The Effects of a Decaying Heat Source in a Rectangular-Shaped Rock Repository

1989 ◽  
Vol 111 (4) ◽  
pp. 264-269 ◽  
Author(s):  
J. C. Small ◽  
J. R. Booker
Keyword(s):  
Solution Method ◽  
Layered Materials ◽  
Surrounding Rock ◽  
Time Dependent ◽  
Numerical Inversion ◽  
Heat Sources ◽  
Rock Formations ◽  
Time Dependent Problem ◽  
High Level ◽  
Finite Difference Techniques

Schemes for the disposal of medium to high level atomic waste involve placing the spent material in repositories deep within stable rock formations. The waste will continue to generate heat after storage underground, and it is of interest to be able to predict the effects of this heating on the surrounding rock, as this may lead to cracking of the rock and the potential contamination of ground water. A solution method is presented for problems involving decaying heat sources of rectangular shape which lie within horizontally layered materials. The method requires very little computer storage (unlike finite element and finite difference techniques) and may easily be implemented on microcomputers. Solution of the time-dependent problem is achieved by applying Laplace transforms to the field variables, solving the resulting equations, and then using numerical inversion to obtain the solution in real time.

scholarly journals An Experimental Study on the Sources of Strontium in Mineral Water and General Rules of Its Dissolution—A Case Study of Chengde, Hebei

Water ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 699
Author(s):  
Ruifeng Wang ◽  
Xiong Wu ◽  
Yanliang Zhai ◽  
Yuxuan Su ◽  
Chenhui Liu
Keyword(s):  
Experimental Study ◽  
Mineral Water ◽  
Surrounding Rock ◽  
Mechanism Of Formation ◽  
High Quality ◽  
General Rules ◽  
Leaching Experiment ◽  
High Level ◽  
Impact Experiments

Chengde City boasts a wealth of high-quality mineral water resources characterized by a high level of strontium (Sr), a low level of sodium, and low alkalinity. In order to study the mechanism of formation of Sr-bearing mineral water in Chengde and to scientifically guide future mineral water exploration, taking three typical mineral water exploration areas in Chengde as examples, this paper studies the sources of Sr in mineral water and the general rules of its dissolution via a laboratory static leaching experiment and impact experiments, and it provides an analysis of the characteristics of typical rock samples. The research results indicate that the content of Sr in surrounding rock and the characteristics of minerals existing in surrounding rock jointly control the dissolution of Sr in water; that CO2 can promote the formation of mineral water containing Sr; and that temperature increases may boost the dissolution of Sr from carbonate minerals but also inhibit the dissolution of Sr from silicate minerals.

scholarly journals Thermo-hydro-mechanical processes in fractured rock formations during a glacial advance

2015 ◽  
Vol 8 (7) ◽  
pp. 2167-2185 ◽  
Author(s):  
A. P. S. Selvadurai ◽  
A. P. Suvorov ◽  
P. A. Selvadurai
Keyword(s):  
Rock Mass ◽  
Fractured Rock ◽  
Fluid Pressure ◽  
Computational Modelling ◽  
Fracture Zones ◽  
Saturated Rock ◽  
Rock Formations ◽  
Geological Formation ◽  
High Level Nuclear Waste ◽  
High Level

Abstract. The paper examines the coupled thermo-hydro-mechanical (THM) processes that develop in a fractured rock region within a fluid-saturated rock mass due to loads imposed by an advancing glacier. This scenario needs to be examined in order to assess the suitability of potential sites for the location of deep geologic repositories for the storage of high-level nuclear waste. The THM processes are examined using a computational multiphysics approach that takes into account thermo-poroelasticity of the intact geological formation and the presence of a system of sessile but hydraulically interacting fractures (fracture zones). The modelling considers coupled thermo-hydro-mechanical effects in both the intact rock and the fracture zones due to contact normal stresses and fluid pressure at the base of the advancing glacier. Computational modelling provides an assessment of the role of fractures in modifying the pore pressure generation within the entire rock mass.

scholarly journals Thermomechanical coupling of ice flow with the bedrock

2003 ◽  
Vol 37 ◽  
pp. 390-396 ◽  
Author(s):  
Richard C.A. Hindmarsh
Keyword(s):  
Temperature Distribution ◽  
Horizontal Velocity ◽  
Time Dependent ◽  
Thermomechanical Coupling ◽  
Positive Anomaly ◽  
Thermal Coupling ◽  
Steady Temperature ◽  
Ice Flow ◽  
Time Dependent Problem ◽  
Geomorphological Processes

