| Abstract |
To provide a sustainable heat extraction rate, an Enhanced Geothermal System (EGS) requires adequate circulation of the working fluid through a heat exchanger, which is comprised of a network of open fractures. The permeability of the fracture network constrains the fluid flux, and the surface area of the matrix rocks in contact with the fluid constrains the power or efficiency of the heat exchanger. Consequently, these parameters (surface area and permeability) are crucial for determining the capacity and longevity of EGS systems. One promising approach to estimate these properties is to analyze natural and/or artificial tracer data that are subject to fracture-matrix interactions including matrix diffusion and a number of chemical reactions within the matrix. Analytical solutions for tracer transport are commonly used to analyze tracer test data. However, precipitation- dissolution reactions can impact the tracer behavior, and analytical solutions for tracer transport associated with precipitation-dissolution reactions are limited in the literature. This study develops analytical solutions for tracer transport in both a single-fracture and a multiple-fracture system associated with precipitation-dissolution reactions under transient and steady state transport conditions. These solutions also take into account advective transport in fractures and molecular diffusion in rock matrix. It is demonstrated that for studying distributions of disturbed tracer concentration (defined as 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 our derivation procedure by taking advantage of the existence of analytical solutions to tracer transport associated with radioactive decay in fractured rock. It is also useful for interpreting tracer breakthrough curves, because impact of decay process is relatively easy to analyze. Several illustrative examples (breakthrough curves obtained from analytical solutions) are presented and show that results are quite sensitive to fracture spacing, fracture surface area, and bulk reaction rate (or “decay” constant), indicating that the relevant flow and transport parameters can be inferred by analyzing tracer signals. |