Alexandre A. Emerick

Ensemble smoother with multiple data assimilation

In the last decade, ensemble-based methods have been widely investigated and applied for data assimilation of flow problems associated with atmospheric physics and petroleum reservoir history matching. This paper focuses entirely on the reservoir history-matching problem. Among the ensemble-based methods, the ensemble Kalman filter (EnKF) is the most popular for history-matching applications. However, the recurrent simulation restarts required in the EnKF sequential data assimilation process may prevent the use of EnKF when the objective is to incorporate the history matching in an integrated geo-modeling workflow. In this situation, the ensemble smoother (ES) is a viable alternative. However, because ES computes a single global update, it may not result in acceptable data matches; therefore, the development of efficient iterative forms of ES is highly desirable. In this paper, we propose to assimilate the same data multiple times with an inflated measurement error covariance matrix in order to improve the results obtained by ES. This method is motivated by the equivalence between single and multiple data assimilation for the linear-Gaussian case. We test the proposed method for three synthetic reservoir history-matching problems. Our results show that the proposed method provides better data matches than those obtained with standard ES and EnKF, with a computational cost comparable with the computational cost of EnKF.

History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations

The ensemble Kalman filter (EnKF) has become a popular method for history matching production and seismic data in petroleum reservoir models. However, it is known that EnKF may fail to give acceptable data matches especially for highly nonlinear problems. In this paper, we introduce a procedure to improve EnKF data matches based on assimilating the same data multiple times with the covariance matrix of the measurement errors multiplied by the number of data assimilations. We prove the equivalence between single and multiple data assimilations for the linear-Gaussian case and present computational evidence that multiple data assimilations can improve EnKF estimates for the nonlinear case. The proposed procedure was tested by assimilating time-lapse seismic data in two synthetic reservoir problems, and the results show significant improvements compared to the standard EnKF. In addition, we review the inversion schemes used in the EnKF analysis and present a rescaling procedure to avoid loss of information during the truncation of small singular values.

Well Placement Optimization Using a Genetic Algorithm With Nonlinear Constraints

Well placement optimization is a very challenging problem due to the large number of decision variables involved and the nonlinearity of the reservoir response as well as of the well placement constraints. Over the years, a lot of research has been done on this problem, most of which using optimization routines coupled to reservoir simulation models. Despite all this research, there is still a lack of robust computer-aided optimization tools ready to be applied by asset teams in real field development projects. This paper describes the implementation of a tool, based on a Genetic Algorithm, for the simultaneous optimization of number, location and trajectory of producer and injector wells. The developed software is the result of a two-year project focused on a robust implementation of a computer-aided optimization tool to deal with realistic well placement problems with arbitrary well trajectories, complex model grids and linear and nonlinear constraints. The developed optimization tool uses a commercial reservoir simulator as the evaluation function without using proxies to substitute the full numerical model. Due to the large size of the problem, in some cases involving more than 100 decision variables, the optimization process may require thousands of reservoir simulations. Such a task has become feasible through a distributed computing environment running multiple simulations at the same time. The implementation uses a technique called Genocop III – Genetic Algorithm for Numerical Optimization of Constrained Problems – to deal with well placement constraints. Such constraints include grid size, maximum length of wells, minimum distance between wells, inactive grid cells and user-defined regions of the model, with non-uniform shape, where the optimization routine is not supposed to place wells. The optimization process was applied to three full-field reservoir models based on real cases. It increased the net present values and the oil recovery factors obtained by well placement scenarios previously proposed by reservoir engineers. The process was also applied to a synthetic case, based on outcrop data, to analyze the impact of using reservoir quality maps to generate an initial well placement scenario for the optimization routine without using an engineer-defined configuration. Introduction The definition of a well placement is a key aspect with major impact in a field development project. In this sense, the use of reservoir simulation allows the engineer to evaluate different placement scenarios. However, the current industry practice is still, in most cases, a manual procedure of trial and error that requires a lot of experience and knowledge from the engineers involved in the project. Considering that, the development of well placement optimization tools which can automate this process is a high desirable goal. Well placement optimization is a very challenging problem due to the large number of decision variables involved and the nonlinearity of the reservoir response as well as of the well placement constraints. Over the years, a lot of research has been done on this problem, most of which using optimization routines coupled to reservoir simulation and economical models. In 1995, Beckner and Song applied a Simulated Annealing algorithm to optimize the location and scheduling of 12 wells with fixed orientation and length. In 1997, Bittencourt and Horner applied a Genetic Algorithm (GA) hybridized with Polytope and Tabu Search methods to optimize the location of 33 vertical and horizontal wells, including wells, producers and injectors. In 1998, Pan and Horner investigated the use of multivariate interpolation algorithms, Least Squares and Kriging, as proxies to reservoir simulations for optimization problems including well placement. In 1999, Cruz et al. introduced the

Estimation of pressure and saturation fields from time-lapse impedance data using the ensemble smoother

This paper introduces the use of the ensemble smoother as a method to invert time-lapse seismic data into pressure and saturation fields. The proposed method uses engineering information described in terms of reservoir flow simulations to generate samples of the prior uncertainty space. Subsequently, these samples are corrected using the time-lapse seismic as conditioning data. The problem is formulated in terms of generating an ensemble of pressure and saturation fields sampling the posterior uncertainty space. The proposed method is very flexible and computationally easy to implement. It has very few requirements in terms of the forward model (reservoir flow simulations and petroelastic modeling). This makes the method straightforward to integrate with existing commercial tools.

