Modeling and Analysis of Seawater Intrusion in the Coastal Aquifer of Eastern Cap-Bon, Tunisia

A numerical model that treats density-dependent variably saturated flow and miscible salt transport is used to investigate the occurrence of seawater intrusion in the Korba aquifer of the eastern coast of Cap-Bon in northern Tunisia. We examine the interplay between pumping regimes and recharge scenarios and its effect on the saline water distribution. More localized simulations are used to examine, in vertical cross sections, the effects of well location and soil type and the role of the vadose zone in possible remediation actions. The exploratory simulations suggest interesting interactions between the unsaturated zone and the saltwater–freshwater interface with possible implications for groundwater exploitation from shallow unconfined coastal aquifers, involving in one case feedback between seawater intrusion and the high pressure head gradients around the pumping-induced drawdown cone and in another case threshold-like interface displacement for tight soils such as clays. The data processing steps undertaken in this GIS and modeling study are described in some detail, and a critical assessment is given of the data availability and of the requirements for successful monitoring and modeling of seawater intrusion risks in heavily exploited coastal aquifers such as those found in the semi-arid regions of the Mediterranean basin. It is shown how, with the aid of GIS, reasonably reliable information can be assembled from maps, surveys, and other sources of geospatial and hydrogeological data, an approach that is necessary in the many regions of the world with acute water resource problems but with limited means for undertaking systematic data acquisition and environmental monitoring actions. Nonetheless the need for more concerted monitoring of relevant parameters and processes and of closer coordination between monitoring and modeling is stressed. An idea of the extent of over-exploitation of the Korba aquifer is obtained by examining the pumping and rainfall/infiltration data, and the simulation results support groundwater pumping as the mechanism for and seawater intrusion as the origin of the salt contamination observed in the soils and subsurface waters of the Korba plain.     

Compressed Air Flow within Aquifer Reservoirs of CAES Plants

A model on the air flow within aquifer reservoirs of Compressed Air Energy Storage (CAES) plants was developed. The design of such CAES plants requires knowledge of the reservoir air pressure distribution during both the charging and discharging phases. Also, it must assure air/water interface stability to prevent water suction during discharge. An approximate analytical solution for the pressure variations within the anisotropic reservoir porous space was developed, subject to the Darcy equation and for conditions of partially penetrating wells. Sensitivity analyses were conducted to identify the dominant parameters affecting the well pressure and the critical flow rate (water suction threshold). It is demonstrated that water coning is a factor that could severely limit the discharge air flow rate. A significant diminishment of that limitation and reduction of the pressure fluctuation can be achieved by enlargement of the air layer height and discharge period. Likewise, aquifers with larger horizontal permeability impose less restrictive critical flows. A conclusion on the preferred screen length could not be merely drawn from technological considerations, but should also involve important economic aspects.     

Uncertainty Analysis of Radionuclide Transport in a Fractured Coastal Aquifer with Geothermal Effects

Groundwater flow and radionuclide transport at the Milrow underground nuclear test site on Amchitka Island are modeled using two-dimensional numerical simulations. A multi-parameter uncertainty analysis is adapted and used to address the effects of uncertainties associated with the definition of the modeled processes and the values of the parameters governing these processes. In particular, we focus on the effects on radioactive transport of uncertainties associated with conduction and convection of heat relative to the uncertainties associated with other flow and transport parameters. These include recharge, hydraulic conductivity, fracture porosity, dispersivity and strength of matrix diffusion. The flow model is conceptualized to address the problem of density-driven flow under conditions of variable salinity and geothermal gradient. The conceptual transport model simulates the advection–dispersion process, the diffusion process from the high-velocity fractures into the porous matrix blocks, and radioactive decay.For this case study, the uncertainty of the recharge-conductivity ratio contributes the most to the output uncertainty (standard deviation of mass flux across the seafloor). The location of the freshwater–saltwater transition zone changes dramatically as this ratio changes with the thickness of the freshwater lens and the location of the seepage face changing as well. In the context of radionuclide transport from the nuclear test cavity that is located in the area where the transition zone is uncertain, travel times of radionuclide mass from the cavity to the seepage face along the seafloor are significantly impacted. The variation in transition zone location changes the velocity magnitude at the cavity location by a large factor (probably an order of magnitude). When this effect is combined with porosity and matrix diffusion uncertainty, the uncertainty of transport results becomes large. Although thermal parameters have an effect on the solution of the flow problem and also on travel times of radionuclides, the effect is relatively small compared to other flow and transport parameters.     

