Uncertainty analysis of numerical inversions of temperature logs from boreholes under injection conditions

Abstract

Abstract Conventional methods to estimate the static formation temperature (SFT) require borehole temperature data measured during thermal recovery periods. This can be both economically and technically prohibitive under real operational conditions, especially for high-temperature boreholes. This study investigates the use of temperature logs obtained under injection conditions to determine SFT through inverse modelling. An adaptive sampling approach based on machine-learning techniques is applied to explore the model space efficiently by iteratively proposing samples based on the results of previous runs. Synthetic case studies are conducted with rigorous evaluation of factors affecting the quality of SFT estimates for deep hot wells. The results show that using temperature data measured at higher flow rates or after longer injection times could lead to less-reliable results. Furthermore, the estimation error exhibits an almost linear dependency on the standard error of the measured borehole temperatures. In addition, potential flow loss zones in the borehole would lead to increased uncertainties in the SFT estimates. Consequently, any prior knowledge about the amount of flow loss could improve the estimation accuracy considerably. For formations with thermal gradients varying with depth, prior information on the depth of the gradient change is necessary to avoid spurious results. The inversion scheme presented is demonstrated as an efficient tool for quantifying uncertainty in the interpretation of borehole data. Although only temperature data are considered in this work, other types of data such as flow and transport measurements can also be included in this method for geophysical and rock physics studies.