Streamline Tracing and Applications in Dual-Porosity Dual-Permeability Models

Streamline-based methods have proven to be effective for various subsurface flow and transport modeling problems. However, the applications are limited in dual-porosity and dual-permeability (DPDK) system due to the difficulty in describing interactions between matrix and fracture during streamline tracing. In this work, we present a robust streamline tracing algorithm for DPDK models and apply the new algorithm to rate allocation optimization in a waterflood reservoir. In the proposed method, streamlines are traced in both fracture and matrix domains. The interfluxes between fracture and matrix are described by switching streamlines from one domain to another using a probability computed based on the ratio of interfluxes to total fluxes within the domain. The approach is fundamentally similar to the existing streamline tracing technique and can be utilized in streamline-assisted applications, such as flow diagnostics, history matching, and production optimization. The proposed method is benchmarked with a finite volume (FV)-based approach where grid-based time-of-flight (TOF) distributions were obtained by solving the stationary transport equation. We first validated our method using simple examples. Visual TOF comparisons as well as tracer concentration and allocation factors at wells show good agreement. Next, we applied the proposed method to field-scale models to demonstrate the robustness. The results show that our method offers reduced numerical artifacts and better represents reservoir heterogeneity and well connectivity with subgrid resolutions. The proposed method is then used for rate allocation optimization in DPDK models. A streamline-based gradient-free algorithm is used to optimize net present value (NPV) by adjusting both injection and production well rates under operational constraints. The results show that the optimized schedule offers significant improvement in recovery factor, NPV, and sweep efficiency compared to the base scenario using equal rate injection and production. The optimization algorithm is computationally efficient, as it requires only a few forward reservoir simulations. A novelty of this work is the streamline tracing algorithm in DPDK reservoir models. The proposed method is simple and easy to implement to existing streamline-based frameworks and is applicable to field-scale reservoir models for flow diagnostics and rate allocation optimization.