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This study presents the mathematical bases of the measurement of internal temperatures within flowing systems using chemically reacting tracers. It considers plugflow (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. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information. apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or othenvise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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