Rafid Al-Khoury

Spectral element technique for efficient parameter identification of layered media. I. Forward calculation

Abstract This contribution deals with the use of spectral analysis as a means of analysing the dynamic behaviour of the axially symmetric multi-layered systems as a result of a transient force. The objective of this research work is to develop an accurate and computationally efficient forward tool suitable for solving inverse problems. The spectral element technique is utilized. Details of the mathematical derivation, implementation and verification of newly developed axi-symmetric and half-space spectral elements are presented. It is shown that the suitability of the spectral element method to such a problem encompasses in its ability to model a whole layer without the need for subdivisions. As a consequence, the size of the modelled structure becomes as large as the number of the layers involved. This reduces the computational requirements substantially and hence enables efficient utilization of the method in iterative algorithms for solving inverse problems.

Efficient numerical modeling of borehole heat exchangers

This paper presents a finite element modeling technique for double U-tube borehole heat exchangers (BHE) and the surrounding soil mass. Focus is placed on presenting numerical analyses describing the capability of a BHE model, previously reported, to simulate three-dimensional heat transfer processes in multiple borehole heat exchangers embedded in a multi-layer soil mass, in a computationally efficient manner. Geothermal problems which require very fine meshes, of the order of millions of finite elements, can be simulated using coarse meshes, of the order of a few hundred to a few thousand elements. Accordingly, significant reduction of CPU time is gained, rendering the model suitable for utilization in engineering practice. A validation example comparing computed results with measured results is presented. Parametric analyses are also presented describing the possible utilization of the model for research works and design optimization.

Spectral element technique for efficient parameter identification of layered media: Part II: Inverse calculation

Abstract In Part I of this series of articles a forward model was presented for the simulation of wave propagation in a multi-layer system by means of the spectral element method. In the current article and, on the basis of the forward model, a procedure is presented for inverse calculation of the system parameters. The proposed procedure is based on iterative comparisons of measured versus theoretically determined system transfer functions. The performance of three minimization algorithms; factored Secant update, modified Levenberg–Marquardt and Powell hybrid for solving the resulting system of nonlinear equations is evaluated. For the problem under consideration, the Powell hybrid algorithm exhibits better stability and convergence characteristics. As an application, the inverse procedure is utilized for the determination of pavement layer moduli and thicknesses via the use of the falling weight deflectometer (FWD) test. The calculations show that the developed procedure is accurate and computationally efficient. As a result of these calculations, modifications to the standard practice of FWD measurements and instrumentation are suggested.

Spectral element technique for efficient parameter identification of layered media. Part III: viscoelastic aspects

This article addresses the issues of wave propagation in elastic–viscoelastic layered systems and viscous parameter identification from non-destructive dynamic tests. A methodology that combines the spectral element technique, for the simulation of wave propagation, with the differential operator technique, for stress–strain relationship in viscoelastic materials, is adopted. The compatibility between the two techniques stems from the fact that both can be treated in the frequency domain, which enables naturally the adoption of Fourier superposition. The mathematical formulation of spectral elements for Burger’s viscoelastic material model is highlighted. Also, an inverse procedure for the identification of the material’s Young’s moduli and complex moduli for layer systems is described. It is shown that the proposed methodology enables the substitution of an expensive laboratory testing procedure for the determination of material complex moduli with non-destructive dynamic testing. 2002 Elsevier Science Ltd. All rights reserved.

An efficient computational model for deep low-enthalpy geothermal systems

In this paper, a computationally efficient finite element model for transient heat and fluid flow in a deep low-enthalpy geothermal system is formulated. Emphasis is placed on coupling between the involved wellbores and a soil mass, represented by a geothermal reservoir and a surrounding soil. The finite element package COMSOL is utilized as a framework for implementing the model. Two main aspects have contributed to the computational efficiency and accuracy: the wellbore model, and the 1D-2D coupling of COMSOL. In the first aspect, heat flow in the wellbore is modelled as pseudo three-dimensional conductive-convective, using a one-dimensional element. In this model, thermal interactions between the wellbore components are included in the mathematical model, alleviating the need for typical 3D spatial discretization, and thus reducing the mesh size significantly. In the second aspect, heat flow in the soil mass is coupled to the heat flow in the wellbores, giving accurate description of heat loss and gain along the pathway of the injected and produced fluid. Heat flow in the geothermal reservoir, and due to dependency of fluid density and viscosity on temperature, is simulated as two-dimensional fully saturated nonlinear conductive-convective, whereas in the surrounding soil, heat flow is simulated as linear conductive. Numerical and parametric examples describing the computational capabilities of the model and its suitability for utilization in engineering practice are presented.

