From time-lapse seismic inversion to history matching of water flooded oil reservoirs

The world energy demand still increases every year. As a consequence, the demand for fossil fuels, by far the first energy source, is increasing, while easily accessible fossil fuel resources are decreasing. This has stimulated research and development to the optimization of hydrocarbon recovery from existing reservoirs over the last decade. Waterflooding for enhanced oil recovery is one approach to increase the recovery of an oil reservoir. In this thesis the monitoring of waterflooding using time lapse seismic data in combination with production data is used to improve the representative flow models of the reservoir. Such models are then used to optimize production strategies. When constraining a reservoir model to observations, the measurement uncertainty plays a key role. The first part of this thesis is dedicated to developing an inversion methodology leading to more accurate estimates of changes in saturation and pore pressure induced by waterflooding from 4D seismic data. Waterflooding processes induce time-lapse changes in reservoir fluid saturation and in pore pressure. These are reflected in 4D variations of seismic attributes like changes in amplitudes and time-shifts. The improvement of the proposed 4D seismic inversion method resides in a more correct, and possibly unbiased, estimate of time-lapse changes in saturation and pore pressure. Existing methods often suffer from bias and leakage between the different estimated parameters. By making use of different combinations of time-lapse seismic attributes based on four equations: two expressing changes in pre-stack AVO attributes (zero-offset and gradient reflectivities), and two expressing post-stack time-shifts of compressional and shear waves as functions of production induced changes in fluid properties, the estimates can be considerably improved. The impact of using different combinations of these equations is tested on a synthetic, though realistic 3D model, where seismic data have been simulated at various steps during the 30 years lifetime of the waterflooded reservoir. Results show that the inversion accuracy increases if higher order terms in the description of the P-wave gradient reflectivity are not neglected, or if, in case S-wave data are available, the S-wave time-shift equation replaces the equation related to the P-wave gradient reflectivity. As in all inversion methods, the influence of prior porosity estimates remains very high and results improve considerably, in case lateral variations of porosity are properly taken into account. The effect of noise on the inversion results is also investigated, with the conclusion that the method seems to be quite robust to random noise, while the introduction of systematic noise decreases the inversion accuracy more severely. The second part of this thesis is dedicated to the investigation of the possibilities to obtain an accurate model characterization, particularly in terms of flow, through the assimilation of seismic measurements with the Ensemble Kalman Filter. The mathematical process which identifies the parameter values that minimize a cost-function representing the mismatch between modeled and observed data is called Data Assimilation (or History Matching). In Data Assimilation, parameter estimations for the entire reservoir model, are often based only on the information related to sparsely distributed production data. It is obvious that in such a case the number of observations is much smaller than the number of parameters to estimate, making history matching a strongly ill-posed problem. The additional information acquired from (time-lapse) seismic data can be utilized to narrow the solution space down when minimizing the misfit between gathered measurements and their forecasts from numerical models. Although in literature numerous data assimilation methods have been presented, in this thesis the Ensemble Kalman Filter has been chosen for several reasons. Firstly, the method is computationally feasible for large systems and is relatively simple to implement making use of existing simulators. Secondly, it presents a flexible treatment of any kind and number of data or uncertain parameters. Thirdly, this method has a large and active research community, and a rigorous theoretical basis. This thesis proposes two innovative approaches to assimilate seismic measurements with the Ensemble Kalman Filter. The first approach concerns the assimilation of time-lapse changes in fluid saturation and pore pressure available for every reservoir gridblock. This method builds directly on the results of the first part of this thesis. In this case the number of observations to assimilate can be very high, causing the problem of ’filter divergence’. Filter divergence is a consequence of an excessive reduction of ensemble parameter covariance. The most effective method to circumvent this problem is Covariance regularization through Localization. This approach consists of multiplying the ensemble covariances element-wise by a local support matrix, resulting in a localized covariance estimate. For a correct application, localization requires the knowledge of the real covariance between measurements and states/parameters to update. Through a 2D synthetic study rules of thumb for the definition of adequate localization functions have been determined. Afterwards these rules have been successfully applied on a 3D reservoir. The second approach of seismic data assimilation is based on the assimilation of fluid front arrival times. The major advantage of the method is, that no full inversion of seismic data to saturations for each grid block is required. The focus is only on the fronts, where changes in time lapse seismic response can be observed. In this case saturation data, impedance maps, or even simple amplitude change maps can be assimilated as waterfront arrival times. This approach enables a very large reduction in number of data while retaining the essential information content. Furthermore, it offers a more linear sensitivity to reservoir properties and a more Gaussian distribution of simulated measurements than using saturation data. This tends to improve the functioning of the EnKF, which represents a multi-model history match that incorporates and retains geological information formulated in terms of two-point geostatistics. This method has also been successfully applied on a slightly modified version of the benchmark Brugge field, a synthetic study reflecting to a great extent the complexity of a real field.