An Efficient Upscaling Process Based on a Unified Fine-scale Multi-Physics Model for Flow Simulation in Naturally Fracture Carbonate Karst Reservoirs
Authors: Qin Guan , Bi Linfeng , Popov Peter , Efendiev Yalchin , Espedal Magne S. 
Published: July 2010

Abstract
Naturally-fractured carbonate karst reservoirs are characterized by various-sized solution caves that are connected via fracture networks at multiple scales. These complex geologic features can not be fully resolved in reservoir simulations due to the underlying uncertainty in geologic models and the large computational resource requirement. They also bring in multiple flow physics which adds to the modeling difficulties. It is thus necessary to develop a method to accurately represent the effect of caves, fractures and their interconnectivities in coarse-scale simulation models. In this paper, we present a procedure based on our previously proposed Stokes-Brinkman model (SPE 125593) and the discrete fracture network method for accurate and efficient upscaling of naturally fractured carbonate karst reservoirs.
The natural fracture networks provide the essential connection between the caves in carbonate karst reservoirs. It is thus very important to resolve the flow involving in the fracture network and the interaction between fractures and caves to better understand the complex flow behavior. On the other hand, the big scale contrast between the fractures and flow domain makes the efficient solution of the flow problem very difficult. The idea is to use Stokes-Brinkman model to represent flow through rock matrix, void caves as well as intermediate flows in very high permeability regions and to use discrete fracture network model to represent flow in fracture network. This unified approach adaptively treats fractures as lower dimensional geometries in the domain with permeabilities assigned according to their apertures. Although the choice of discrete fracture network method in dealing with natural fractures is straightforward, the numerical solution of discrete fracture network in association with Stokes-Brinkman equations is not as trivial. We present mixed finite element solution strategies for improved computational efficiency in flow simulations especially when there exist a relatively large number of interconnecting fractures.
We have applied the proposed procedure in scale-up computations of naturally fractured carbonate karst reservoirs. Since the fractures and caves are globally connected, global scale-up is used for better upscaling accuracy. The resulting effective properties are further used for coarse-scale flow simulations. Our results show that the coarse-scale permeability field is greatly affected by the configuration of the interconnecting caves and fractures. The coarse-scale solutions are compared with fine-scale simulation results. The good agreements indicate the proposed upscaling procedure can accurately and efficiently account of the complex flow behavior in naturally fractured carbonate karst reservoirs.
The proposed upscaling procedure flexibly adapts to the different flow physics in naturally-fractured carbonate karst reservoirs in a simple and effective way. It certainly extends modeling and predicting capability in efficient development of this important type of reservoir.