A significant number of naturally fractured reservoirs (NFRs) discovered in the world contain heavy and extra heavy oil. These reservoirs are important resources; however, the nature of naturally fractured reservoirs, especially those containing heavy and extra heavy oil, presents many unique and complex challenges for reservoir modeling and simulation. There have been a number of attempts over the last 50 years to develop methods to improve our understanding as to how the fracture systems impact oil recovery. For many decades, the dual-porosity approach has been the most popular and effective technique in modeling of NFRs. This approach separates the fracture and matrix systems into two different continua, each with its own set of properties. Fluid exchange between matrix and fractures is modeled through a Transfer Function (TF), while a shape factor describes the fracture-matrix surface area. However, the fracture-matrix fluid interaction is not yet fully understood for thermal processes, which represents a significant unknown in thermal reservoir simulation of NFRs containing (ultra) heavy oil.

In this paper an extensive literature survey was initiated to establish a detailed understanding as to how shape factors are utilized for modeling non-isothermal, fracture-matrix fluid exchange in fractured reservoirs. The most appropriate way is to treat the shape factor as a time-dependent quantity to capture the pertinent features of non-isothermal fluid flow in fractured reservoirs. A series of numerical simulations have been conducted using the simulator STARS from Computer Modeling Group Ltd. in order to analyze the performance of existing transfer functions and shape factor formulations for dual-porosity, multiphase flow systems in thermal reservoir simulation. Based on this analysis, we introduce the concept of a new, transient shape factor for non-isothermal, dual-porosity models and compare our new concept with the existing shape factor models. The results from this study clearly confirm that a transient shape factor is required for an appropriate modeling of a thermal recovery process in NFRs when using dual-porosity formulations.

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