Hydrothermal Conditions around a Radioactive Waste Repository
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ROGER THUNVIK
AND CAROL BRAESTER++
+Royal Institute of Technology, S-100 44 Stockholm, Sweden Israel Institute of Technology, Haifa 32000, Israel
INTRODUCTION The possibility of permanent burial of radioactive waste from nuclear power plants,
is
studied in Sweden at
the KBS
(Nuclear Fuel Safety)
Definite repository sites have not yet been selected,
- project.
but the general principles
of construction regarding the layout have been devised (KBS'). The feasibility of a prospective site for radioactive waste disposal is highly dependent on the geohydrological conditions. Heat emitted by the decaying waste will increase the temperature of the rock, changing groundwater density gradients and creating convective currents. Under certain conditions water particles passing through the repository may reach the ground surface.
It
is
therefore of significant interest in
the safe-
ty analysis to predict pathlines and travel times of water particles,
should
any of the waste canisters be breached and the groundwater be contaminated. The solutions presented illustrate the effect of heat released from a hypothetical repository on the groundwater movements around the repository.
THE FLOW MODEL The prospective sites for radioactive waste repositories in Sweden are fractured hard rock formations.
The fractured rock is
conceptualized as a configu-
ration of interconnected fractures surrounding the solid blocks. It
is
assumed in the present investigation that the fractured rock formation
in consideration can be treated by the continuum approach. The water volume in volume.
the fractures is
As a consequence,
small in comparison with the solid rock
one may assume that thermal equilibrium between fluid
and rock takes place instantaneously. The governing equations for simultaneous flow of fluid and heat, from the basic conservation
laws and Darcy-s law,
derived
are the equation for the
conservation of fluid mass: •
f (c f+c r)p,
- 0fp Tt
-
k. (pfii 1t P
f (p,j- p gj)),i = 0 ,J
(1)
588 and the equation for the conservation of thermal energy: ((c*r,
(*
((PC)T)
-
( ff
(X*
•1k'"
)T, + (pf Cf(
-f
-j (p
.-
p gj))T),i = 0
where * denotes the equivalent properties of the composite,
(2)
solid and fluid.
Water density and viscosity are considered functions of pressure and temperature through the equations of state:
pf= Eqs.
11 = 1f (p,T)
(p,T),
(1) to (3)
(3)
form a system of coupled non-linear partial differential
equations.
METHOD OF SOLUTION The equations are solved with the appropriate boundary conditions by the Galerkin finite element method.
The flow domain is
discretized in a graded size
mesh of eight node quadrilateral elements. According to the Galerkin method, one introduces the trial
p _ Tjpj ,
T=_T iT
(4)
where Tj = Tj(xi) are basis functions, conditions.
functions
chosen to satisfy the essential boundary
The same basis functions are used to represent the variations in the
material properties over the elements. Making use of the orthogonality conditions in Galerkin
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