We have developed an efficient approach of petroleum reservoir model calibration that integrates 4D seismic surveys together with well-production data. The approach is particularly well-suited for the calibration of high-resolution reservoir properties (permeability) because the field-scale seismic data are areally dense, whereas the production data are effectively averaged over interwell spacing. The joint calibration procedure is performed using streamline-based sensitivities derived from finite-difference flow simulation. The inverted seismic data (i.e., changes in elastic impedance or fluid saturations) are distributed as a 3D high-resolution grid cell property. The sensitivities of the seismic and production surveillance data to perturbations in absolute permeability at individual grid cells are efficiently computed via semianalytical streamline techniques. We generalize previous formulations of streamline-based seismic inversion to incorporate realistic field situations such as changing boundary conditions due to infill drilling, pattern conversion, etc. A commercial finite-difference flow simulator is used for reservoir simulation and to generate the time-dependent velocity fields through which streamlines are traced and the sensitivity coefficients are computed. The commercial simulator allows us to incorporate detailed physical processes including compressibility and nonconvective forces, e.g., capillary pressure effects, while the streamline trajectories provide a rapid evaluation of the sensitivities. The efficacy of our proposed approach was tested with synthetic and field applications. The synthetic example was the Society of Petroleum Engineers benchmark Brugge field case. The field example involves waterflooding of a North Sea reservoir with multiple seismic surveys. In both cases, the advantages of incorporating the time-lapse variations were clearly demonstrated through improved estimation of the permeability heterogeneity, fluid saturation evolution, and swept and drained volumes. The value of the seismic data integration was in particular proven through the identification of the continuity in reservoir sands and barriers, and by the preservation of geologic realism in the calibrated model.
Characterization of the Measurement Error in Time-Lapse Seismic Data and Production Data with an EM Algorithm