Effects of Clay Dispersion on Aquifer Storage and Recovery in Coastal Aquifers

Cyclic injection, storage, and withdrawal of freshwater in brackish aquifers is a form of aquifer storage and recovery (ASR) that can beneficially supplement water supplies in coastal areas. A 1970s field experiment in Norfolk, Virginia, showed that clay dispersion in the unconsolidated sedimentary aquifer occurred because of cation exchange on clay minerals as freshwater displaced brackish formation water. Migration of interstitial clay particles clogged pores, reduced permeability, and decreased recovery efficiency, but a calcium preflush was found to reduce clay dispersion and lead to a higher recovery efficiency. Column experiments were performed in this study to quantify the relations between permeability changes and clay mineralogy, clay content, and initial water salinity. The results of these experiments indicate that dispersion of montmorillonite clay is a primary contributor to formation damage. The reduction in permeability by clay dispersion may be expressed as a linear function of chloride content. Incorporating these simple functions into a radial, cross-sectional, variable-density, ground-water flow and transport model yielded a satisfactory simulation of the Norfolk field test – and represented an improvement over the model that ignored changes in permeability. This type of model offers a useful planning and design tool for ASR operations in coastal clastic aquifer systems.     

CO2 Injection into Saline Carbonate Aquifer Formations II: Comparison of Numerical Simulations to Experiments

Sequestration of carbon dioxide in geological formations is an alternative way of managing extra carbon. Although there are a number of mathematical modeling studies related to this subject, experimental studies are limited and most studies focus on injection into sandstone reservoirs as opposed to carbonate ones. This study describes a fully coupled geochemical compositional equation-of-state compositional simulator (STARS) for the simulation of CO₂ storage in saline aquifers. STARS models physical phenomena including (1) thermodynamics of sub- and supercritical CO₂, and PVT properties of mixtures of CO₂ with other fluids, including (saline) water; (2) fluid mechanics of single and multiphase flow when CO₂ is injected into aquifers; (3) coupled hydrochemical effects due to interactions between CO₂, reservoir fluids, and primary mineral assemblages; and (4) coupled hydromechanical effects, such as porosity and permeability change due to the aforementioned blocking of pores by carbonate particles and increased fluid pressures from CO₂ injection. Matching computerized tomography monitored laboratory experiments showed the uses of the simulation model. In the simulations dissolution and deposition of calcite as well as adsorption of CO₂ that showed the migration of CO₂ and the dissociation of CO₂ into HCO₃ and its subsequent conversion into carbonate minerals were considered. It was observed that solubility and hydrodynamic storage of CO₂ is larger compared to mineral trapping.     

Large Eddy Simulation of Flow Control Around a Cube Subjected to Momentum Injection

The concept of Momentum Injection (MI) through Moving Surface Boundary layer Control (MSBC) applied to a cubic structure is numerically studied using Large Eddy Simulation at a Reynolds number of 6.7×10⁴. Two small rotating cylinders are used to add the momentum at the front vertical edges of the cube. Two configurations are studied with the yaw angle of 0° and 30°, respectively, with ratio of the rotation velocity of cylinders and the freestream velocity of 2. The results suggest that MI delays the boundary layer separation and reattachment, and thus reduces the drag. A drag reduction of about 6.2 % is observed in the 0° yaw angle case and about 44.1 % reduction in the 30° yaw angle case. In the case of 0° yaw angle, the main change of the flow field is the disappearance of the separation regions near the rotating cylinders and the wake region is slightly changed due to MI. In the 30° yaw angle case, the flow field is changed a lot. Large flow separations near one rotating cylinder and in the wake is significantly reduced, which results in the large drag reduction. Meanwhile, the yaw moment is increased about 50.5 %.     

