-dispersion equation (ADE) and the continuous-time random walk (CTRW) were used to simulate the breakthrough curves (BTCs) of the solute transport. The results show that the media and hydrodynamic conditions are two important factors affecting solute transport and are related to the degree of non-Fickian transport. The simulation results show that CTRW can more effectively describe the non-Fickian phenomenon in the solute transport process than ADE. The sensitive parameter in the CTRW simulation process is , which can reflect the degree of non-Fickian diffusion in the solute transport. Understanding the relationship of with velocity and media particle size is conducive to improving the reactive solute transport model. The results of this study provide a theoretical basis for better prediction of pollutant transport in groundwater.     

Grain Size Analysis and Permeametry for Estimating Hydraulic Conductivity in Engineered Porous Media

Grain size analysis and permeametry are common methods for estimating the hydraulic conductivity (K) of porous media. It is well known that these methods have limited accuracy when they are used to characterize natural sediments. However, hydrogeological research has increasingly introduced technologies dependent on engineered porous media that may be less problematic because complex geologic structures are eliminated in the lab and field-scale packings. The recently introduced Horizontal Reactive Media Treatment Wells (HRX® Wells), for in situ, passive remediation of groundwater is one such example. The HRX Well passively collects groundwater and directs it through a horizontal pipe packed with an engineered porous medium. In this project, grain size analysis was conducted for sand and sand-iron mixtures to estimate K using the 16 algorithms provided in the HydrogeoSieveXL2.3.2 software. The results were compared to K determined by permeametry and a field-scale column, 30 cm long and 25 cm in diameter, representing an HRX Well. The best comparability of K estimates from grain size analysis and permeametry were obtained using the USBR, Slichter, and Shepherd K estimation methods. These also showed good agreement between lab-scale and field-scale K estimations, with reproducibility within the range ±20%. This study shows that laboratory K estimations can be representative across various relevant scales, including the field-scale, for engineered porous media. This finding extends to filter packs, and other engineered porous media design methods by emphasizing and demonstrating one case of accuracy in lab-scale permeability estimation for field-scale implementations.     

Specification of Matrix Cleanup Goals in Fractured Porous Media

Semianalytical transient solutions have been developed to evaluate what level of fractured porous media (e.g., bedrock or clay) matrix cleanup must be achieved in order to achieve compliance of fracture pore water concentrations within a specified time at specified locations of interest. The developed mathematical solutions account for forward and backward diffusion in a fractured porous medium where the initial condition comprises a spatially uniform, nonzero matrix concentration throughout the domain. Illustrative simulations incorporating the properties of mudstone fractured bedrock demonstrate that the time required to reach a desired fracture pore water concentration is a function of the distance between the point of compliance and the upgradient face of the domain where clean groundwater is inflowing. Shorter distances correspond to reduced times required to reach compliance, implying that shorter treatment zones will respond more favorably to remediation than longer treatment zones in which back‐diffusion dominates the fracture pore water response. For a specified matrix cleanup goal, compliance of fracture pore water concentrations will be reached sooner for decreased fracture spacing, increased fracture aperture, higher matrix fraction organic carbon, lower matrix porosity, shorter aqueous phase decay half‐life, and a higher hydraulic gradient. The parameters dominating the response of the system can be measured using standard field and laboratory techniques.     