Deterministic ensemble smoother with multiple data assimilation as an alternative for history-matching seismic data

This paper reports the results of an investigation on the use of a deterministic analysis scheme combined with the method ensemble smoother with multiple data assimilation (ES-MDA) for the problem of assimilating a large number of correlated data points. This is the typical case when history-matching time-lapse seismic data in petroleum reservoir models. The motivation for the use of the deterministic analysis is twofold. First, it tends to result in a smaller underestimation of the ensemble variance after data assimilation. This is particularly important for problems with a large number of measurements. Second, the deterministic analysis avoids the factorization of a large covariance matrix required in the standard implementation of ES-MDA with the perturbed observations scheme. The deterministic analysis is tested in a synthetic history-matching problem to assimilate production and seismic data.

Investigation on Principal Component Analysis Parameterizations for History Matching Channelized Facies Models with Ensemble-Based Data Assimilation

Preserving plausible geological features when updating facies models is still one of the main challenges with ensemble-based history matching. This is particularly evident for fields with complex geological description (e.g., fluvial channels). There is an impressive amount of research published in the last few years about this subject. However, it appears that there is no definitive solution and both, academia and industry, are looking for practical and robust methods. Among the parameterizations traditionally investigated for history matching, the principal component analysis (PCA) of the prior covariance matrix is an efficient alternative to represent models described by two-point statistics. However, there are some recent developments extending PCA-based parameterizations for models described by multiple-point statistics. The first part of this paper presents an investigation on PCA-based schemes for parameterizing channelized facies models for history matching with ensemble-based methods. The following parameterizations are tested: standard PCA, two alternative implementations of kernel PCA and optimization-based PCA. In the second part of the paper, the optimization-based PCA is modified to allow the use of covariance localization and adapted for simultaneously adjusting the facies type and the permeability values within each facies when history matching production data with an ensemble-based method.

Towards a hierarchical parametrization to address prior uncertainty in ensemble-based data assimilation

Ensemble-based methods are becoming popular assisted history matching techniques with a growing number of field applications. These methods use an ensemble of model realizations, typically constructed by means of geostatistics, to represent the prior uncertainty. The performance of the history matching is very dependent on the quality of the initial ensemble. However, there is a significant level of uncertainty in the parameters used to define the geostatistical model. From a Bayesian viewpoint, the uncertainty in the geostatistical modeling can be represented by a hyper-prior in a hierarchical formulation. This paper presents the first steps towards a general parametrization to address the problem of uncertainty in the prior modeling. The proposed parametrization is inspired in Gaussian mixtures, where the uncertainty in the prior mean and prior covariance is accounted by defining weights for combining multiple Gaussian ensembles, which are estimated during the data assimilation. The parametrization was successfully tested in a simple reservoir problem where the orientation of the major anisotropic direction of the permeability field was unknown.

Intelligent Optimization System for Selecting Alternatives for Oil Field Exploration by Means of Evolutionary Computation

The problem of selecting alternatives for the development of an oil field consists of finding the suitable number of production and injection wells and their suitable locations in the field. This is basically an optimization problem, since one wishes to find the alternative that offers the highest NPV. In order to solve this problem, this project makes use of evolutionary algorithms: genetic algorithms [1] [2] [3] [4], cultural algorithms [5] [6] and coevolutionary algorithms [7]. Optimization systems were developed and tested using these optimization algorithms [8] [9] [10].

Analysis of Alternatives for Oil Field Development under Uncertainty

The objective of this area of the project was to develop the foundations of a modular system for alternatives analysis that would allow the integration of the models presently studied (models for investment alternatives, expansion options and options to invest in information). The system makes it possible to work with several different oil fields, where each field can have several investment alternatives and each investment alternative can, for example, present options to invest in information and options to invest in several expansion wells. Technical uncertainties are represented by fuzzy numbers and the problem is solved by Monte Carlo simulation.

ANEPI: Economic Analysis of Oil Field Development Projects under Uncertainty

The analysis of an option to develop (set up for production) a previously delimited oil field requires investments whose costs and whose benefits depend on the alternative chosen. Some alternatives include more wells than others; others present a different geometric distribution of the wells. There are also different types of wells (vertical, directional, horizontal, multilateral, etc.) which involve different types of investments and benefits. The combination of these aspects with others, such as: platform types; production flow system; drilling speed (rig availability); lifting method (gas lift, centrifugal pumping, etc.), oil recovery method, etc., makes this a complex optimization problem. In addition, alternatives to invest in information and even alternatives to simply wait for market conditions to improve must be taken into account. Flexibility is another aspect that needs to be considered in the concept of oil field development as a means by which to ensure that it will be possible to incorporate a future increase in production (expansion option) through additional optional wells, depending on the market conditions and on how the reservoir responds to the first months/years of production.