A computationally efficient method to estimate the value of information (VOI) in the context of subsurface energy resources applications is proposed. VOI is a decision analytic metric quantifying the incremental monetary value that would be created by collecting information prior to making a decision under uncertainty. The VOI has to be computed before collecting the information and can be used to justify its collection. Previous work on estimating the VOI of geophysical data has involved explicit approximation of the posterior distribution of reservoir properties given the data and then evaluating the prospect values for that posterior distribution of reservoir properties. Here, we propose to directly estimate the prospect values given the data by building a statistical relationship between them using regression and machine learning techniques. For a 2D reservoir case, the VOI of time-lapse seismic data has been evaluated in the context of spatial decision alternatives and spatial heterogeneity of reservoir properties. Different approaches are employed to regress the values on the data: Partial Least Squares Regression (PLSR) and Principal Components Regression (PCR) regress the values on the important linear combinations of the seismic data. Random forests regression (RFR) is employed to regress the values on a few features extracted from the seismic data. The uncertainty in the VOI estimation has been quantified using bootstrapping. Estimating VOI by simulation-regression is much less computationally expensive than other approaches that fully describe the posterior distribution. This method is flexible since it does not require rigid model specification of the posterior but rather fits conditional expectations non-parametrically from samples of values and data.
Value of information analysis is useful for helping a decision maker evaluate the benefits of acquiring or processing additional data. Such analysis is particularly beneficial in the petroleum industry, where information gathering is costly and time-consuming. Furthermore, there are often abundant opportunities for discovering creative information gathering schemes, involving the type and location of geophysical measurements. A consistent evaluation of such data requires spatial modeling that realistically captures the various aspects of the decision situation: the uncertain reservoir variables, the alternatives and the geophysical data under consideration. The computational tasks of value of information analysis can be daunting in such spatial decision situations; in this paper, a regression-based approximation approach is presented. The approach involves Monte Carlo simulation of data followed by linear regression to fit the conditional expectation expression that is needed for value of information analysis. Efficient approximations allow practical value of information analysis for the spatial decision situations that are typically encountered in petroleum reservoir evaluation. Applications are presented for seismic amplitude data and electromagnetic resistivity data, where one example includes multi-phase fluid flow simulations.
Simulation-regression is a computationally efficient methodology to estimate the value of information (VOI), as it involves directly estimating the value outcomes corresponding to different data realizations by building a statistical relationship between the prospect values and the data, rather than estimating the model parameters from the data and then estimating the value outcomes given the model parameters. The simulation-regression workflow is applied to estimate the VOI of time-lapse seismic data in a 2D reservoir case using Partial Least Squares Regression (PLSR) and Principal Components Regression (PCR), and the variance in the VOI result is estimated using bootstrapping for varying number of realizations. The VOI results from the two regression techniques are found to be consistent, and it is seen from the bootstrap results that the variance in the VOI decreases with increasing number of realizations and the VOI ranges obtained by higher number of realizations are captured by those obtained by fewer realizations. The VOI results from simulation-regression are then compared with those obtained by a rigorous Monte Carlo method, where the posterior model realizations are sampled using rejection sampling for each possible data realization, and then the prospect values are estimated for each model realization using flow simulation. Finally, the simulation-regression method is applied to estimate the VOI of timelapse seismic data in a complex production optimization case involving sequential well placement and control decisions.
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