A novel concept for estimating inflow profiles in oil wells is based on introducing heatwaves at known times and locations and measure the temperature waves further downstream. The heatwaves arrival times and shapes are known to depend on the source location and inflow profile along the traveled path. Estimating the inflow profile is then done by fitting an inverse model to multiple measured waves. This study aims at introducing a 1D physics-driven model that may be used for this estimation purpose and validate & optimize it by means of experimental data.

We assume the presence of uncertainty in both the model and the data. The former arises from both simplifications needed to achieve acceptable computational time, and several assumptions on the governing processes. Uncertainty in the data stems instead from measurement noise and preprocessing steps necessary to transform non-stationary time-series data so to be suitable for fitting the model. To account for these uncertainties, we cast the problem in a Bayesian framework by applying Markov Chain Monte Carlo approaches to infer the distribution of the model parameters.

The results show that the uncertainties introduced in the model through dimensionality reduction from 3D to 1D are largely Gaussian in nature with the mode close to the original estimate. This indicates that the model matches the data to a satisfactory degree given the available experimental data quality. Overall this is an indication both towards the validity of the model, and towards the fact that a purely physics-driven approach matches measurements resulting from a wide variety of system inputs (a further evidence that the concept is valid).

The most challenging aspect of this study has been that of processing and fitting the data in a satisfactory manner. Especially the observed difference in time constants of the different sensors used in the flow loop experiments introduced challenges related to averaging/combining data from several sensors. Further exploration into methods of combining cross-sectional measurements to 1D along with parameterizations or alternative methods of fitting are perhaps the most clear-cut areas for further research. In the paper we present both novel methods for data preprocessing and illustrate how advanced probability-based methods may be used in a fruitful way for development of improved and computationally fast well inflow estimation models.

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