Parameter Estimation Applied To Thermal Data From In Situ Coal Gasification Experiments
Authors: Hommert Paul J. 
Published: December 2007

Abstract
Parameter estimation techniques that allow quantitative treatment of thermal data from an in situ coal gasification experiment are presented. After a discussion of the important aspects of using parameter estimation, the specific models used for parameter estimation, the specific models used for the Hanna II and Hanna IV test data are outlined. In particular, conduction models have been useful for describing the reverse combustion process and a formal mapping procedure has provided quantitative detail of cavity growth during forward gasification.

Introduction
Since 1973 Sandia Laboratories has been associated with a series of Underground Coal Gasification (UCG) experiments conducted by the Laramie Energy Technology Center (LETC) at Hanna, Wyoming. There has been a variety of instrumentation fielded by Sandia for these tests. The instrumentation has included the conventional in situ diagnostic tools, gas sampling and thermometry, in addition to remote monitoring techniques such as electrical resistivity, seismic and acoustic. An assessment of these various techniques has been compiled. This paper limits itself to a discussion of the techniques developed to analyze thermocouple data from UCG experiments.
Sandia Laboratories' approach to in situ thermometry has been shaped to a large degree by two simple facts of life regarding measurements for UCG. First, the test environment is extremely hostile with severe chemical, thermal, and mechanical effects. Thermocouple failure is almost inevitable. Extreme attempts to prolong thermocouple lifetime with the often accompanying loss of measurement resolution are not cost effective. A different approach is to accept thermocouple failure and instead of survivability, emphasize thermocouple diagnostics and accurate data. Thus the experimenter knows when his data is reliable and because it is accurate he can use it quantitatively. Sandia Laboratories fielded a diagnostic oriented thermometry system on the Hanna IV experiment. Results indicate that appropriate diagnostics are not a luxury for UCG experiments; they are a necessity. The second fact of life is that thermal instrumentation from vertical boreholes is expensive. The number of wells, and consequently spatial resolution, is often limited by cost considerations. Thus every effort must be made to maximize the information from the available instrumentation. This necessity naturally leads to using the data for quantitative analysis. Such an approach can extend the information obtained from the data base. It also can rule out some of the erroneous explanations for data sequences that can be made on the basis of purely qualitative inspection of the data.
In-situ temperature data poses a natural inverse problem. That is one desires to describe a source, problem. That is one desires to describe a source, be it a reverse combustion path or an expanding gasification cavity, by observation of its output. Parameter estimation or non-linear least squares is a Parameter estimation or non-linear least squares is a very effective method for solving the non-linear inverse problems the data presents. For work in UCG this author has found parameter estimation useful in two areas; first, for the analysis of low temperature (less than 100 deg. C) responses and, second, for mapping cavity growth during forward gasification. The models are described in detail, herein, and results from both the Hanna II and Hanna IV experiments are given.
PARAMETER ESTIMATION PARAMETER ESTIMATION Before discussing the particular models appropriate for UCG, it is useful to point out some of the problems associated with parameter estimation in a problems associated with parameter estimation in a more general sense. Of course, parameter estimation has been the subject of considerable work with respect to both the statistical inferences of least squares problems and solution techniques. The reader is referred to one of the many texts on the subject [4]. For the engineer engaged in data analysis two problem areas standout; parameter identification and model appropriateness. Let us consider these with practical examples of germane to UCG data.