Data-Space Inversion with Ensemble Smoother

TL;DR

This paper tackles the uncertainty inherent in reservoir forecasting by improving data-space inversion (DSI) with an iterative ensemble smoother (DSI-ESMDA). By updating predicted data directly through a multi-step ensemble-smoother framework and incorporating localization, the method becomes faster and more robust than the PCA-based DSI, while delivering forecasts comparable to traditional ensemble history matching in field-scale problems. The authors demonstrate success on synthetic and benchmark cases, and show that localization is crucial for handling large data volumes. Overall, DSI-ESMDA offers a practical, scalable approach for uncertainty quantification in production forecasts without requiring model inversions.

Abstract

Reservoir engineers use large-scale numerical models to predict the production performance in oil and gas fields. However, these models are constructed based on scarce and often inaccurate data, making their predictions highly uncertain. On the other hand, measurements of pressure and flow rates are constantly collected during the operation of the field. The assimilation of these data into the reservoir models (history matching) helps to mitigate uncertainty and improve their predictive capacity. History matching is a nonlinear inverse problem, which is typically handled using optimization and Monte Carlo methods. In practice, however, generating a set of properly history-matched models that preserve the geological realism is very challenging, especially in cases with complicated prior description, such as models with fractures and complex facies distributions. Recently, a new data-space inversion (DSI) approach was introduced in the literature as an alternative to the model-space inversion used in history matching. The essential idea is to update directly the predictions from a prior ensemble of models to account for the observed production history without updating the corresponding models. The present paper introduces a DSI implementation based on the use of an iterative ensemble smoother and demonstrates with examples that the new implementation is computationally faster and more robust than the earlier method based on principal component analysis. The new DSI is also applied to estimate the production forecast in a real field with long production history and a large number of wells. For this field problem, the new DSI obtained forecasts comparable with a more traditional ensemble-based history matching.

Figures (14)

• Figure 1: Histogram transformation used in DSI.
• Figure 2: Test case 1.
• Figure 3: Water production rate in m$^\text{3}$/days for wells P1 (first row) and P2 (second row). Test case 1. (a) and (c) DSI, (b) and (d) DSI-ESMDA. The red dots are the observed data points and the red line is the prediction from the reference model. The grey region corresponds to the predictions within the percentiles P10--P90 obtained with the prior ensemble. The light blue region corresponds to the predictions within the percentiles P10--P90 obtained with DSI or DSI-ESMDA. The blue line corresponds to the percentile P50 obtained with DSI or DSI-ESMDA. The black lines correspond to the percentiles P10, P50 and P90 obtained by the history-matched models using ES-MDA. The vertical dashed line indicates the end of the history and beginning of the forecast period.
• Figure 4: Field cumulative production in $\text{10}^\text{6}$ m$^\text{3}$. (a) Oil and (b) water. Test case 1. The dashed red line indicates the cumulative production of the reference case.
• Figure 5: Water production rate in m$^\text{3}$/days for well P1 considering different number of observed data points 20 (first row), 51 (second row) and 70 data points (third row). Test case 1. (a), (c) and (e) DSI, (b), (d) and (f) DSI-ESMDA. See Fig. \ref{['Fig:WaterRateTestCase1']} for description.