Effect of Scale Dependent Data Correlations in an Integrated History Matching Loop Combining Production Data and 4D Seismic Data

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe use of time-lapse data, or 4D seismic, in conjunction with production data in computer aided history matching of reservoir models requires that the various types of data are incorporated in a single objective function measuring the mismatch between the simulated and measured data. In the context of linear maximum likelihood estimation, the contribution of seismic data and production data to the objective function can be balanced on the basis of the sum of the inverse of the data and model error covariance matrices. Methods to estimate these covariance matrices for the combined set of production data and seismic impedance are presented. Generally, the seismic data will be correlated leading to a nondiagonal error covariance matrix. This matrix will also be very large, and efficient methods to invert this matrix are required. This is done using a very fast discrete convolution inverse based on multiplication of block Toeplitz matrices. It is shown that the regression may converge to a wrong solution if incorrect values for the data correlations are used.The presented methodology is applied to an actual historymatching project using data from a North Sea oil field, and a procedure for mapping the time-lapse seismic data and covariance matrix from the seismic grid to the simulation grid is presented.

Advanced Integrated Workflows for Incorporating Both Production and 4D Seismic-Related Data into Reservoir Models

“…First, the weights balancing datasets as different as production and 4D seismic data must be properly estimated. Second, the least-square formulation used to measure the seismic error may be inappropriate to capture the relevant information (Aanonsen et al, 2003). Difficulties to achieve significant decrease in the seismic data mismatch were reported in several studies .…”

Reservoir description using a binary level set model

“…Let us first assume that needs to be divided into two subdomains, 1 and 2 , such that 1 ∩ 2 = ∅ and = 1 ∪¯ 2 , where¯ j is the closure of j . A representation of this domain can be given by…”

“…As in [1,2] we apply the following objective function to measure the misfit between the measured and the simulated data The problem of recovering q(x) is an inverse problem which can be highly ill-posed. Because of the ill-posedness, a proper regularization is required to restrict the solution space.…”

“…A quantitatively incorporation of these data has been discussed by Gosselin et al [16]. Aanonsen et al [1,2] have taken this approach further and considered the effect of using proper weights for the seismic data in the objective function.…”

Sampling error distribution for the ensemble Kalman filter update step

“…Time-lapse seismic data can also be used in updating reservoir models, see, e.g., [1,6,13]. Adjusting the model parameters based on the observed data is known as history matching.…”