Practical simulation of multi-porosity reservoirs through existing reservoir simulator

Abstract

Complex heterogeneous reservoir exhibits special characteristics, such as multiple storage types, wide range of storage sizes, complicated storage combinations, and various flow behaviors. Multi-continuum model is needed to rigorously simulate this type of reservoir. However most reservoir simulators use dual porous media model, and the theory of the models is mainly focused on matrix-fracture system. Therefore when porous media is more complex than matrix-fracture system, such software cannot be utilized to simulate these reservoirs directly. Some studies have been proposed to solve the problem, but most of them are either at the theoretical level or cannot been used widely in the simulation softwares. The goal of this paper is not to develop new numerical simulation software, but to obtain appropriate ways to improve performance of current simulation software for complex reservoir.Our approach is theoretically based on multi-continuum seepage theory. By comparing the microscopic seepage model and multi-continuum seepage model, we find that the conventional theory becomes improper because of the absence of an important restriction to the interporosity flow. In the conventional way, an N-multiple flow model always can be established based on N types of continuous media. In fact, one more restrictive condition needs to be added to make it valid: all the crossflow between any two types of continuum can be simplified into a source or sink terms in the seepage model. Consequently, the multiplicity of the seepage model is always less or equal to the number of the continuum types. In addition, because different type of dual-medium has different crossflow, it is required to construct their crossflow models respectively and derive corresponding calculation formula.Several steps developed in this paper are as follows on the basis of multi-continuum theory and the restrictions appended: First, reservoir storage is categorized into continuous and non-continuous media according to storage scale characteristics, distribution and intensity. In general, small cavities, small fractures, and pores in the rock are continuous while large-scale fractures, big cavities or caves are non-continuous. The whole reservoir is therefore classified into continuum region and dis-continuum region. Second, in the continuum region, multi-media model and its multiplicity are determined by using the new theory proposed in this paper. Third, calculation formulae are constructed for each type of crossflow. This research takes fractured vuggy reservoirs as an example. A new calculation for the flux transfer is derived for such fracture-vug dual-porosity system. Forth, in the discrete region, flow in a filled non-continuous medium is described by Darcy's law and free flow in large unfilled cavities or caves follows Navier-Stokes equation and an approximate approach to using Darcy flow simulation is provided. Lastly, this paper introduces the methods how to simplify multi-media into two media and how to simulate the complex reservoir by using the existing simulators.The proposed method is applied to a naturally fractured carbonate reservoir with cavities in the Tarim Basin in China. The simulation results illustrate the production mechanisms of reservoir development using water flooding, including water injection and shut-in, stairs-shaped line of water cut with time, high production with low water cut for long time.