Real-Time Model Parameter Estimation for Analyzing Transport in Porous Media
This work describes the integration of data acquisition (DAQ) hardware and software for the purpose of acquiring not only data but real-time transport model parameter estimates in the context of subsurface flow and transport problems. Integrated DAQ parameter estimation systems can be used to reduce data storage requirements, trigger event recognition and more detailed sampling actions, and otherwise enhance remote monitoring capabilities. The contaminant transport problem is posed here as the analogous heat transfer problem in a three-dimensional, intermediate-scale physical aquifer model. A constant source of warm water is fed into a sandy aquifer undergoing steady, unidirectional flow. The spatial distribution of temperature in the medium is monitored over time using 17 thermocouples embedded in the medium. These sensors log temperatures via conventional analog-to-digital conversion hardware driven by commercially available DAQ software (LabVIEW™). Parameter estimation routines programmed in MATLAB™-based M-files are embedded in the LabVIEW DAQ routine and access parameter estimation libraries, such as the descent method employed here, via the Internet. The integrated DAQ parameter estimation system is demonstrated for the estimation of (1) the thermal dispersion coefficients (analogous to mass dispersion coefficients), given a known heat source; and (2) the location of a heat source, given known thermal dispersion coefficients. In both cases, the parameter estimation procedure is executed repeatedly as the data are acquired. For the case of source location, the effect of the number of sensors on the parameter estimation procedure is also demonstrated. Reasonable parameter estimates are provided rapidly during both the transient and steady-state phases of the experiments, with accuracy increasing with time and with the number of observations employed.