An Investigation of the Pressure Pulsing Reagent Delivery Approach

Pressure pulsing technology is an innovative method that has been developed with the aim of overcoming preferred flow paths associated with remediation techniques that rely on the injection of reagents. Numerical and field experiments were conducted to assess how pressure pulsing affects groundwater flow and solute transport during reagent injection. A series of field experiments were performed at two field sites where a monitoring network designed to capture the breakthrough of solutes delivered from an injection well was installed. Pressure pulsing and conventional injection methods were used at each site. One site was comprised of fine sand with low heterogeneity, while the other was moderately heterogeneous with discrete layers varying from fine sand to silt. The data suggest that breakthrough was more uniform for the pressure pulsing injections; however, this difference was minor and complicated by sorption of some of the tracers employed. The groundwater flow and solute transport modeling exercise simulated the rapid boundary pressure modulation that occurs in association with pressure pulsing. Two‐dimensional (2D) simulations revealed that repeated sudden onset of injection cessation produces brief periods of gradient reversal and the development of a mixing zone near the injection well. The spatial extents of this mixing zone were found to be highly dependent upon the hydraulic diffusivity of the medium, with medium heterogeneity and pulsing frequency playing secondary roles. Three‐dimensional (3D) numerical simulations were used to benchmark the observations from one of the field sites. The results from the modeling effort showed that solute breakthrough from a pressure pulsing injection is more dispersed relative to a conventional injection as a result of the mixing zone phenomenon; however, we were unable to directly observe this mixing zone using the instrumentation deployed at the two field sites.     

Simulation of Tidal Effects on Contaminant Transport in Porous Media

A one-dimensional numerical model is developed with oscillating velocities and dispersions to simulate the migration process of a contaminant plume within tidally influenced aquifers. Model simulations demonstrate that a major effect the tidal fluctuation has on the migration process of a contaminant plume is the exit concentration discharging to the tidal estuary. Tidal fluctuation causes the exit concentration levels to be significantly diluted by the surface-water body of the estuary. Sensitivity analyses demonstrate that tidal fluctuation hastens the rate of plume migration near the bank of the estuary because of the relatively high advective and dispersive fluxes induced by tides. However, tides affect the migration process only over a short distance from the tidal-water interface (about 40 ft for the parameters used in this study). If the contaminant plume is located far beyond the interface, tidal fluctuations will not affect the rate of plume migration until an existing regional ground-water flow velocity brings the plume to the tidally active zone. With or without tides, the rate of contaminant migration increases with higher regional hydraulic gradient. Furthermore, the effects of tidal fluctuations on the transport process become insignificant with higher regional hydraulic gradients.     

The Effect of Toluene-Substrate Concentration on Biological Clogging and Sloughing in Porous Media

One-dimensional flow experiments on biological clogging were carried out by biostimulating columns packed with glass beads, sterilized, and inoculated with toluene-utilizing bacteria. Biostimulation consisted of continuously injecting toluene at four concentrations (3.0 ± 0.9, 6.1 ± 0.8, 8.7 ± 1.6, and 11.3 ± 0.8 mg/L). The results of column flow experiments indicated that a threshold concentration of toluene exists below which the total biomass in the column can be kept at a steady-state level. The column cores were extruded and segmented to determine the biomass distribution throughout the column at clogging. Clogging resulted in a significant buildup of filamentous bacteria close to the inlet end. Based on the nucleotide sequence of 16S rRNA genes, the dominant filamentous bacteria were identified as Nocardia farcinica. A 235-d column experiment demonstrated that the clogging near injection points can be controlled by keeping the influent concentration of toluene below the threshold.     

Reformulated Kinematic and Dynamic Ray Tracing Systems for Arbitrarily Anisotropic Media

I reformulate well-established systems for kinematic and dynamic ray tracing in 3D heterogeneous media with arbitrary anisotropy. Matrices of size 3 × 3, e.g. the Christoffel matrix, are substituted by six-component vectors, and the Christoffel matrix elements are expressed explicitly in terms of the elements of the 6 × 6 matrix of elastic coefficients, written in Voigt notation. Thereby, I find it easier to see the effects on the ray tracing systems of vanishing elastic coefficients and Christoffel matrix elements and of vanishing derivatives with respect to spatial coordinates and slowness vector components. The eigenvalue of the current wave and its derivatives with respect to the ray parameters are included explicitly, which may be favorable for ray tracing processes optimized with respect to speed. With the ANRAY program as a reference, I show that the new formulation requires less optimization than the conventional one.