Streamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models.
Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, based on a defined flux field, are computed on the native finite volume grid. The information embedded in these metrics are utilized in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation utilized in the well-established Generalized Travel Time Inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR system composed of the computed analytical sensitivity and the optimal water travel time shift, augmented with regularization and smoothness constraints.
The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatio-temporal trends. Furthermore, the desirable quasi-linear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multi-continuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models.
This work presents, for the first time, an application of the Generalized Travel Time Inversion (GTTI) to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel time sensitivity computations directly on finite volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.