“…Details about the PEM implementation can be found in Emerick et al [8]. Among the elastic properties typically used for seismic data history matching, the most common choices are pressure-wave impedance (P-impedance or acoustic impedance) and Poisson's ratio; see, e.g., [15,21,22,40,47]. However, other seismic attributes such as amplitudes [23] and time shifts [27,41] have also been used.…”
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 linearGaussian 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.
“…Details about the PEM implementation can be found in Emerick et al [8]. Among the elastic properties typically used for seismic data history matching, the most common choices are pressure-wave impedance (P-impedance or acoustic impedance) and Poisson's ratio; see, e.g., [15,21,22,40,47]. However, other seismic attributes such as amplitudes [23] and time shifts [27,41] have also been used.…”
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 linearGaussian 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.
“…In some cases, the relationship between s andĉ can be determined empirically [19], though this requires elaborate laboratory work and cannot be generated for the general case.…”
Section: Variational Imaging Of Fluid Flow Problemsmentioning
Imaging and prediction of fluid flow in the subsurface provides information that is crucial for decision making processes in fields such as groundwater management and enhanced oil recovery. The flow of an injected fluid through a reservoir depends primarily on the hydraulic conductivity, which is in general unknown or known only with low accuracy. A common way of imaging the flow is thus to intelligently modify the hydraulic conductivity model and simulate the fluid flow and geophysical imaging data that approximately match the observations over time. This process is also known as history matching. As the imaging process is a highly underdetermined inverse problem, we propose a new technique that avoids estimation of hydraulic conductivities. Instead, our approach directly estimates the flow field and initial distribution of the fluid from a time series of geophysical imaging data. Our method combines the flow equations with geophysical imaging to form a single inverse problem, where the unknowns are the initial state of the reservoir and the flow field. We discuss consistent discretization techniques, tailor specific regularizations, and use a modification of the variable projection method to solve the discrete optimization problem. We demonstrate the potential of our method on a model problem and show that our approach yields an improved flow estimate as well as an improved image quality. Finally, we show that the estimated flow field allows for the reconstruction of the subsurface structure.
“…Recently, time-lapse (repeated) seismic data has been added for better conditioning of the models; see, e.g., Gosselin et al [11], Waggoner et al [30], Lygren et al [22], and Skjervheim et al [27]. Although some authors use seismic amplitude differences, most of the work on seismic history matching has focused on inverted seismic data, such as acoustic impedance and/or Poisson's ratio.…”
A method for history matching of an in-house petroleum reservoir compositional simulator with multipoint flux approximation is presented. This method is used for the estimation of unknown reservoir parameters, such as permeability and porosity, based on production data and inverted seismic data. The limitedmemory Broyden-Fletcher-Goldfarb-Shanno method is employed for minimization of the objective function, which represents the difference between simulated and observed data. In this work, we present the key features of the algorithm for calculations of the gradients of the objective function based on adjoint variables. The test example shows that the method is applicable to cases with anisotropic permeability fields, multipoint flux approximation, and arbitrary fluid compositions.
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