Summary Recently, Emerick and Reynolds (2012) introduced the ensemble smoother with multiple data assimilations (ES-MDA) for assisted history matching. With computational examples, they demonstrated that ES-MDA provides both a better data match and a better quantification of uncertainty than is obtained with the ensemble Kalman filter (EnKF). However, similar to EnKF, ES-MDA can experience near ensemble collapse and results in too many extreme values of rock-property fields for complex problems. These negative effects can be avoided by a judicious choice of the ES-MDA inflation factors, but, before this work, the optimal inflation factors could only be determined by trial and error. Here, we provide two automatic procedures for choosing the inflation factor for the next data-assimilation step adaptively as the history match proceeds. Both methods are motivated by knowledge of regularization procedures—the first is intuitive and heuristical; the second is motivated by existing theory on the regularization of least-squares inverse problems. We illustrate that the adaptive ES-MDA algorithms are superior to the original ES-MDA algorithm by history matching three-phase-flow production data for a complicated synthetic problem in which the reservoir-model parameters include the porosity, horizontal and vertical permeability fields, depths of the initial fluid contacts, and the parameters of power-law permeability curves.

Fingerprint image enhancement is a key aspect of an automated fingerprint identification system. This paper describes an effective algorithm based on a novel lighting compensation scheme. The scheme involves the use of adaptive higher-order singular value decomposition on a tensor of wavelet subbands of a fingerprint (AHTWF) image to enhance the quality of the image. The algorithm consists of three stages. The first stage is the decomposition of an input fingerprint image of size 2M × 2N into four subbands at the first level by applying a two-dimensional discrete wavelet transform. In the second

Given a suite of potential surveillance operations, we define surveillance optimization as the problem of choosing the operation that gives the minimum expected value of P90 minus P10 of a specified reservoir variable J (e.g. cumulative oil production) that will be obtained by conditioning J to the observed data. Two questions can be posed, namely: (1.) Which surveillance operation is expected to provide the greatest uncertainty reduction in J ? (2.) What is the expected value of the reduction in uncertainty that would be achieved if we were to undertake each surveillance operation to collect the associated data and then history-match the data obtained? In this work, we extend and apply a conceptual idea that we recently proposed for surveillance optimization to 2-D and 3-D water flooding problems. Our method is based on information theory where the mutual information between J and the random observed data vector Dobs is estimated using an ensemble of prior reservoir models. This mutual information reflects the strength of the relationship between J and the potential observed data and provides a qualitative answer to question 1. Question 2 is answered by calculating the conditional entropy of J in order to generate an approximation of the expected value of the reduction in P90 - P10 of J. The reliability of our method depends on obtaining a good estimate of the mutual information. We consider several ways to estimate the mutual information and suggest how a good estimate can be chosen. We validate the results of our proposed method with an exhaustive history-matching procedure. The methodology provides an approximate way to decide which data should be collected to maximize the uncertainty reduction in a specified reservoir variable and to estimate the reduction in uncertainty that could be obtained. We expect this paper will stimulate significant research on the application of information theory and lead to practical methods and workflows for surveillance optimization.

No abstract

Summary Given a suite of potential surveillance operations, we define surveillance optimization as the problem of choosing the operation that gives the minimum expected value of P90 minus P10 (i.e., P90 – P10) of a specified reservoir variable J (e.g., cumulative oil production) that will be obtained by conditioning J to the observed data. Two questions can be posed: (1) Which surveillance operation is expected to provide the greatest uncertainty reduction in J? and (2) What is the expected value of the reduction in uncertainty that would be achieved if we were to undertake each surveillance operation to collect the associated data and then history match the data obtained? In this work, we extend and apply a conceptual idea that we recently proposed for surveillance optimization to 2D and 3D waterflooding problems. Our method is based on information theory in which the mutual information between J and the random observed data vector Dobs is estimated by use of an ensemble of prior reservoir models. This mutual information reflects the strength of the relationship between J and the potential observed data and provides a qualitative answer to Question 1. Question 2 is answered by calculating the conditional entropy of J to generate an approximation of the expected value of the reduction in (P90 – P10) of J. The reliability of our method depends on obtaining a good estimate of the mutual information. We consider several ways to estimate the mutual information and suggest how a good estimate can be chosen. We validate the results of our proposed method with an exhaustive history-matching procedure. The methodology provides an approximate way to decide the data that should be collected to maximize the uncertainty reduction in a specified reservoir variable and to estimate the reduction in uncertainty that could be obtained. We expect this paper will stimulate significant research on the application of information theory and lead to practical methods and workflows for surveillance optimization.