Numerical Determination of Temperature Profiles in Flowing Systems from Conversions of Chemically Reacting Tracers

摘要

This study presents the mathematical bases of the measurement of internal temperatures within flowing systems using chemically reacting tracers. It considers plug-flow (or piston-flow) systems. The differential equation for reactant conversion can be reformulated into a Fredholm integral equation of the first kind. In the Fredholm integral equation the unknown is the temperature distribution function, which characterizes the internal temperature profile of the flowing system. Due to nonlinearity of the kernel, the usual technique of regularization has been modified into an iterative approach. This new approach is employed to solve this Fredholm integral equation. The iterative approach successfully overcomes the usual difficulty of determining the optimal value of the regularization smoothing parameter. Advantages and disadvantages of this method are discussed, and the results are compared with those obtained by optimization of undetermined parameters in a postulated temperature distribution function. The insight acquired from this study can be used to determine temperature profiles for many existing systems, and can form a basis for analysis of the more complicated dispersed-flow systems. The iterative Fredholm integral equation method is tested to see what is required to discriminate between two models of the temperature behavior of Hot Dry Rock geothermal reservoirs. It is found that using as few as two reacting tracers can distinguish between the models and provide a reasonable approximation of the temperature profile within a reservoir. 10 refs., 6 figs., 2 tabs. (ERA citation 14:017242)