Fixed and random effects error models for geothermal simulator calibration

Abstract

Standard approaches to geothermal model calibration typically assume independent, identically distributed
Gaussian measurement noise about the model. However, in practice, models usually exhibit systematic errors, such as well-to-well offsets between measured data and the best-fit (calibrated) simulation model. Failure to account for these systematic errors can lead to bias and overconfidence in parameter estimates and predictions. The statistical regression literature often handles these issues using fixed or random effects error models; petroleum reservoir modelling and related fields have recently incorporated similar ideas. However, geothermal reservoir modellers have not yet adopted these methods, neglecting systematic errors or using ad-hoc methods of weighting observations. Here we review basic concepts of fixed and random effects error modelling and show how to apply them to account for the kinds of well-to-well discrepancies expected between models and realworld data. This approach relies on fairly straightforward mathematics and statistics but generally leads to much more reasonable results. Furthermore, these methods can easily be implemented in existing frameworks and software and typically require only minor additional computational costs.