Fluid Flow and Solute Transport though a Fracture Intersecting a Canister - Analytical Solutions for the Parallel Plate
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)OXLG)ORZDQG6ROXWH7UDQVSRUWWKRXJKD)UDFWXUH,QWHUVHFWLQJD&DQLVWHU $QDO\WLFDO6ROXWLRQVIRUWKH3DUDOOHO3ODWH0RGHO L. Liu and I. Neretnieks Department of Chemical Engineering and Technology, Royal Institute of Technology S-100 44 Stockholm, Sweden $%675$&7 In this paper, we are concerned with a specific scenario where a large fracture intersects, at its center, a canister that contains spent nuclear fuel. Assuming that a nuclide is free to release from the canister into groundwater flowing through the fracture, a detailed formulation of the volumetric flow rate and the equivalent flow rate are made for the parallel plate model. The formulas proposed have been validated by numerical examinations; they are not only simple in forms but also universal in applications where the flow may be taken normal, inclined or parallel to the axis of the canister. Of great importance, they provide a convenient way to predict the average properties of fluid flow and solute transport through a single fracture with spatially variable apertures. ,1752'8&7,21 Fluid flow and solute transport through fractured rock is important in many areas, such as extraction of geothermal energy, production of oil and gas from fractured reservoirs and disposal of nuclear waste in underground repositories. For this reason considerable effort has been placed on characterization and modelling of fractures and fracture systems [1], and in particular, on quantification of the hydraulic behaviour of a single fracture [2], which constitutes the basic building block of realistic models of fluid flow and solute transport in fractured media. To describe adequately the statistical properties of fluid flow and solute transport through a single fracture with spatially variable apertures, the concept of the volumetric flow rate [3] 4=∫
∂Ω outflow
Q ⋅ T EGV
(1)
is commonly used to quantify the ability of the fracture to transmit fluid through its connected space. Similarly, the concept of the equivalent flow rate [4] 4HT =
1 F0
∫
∂Ω outflow
Q ⋅ - EGV
(2)
is frequently introduced to quantify the ability of the fracture to transmit solute (contaminated water) through its aperture field. Using these two concepts, one can explore conveniently by numerical methods how the flow and transport properties of a fracture are influenced by e.g. the flow direction, the fracture type, the roughness and the degree of spatial correlations of the aperture field. The results obtained, with respect to the distribution of the volumetric and the equivalent flow rate, should, however, be compared with that determined from the simplest case where the fracture is assumed to consist of two perfectly smooth parallel plates. In addition, for the purpose of safety assessment 1
of deep repositories for spent nuclear fuel [5], it is desirable to develop simple expressions, based on that for the parallel plate model [3], to assess the stochastic properties of fluid flow and solute transport through variable aperture fractures, without making detailed calculations in every
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