Pressure Buildup During CO<Subscript>2</Subscript> Injection into a Closed Brine Aquifer

CO₂ injected into porous formations is accommodated by reduction in the volume of the formation fluid and enlargement of the pore space, through compression of the formation fluids and rock material, respectively. A critical issue is how the resulting pressure buildup will affect the mechanical integrity of the host formation and caprock. Building on an existing approximate solution for formations of infinite radial extent, this article presents an explicit approximate solution for estimating pressure buildup due to injection of CO₂ into closed brine aquifers of finite radial extent. The analysis is also applicable for injection into a formation containing multiple wells, in which each well acts as if it were in a quasi-circular closed region. The approximate solution is validated by comparison with vertically averaged results obtained using TOUGH2 with ECO2N (where many of the simplifying assumptions are relaxed), and is shown to be very accurate over wide ranges of the relevant parameter space. The resulting equations for the pressure distribution are explicit, and can be easily implemented within spreadsheet software for estimating CO₂ injection capacity.     

Radial Flow in a Bounded Randomly Heterogeneous Aquifer

Flow to wells in nonuniform geologic formations is of central interest to hydrogeologists and petroleum engineers. There are, however, very few mathematical analyses of such flow. We present analytical expressions for leading statistical moments of vertically averaged hydraulic head and flux under steady-state flow to a well that pumps water from a bounded, randomly heterogeneous aquifer. Like in the widely used Thiem equation, we prescribe a constant pumping rate deterministically at the well and a constant head at a circular outer boundary of radius L. We model the natural logarithm Y = lnT of aquifer transmissivity T as a statistically homogeneous random field with a Gaussian spatial correlation function. Our solution is based on exact nonlocal moment equations for multidimensional steady state flow in bounded, randomly heterogeneous porous media. Perturbation of these nonlocal equations leads to a system of local recursive moment equations that we solve analytically to second order in the standard deviation of Y. In contrast to most stochastic analyses of flow, which require that log transmissivity be multivariate Gaussian, our solution is free of any distributional assumptions. It yields expected values of head and flux, and the variance–covariance of these quantities, as functions of distance from the well. It also yields an apparent transmissivity, T _a, defined as the negative ratio between expected flux and head gradient at any radial distance. The solution is supported by numerical Monte Carlo simulations, which demonstrate that it is applicable to strongly heterogeneous aquifers, characterized by large values of log transmissivity variance. The two-dimensional nature of our solution renders it useful for relatively thin aquifers in which vertical heterogeneity tends to be of minor concern relative to that in the horizontal plane. It also applies to thicker aquifers when information about their vertical heterogeneity is lacking, as is commonly the case when measurements of head and flow rate are done in wells that penetrate much of the aquifer thickness. Potential uses include the analysis of pumping tests and tracer test conducted in such wells, the statistical delineation of their respective capture zones, and the analysis of contaminant transport toward fully penetrating wells.     

The Application of a Laminar Flamelet Model to Confined Explosion Hazards

The majority of computational studies of confined explosion hazards apply simple and inaccurate combustion models, requiring adhoc corrections to obtain realistic flame shapes and often predicting an order of magnitude error in the overpressures. This work describes the application of a laminar flamelet model to a series of two-dimensional test cases. The model is computationally efficient applying an algebraic expression to calculate the flame surface area, an empirical correlation for the laminar flame speed and a novel unstructured, solution adaptive numerical grid system which allows important features of the solution to be resolved close to the flame. Accurate flame shapes are predicted, the correct burning rate is predicted near the walls, and an improvement in the predicted overpressures is obtained. However, in these fully turbulent calculations the overpressures are still too high and the flame arrival times too low, indicating the need for a model for the early laminar burning phase. Due to the computational expense, it is unrealistic to model a laminar flame in the complex geometries involved and therefore a pragmatic approach is employed which constrains the flame to propagate at the laminar flame speed. Transition to turbulent burning occurs at a specified turbulent Reynolds number. With the laminar phase model included, the predicted flame arrival times increase significantly, but are still too low. However, this has no significant effect on the overpressures, which are predicted accurately for a baffled channel test case where rapid transition occurs once the flame reaches the first pair of baffles. In a channel with obstacles on the centreline, transition is more gradual and the accuracy of the predicted overpressures is reduced. However, although the accuracy is still less than desirable in some cases, it is much better than the order of magnitude error previously expected. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling of Gas Migration Through Low-Permeability Clay Rock Using Information on Pressure and Deformation from Fast Air Injection Tests

