Arieh Pistiner

Similarity solutions for immiscible phase migration in porous media: an analysis of free boundaries

A fuel pollutant migrating in a water flow throughout a porous medium is distributed between the moving (continuous) and residual (discontinuous) phases. Usually, there is an equilibrium condition between these phases. In this study, the migration of a fuel slug confied within free boundaries moving in the porous medium is considered. This type of fuel migration pertains to circumstances in which convective fuel transport dominates fuel dispersion when fuel saturation approaches zero. A one-dimensional self-similar model is developed, describing the movement of fuel saturation fronts in a porous medium against and with the water flow direction. Several analytical solutions are found revealing the effects of the pore size, fuel viscosity, fuel mass, and the capillary number on the fuel migration in the porous medium.

Modelling fresh water injection into a partially saline partially fresh (PASPAF) aquifer

Abstract This paper concerns the study of physical phenomena typical to injection of fresh water, like treated effluents, into an aquifer whose deep layers are saturated with saline water, and its upper layers are saturated with fresh water. Such a partially saline partially fresh aquifer is termed by the present paper as a PASPAF aquifer. The study concerns infiltration by recharge wells as well as over an infiltrating area. The framework of the present study includes the development of the appropriate numerical model as well as the performance of various numerical simulations demonstrating the applicability of the model and representing the possible physical phenomena associated with the fresh water injection. The numerical model is able to simulate the downconing process and the formation of the transition zone in the aquifer. The numerical experiments with the model indicate that the fresh water injection may lead to degradation of the groundwater quality mainly around the injection site. Quantitative calculations of such an effect and the appropriate conclusions obtained by these calculations are represented in this paper.

A model for a moving interface in a layered coastal aquifer

The framework of the present study is the development of a new approach to describe the displacement of fresh water by salt water in a layered coastal aquifer. The aquifer is composed of horizontal layers possessing different hydraulic conductivities, which are also different in the saltwater and the freshwater zones. A one-dimensional analysis is performed, describing the displacement of the saltwater-freshwater interface under the influence of freshwater flow toward the sea. Several analytical solutions are found revealing the effects of various parameters on the interface displacement process. On the basis of these solutions, several type curves for different freshwater saltwater hydraulic conductivity are drawn. The model is calibrated by matching a type curve with field data taken from an observation well and is further used to predict the evolution of the interface shape and position.

A new solution for the nonlinear diffusion-convection equation

The Cauchy problem for a one-dimensional nonlinear porous-media diffusion-convection differential equation is considered. A self similar solution is derived that, after the Riccati transformation, is described in terms of the Airy functions. The asymptotic behavior of the solution for a small amount of species introduced into the porous media is investigated.

Capillary end effect in a water saturated porous layer

The uni-directional propagation of oil injected into water flowing through a water wetted porous slab of a finite length is investigated. The inlet and outlet edges of the slab are impermeable to the oil flux. Hence, the oil accumulates within the slab, thereby leading to a saturation build-up-capillary end effect. This phenomenon is studied analytically on the basis of a nonlinear equation describing oil-water transport in porous media. A dimensionless criterion is derived, which governs the appearance and relative strength of the capillary end effect. For weak oil-water interfacial tension (large capillary number) and long porous slabs the above effect is not observed and the temporal evolution of the oil saturation is described by the Buckley-Leverett solution. Short porous slabs are found to be almost entirely subjected to the capillary end effect. Intermediate situations are identified and quantitatively described, in which the downstream part of the slab may be divided into two zones: one-characterized by the capillary end effect, and the other being a Buckley-Leverett zone.It is shown, that the oil flux injected into the slab is limited by a maximum value which depends upon the location of the injection point. The partition of the inlet flux between the upstream and downstream directions is investigated. In the upstream side of the porous slab the oil moves under the action of free imbibition only. It is found that the upstream flux is limited by the value, which is independent of the slabs length and of the location of the injection point.

Gravitational migration of fuel in porous media

Fuel migration in a water flowing through a porous medium generally occurs parallel to porous strata, which may not be horizontal. In this case, gravity tends to cause vertical segregation of fluids, depending on their densities. This phenomenon can exert a strong effect on fuel migration. The gravitational force creates the buoyancy force which acts upon the fuel, and may be either parallel or anti-parallel to the water flow direction.In this study, the above effects are investigated using the one-dimensional model of Pistineret al. We go beyond the latter investigation in describing the influence of the gravitational forces upon the movement of fuel saturation fronts in a vertical porous layer against and along the water flow direction.It is found that when the directions of the buoyancy force and of the water flow are anti-parallel, fuel migrates in the direction of the buoyancy force, provided the latter is strong enough. However, in the case of a weak buoyancy force, the direction of migration of the fuel depends on its mass. Small fuel masses move mainly in the direction of the water flow. However, big fuel slugs possessing large masses will move mainly in the direction of the buoyancy force. Slugs, characterized by intermediate masses, have no preferable moving direction and are almost stagnant.

Radial fuel-water transport in aquifer near an injection well

Abstract A new physico-mathematical approach is developed for modelling of fuel migration in an axisymmetric groundwater flow by considering the various dimensionless parameters governing the transport processes. The self-similar solution scheme developed for a time-dependent water injection rate describes the evolution of the fuel saturation in the aquifer near a single recharge well. It is found that the capillary forces prevent the fuel from being removed downstream by injecting water through the well. The time dependent saturation profiles calculated from several exact analytical solutions exhibit the effects of various dimensionless parameters in fuel migration in radial water flow.

Radial Oil–Water Transport Toward an Extraction Well

A plane axisymmetric (radially converging) flow occurs in case of water extraction from an aquifer through a well. A new physico-mathematical approach is developed for modeling oil pollutant migration near an extraction well in the aquifer. This is done by considering the various dimensionless parameters governing the transport processes and by applying a self-similar scheme. The time-dependent saturation profiles, calculated from several exact analytical solutions, exhibit the effects of various dimensionless parameters related to oil migration, directed to a water extraction well. By using hypothetical saturation data, the model was calibrated and a predication of the temporal oil saturation distribution around the well was calculated.