Using conversions of chemically reacting tracers for numerical determination of temperature profiles in flowing systems and temperature histories in batch systems

摘要

This report presents the mathematical bases for measuring internal temperatures within batch and flowing systems using chemically reacting tracers. This approach can obtain temperature profiles of plug-flow systems and temperature histories within batch systems. The differential equations for reactant conversion can be converted into Fredholm integral equations of the first kind. Effects of tracer-reaction activation energy, number of tracers used, and error in the data are evaluated. The methods can determine temperature histories and profiles for many existing systems, and can be a basis for analysis of the more complicated dispersed-flow systems. An alternative to using the Fredholm-equation approach is the use of an assumed temperature-distribution function and incorporation of this function into the basic integral equation describing tracer behavior. The function contains adjustable parameters which are optimized to give the temperature distribution. The iterative Fredholm equation method is tested to see what is required to discriminate between two models of the temperature behavior of Hot Dry Rock (HDR) geothermal reservoirs.