Christos Tzimopoulos

Hydraulic behavior and contaminant transport in multiple porosity media

The hydraulic behavior and contaminant transport of aquifers containing distinct families of fractures are investigated by using the multiple porosity continuum model. We consider that the conditions are such that a horizontal 2D flow takes place. By writing the continuity of mass (including exchange terms between the various families of fractures) and Darcys law for each family of fractures, macroscopic equations for both confined and unconfined flow are obtained. A classification procedure and geometrical idealization of the individual fractures for each family is proposed which enables the calculation of the exchange coefficients. Equations for the description of the contaminant transport in the field scale for both confined and unconfined aquifer are developed. It turns out that the adequate formulation of the macroscopic equations and their sink-source term depends on whether the aquifer investigated is confined or unconfined, and also on the value of an nondimensional parameter describing the transfer process at the microscopic scale (connection Peclet number). Numerical investigation of representative problems offers some insight into the behavior of double and triple porosity aquifers.

Analysis of a closed-form analytical model to predict the hydraulic conductivity function

As measurements of the hydraulic conductivity relationship, K(Θ), are time-consuming, many researchers have suggested the use of prediction models. Recently a closed form model was proposed∗, derived from an integral relation∗∗. In this paper an attempt was made to check this model for ten soils described in the literature, especially the existence of hysteresis in the predicted Kr(Θ) relations. It was concluded that the magnitude of the parameter n is a determining factor in whether or not hysteresis will occur in the Kr(Θ) relation. Sensitivity analysis showed that Kr is relatively insensitive to n when the soil is not too dry. The exponent n — as with a parameter λ∗∗∗ — defines the pore size distribution which becomes uniform at large values of n. Comparison of Kr(Θ) as predicted for wet and dry conditions showed that the proposed model is reasonably accurate: (1) when values of the ultimate boundary characteristic curves of the hysteretic loop are small and have approximately the same value; and (2) for larger n values differing in n.

Estimation of soil moisture profile and diffusivity using simple laboratory procedures.

Diffusivity is one of the main soil hydraulic properties. It is a critical parameter for the prediction of water transport within the vadose zone. The aim of this research was to generate the soil moisture profile from very simple measurements such as sorptivity, distance of the wetting font in transformed coordinates, and initial and final water contents. The objective was to use a complex empirical function with three constants to generate the transformed soil moisture profile by treating the whole process as an optimization problem. The required conditions are that the constants of the empirical function are computed so that the analytically computed sorptivity agrees with the experimental one, and at the beginning and at the end of the transformed soil moisture profile, the water content is the final and the initial correspondingly. Once an analytic function for the transformed soil moisture profile is determined, then diffusivity is calculated analytically. As an added verification of the accuracy of the analytic diffusivity function produced by this method, diffusivity results were used as input in Philips semianalytic method to verify that the transformed soil moisture profiles can be regenerated. Integral continuity is preserved throughout the process.

Solution de l'équation de Boussinesq par une méthode des éléments finis

Abstract A mathematical model is presented which enables the solution of various problems of free water surface flow in porous media. Galerkins method was used for the finite-element formulation. The studied physical problem was that of a free surface flow towards a ditch or a river. The flow in that case is described by the Boussinesq equation, which is a partial differential equation of parabolic type. The application of Galerkins method leads to a system of non-linear equations, which are solved by using the Gaussian algorithm. The results have been compared with solutions published elsewhere. For the special case solved by Boussinesq in 1904, the exact solution has been compared with its finite-element and finite-difference approximations. The former require slightly less computer time.

FLUX-SATURATION RELATIONSHIP FOR UNSATURATED HORIZONTAL FLOW

The prediction of unsaturated flow is a never-ending quest for many scientists. Many methods exist with their corresponding advantages and disadvantages, such as semianalytic, finite difference, finite element, finite control volume, and flux-saturation. The last one, even though it belongs to the semianalytic group, is very interesting due to its simplicity and the way it approaches the physical problem. During laboratory research, a new intuitive monoparametric fitting function was used for F(Θ). The purpose of this research was to examine the range of variation of the new fitting function coefficient and the feasibility to replace it with a constant. A series of experiments was carried out on horizontal absorption under constant-head conditions, using three different soil types, to measure their F(Θ) function. F(Θ) values were also obtained for four other soils, using different methods. The soils that were examined were characterized from silt to sand, according to the textural triangle of the United States Department of Agriculture. Actual F(Θ) functions were then calculated in each soil. The proposed F(Θ) function was compared with the limiting F(Θ) function for linear and Dirac soil and with preexisting ones. The results were satisfactory both in shape and in quantity, leading to a new expression for F(Θ) for all soil types.

