Two-Valued Solutions in the Problem of Salt Precipitation during Groundwater Evaporation

The problem of the evaporation of groundwater containing a dissolved admixture is studied. It is shown that in the salt precipitation regime the solution is nonunique. At critical parameter values the solutions merge and in a certain region the solution of the problem disappears. The nonexistence of a solution corresponds to clogging of the pore space with precipitated salt.     

Effects of Evaporation and Different Flow Regimes on Solute Distribution in Soil

Water evaporation and solute transport processes were studied in large soil columns filled with a sandy clay loam (SCL) and a clay loam (CL) soils. To create different water flow velocity through the soil column, the 3 cm (Treatment I) and 6 cm (Treatment II) depths of water were ponded at the soil surface during leaching. After leaching, soils were left for evaporation for 10 days. Some salinity parameters were monitored during three leaching and evaporation periods. To achieve the same degree of leaching more water was needed in Treatment II than in Treatment I for both soils. The electrical conductivity (EC) at the soil surface after evaporation increased, to 41–46% of the pre-drying level for the SCL and 28–31% for the CL. Although very low concentrations of Cl^– were detected at the soil surface after the first leaching in both soils, high increase was monitored after the evaporation period, due to the high mobility of this anion. The fluctuation of exchangeable sodium percentage (ESP) during the leaching and evaporation periods was attributed to the different transportation rates of Na⁺, Ca²⁺ and Mg²⁺. The boron leaching in Treatment I was more effective than that in Treatment II for both soils.     

The Effect of Asphalt Precipitation on Flow Behavior and Production of a Fractured Carbonate Oil Reservoir During Gas Injection

The first field data, collected over an 11 year period, are presented which indicate the possible effect of asphalt precipitation on the permeability and injectivity index of a fractured carbonate oil reservoir. The asphalt aggregates were formed during enhanced oil recovery by injection of a rich gas into the reservoir. The data indicate that, while at the initial stages of the operations the permeability and injectivity index decrease, at later times they appear to oscillate with the process time, with apparent oscillations' periods that depend on the heterogeneity of the reservoir. Two classes of plausible mechanisms that give rise to such oscillatory behavior are discussed. One relies on the changes in the structure of the reservoir's fractures, while the other one is based on asphalt precipitation in the reservoir. Computer simulations of flow and precipitation of asphalt aggregates in a pore network model of the reservoir are carried out. The results appear to support our proposition that asphalt formation and precipitation in the reservoir are the main mechanism for the observed behavior of the injectivity index. We also develop a stochastic continuum model that accurately predicts the time-dependence of the reservoir's permeability and injectivity index during the gas injection process.     

Use of Synchrotron Tomographic Techniques in the Assessment of Diffusion Parameters for Solute Transport in Groundwater Flow

This technical note describes the use of time-resolved synchrotron radiation tomographic energy dispersive diffraction imaging (TEDDI) and tomographic X-ray fluorescence (TXRF) for examining ion diffusion in porous media. The technique is capable of tracking the diffusion of several ion species simultaneously. This is illustrated by results which compare the movement of Cs⁺, Ba²⁺ and La³⁺ ions from solution into a typical sample of English chalk. The results exhibited somewhat anomalous (non-Fickian) behaviour and revealed heterogeneities (in 1D) on the scale of a few millimetres.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

Evaporation phenomenon past a rotating hydrocarbon droplet of ternary components

A numerical study of heat and mass transfer from an evaporating fuel droplet rotating around its vertical axis was performed in forced convection only on the side opposite to the flow. The flow was assumed to be laminar, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on the abovementioned assumption, the conservation equations in a general curvilinear coordinate were solved numerically. The behavior of rotating droplet evaporation in the forced convection flow can be investigated by analyzing the effects of the rotation of the droplet on the evaporation process of multi-component hydrocarbons droplet. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method. Thomas algorithm is used to solve the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hydrocarbon droplet were determined. The thickness of the boundary layer is unknown for this model and therefore, it was determined in function of time. Additionally, the study concerns “Dgheim dimensionless number” which is the ratio of the rotation forces over the viscosity forces. Dgheim dimensionless number is correlated to Nusselt and Sherwood numbers for multi-component hydrocarbon droplets in evaporation by taking into account the effect of heat and mass Spalding, Prandtl and Schmidt numbers respectively. Also, correlations for Nusselt and Sherwood numbers in terms of Reynolds, Prandtl and Schmidt numbers are proposed. These correlations consider the rotation phenomenon and advance the variation of the thermophysical and transport properties in the vapor phase of multi-component blends.     