AbstractTwo aspects of thermal coupling with bedrock are considered: the coupled time-dependent problem of co-evolving temperatures in lithosphere and ice; and the influence of basal topography on steady temperature distribution within the ice. The nature of the time-dependent coupling is found to depend on the horizontal velocity. As has been suggested, there is a cooling of steady temperatures on bedrock highs, but this is phase-shifted downstream when horizontal velocities increase. This observation may have consequences for geomorphological processes such as plucking and protection. The effect of bedrock channelling on steady temperature is considered. The positive anomaly of basal temperature due to channelling increases as the transverse wavelength decreases, but not monotonically, reaching a plateau when both the wavelengths of the basal topography are around 100 km.

Time-dependent tunnel deformations in homogeneous and heterogeneous weak rock formations

2017 ◽  
Vol 92 ◽  
pp. 186-200 ◽  
Author(s):  
Atsushi Sainoki ◽  
Shingo Tabata ◽  
Hani S. Mitri ◽  
Daisuke Fukuda ◽  
Jun-ichi Kodama
Keyword(s):  
Time Dependent ◽  
Weak Rock ◽  
Rock Formations

On the principle of exchange of stabilities

1969 ◽  
Vol 310 (1502) ◽  
pp. 341-358 ◽  
Keyword(s):  
Growth Rate ◽  
Couette Flow ◽  
Equations Of State ◽  
Travelling Waves ◽  
Time Dependent ◽  
Heat Sources ◽  
Constant Heat ◽  
Perturbation Theorem ◽  
Adjoint Operators ◽  
Real Self

A perturbation theorem is proved: a class of real, bounded (non-self-adjoint) perturbations of norm ϵ to real self-adjoint operators preserve the reality of the simple eigenvalues for ϵ sufficiently small. A bound is obtained on ϵ. Application is made to Bénard convection with constant heat sources, radiation, particular time-dependent profiles and nonlinear equations of state and to instability of circular Couette flow for a range of gap widths. In each case the growth rate is the eigenvalue and hence if ϵ < ϵ c , travelling waves (either growing or decaying) are forbidden.

scholarly journals hp-FEM for the fractional heat equation

2020 ◽  
Author(s):  
Jens Markus Melenk ◽  
Alexander Rieder
Keyword(s):  
Finite Elements ◽  
Heat Equation ◽  
Exponential Convergence ◽  
Time Dependent ◽  
Nonlocal Operator ◽  
Time Stepping ◽  
Fractional Heat Equation ◽  
Time Dependent Problem ◽  
Hp Finite Elements ◽  
Abstract Framework

Abstract We consider a time-dependent problem generated by a nonlocal operator in space. Applying for the spatial discretization a scheme based on $hp$-finite elements and a Caffarelli–Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-discontinuous Galerkin based time stepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the spatial domain $\varOmega $.

scholarly journals Thermal ignition in a reactive slab with unsymmetric boundary temperatures

1983 ◽  
Vol 24 (3) ◽  
pp. 279-288 ◽  
Author(s):  
K. K. Tam ◽  
P. B. Chapman
Keyword(s):  
Steady State ◽  
Critical Role ◽  
Upper And Lower Solutions ◽  
Lower Solution ◽  
Time Dependent ◽  
Thermal Ignition ◽  
Time Dependent Problem ◽  
Steady State Solutions

AbstractThe problem of thermal ignition in a reactive slab with unsymmetric temperatures equal to 0 and T is considered. Steady state upper and lower solutions are constructed. It is found that T plays a critical role. Results similar to the case with symmetric boundary temperatures are expected when T is small. When T is sufficiently large, there is only one steady state upper or lower solution. The time dependent problem is then considered. Phenomena suggested by studying the upper and lower steady state solutions are confirmed.

scholarly journals Exact Analytical Solution for 3D Time-Dependent Heat Conduction in a Multilayer Sphere with Heat Sources Using Eigenfunction Expansion Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nemat Dalir
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Radial Direction ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Expansion Method ◽  
Time Dependent ◽  
Heat Sources ◽  
Eigenfunction Expansion Method

An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed.

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