Investigating the impact of geological uncertainty (i.e., spatial distribution of fractures) on reservoir performance may aid management decisions. The conventional approach to address this is to build a number of possible reservoir models, upscale them, and then run flow simulations. The problem with this approach is that it is computationally very expensive. In this study, we use another approach based on the permeability contrasts that control the flow, called percolation approach. This assumes that the permeability disorder of a rock can be simplified to either permeable or impermeable. The advantage is that by using some universal laws from percolation theory, the effect of the complex geometry which influences the global properties (e.g., connectivity or conductivity) can be easily estimated in a fraction of a second on a spreadsheet.The aim of this contribution is to establish the percolation framework to examine the connectivity of fracture systems at a given finite observation scale in 2D and 3D. In particular, we use numerical simulation to show how the scaling laws of the connectivity derived originally for constant-length isotropic systems can be expanded to cover more realistic cases including fracture systems with anisotropy and fracture-length distribution. Finally, the outcrop data of mineralized fractures exposed on the southern margin of the Bristol Channel Basin was used to show that the predictions from the percolation approach are in agreement with the results calculated from field data but can be obtained very quickly. As a result, this may be used for practical engineering purposes for decision making.

Summary Uncertainty in geometrical properties of fractures, when they are considered as the conductive paths for flow movement, affects all aspects of flow in fractured reservoirs. The connectivity of fractures, embedded in low-permeability zones, can control fluid movement and influence field performance. This can be analyzed using percolation theory. This approach uses the hypothesis that the permeability map can be split into either permeable (i.e., fracture) or impermeable (i.e., matrix) portions and assumes that the connectivity of fractures controls the flow. The analysis of the connectivity based on finite-size scaling assumes that fractures all have the same sizes. However, natural fracture networks involve a relatively wide range of fracture lengths, modeled by either scale-limited laws (e.g., log normal) or power laws. In this paper, we extend the applicability of the percolation approach to a system with a distribution of size. For scale-limited distributions, we use the hypothesis seen in the literature that the connectivity of fractures of variable size is identical to the connectivity of fractures of the same size whose length is given by an appropriate effective length. It is then necessary to define the percolation probability based on the excluded area arguments. In this research work, we also validate the applicability of this idea to fracture networks having a uniform, Gaussian, exponential, and log-normal length distribution. However, in the case of the power-law length distribution, we have found that the scaling parameters (e.g., correlation length exponent) have to be modified. The main contribution is to show how the critical exponents vary as a function of the power-law exponent. To validate the approach, we used outcrop data of mineralized fractures (vein sets) exposed on the southern margin of the Bristol Channel basin. We show that the predictions from the percolation approach are in good agreement with the results calculated from field data with the advantage that they can be obtained very quickly. As a result, they may be used for practical engineering purposes and may aid decision-making for real field problem. Introduction Many hydrocarbon reservoirs are naturally fractured. The conventional approach to investigate the impact of geological uncertainties on reservoir performance is to build a detailed reservoir model using available geophysical and geological data, upscale it, and then perform flow simulation. In fractured reservoirs, this can be done by using equivalent continuum models (i.e., dual porosity), discrete network models, or a combination of both [see Warren and Root (1963), Quenes and Hartley (2000), and Dershowitz et al. (2000)]. The nature of fluid flow in fractured reservoirs of low matrix permeability depends strongly on the spatial distribution of the conductive natural fractures. We use the term "fracture" to mean any discontinuity within a rock mass that developed as a response to stress. Fractures exist on various length scales from microns to kilometres. They appear as tensile (e.g., joints or veins) or shear (e.g., faults) and can act as hydraulic conductors or barriers to flow movement. Conductive fractures may be connected in a complicated manner to form a complex network. The connectivity of such networks is a crucial parameter in controlling flow movement, which in turn depends on the geometrical properties of the network such as fracture orientation, spacing, or length distribution.

We investigate the effects of anisotropy on finite-size scaling of site percolation in two dimensions. We consider a lattice of size n(x) x n(y). We define an aspect ratio omega=n(x)/n(y) and consider the mean connected fraction P (averaged over the realizations) as a function of the site occupancy probability (p), the system size (n(x)), and this aspect ratio. It is clear that there is an easy direction for percolation, which is in the short direction (i.e., y if omega>1) and a difficult direction which is along the long axis. We define an apparent percolation threshold in each direction as the value of p when 50% of realizations connect in that direction. We show that standard finite-size scaling applies if we use this apparent threshold. We also find a finite-size scaling for the fluctuations about this mean connected fraction.

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...

This paper presents the analyses of well tests and production logging carried out on three multi-fractured horizontal wells in the Babbage tight gas field, UK Southern North Sea. The actual performance observed in these wells was compared to the forecasts made based on open-hole well data and the data gathered during hydraulic fracturing operations. Some of the drawbacks in analysing well test data are discussed along with the uncertainties in modelling hydraulic fractures. Horizontal wells with multiple hydraulic fractures are used to increase productivity and recovery in tight reservoirs. Understanding and predicting fracture performance is essential to the field commerciality considering the associated high development costs, especially in the North Sea.The results of this study indicate that based on several pressure transient analyses, the clean-up time can be up to several months, which was observed in the form of gradual skin reduction over time. The PLT data also confirmed that there is cross flow during the shut in periods, usually flowing from the outer fractures into the inner fractures. This was believed to have an impact on the interpretation of the build-ups. Moreover it was shown that during build-up tests of more than 500 hours, linear flow was the dominant flow regime and therefore the final radial flow stabilization had not yet been reached.There are many studies in the literature on the design, operations, characterization and numerical modelling of similar multifractured horizontal wells. However there are not many publications presenting real field data and the performance of these wells. This paper covers the well performance data in addition to the design, modelling and operations of the multi-fractured horizontal wells.