Streamline-based production data integration in naturally fractured reservoirs

Abstract

Streamline-based models have shown great potential in reconciling high resolution geologic models to production data. In this work we extend the streamline-based production data integration technique to naturally fractured reservoirs. We use a dualporosity streamline model for fracture flow simulation by treating the fracture and matrix as separate continua that are connected through a transfer function. Next, we analytically compute the sensitivities that define the relationship between the reservoir properties and the production response in fractured reservoirs. Finally, production data integration is carried out via the Generalized Travel Time inversion (GTT). We also apply the streamline-derived sensitivities in conjunction with a dual porosity finite difference simulator to combine the efficiency of the streamline approach with the versatility of the finite difference approach. This significantly broadens the applicability of the streamlinebased approach in terms of incorporating compressibility effects and complex physics. The number of reservoir parameters to be estimated is commonly orders of magnitude larger than the observation data, leading to non-uniqueness and uncertainty in reservoir parameter estimate. Such uncertainty is passed to reservoir response forecast which needs to be quantified in economic and operational risk analysis. In this work we sample parameter uncertainty using a new two-stage Markov Chain Monte Carlo (MCMC) that is very fast and overcomes much of its current limitations. The computational efficiency comes through a substantial increase in the acceptance rate during MCMC by using a fast linearized approximation to the flow simulation and the likelihood function, the critical link between the reservoir model and production data. The Gradual Deformation Method (GDM) provides a useful framework to preserve geologic structure. Current dynamic data integration methods using GDM are inefficient due to the use of numerical sensitivity calculations which limits the method to deforming two or three models at a time. In this work, we derived streamline-based analytical sensitivities for the GDM that can be obtained from a single simulation run for any number of basis models. The new Generalized Travel Time GDM (GTT-GDM) is highly efficient and achieved a performance close to regular GTT inversion while preserving the geologic structure.