The characterization of gas migration through low-permeability clay formations has been a focus of R&D programs for radioactive waste disposal, which is also of great importance for shale gas exploration, cap-rock behavior of hydrocarbon reservoirs, and \(\hbox {CO}_{2}\) sequestration. Laboratory tests have been performed on Opalinus Clay, a Mesozoic claystone that is being investigated in Switzerland as a potential host rock for the storage of nuclear waste. The laboratory program included specific water and air injections tests, as well as oedometer and isotropic compression tests. Undisturbed core samples have been retrieved from a shallow borehole in the Mont Terri Underground Research Laboratory (URL) and from a deep borehole in northern Switzerland. For the shallow cores from Mont Terri URL, largely linear-elastic deformations associated with the gas injection test could be inferred and the change in void ratio was accounted for by the pore compressibility. The corresponding change in permeability was obtained from the results of the water tests, indicating a log-linear relation between permeability and porosity. The derived porosity change and the corresponding change in permeability were implemented in the standard TOUGH2 code, which reproduced the measured gas test results using fitted water retention data derived from laboratory measurements. Similar air injection tests performed on Opalinus Clay cores from the borehole at greater depth showed overall similar behavior, but at lower porosities, lower permeability values, and lower compressibility. These cases indicated nonlinear behavior which was implemented using an effective stress-dependent porosity change and the associated change in permeability. In addition, the anisotropy associated with the bedding planes of the clay formation was considered by assuming different properties for “soft” and “hard” layers to account for storage capacity for the injected gas prior to gas breakthrough. The computed change in the overall porosity could be compared to the measured axial deformation during the gas injection test and was used for calibration of the parameters describing the relationship between the effective stress and porosity, as well as the corresponding change in permeability and capillary pressure.     

Water Injection into a Low-Permeability Rock - 2: Control Model

In Part 1, we have demonstrated the inevitable growth of the fluid injection hydrofractures in low-permeability rocks. Thus, a smart controller that manages fluid injection in the presence of hydrofracture extension is highly desirable. Such a controller will be an essential part of automated waterflood project surveillance and control. Here we design an optimal injection controller using methods of optimal control theory. The controller inputs are the history of the injection pressure and the cumulative injection, along with the fracture size. The output parameter is the injection pressure and the control objective is the injection rate. We demonstrate that the optimal injection pressure depends not only on the instantaneous measurements, but it is determined by the whole history of the injection and of the fracture area growth. We show the controller robustness when the inputs are delayed and noisy and when the fracture undergoes abrupt extensions. Finally, we propose a procedure that allows estimation of the hydrofracture size at no additional cost.     

Control of a Nonlinear System Using the Saturation Phenomenon

In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore, the second-order solution is presented and the corresponding results are compared with those of the first-order solution. It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding numerical results. Good agreement between the two sets of results is observed.     

Feedback Control of a Thermal Fluid Using State Estimation

Abstract

In his paper we consider the problem of designing a feedback controller for a thermal fluid. Any practical feedback controller for a fluid flow system must incorporate some type of state estimator. Moreover, regardless of the approach, one must introduce approximations at some point in the analysis. The method presented here uses distributed parameter control theory to guide the design and approximation of practical slate estimators. Wc use finite clement techniques to approximate optimal infinite dimensional controllers based on linear quadratic Gaussian lpar;LQG) and MinMax theory for the Bonssincsq equations. These designs are then compared to full state feedback. We present several numerical experiments and we describe how these techniques can also be applied to sensor placement problems.     