Poroelastic spectral element for wave propagation and parameter identification in multi-layer systems

Abstract This contribution deals with the use of Biots theory of propagation of elastic waves in a fluid-saturated porous solid in conjunction with the computationally efficient spectral element technique as a means for forward analysis of the dynamic behavior of multi-layer systems consisting of both one- and two-phase material layers. Details of the mathematical formulation and verification of an axi-symmetric semi-infinite spectral element for a fully saturated porous medium are presented. The spatial domain of the element in the vertical direction is assumed to extend to infinity. In the radial direction it extends to a finite distance. In the last part of this contribution an example is presented of the use of the developed element for parameter identification of pavement layers via the use of falling weight deflectometer test.

An efficient finite volume model for shallow geothermal systems-Part II: Verification, validation and grid convergence

This part of the series of two papers presents the computational capability of the finite volume model, described in Part I, to simulate three-dimensional heat transfer processes in multiple borehole heat exchangers embedded in a multi-layer soil mass. Geothermal problems which require very fine grids, of the order of millions of finite volumes, can be simulated using coarse grids, of the order of few to tens of thousands elements. Accordingly, significant reduction of CPU time is gained, rendering the model suitable for utilization in engineering practice. A verification example comparing the computational results with an analytical solution of a benchmark case is given. A validation example comparing computed results with measured results is presented. Furthermore, numerical examples are presented describing the possible utilization of the model for research works and design.

An efficient finite volume model for shallow geothermal systems. Part I: Model formulation

This series of two papers presents a three-dimensional finite volume model for shallow geothermal systems. In this part, an efficient computational model describing heat and fluid flow in ground-source heat pumps is formulated. The physical system is decomposed into two subdomains, one representing a soil mass, and another representing one or a set of borehole heat exchangers. Optimization of the computational procedure has been achieved by, first, using a pseudo three-dimensional line element for modeling the borehole heat exchanger, and second, using a combination of a locally refined Cartesian grid and a multigrid with hierarchal tree data structure for discretizing and solving the soil mass governing equations. This optimization made the model computationally efficient and capable of simulating multiple borehole heat exchangers embedded in a multilayer system, in relatively short CPU time. In Part II of this series, verifications and numerical examples describing the computational capabilities of the model are presented.

Experimental Calibration Of A Viscoplastic-Fracturing Computational Model

An extensive experimental and analytical investigation is currently being carried out on the mechanisms leading to the initiation and propagation of damage in viscoplastic materials. One of the major goals of the investigation is the development and the finite elements implementation of a generalised triaxial, strain rate sensitive, history and temperature dependent constitutive model. Explicit procedures have been formulated for the experimental determination of the model parameters. As a minimum, only uniaxial test results are needed for determination of the basic parameters. The model has been implemented in the finite element code CAPA-3D. Results of the utilization of CAPA-3D for the investigation of the dynamic non-linear response of a road pavement are reviewed in the last part of this contribution.

Spectral framework for geothermal borehole heat exchangers

Purpose – This paper aims to present a framework for deriving analytical and semi‐numerical models for coupled conductive‐convective heat transfer processes in a borehole heat exchanger subjected to general initial and boundary conditions.Design/methodology/approach – The discrete Fourier transform and the spectral element method have been utilized for deriving two spectral models for a single U‐tube borehole heat exchanger in contact with a soil mass.Findings – Verification and numerical examples have shown that the developed models are accurate and computationally very efficient. It is illustrated that one spectral element is capable of producing results which are more accurate than those produced by 200 finite elements.Practical implications – The gained computational efficiency and accuracy will boost considerably the possibilities for more insight into geothermal analysis, which will improve the procedure for designing competitive energy extraction systems.Originality/value – The models are capable o...