Flexible and Efficient N-Porosity, Full-Featured Simulator Design, and Application

Abstract

The need for flexible and efficient multi-porosity, reservoir-simulation capabilities has never been greater. Much of the world's oil reserves are contained in highly variable fractured reservoirs. Moreover, there is now unprecedented interest in the simulation of unconventional gas reservoirs, where up to four porosity types may be required. This paper discusses the design of an N-porosity, full-featured reservoir simulator capable of handling these diverse scenarios. Essential to the design is the programming data-structure paradigm of the SubGrid. SubGrids represent collections of simulation nodes within spatial regions of interest and encapsulate all data and variables required. Any number of associated SubGrids may coexist, representing N-porosities. Inter-and intra-SubGrid connections may be arbitrarily specified. Because the linear solver operates on the associated SubGrids as distinct entities, the design has tremendous flexibility. For example, regions with simple connectivity, such as in dual-porosity, single-permeability models, can have simple pre-solver elimination performed while other regions with uniform intra-porosity connectivity require a merged SubGrid solution. The scheme efficiently treats regions with different numbers of porosities, levels of interconnectivity, and levels of implicitness. Applications may be applied across multiple reservoirs simultaneously. Treatment of missing "fracture" zones has always been an important feature in the dual-porosity, single-permeability simulation. The traditional approach is to treat the matrix within missing fracture zones effectively as though it were an interconnected portion of the fracture porosity. This preserves connectivity within the fracture-free zones and the more computationally efficient single-permeability solver pre-elimination step. A second missing "fracture" scheme is introduced, which differs in the way that the connections between the fracture and matrix blocks are computed at the boundary of fracture-free zones. Flexible transfer-function application and porosity dependency during equilibrium initialization are discussed. Computational DesignThe extension of the classic industry-standard, dual-porosity simulation scheme to more porosity types began with tripleporosity models (Abdassah and Ershaghi 1986;Lee et al. 1987). More recently, Fung et al. (2011) have demonstrated applications with Middle Eastern carbonates of up to three porosity types within their generalized multi-porosity scheme. Moreover, interest in the simultaneous simulation of four porosity types for unconventional gas reservoirs is now under active study (Andrade et al. 2011). This paper presents the design of our simulator with respect to the challenges of modeling multiple porosity types. Treatment of Multiple Porosities.Our reservoir data architecture expresses the simulation domain into one or many SubGrids, as depicted in Fig. 1. SubGrids are collections of structured or unstructured simulation nodes that ordinarily represent distinct and contiguous regions. ...

General Multi-Porosity simulation for fractured reservoir modeling

“…There are two different configurations in the Multi-Porosity Model. The first configuration is conventional Multi-Porosity Model, which is similar to the model from Hinkley et al (2013). This configuration is naturally compatible with the formulation above.…”

“…Specifically, all grid-based properties are stored through an ordered list, such as grid name, pore volume, rock type, phase saturation etc, and all connection-based properties are stored through a connection list, such as names of two grids in a connection, connection type, and transmissibilities etc. As for the ordering of porosity types, Hinkley et al (2013) recommended that the porosity type with the highest permeability is first and the one with the lowest permeability comes last, and this facilitates the LU factorization process.…”

“…Similar to Hinkley et al (2013), this model honors any number of porosity systems with different properties. Besides, the high contrast of fluid conductivity in different porosity systems results in a multi-scale fluid transfer in different porosity systems, so a hierarchical porosity subdivision discretization scheme is proposed to solve the problem.…”

“…After all, those approaches are still based on the framework of Dual-Porosity Model, and the number of simulated porosity systems is increased but still limited. On the other hand, Hinkley et al (2013) recently extended the traditional Dual-Porosity Model and designed a Multi-Porosity Model to honor the multiple porosity types. Theoretically the method was able to simulate any number of porosity systems and different physics among them, and it shows great application potential in carbonate reservoirs and fractured shale reservoirs.…”

Extended Abstract: Advanced Multiple Porosity Model for Fractured Reservoirs

“…Based on those approaches, the multiple porosity systems in shale reservoirs are conveniently but not yet comprehensively simulated. More recently, Hinkley et al (2013) extended dual porosity model to multiple porosity model. Theoretically the method was able to simulate any number of porosity systems and different physics among them, and it showed good potential to simulate multiple porosity systems in shale reservoirs or carbonate reservoirs.…”