Large Scale Experiment on Transport of Trichloroethylene in a Controlled Aquifer

Pollution by dense non-aqueous phase liquids (DNAPLs) represents a major threat to groundwater resources. In a real case of site contamination, the efficiency of remediation techniques is often limited by a lack of knowledge of both the extent of the pollution and the behavior of the different phases of the pollutant in the subsurface. An experiment simulating pollution of an aquifer by a chlorinated solvent (Trichloroethylene: TCE) was conducted on a large controlled experimental site called SCERES. The experiment consisted of an injection of 8.9 liters of TCE under controlled conditions at 35cm below the soil surface with an appropriate set up. The goal was to study the behavior of the three phases of the pollutant (trapped TCE phase forming the impregnation body, vapors in the vadose zone, and dissolved traces in the aquifer) in order to better comprehend the mechanisms which govern the propagation and the transfer of this type of pollution underground. The SCERES experimental data indicate that mass transfer from the saturated zone to the vadose zone is important, affecting the repartition of the vapor plume and causing a significant decrease of dissolved TCE concentrations in the groundwater. Furthermore, vertical leaching of TCE vapors due to rainfall strongly influences the degree of groundwater pollution and its lateral extent. The transient mass balance of the experiment is very satisfactory and shows that the main part of the spilled quantity is lost to the atmosphere.     

Numerical Modeling of Two-Dimensional Flow of a Nonhomogeneous Fluid in a Confined Domain

The pattern of the two-dimensional vortex flow of a nonhomogeneous fluid in a confined domain is studied using two-dimensional numerical calculations. It is found that in the case of a nonhomogeneous initial density distribution the kinetic energy decay rates are proportional to the square root of viscosity at the active stage of flow restructuring. The correlation functions of the velocity and the density are derived for different moments of time in the inertial range. All these results indicate the choice of the two-dimensional turbulence development scenario in a nonhomogeneous fluid.     

Investigation of the Flow Structure in a Model Scramjet Air Intake with Transverse Hydrogen Fuel Injection into Supersonic Crossflow

Fluid Dynamics - Combustion flow inside the channel of a model scramjet air inlet with transverse hydrogen fuel injection from the bottom wall is investigated. The OH-concentration and pressure...     

Large Eddy Simulation of Scalar Mixing in a Coaxial Confined Jet

The highly turbulent flow occurring inside gas-turbine combustors requires accurate simulation of scalar mixing if CFD methods are to be used with confidence in design. This has motivated the present paper, which describes the implementation of a passive scalar transport equation into an LES code, including assessment/testing of alternative discretisation schemes to avoid over/undershoots and excessive smoothing. Both second order accurate TVD and higher order accurate DRP schemes are assessed. The best performance is displayed by a DRP method, but this is only true on fine meshes; it produces similar (or larger) errors to a TVD scheme on coarser meshes, and the TVD approach has been retained for LES applications. The unsteady scalar mixing performance of the LES code is validated against published DNS data for a slightly heated channel flow. Excellent agreement between the current LES predictions and DNS data is obtained, for both velocity and scalar statistics. Finally, the developed methodology is applied to scalar transport in a confined co-axial jet mixing flow, for which experimental data are available. Agreement with statistically averaged fields for both velocity and scalar, is demonstrated to be very good, and a considerable improvement over the standard eddy viscosity RANS approach. Illustrations are presented of predicted time-resolved information e.g. time histories, and scalar pdf predictions. The LES results are shown, even using a simple Smagorinsky SGS model, to predict (correctly) lower values of the turbulent Prandtl number in the free shear regions of the flow, compared to higher values in the wall-affected regions. The ability to predict turbulent Prandtl number variations (rather than input these as in combustor RANS CFD models) is an important and promising feature of the LES approach for combustor flow simulation since it is known to be important in determining combustor exit temperature traverse.