A theoretical look at ensemble-based optimization in reservoir management

Ensemble-based optimization has recently received great attention as a potentially powerful technique for life-cycle production optimization, which is a crucial element of reservoir management. Recent publications have increased both the number of applications and the theoretical understanding of the algorithm. However, there is still ample room for further development since most of the theory is based on strong assumptions. Here, the mathematics (or statistics) of Ensemble Optimization is studied, and it is shown that the algorithm is a special case of an already well defined natural evolution strategy known as Gaussian Mutation. A natural description of uncer-tainty in reservoir management arises from the use of an ensemble of history-matched geological realizations. A logical step is therefore to incorporate this uncertainty description in robust life-cycle production optimization through the expected objective function value. The expected value is approximated with the mean over all geological realizations. It is shown that the frequently advocated strategy of applying a different control sample to each reservoir realization delivers an unbiased estimate of the gradi-ent of the expected objective function. However, this procedure is more variance prone than the deterministic strategy of applying the entire ensemble of perturbed control samples to each reservoir model realization. In order to reduce the variance of the gradient estimate, an importance sampling algorithm is proposed and tested on a toy problem with increasing dimensionality.acceptedVersio

The Effect of Ocean Currents on Sea Surface Temperature Anomalies

We investigate regional and global-scale correlations between observed anomalies in sea surface temperature and height. A strong agreement between the two fields is found over a broad range of latitudes for different ocean basins. Both time-longitude plots and wavenumber-frequency spectra suggest an advective forcing of SST anomalies by a first-mode baroclinic wave field on spatial scales down to 400 km and time scales as short as 1 month. Even though the magnitude of the mean background temperature gradient is determining for the effectiveness of the forcing, there is no obvious seasonality that can be detected in the amplitudes of SST anomalies. Instead, individual wave signatures in the SST can in some cases be followed over periods of two years. The phase relationship between SST and SSH anomalies is dependent upon frequency and wavenumber and displays a clear decrease of the phase lag toward higher latitudes where the two fields come into phase at low frequencies. Estimates of the damping coefficient are larger than generally obtained for a purely atmospheric feedback. From a global frequency spectrum a damping time scale of 2-3 month was found. Regionally results are very variable and range from 1 month near strong currents to 10 month at low latitudes and in the sub-polar North Atlantic. Strong agreement is found between the first global EOF modes of 10 day averaged and spatially smoothed SST and SSH grids. The accompanying time series display low frequency oscillations in both fields

Editorial: Data Science Applications to Inverse and Optimization Problems in Earth Science

Petroleum Engineerin

Seismic History Matching of Fluid Fronts Using the Ensemble Kalman Filter

SummaryTime-lapse seismic data provide information on the dynamics of multiphase reservoir fluid flow in places where no production data from wells are available. This information, in principle, could be used to estimate unknown reservoir properties. However, the amount, resolution, and character of the data have long posed significant challenges for quantitative use in assisted-history-matching workflows. Previous studies, therefore, have generally investigated methods for updating single models with reduced parameter-uncertainty space. Recent developments in ensemble-based history-matching methods have shown the feasibility of multimodel history and matching of production data while maintaining a full uncertainty description. Here, we introduce a robust and flexible reparameterization for interpreted fluid fronts or seismic attribute isolines that extends these developments to seismic history matching. The seismic data set is reparameterized, in terms of arrival times, at observed front positions, thereby significantly reducing the number of data while retaining essential information. A simple 1D example is used to introduce the concepts of the approach. A synthetic 3D example, with spatial complexity that is typical for many waterfloods, is examined in detail. History-matching cases based on both separate and combined use of production and seismic data are examined. It is shown that consistent multimodel history matches can be obtained without the need for reduction of the parameter space or for localization of the impact of observations. The quality of forecasts based on the history-matched models is evaluated by simulating both expected production and saturation changes throughout the field for a fixed operating strategy. It is shown that bias and uncertainty in the forecasts of production both at existing wells and in the flooded area are reduced considerably when both production and seismic data are incorporated. The proposed workflow, therefore, enables better decisions on field developments that require optimal placement of infill wells.</jats:p