Theoretical and Experimental Research of Cumulative Infiltration

The main object of this study is the comparative evaluation of Green & Ampt’s (G & A) and Parlange’s (P’s) models and their ability to describe cumulative infiltration of water through various soil types. Three soil samples of different hydraulic properties were packed separately into a transparent vertical column. A constant head boundary condition was applied at the surface of the soil and the incoming amount of water was measured volumetrically. Soil moisture was measured using TDR waveguides at certain locations of the column. At the early times of cumulative infiltration, sorptivity of each soil sample was estimated. Theoretical research showed that both models converge to the same equation at the early times of infiltration and that the slopes of the two models are the same for large times of infiltration, but the curves of the two models are parallel shifted. P’s and G & A’s models approximate well the experimental points of cumulative infiltration of the three soil samples at small times of infiltration, but P’s model approximates better the experimental points at large times of infiltration.

A new analytical model to predict the hydraulic conductivity of unsaturated soils

A new analytical model is presented for the prediction of hydraulic conductivity. The new model is based on the Brutsaert characteristic curve ψ(θ) and the Mualem integral relation. It is presented by a series expansion of the effective saturation (Θ) power and given in a simple algebraic relation. For checking the new model, twelve soils were selected from the available literature and a comparison was made between the new model, the experimental curve and the van Genuchten model as well. The suggested model is very close to the van Genuchten model in all cases except one and it exhibits hysteresis, due to the different values of the parameter b of Brutsaert equation for the wetting and drainage curves. Also a second model is presented, based on the Burdine integral relation.

Sensitivity analysis of a coupled heat and mass transfer model in unsaturated porous media

Abstract Heat and moisture transfer equations are solved and a sensitivity analysis is presented. Physical models based on equilibrium thermodynamics and models based on irreversible thermodynamics are reviewed. The governing equations are reduced to a non-dimensional form. Finite-difference and finite-element solutions are given; they are compared with analytical ones, obtained after linearization of these equations through Fourier and Laplace transforms. Moisture profiles for the linearized case are produced both for isothermal and non-isothermal conditions, demonstrating an excellent agreement between the different numerical and analytical methods. The non-isothermal profiles are seen to advance more rapidly. The small influence of the phase conversion coefficient is observed in numerical experiments. An analytical treatment of sensitivity with respect to this coefficient is presented. Sensitivity is further demonstrated by means of a numerical example. Establishment of the small effect of the above coefficient leads to significant reductions.

A Method for the Detection of the Most Suitable Fuzzy Implication for Data Applications

Fuzzy implications are widely used in applications where propositional logic is applicable. In cases where a variety of fuzzy implications can be used for a specific application, it is important that the optimal candidate be chosen in order valuable inference be drawn from a given set of data. This study introduces a method for detecting the most suitable fuzzy implication among others under consideration, which incorporates an algorithm forthe separation of two extreme cases. According to the truth values of the corresponding fuzzy propositions the optimal implication is one of these two extremes. An example involving five such relations is used to illustrate the procedure of the method. The results obtained verify that the resulting implication is the optimal operator for inference making from the data.

The artificial recharge of groundwater: A solution by successive variations of steady states

The artificial recharge of groundwater aims at the modification of water quality, an increase of groundwater resources, and the optimization of the exploitation and recovery of contaminated aquifers. The purpose of this work is to develop a new mathematical model for the problem of an artificial recharge well, using the method of successive variations of steady states. Applying this method, one arrives at an expression of time as a double integral. This integral contains the time-dependent radius of the recharge boundary and the piezometric head of the well, calculated with the finite-element method. The new model is simple and useful, and can be applied to many practical problems, using the designed dimensionless graphs.