Jacob Bensabat

An adaptive pathline-based particle tracking algorithm for the Eulerian–Lagrangian method

Abstract The accuracy in determining the Lagrangian concentration in the Eulerian–Lagrangian method depends on both the particle tracking algorithm and concentration interpolation. In most existing particle tracking algorithms, accurate tracking cannot be achieved, particularly in a complicated unsteady flow. Also mechanisms for error estimation and accuracy control are not available. A new algorithm is developed by refining the process of particle tracking, making use of a series of available travel time increments (ATTIs). The ATTIs are selected on the basis of tracking accuracy and efficiency. These are controlled by practical indices related to the rate of particle velocity variation (magnitude and direction). The particle velocity is determined by bilinear interpolation in space and time. The proposed algorithm combines an inter-element refinement, consistent with the piecewise interpolation of velocity, and an in-element pathline-based refinement. No mesh refinement is needed. Numerical simulations have been used to demonstrate the accuracy of the proposed algorithm. A comparison between the results obtained by using the proposed algorithm and by some existing techniques shows that the new algorithm can provide an accurate and efficient particle tracking, especially in a complicated unsteady heterogeneous flow.

Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model

We present a model of heat and mass transfer in an unsaturated zone of sand and silty clay soils, taking into account the effects of temperature gradients on the advective flux, and of the enhancement of thermal conduction by the process of latent heat transfer through vapor flow. The motivation for this study is to supply information for the planned storage of thermal energy in unsaturated soils and for hot waste storage. Information is required on the possibility of significant drying at a hot boundary, as this would reduce the thermal conductivity of a layer adjacent to the boundary and, thus, prevent effective heat transfer to the soil. This study indicates the possibility that the considered system may be unstable, with respect to the drying conditions, with the occurrence of drying depending on the initial and the boundary conditions. An analysis performed for certain boundary conditions of heat transfer and for given soil properties, disregarding the advective flux of energy, indicated that there are initial conditions of water content for which heating will not cause significant drying. Under these conditions, fine soils may be better suited for heat transfer at the hot boundary, due to their higher field capacity, although their heat conduction coefficients at saturation are lower than those of sandy soils. At present, these conclusions are limited to the range of 50–80°C. Potential effects of solute concentration at the hot boundary are indicated.

Optimal management of a regional aquifer under salinization conditions

Salinization of an aquifer results from the movement and dispersion of saline water bodies within it and/or from inflow of saline waters across boundaries, including through recharge. Salinity does not exceed a few thousand parts per million, so the effects of density on the flow can be neglected. The objective of management is to maximize the net benefit from the water extracted subject to constraints on the amount of salt taken out with the water. The management model presented in this paper contains simulation of flow and transport of salinity, developed for a two-dimensional essentially horizontal confined aquifer, linked to a nonsmooth optimization algorithm. The simulator is based on a finite element formulation, in which the convective term is treated by the streamlineupwind Petrov-Galerkin (SUPG) method. SUPG is shown to reduce substantially the oscillations present in conventional finite element solutions of the transport equation, especially when the advective term dominates. The derivatives of the dependent variables, heads and concentrations at points in the field, with respect to the decision variables, the pumping rates, are computed in the simulator, using analytical expressions based on sensitivity theory. These derivatives are transmitted to the optimization algorithm, which uses the bundle-trust method for nonsmooth optimization. Application to a synthetic aquifer is demonstrated and analyzed.

Accurate calculation of specific discharge in heterogeneous porous media

Existing continuous schemes for computing the specific discharge in heterogeneous porous media result in inaccuracy in simulating the local specific discharge field at and in the vicinity of an interface between subdomains of different material properties. The domain decomposition method used in multilayered systems and a consistent scheme in a randomly heterogeneous domain are applicable only to some particular cases, such as when the material interfaces are parallel to an axis. Along a material interface, the law of refraction of streamlines, related to both the tangential and the normal specific discharge components, should be satisfied. By incorporating these interface conditions into the weak formulation of Darcys law, two consistent numerical schemes have been developed. These schemes can be applied to accurately and efficiently simulate the specific discharge field in a heterogeneous domain with different values of the ratio of hydraulic conductivities between adjacent elements. In particular, they provide an easy way for treating aquifers with semipervious layers as a single system. Numerical simulations have been used to demonstrate the capability and accuracy of the proposed schemes. Comparison between the specific discharge fields computed by the proposed schemes and by other techniques shows that the new schemes are superior to the traditional ones.

Advective fluxes in multiphase porous media under nonisothermal conditions

We consider the case in which more than one fluid phase occupies the void space of a porous medium. The advective flux law is formulated for a fluid phase, under nonisothermal conditions and with the presence of solutes in the fluid phases. The derivation of the flux laws is based on an approximated version of the averaged balance equation for linear momentum. Taking into account momentum transfer through the interface between the fluid phases, leads to coupling between the flow in adjacent phases. Fluxes are also shown to depend on the surface tension at the interface between the adjacent fluid phases. Since the latter depends on temperature and solute concentration in the two phases, the advective flux is shown to depend on both temperature and solute concentration gradients in the two phases. A preliminary order of magnitude analysis gives conditions under which the coupling phenomena are not negligible. The approach is applied to the unsaturated zone, as a typical example of a multiphase porous medium.The main conclusion is that the well known Darcy law for single phase flow, may have to be modified for a multi fluid phase system, especially when temperature and solute concentration are not uniform.

