Estimation of Fracture Aperture in Naturally Fractured Reservoirs Using an Ensemble Smoother with Multiple Data Assimilation

Abstract

Summary Accurate modelling of flow in geothermal and hydrocarbon reservoirs is necessary for performance prediction. When fractures are naturally present as in many brittle reservoir rocks, they can control flow. In this case, a thorough knowledge of fracture location, orientation, density, abutting relationships and geologic attributes is crucial. In the subsurface, these parameters usually are associated with a high degree of uncertainty because their observability is limited. Fractures intersected by boreholes can be detected and characterized to some extent using established measurement techniques such as image logging, core analysis or spinner logs. Yet, the majority are not sampled, hampering modelling. In this conceptual study, we focus on fracture aperture as the only unknown parameter, while assuming that location, orientation and length of all fractures are known a priori. While this assumption usually is not fulfilled, it allows us to study effects of fracture aperture on flow independently. We extract fracture patterns from mapped outcrops serving as reservoir analogues. The resulting detailed 2.5-dimensional models contains hundreds of natural fractures evolved over geologic time. We estimate fracture aperture from the in situ stress in the reservoir of interest using a modified version of the method of Barton & Bandis, acknowledging the limitations of this method by increasing the uncertainty in stress state, material properties of the rock, and other input quantities. These estimates are then used as prior for inverse modelling. We apply an iterative Ensemble Kalman Filter, the Ensemble Smoother with Multiple Data Assimilation (ES-MDA), to reduce the uncertainty of fracture aperture and improve simulation results. Ensemble Kalman Filters are widely used for data assimilation or history matching in the context of sub-surface flows. Here, we use synthetic flow and transport data from a separate simulation with known fracture aperture as reference data in the ES-MDA framework. The modified Barton-Bandis model provides prior realisations for an ensemble-based data assimilation framework at low computational cost. First results suggest that the realisations have some variety and reproduce physical relations such as the correlation of fracture aperture to fracture length and shear displacement to fracture orientation. Future work needs to validate the modified model with a mechanical simulator. Preliminary results of our ES-MDA framework with plausible flow model parameterizations indicate that valuable information about the aperture distribution in the considered fracture geometry could be obtained. This amounts to one step forward towards a satisfying characterization of fracture parameters with dynamic data from a geological reservoir.