Optimal experimental estimation of thermal dispersion coefficients in porous media

In this work, thermal dispersion coefficients, as they appear in the one-temperature model, are estimated for a packed bed of glass spheres through which water is flowing with Péclet numbers up to 130. Thermocouples in the downstream neighborhood of a line heat source measure the temperature response to a step heat input. Due to experimental uncertainties in fluid velocity and thermocouple positions, ordinary least squares estimation on the thermocouple signal alone is of poor quality. Optimal experimental design and simultaneous estimation of velocities and thermocouple positions by the Gauss–Markov method––using prior (but uncertain) information on the thermocouple locations––allow for highly improved estimation of the longitudinal thermal dispersion coefficient. The lateral coefficient can only be roughly estimated by the presented method. Monte Carlo simulations of measurements allow one to assess the level of estimation errors. Excellent temperature residuals in the whole range of Péclet numbers suggest that the assumption of the one-temperature model is reasonable even in the case of local thermal non-equilibrium.