Real‐time model parameter estimation for analyzing transport in porous media

Abstract

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 (LabVIEWä). Parameter estimation routines programmed in MATLABä-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.

On Integrating Groundwater Transport Models with Wireless Sensor Networks

“…Emerging sensing and network technology is also motivating researchers to develop data assimilation techniques, that is, readjusting model parameters (usually automatically) as new data become available. Kim et al (2005) performed real-time model parameter estimation of simplified (diffusive-only) transport in porous media; Liu et al (2008) assimilated concentration data from the MADE site to validate tritium concentrations. Graham and McLaughlin (1991) and McLaughlin et al (1993) gave early examples of concentration data assimilation.…”

“…Given this, it may be surprising that few studies exist that are designed to establish model credibility (Anderson and Woessner 1992; Hassan 2004). There is a growing belief that models will become more effective if model parameters are periodically updated or recalibrated as new data become available (Anderson and Woessner 1992; Kim et al 2005). However, the effect that erroneous data may have on simulation results is largely overlooked—especially in light of the above pioneering WSN studies.…”

Recent Developments and Future Directions for MT3DMS and Related Transport Codes

“…Heat is increasingly being recognized as an excellent ground water tracer because of its usefulness in identifying multiple hydrologic processes and recent availability of improved temperature sensors and measurement technologies (Anderson 2005). The mathematical equivalency between the heat and solute transport equations has been established in numerous studies (e.g., Healy and Ronan 1996;Kim et al 2005;Prommer and Stuyfzand 2005;Greskowiak et al 2006;Thorne et al 2006;Bayer et al 2008). As a result, MT3DMS can be used directly and efficiently to simulate heat transport with simple variable conversion.…”

Continuous time random walks and heat transfer in porous media

“…In the case of solute transport, this disorder causes the breakthrough curves of tracer tests to deviate from "Fickian" behavior, and, accordingly, such transport is often referred to as "anomalous" or "non-Fickian". Attempts to model thermal breakthrough in an experimental sandy aquifer with an equilibrium approach revealed that the inferred effective thermal dispersion coefficients changed with time during the course of the experiment (Kim et al 2005). Furthermore, several studies of heat transfer in soils have noted that Eq.…”