Evaporation of Falling and Shear-Driven Thin Films on Smooth and Grooved Surfaces

One of the most important tasks in development of modern gas turbine combustors is the reduction of NO_x emissions. An effective way to reduce the NO_x emission is using the lean premixed prevaporization (LPP) concept. An important phenomenon taking place in LPP chambers is the evaporation of thin fuel films. To increase the fuel evaporation rate, the use of microstructured walls has been suggested. The wall microstructures make use of the capillary forces to evenly distribute the liquid fuel over the wall, so that the appearance of uncontrolled dry patches can be avoided. Moreover, the wall structures promote the thin film evaporation characterized by ultra-high evaporation rates. An experimental setup was built for the investigation of thin liquid films falling down on the outer surface of vertical tubes with either a smooth or structured surface. In the first testing phase water is used, fuel like liquids will be used later on. The thin film can be heated from both sides, by hot oil flowing inside the tube, and by hot compressed air flowing in co-current direction to the thin film. The film is partly evaporated along the flow. Results for the wavy film structure at different Reynolds numbers are reported. For theoretical investigations a model describing the hydrodynamics and heat transfer due to evaporation of the gravity- and shear-driven undisturbed liquid film on structured surfaces was developed. For low Reynolds numbers or low liquid mass fluxes the wall surface is only partly covered with liquid and the heat transfer is shown to be governed by the evaporation of the ultra-thin film in the vicinity of the three-phase contact line. A numerical model for the solution of a two-dimensional free-surface flow of a liquid film over a structured wall was also developed. The Navier–Stokes equations are solved using the Volume of Fluid (VOF) technique. The energy equation is included in the model. The model is verified by comparison with data from the literature showing favorable agreement. In particular, the proposed model predicts the formation of capillary waves observed in the experiments. The model is used to investigate the flow of liquid on a structured wall. This calculation is the first step towards the modeling of a three-dimensional wavy flow of a gravity- and shear-driven film along a wall with longitudinal grooves. It is found that due to the Marangoni effect, a circulating flow arises within the cavity, thereby leading to an enhancement in the evaporation rate.     

Effect of the Nature of the Interaction between a Gas and a Surface on the Relations for the Knudsen Layer in the Case of Strong Evaporation

The effect of the temperature accommodation coefficient _T on the relations at the Knudsen layer edge is investigated for strong evaporation using the moment method. An explicit expression for the dimensionless density as a function of the temperature and the Mach number M is obtained for 0 < _T < 1. For _T = 0 the entire solution is obtained in explicit form. It is shown that for = 0 and a condensation coefficient << 1 the temperature outside the Knudsen layer changes sharply as M varies from 0 to a certain value much less than unity after which the temperature ceases to depend on . For the model of specular reflection of the molecules from the surface the density and the temperature outside the Knudsen layer are found in explicit form as functions of the Mach number.     

Pore Network Simulation of Evaporation of a Binary Liquid from a Capillary Porous Medium

A pore-network model of evaporation of a binary liquid mixture into a ternary gas phase is developed. The model is applied to study the influence of surface tension gradients induced by composition variations of the liquid on the phase distribution within a capillary porous medium. Numerical simulations based on the proposed model show that the surface tension gradients lead to the accumulation of liquid near the open edge of the network. This surface tension gradient effect is only significant for weakly disordered porous media.     

Modeling of Liquid Fuel Injection, Evaporation and Mixing in a Gas Turbine Burner Using Large Eddy Simulations

The interaction of turbulence, temperature fluctuation, liquid fuel transport, mixing and evaporation is studied by using Large Eddy Simulations (LES). To assess the accuracy of the different components of the methods we consider first isothermal, single phase flow in a straight duct. The results using different numerical methods incorporating dynamic Sub-Grid-Scale (SGS) models are compared with DNS and experimental data. The effects of the interactions among turbulence, temperature fluctuation, spray transport, evaporation and mixing of the gaseous fuel are studied by using different assumptions on the temperature field. It has been found that there are strong non-linear interactions among temperature-fluctuation, evaporation and turbulent mixing which require additional modeling if not full LES is used. The developed models and methods have been applied to a gas turbine burner into which liquid fuel is injected. The dispersion of the droplets in the burner is described. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some Analytical Solutions for Groundwater Flow and Transport Equation

This paper presents the use of symmetry reduction method resulting in new exact solutions for the groundwater flow and transport equation. It is assumed that the radionuclides are transported by advection-diffusion in a single fracture and diffusion in the surrounding rock-matrix. The application of one-parameter group reduces the number of independent variables, and consequently the governing PDE of (1+2)-dimension reduces to set of ODEs which are solved analytically. This enables us to present some new exact time-dependent solutions of the advection-diffusion equation.     

