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

Using underground gas storage to replace the swing capacity of the giant natural gas field of Groningen in the Netherlands. A reservoir performance feasibility study

In this study we probe the ultimate potential Underground Gas Storage (UGS) capacity of the Netherlands by carrying out a detailed feasibility study on inflow performances of all onshore natural gas reservoirs. The Netherlands is one of the largest natural gas producers in Western Europe. The current decline of its national production and looming production restrictions on its largest field of Groningen -owing to its induced seismicity- have recently made necessary to upgrade the two largest UGS of Norg and Grijpskerk. The joined working volume of these two UGS is expected to replace the swing capacity of the Groningen field to continue guaranteeing the security of supply of low calorific natural gas. The question is whether this UGS configuration will provide the expected working storage capacity unrestricted by issues on reservoir performances and/or induced seismicity. This matter will be of paramount importance in the near future when production restrictions and/or the advance state of depletion of the Groningen field will turn the Netherlands into a net importer of high calorific natural gas. By then, the question will be whether the available UGSs will still be economically attractive to continue operating, or if additional or alternative UGSs will be needed?. Hence the characterization and ranking of the best potential reservoirs available today is of paramount importance for future UGS developments. We built an in-house automated module based on the application of the traditional inflow performance relationship analysis to screen the performances of natural gas reservoirs in onshore Netherlands. Results enable identifying the 72 best candidates with an ultimate total working volume capacity of 122±30 billion Sm 3 . A detailed sensitivity analysis shows the impact of variations in the reservoir properties or wellbore/tubing configurations on withdrawal performances and storage capacity. We validate our predictions by comparing them to performances of the UGSs currently operating in the Netherlands. Our results show that although Norg and Grijpskerk stand midst the best candidates, their working:cushion gas volume (wv:cv) ratios appear amongst the lowest. We found many other reservoir candidates with higher wv:cv ratios ("1) and working volumes between 3 and 10 billion Sm 3 geographically distributed across the Netherlands. Any of the current and future UGSs will have to compete with economically more attractive means of gas import via pipelines and liquefied natural gas. We suggest that only the strategic development of a network of efficient underground gas storages with wv:cv ratios "1, could increase its economical attractiveness. This can reduce future dependence on foreign gas supply for cases of import disruption or shortages during peak demand in winter periods. Future political and economic decisions and societal acceptance will determine the role that UGS will play in the security of supply of natural gas in the Netherlands and Western Europe

Estimation of changes in saturation and pressure from 4D seismic AVO and time-shift analysis

A reliable estimate of reservoir pressure and fluid saturation changes from time-lapse seismic data is difficult to obtain. Existing methods generally suffer from leakage between the estimated parameters. We propose a new method using different combinations of time-lapse seismic attributes based on four equations: two expressing changes in prestack AVO attributes (zero-offset and gradient reflectivities), and two expressing poststack time-shifts of compressional and shear waves as functions of production-induced changes in fluid properties. The effect of using different approximations of these equations was tested on a realistic, synthetic reservoir, where seismic data have been simulated during the 30-year lifetime of a water-flooded oil reservoir. Results found the importance of the porosity in the inversion with a clear attenuation of the porosity imprint on the final estimates in case the porosity field or the vertically averaged porosity field is known a priori. The use of a first-order approximation of the gradient reflectivity equation leads to severely biased estimates of changes in saturation and leakage between the two different parameters. Both the bias and the leakage can be reduced, if not eliminated, by including higher-order terms in the description of the gradient, or by replacing the gradient equation with P- and/or S-wave time-shift data. The final estimates are relatively robust to random noise, as they present fairly high accuracy in the presence of white noise with a standard deviation of 15%. The introduction of systematic noise decreases the inversion accuracy more severely.Geoscience & EngineeringCivil Engineering and Geoscience