Fast Estimation of Performance Parameters in Fractured Reservoirs Using Percolation Theory

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractFractured reservoirs have heterogeneities on all length scales which affect all aspects of flow and make the reliable prediction of reservoir performance extremely difficult. The conventional approach to this is to build a number of possible reservoir models (with associated probabilities) then upscale them and run flow simulations. The problem with this approach is that it is computationally very expensive.An alternative approach derived from percolation theory to make a very rapid estimation of reservoir performance and its uncertainty using sandbodies as flow unit was introduced by King et.al 1-2 . This approach is based on the permeability contrasts that control the flow and assumes that the permeability disorder can be approximated by either permeable or impermeable rock. The advantage is that by using some semi-analytical universal curves from percolation theory the effect of the complex geometry which influences the performance parameters can be easily estimated in a fraction of second on a spread sheet.This study extends the application of this approach to fractured reservoirs where we can assume that matrix is almost impermeable and fracture is highly permeable. The problem with this extension is that classic percolation can not be used due to spatial correlation of fractures. However for correlated systems, the basic methodology with some modifications, which in turn depend on the nature of correlation, can be applied. We develop a stochastic methodology based on the derived spatial correlation by Heffer et.al. 3 to generate fracture network realizations. Then by using this spatially correlated model we use the same basic algorithm of percolation theory in 2 and 3D. Simulation results show the applicability of this approach to fractured reservoirs. Moreover we show how to include the effect of anisotropy in the universal curves in order to assess uncertainty in anisotropic reservoirs. IntroductionThere are many oil and gas reservoirs throughout the world that are naturally fractured or will be fractured during development process. Fractured reservoirs are by nature extremely complex, containing geological features on all length scales from micron to tens of metres. These heterogeneities affect all aspects of the flow behaviour and have to be modelled to make reliable prediction of reservoir performance. However, we have very few direct measurements of the flow properties (e.g., core and image-log data) which are 1D and represent a volume of 10 -13 of a typical reservoir. Other type of data are more widespread (e.g., well test and seismic data) but generally are related indirectly to fracture distribution. So there is a great deal of uncertainty about the spatial distribution of the features which influence the flow. A major factor in analysis of flow and transport in these reservoirs is the appropriate representation of the heterogeneities that control flow.The conventional approach in flow modeling is to build a detailed reservoir model using geophysi...

Facies Connectivity Modelling: Analysis and Field Study

“…Well configurations, pressure variations and relative permeability effects can be matter of interest for further works. The extension of this work for fracture networks (line segments) is under a current research and achieved good results 23,24 . …”

A correlated fracture network: Modeling and percolation properties

“…Around p c ∞ typical cluster size is comparable to the system size (i.e., ξ ∼ L ). Using this along with the previously stated scaling for the correlation length ξ ( p ) and the mean connected fraction P ( p ) of infinite systems lead to the following scaling transformation for finite size systems [ Stauffer and Aharony , 1992], Although the above scaling laws are derived for the region close to the threshold, the previously obtained numerical results [ Berkowitz , 1995; Masihi et al , 2005] have shown that the data collapse achieved for a relatively wide range of occupancy probabilities except p close to unity. Hence different mean connectivity curves are collapsed onto a single curve called universal mean connectivity curve and different standard deviation of connectivity curves is collapsed onto a single curve ℜ called universal standard deviation of connectivity curve.…”

“…Extensive studies have addressed the effects of fracture geometrical properties on the connectivity and percolation properties of fracture networks. In particular, the effects of fracture length [e.g., Charlaix et al , 1984; Berkowitz , 1995; Bour and Davy , 1997; Mourzenko et al , 2005; Masihi et al , 2006] and orientation distribution [e.g., Robinson , 1984; Balberg et al , 1984; Masihi et al , 2005] on the scaling laws of the connectivity have been investigated. However, there has been little investigation on the spatial correlation of fractures which mainly concentrated on the long‐range fracture density correlations modeled by fractal geometry [ Berkowitz et al , 2000; Darcel et al , 2003b].…”

Generation of spatially correlated fracture models for seismic simulations

“…We will therefore assume that the fractures extend from top to bottom of the layer and that the figure represents a cross‐section at an arbitrary depth within that layer. The SA procedure determining the locations and orientations of the fractures thus ignores this thickness, which in principle could be taken into account with a significant increase in computational time (Masihi et al 2007). However, as long as the reservoir thickness is relatively small compared to the lateral distances in the model, variations in depth will not have a major affect on the energy in and can be ignored.…”