Calibration and prediction improvement of imperfect subsurface flow models

In this thesis, problems related to calibration of imperfect reservoir models, biased parameter estimation and prediction reliability have been addressed. The main objective of this thesis is to avoid overconfident, inaccurate and unreliable predictions while accounting for model-error during the calibration process. Accounting for reservoir model-error in calibration (history matching) can correct/reduce the bias in parameter estimation and improves the prediction of the subsurface flow model. In this thesis, several approaches and algorithms have been developed and investigated which could be applied at different conditions depending on the modelling assumptions. In the first approach, the parameter estimation problem is formulated as a joint estimation of the imperfect model parameters and the error-model parameters. The prior distributions of the error-model parameters are evaluated before calibration through analysis of leading sources of the modelling errors using pairs of high-fidelity and low-fidelity simulation models. A Bayesian framework is adopted for solving the inverse problem, where the ensemble smoother with multiple data assimilation (ES-MDA) is utilized as a calibration algorithm. In the second approach, two new algorithms to account for model-error during calibration are developed which are the variants of the first approach and existing algorithms. The main aim is to develop flexible algorithms that can handle strong serially correlated outputs of the physical model, variable boundary conditions (i.e. variable well open/shut schedules and rate/pressure controls) and structured model-errors (i.e. strong correlation in time). In the third approach, the model-error during calibration is accounted for without knowing any prior statistics of model-discrepancy. For this purpose, a flexible ensemble-based algorithm is developed which can reduce bias in parameter estimation after calibration of imperfect models in order to improve the prediction capacity/reliability of the calibrated physical model. The flexible ensemble-based algorithm is quite general and has the capability to capture unknown model-error uncertainty by relaxing many of the assumptions commonly introduced in the literature

Strategic Geosteeering Workflow with Uncertainty Quantification and Deep Learning: A Case Study on the Goliat Field

The real-time interpretation of the logging-while-drilling data allows us to estimate the positions and properties of the geological layers in an anisotropic subsurface environment. Robust real-time estimations capturing uncertainty can be very useful for efficient geosteering operations. However, the model errors in the prior conceptual geological models and forward simulation of the measurements can be significant factors in the unreliable estimations of the profiles of the geological layers. The model errors are specifically pronounced when using a deep-neural-network (DNN) approximation which we use to accelerate and parallelize the simulation of the measurements. This paper presents a practical workflow consisting of offline and online phases. The offline phase includes DNN training and building of an uncertain prior near-well geo-model. The online phase uses the flexible iterative ensemble smoother (FlexIES) to perform real-time assimilation of extra-deep electromagnetic data accounting for the model errors in the approximate DNN model. We demonstrate the proposed workflow on a case study for a historic well in the Goliat Field (Barents Sea). The median of our probabilistic estimation is on-par with proprietary inversion despite the approximate DNN model and regardless of the number of layers in the chosen prior. By estimating the model errors, FlexIES automatically quantifies the uncertainty in the layers' boundaries and resistivities, which is not standard for proprietary inversion

Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements

The advent of fast sensing technologies allow for real-time model updates in many applications where the model parameters are uncertain. Once the observations are collected, Bayesian algorithms offer a pathway for real-time inversion (a.k.a. model parameters/inputs update) because of the flexibility of the Bayesian framework against non-uniqueness and uncertainties. However, Bayesian algorithms rely on the repeated evaluation of the computational models and deep learning (DL) based proxies can be useful to address this computational bottleneck. In this paper, we study the effects of the approximate nature of the deep learned models and associated model errors during the inversion of borehole electromagnetic (EM) measurements, which are usually obtained from logging while drilling. We rely on the iterative ensemble smoothers as an effective algorithm for real-time inversion due to its parallel nature and relatively low computational cost. The real-time inversion of EM measurements is used to determine the subsurface geology and properties, which are critical for real-time adjustments of the well trajectory (geosteering). The use of deep neural network (DNN) as a forward model allows us to perform thousands of model evaluations within seconds, which is very useful to quantify uncertainties and non-uniqueness in real-time. While significant efforts are usually made to ensure the accuracy of the DL models, it is widely known that the DNNs can contain some type of model-error in the regions not covered by the training data, which are unknown and training specific. When the DL models are utilized during inversion of EM measurements, the effects of the model-errors could manifest themselves as a bias in the estimated input parameters and as a consequence might result in a low-quality geosteering decision. We present numerical results highlighting the challenges associated with the inversion of EM measurements while neglecting model-error. We further demonstrate the utility of a recently proposed flexible iterative ensemble smoother in reducing the effect of model-bias by capturing the unknown model-errors, thus improving the quality of the estimated subsurface properties for geosteering operation. Moreover, we describe a procedure for identifying inversion multimodality and propose possible solutions to alleviate it in real-time

Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements

The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting for uncertainties. However, they rely on the repeated evaluation of the computational models, and deep neural network (DNN) based proxies can be useful to address this computational bottleneck. This paper studies the effects of the approximate nature of the deep learned models and associated model errors during the inversion of extra-deep borehole electromagnetic (EM) measurements, which are critical for geosteering. Using a deep neural network (DNN) as a forward model allows us to perform thousands of model evaluations within seconds, which is very useful for quantifying uncertainties and non-uniqueness in real-time. While significant efforts are usually made to ensure the accuracy of the DNN models, it is known that they contain unknown model errors in the regions not covered by the training data. When DNNs are utilized during inversion of EM measurements, the effects of the model errors could manifest themselves as a bias in the estimated input parameters and, consequently, might result in a low-quality geosteering decision. We present numerical results highlighting the challenges associated with the inversion of EM measurements while neglecting model error. We further demonstrate the utility of a recently proposed flexible iterative ensemble smoother in reducing the effect of model bias by capturing the unknown model errors, thus improving the quality of the estimated subsurface properties for geosteering operation. Moreover, we describe a procedure for identifying inversion multimodality and propose possible solutions to alleviate it in real-time