Determination of Salt Diffusion Coefficient in Brick: Analytical Methods

This paper presents an investigation into salt diffusion in new, fully saturated brick under isothermal conditions. A commonly used experiment methodology, diffusion cell method, is adopted. The analytical and numerical solutions are obtained. The analytical solution is simple and straightforward, which determines temporally salt concentrations in the monitored chamber. It enables us to estimate salt diffusion coefficients in a fast and accurate way.     

Injection of a salt solution into a geothermal reservoir saturated with superheated vapor

The injection of water containing a dissolved admixture into a high-temperature geothermal reservoir saturated with superheated vapor is considered. Behind the evaporation front on which the admixture precipitates a dissolution front separating regions with the initial concentration and with the concentration of the saturated solution coexisting with the solid salt phase is formed. It is found that the self-similar solution of the problem with two moving boundaries is two-valued. With variation of the parameters and the initial and boundary conditions the solutions may approach each other and at certain critical values merge. In the supercritical region the self-similar solution does not exist. The non-existence of a solution can be interpreted as the filling of the pores with precipitated salt and the cessation of the phase motion.     

波纹竖板层流降膜蒸发传热的分析

对高粘度液体在等温正弦形波纹壁面上的自由降落与蒸发建立了摄动分析模型。得到了流动的分析解和蒸发传热的数值解。考察了壁面波纹的波幅和波数、液膜表面张力及贝克利数对流动与传热的影响,结果表明,加大波纹的波幅、适当选择波数、减小贝克利数可增强传热,而表面张力对蒸发传热的影响较小。     

Calculation of Groundwater Flows in Coastal Pressurized Reservoirs

A model of a fresh groundwater flow through a rectangular horizontal pressurized reservoir toward a salt-water sea (basin, reservoir, trench, etc.) is examined within the framework of two-dimensional steady-state flow theory. In order to study the model, a mixed multi-parameter boundary value problem of the theory of analytic functions is formulated and solved using the Polubarinova-Kochina method. The structure and the characteristic features of the simulated process and the effect of all the determining physical parameters of the model on the nature of the flow are analyzed using the analytic dependences obtained and numerical calculations. An approximate hydraulic solution of the problem is compared with the exact solution obtained.     

Permeability Changes During the Evolution of a Geothermal Field Due to the Dissolution and Precipitation of Quartz

The changes in permeability and porosity associated with quartz deposition in an evolving geothermal reservoir are investigated. We review the processes associated with permeability changes in a geothermal reservoir and also review recent work on quartz solubility and deposition rates. Porosity and permeability changes are calculated for two reservoir models. The first is a generic model of a Taupo Volcanic Zone geothermal reservoir and the second is based on the model of the deep circulation system at Kakkonda published by Hanano. We find that when a reservoir experiences BPD conditions during part of its lifetime the lower reservoir becomes impermeable and a hydrothermal circulation system is only present in the upper part of the reservoir.     

Flow of electrolytes in a porous medium

A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient and external electric field, and the coefficients in this linear relation are calculated with the use of microequations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008.     

Thermodynamic Automaton Simulations of Fluid Flow and Diffusion in Porous Media

A thermodynamic automaton model of fluid flow in porous media is presented. The model is a nonrelativistic version of a Lorentz invariant lattice gas model constructed by Udey et al. (1998). In the previous model it was shown that the energy momentum tensor and the relativistic Boltzman equation can be rigorously derived from the collision and propagation rules. In the present paper we demonstrate that this nonrelativistic model can be used to accurately simulate well known results involving single phase flow and diffusion in porous media. The simulation results show that (1) one-phase flow simulations in porous media are consistent with Darcy's law; (2) the apparent diffusion coefficient decreases with a decrease in permeability; (3) small scale heterogeneity does not affect diffusion significantly in the cases considered.