We propose a generalized travel time inversion method for production data integration into reservoir models using finite-difference reservoir simulators. Our approach is motivated by seismic waveform imaging and is particularly well-suited for large-scale field applications because the computation cost depends only on the number of wells regardless of the number of parameters or the amount of observed data. Instead of matching the production data directly, we minimize a 'travel time shift‘ at each well derived by maximizing the cross-correlation between the observed and calculated production response. An optimal control method is used to compute the sensitivity of the travel time with respect to reservoir parameters. Finally, data integration is carried out via a modified Gauss-Newton method.

There are several advantages associated with the proposed travel time inversion method. First, it is robust and computationally efficient. The travel time misfit function is quasilinear with respect to changes in reservoir properties. As a result, the minimization is relatively insensitive to the choice of the prior model. Second, the computational cost associated with the sensitivity computation depends only on the number of wells which can be orders of magnitude lower than the number of parameters or the amount of observed data. This offers tremendous advantage over the commonly used gradient simulator method or the conventional adjoint methods that attempt to minimize the production data directly. Furthermore, the travel time approach also offers computational advantage during minimization of the misfit function using the Gauss-Newton algorithm. We have presented several examples to demonstrate the power, generality and practical feasibility of our proposed approach for large-scale field applications.

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