Analytical solutions of tracer transport in fractured rock associated with precipitation-dissolution reactions |
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| Authors: | Hui-Hai Liu Sumit Mukhopadhyay Nicolas Spycher Burton M Kennedy |
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| Institution: | 1. Earth Sciences Division Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, USA
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| Abstract: | Precipitation-dissolution reactions are important for a number of applications such as isotopic tracer transport in the subsurface. Analytical solutions have been developed for tracer transport in both single-fracture and multiple-fracture systems associated with these reactions under transient and steady-state transport conditions. These solutions also take into account advective transport in fractures and molecular diffusion in the rock matrix. For studying distributions of disturbed tracer concentration (the difference between actual concentration and its equilibrium value), effects of precipitation-dissolution reactions are mathematically equivalent to a “decay” process with a decay constant proportional to the corresponding bulk reaction rate. This important feature significantly simplifies the derivation procedure by taking advantage of the existence of analytical solutions for tracer transport associated with radioactive decay in fractured rock. It is also useful for interpreting tracer breakthrough curves, because the impact of a decay process is relatively easy to analyze. Several illustrative examples are presented, which show that the results are sensitive to fracture spacing, matrix diffusion coefficient (fracture surface area), and bulk reaction rate (or “decay” constant), indicating that the relevant flow and transport parameters may be estimated by analyzing tracer signals. |
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