Dual-Porosity Flow Diagnostics for Spontaneous Imbibition in Naturally Fractured Reservoirs

We extend single-porosity flow diagnostics to dual-porosity systems using a novel retardation factor R to account for the effect of fracture-matrix transfer on breakthrough times and displacement efficiency during two-phase flow in fractured reservoirs. R is based on an analytical solution for capillary-driven fluid exchange between the fractures and rock matrix. By linearizing R the time-of-flight τ^⋆ is adjusted to include fracture-matrix transfer and derive new metrics, the dynamic Lorenz coefficient (Formula presented.) to quantify the dynamic heterogeneity, and the dual-porosity sweep efficiency Ev^⋆ to estimate how efficiently the injected fluid displaces the reservoir fluid over time. We have tested different formulations of R across three case studies with increasing complexity to analyze the applicability and limitations of dual-porosity flow diagnostics. This analysis reveals that as long as flow in the fractures is faster than fracture-matrix transfer, dual-porosity flow diagnostics provide useful approximations when assessing displacement efficiencies and identifying the wells that are at most and least likely to experience early breakthrough. We show that (Formula presented.) and Ev^⋆ can be combined with stochastic optimization algorithms to improve the displacement efficiency in a 3D reservoir case study. Since a single dual-porosity flow diagnostics calculation requires less than 1 min while a full-physics simulation takes 2 h, we can now quickly screen a large parameter space to identify scenarios that need to be studied in more detail using full-physics simulations. Hence, our new dual-porosity flow diagnostics complement and accelerate state-of-the-art uncertainty quantification and optimization workflows for fractured reservoirs.