Simulation of immiscible multiphase flow in porous media: A focus on the capillary fringe of oil-contaminated aquifers

This paper deals with the analysis of some aspects of the vertical and lateral migration of oil spills in the unsaturated and the capillary zone of a phreatic aquifer. Our motivation stems from the fact that such contamination represents a severe danger for ground-water resources all over the world and from the present acute problem of jet-fuel contamination in some location of Israel. In the present study, we shall focus our efforts on the analysis of the upper layers of the aquifer which are often subjected to the most significant oil contamination. Neglecting coupled processes effects such as dilution, adsorption and volatilization, also adopting Richards assumption, a three-phase flow model is introduced with capillary heads of the water and the oil as variables. The resulting model which is coupled and strongly non-linear is solved using a vertical two-dimensional Finite-Element procedure together with a quasi-Newton optimization algorithm. Applying that scheme, various scenarios of oil migration in the unsaturated and the capillary zone were simulated. Some migration characteristics prediced by the numerical simulations are discussed. In particular, the dynamics of the water and oil phases during the migration process is discussed.

Field Injection Operations and Monitoring of the Injected CO2

Monitoring the fate of the injected CO2 and possible associated effects, such as hydro-mechanical and chemical effects in the target reservoir and its surroundings, is essential for safe operation of a storage facility. In this chapter, we shall first provide an overview of the technologies available and used for monitoring of CO2. We shall then proceed to describe specific methods and finally present some important case studies that will demonstrate the use of the discussed monitoring technologies under specific field settings.

Large scale modeling of seawater intrusion in a coastal aquifer: application to the North Sharon and Heffer Valley areas, Israel.

Seawater intrusion, in the form of a wide transition zone from fresh water to seawater, is a well-known phenomenon occurring in most coastal aquifers, as a result of unbalanced freshwater extraction practices. The prediction of seawater intrusion resulting from planned water extraction scenarios is of crucial importance as it allows maximization of freshwater sustainable extraction, while preserving the coastal aquifers viability by minimizing adverse salinization processes. Seawater intrusion can be monitored by observation wells. However, the number of such wells needed for the construction of a reliable three-dimensional picture of the transition zone between fresh water and seawater would be so large that it is practically infeasible. Therefore, simulation models are used, in combination with the available observed data. This work presents the development, application, and validation of a three- dimensional model, FEAS, for the simulation of seawater intrusion, formulated as a density dependant groundwater flow and salt transport problem in 3-D heterogeneous and anisotropic formations. FEAS was applied to the North Sharon – Heffer Valley region of the Israel coastal aquifer. This is a heterogeneous anisotropic aquifer, covering an area of over 300 km2. The model was first calibrated to identify the values of its hydraulic parameters (hydraulic conductivity, porosity, specific yield, and replenishment coefficients). It was then run for flow and salt transport for three time periods: 1) 1800-1933, pristine conditions (prior to any pumping), in order to obtain a picture of seawater wedge prior to the aquifer exploitation; 2) 1933-1974 rapid development of pumping from the aquifer, and 3) 1975-2002 current conditions, with significant sea water intrusion. The results obtained at the end of the simulation periods were in satisfactory agreement with the available data. The model was then used for estimating the impact of a number of exploitation and replenishment scenarios.

An Optimal control least-squares method for the solution of advection dispersion problems

This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H1, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.At each time step, the discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization one, whose objective function allows the capture of the advective behavior of the equation for high values of the Pe number.A general presentation is made of the optimization algorithm. Validation runs, for a one-dimensional example, show fairly accurate results for a wide range of Péclet and Courant numbers. Comparisons with several numerical schemes are also presented.

Heat and Mass Transfer in Unsaturated Porous Media with Application to Thermal Energy Storage

The objective of the paper is to present a model of heat and mass transfer in the unsaturated zone, taking into account the effect of a temperature gradient on the advective water flux and of enhanced thermal conduction by the processes of latent heat transfer with the vapor flow. The flow of the vapor is enhanced by its transfer through the water phase following a process of simultaneous evaporation and condensation at the air water interfaces. The motivation for the study is to provide the information required for planning heat storage in the unsaturated zone, especially information is required on the possibility of drying near the heat input boundary. The study shows that the considered system is unstable, with the occurence of drying depending on the initial and boundary conditions. For given boundary conditions of heat transfer, there are initial conditions of water content for which heating will not cause significant drying. Therefore, fine soils may be better suited for heat transfer at the boundaries, due to their higher field capacity, although their heat conduction coefficients are lower than those of sandy soils. At present, these conclusions are limited to the range to 50° C – 70° C.