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Data Assimilation of Coupled Fluid Flow and Geomechanics via Ensemble Kalman Filter

In reservoir history matching or data assimilation, dynamic data such as production rates and pressures are used to constrain reservoir models and to update model parameters. As such, even if under certain conceptualization the model parameters do not vary with time, the estimate of such parameters may change with the available observations and thus with time. In reality, the production process may lead to changes in both the flow and geomechanics fields, which are dynamically coupled. For example, the variations in the stress/strain field lead to changes in porosity and permeability of the reservoir and hence in the flow field. In weak formations such as the Lost Hills oilfield, fluid extraction may cause a large compaction to the reservoir rock and a significant subsidence at the land surface, resulting in huge economic losses and detrimental environmental consequences. The strong nonlinear coupling between reservoir flow and geomechanics possesses a challenge to construct a reliable model for predicting oil recovery in such reservoirs. On the other hand, the subsidence and other geomechanics observations can provide additional insight into the nature of the reservoir rock and help constrain the reservoir model if used wisely. In this study, the Ensemble Kalman filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations and for mitigating the land subsidence. The use of surface displacement observations improves the match to both production and displacement data. Localization is used to facilitate the assimilation of a large amount of data and to mitigate the effect of spurious correlations resulting from small ensembles. Since the stress, strain, and displacement fields are updated together with the material properties in The EnKF, the issue of consistency at the analysis step of the EnKF is investigated. A 3D problem with reservoir fluid-flow and mechanical parameters close to those of the Lost Hills oilfield is used to test the applicability. Introduction The geomechanical behavior of a reservoir is usually only considered through rock compressibility in reservoir simulators. Rock compressibility determines the change of reservoir pore volume with respect to the change of pressure. The stress fields change, however, dramatically during depletion, water injection or different applications of enhanced oil recovery techniques. The changes in the stress field induce various geomechanical phenomena, such as land subsidence, abrupt compaction of the reservoir, induced fracturing, enhancement of natural fractures and fault activation. Among these phenomena, reservoir compaction and surface subsidence are most commonly seen. Well know examples include the sea floor subsidence in the Ekofisk field and Valhall field in the North Sea (Pattillo et al. 1998), subsidence in the Lost Hill field, California (Wallace and Pugh 1993) and in the region of the Boliva Coast and Lagunillas in Venezuela (van der Knapp and van der Vlis 1967). These complicated geomechanical situations require more sophisticated methods to take them into account in order to better predict the production and avoid facility failures. In the past ten years, extensive efforts have been made to couple the fluidflow and geomechanics simulations to model the complex process during hydrocarbon production (Chin et al. 2000; Dean et al. 2006; Samier et al. 2006). Geomechanics module is available in several commercial reservoir simulators to facilitate the coupled modeling of fluid-flow and geomechanical processes. Both multiphase flow problems and geomechanical processes require some parameters to describe the flow or mechanical properties of the reservoir. Typical primary parameters for multiphase phase flow simulation are permeability and porosity. The primary parameters for elastical geomechanical processes are Young's modulus and Poisson's ratio. Both flow and geomechanical parameters exhibit spatial variabilities and none of them can be measured extensively and accurately, thus these parameters are subject to large uncertainty. In contrast, model responses normally can be measured relatively precisely. For example, oil and water production rates are usually measured and recorded regularly. Down hole pressure gauges can