Optimizing Subsurface Field Data Acquisition Using Information Theory

Oil and gas reservoirs or subsurface aquifers are complex heterogeneous natural structures. They are characterized by means of several direct or indirect field measurements involving different physical processes operating at various spatial and temporal scales. For example, drilling wells provides small plugs whose physical properties may be measured in the laboratory. At a larger scale, seismic techniques provide a characterization of the geological structures. In some cases these techniques can help characterize the spatial fluid distribution, whose knowledge can in turn be used to improve the oil recovery strategy. In practice, these measurements are always expensive. In addition, due to their indirect and incomplete character, the measurements cannot give an exhaustive description of the reservoir and several uncertainties still remain. Quantification of these uncertainties is essential when setting up a reservoir development scenario and when modelling the risks due to the cost of the associated field operations. Within this framework, devising strategies that allow one to set up optimal data acquisition schemes can have many applications in oil or gas reservoir engineering, or in the CO2 geological storages. In this paper we present a method allowing us to quantify the information that is potentially provided by any set of measurements. Using a Bayesian framework, the information content of any set of data is defined by using the Kullback–Leibler divergence between posterior and prior density distributions. In the case of a Gaussian model where the data depends linearly on the parameters, explicit formulae are given. The kriging example is treated, which allows us to find an optimal well placement. The redundancy of data can also be quantified, showing the role of the correlation structure of the prior model. We extend the approach to the permeability estimation from a well-test simulation using the apparent permeability. In this case, the global optimization result of the mean information criterion gives an optimal acquisition time frequency.