History Matching of a Stochastic Model of Field-Scale Fractures: Methodology and Case Study

History matching of a stochastic model of field-scale fractures: methodology and case study — This paper focuses on the history matching of stochastic models of large-scale fractures under seismic resolution, namely sub-seismic faults and fracture swarms. First, we propose an object-based stochastic model for describing geological features of large-scale fractures. This model accounts for static constraints derived from seismic attributes, fault-related-strain-field, structural information (curvature), etc. Second, we review an upscaling procedure for performing fluid flow simulation in the presence of networks of large-scale fractures. Third, we present an algorithm for gradually moving and deforming Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 2, pp. 265-276 Copyright © 2007, Institut français du pétrole DOI : 10.2516/ogst:2007022 Quantitative Methods in Reservoir Characterization Méthodes quantitatives de caractérisation des réservoirs IFP International Conference Rencontres Scientifiques de l’IFP Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 2 INTRODUCTION Fractures radically affect sub-surface fluid flow and can act as preferential flow paths if they remain open after their formation or as flow barriers if they are sealed by impervious material. The unexpected production behavior of many fields (early water breakthrough, compartmentalization, dual permeability effects, etc.), arising from an insufficient consideration of fracture effects on flow, emphasizes the need for better characterizing the distribution of fractures at various scales and transferring the meaningful part of this information into field flow simulation models. During the last decade, tremendous advances have been made in the modeling of fractured reservoirs, both with respect to geological characterization and fluid flow simulation. Modern geological modeling of fracture networks [1, 2], based on a fractal or stochastic approach, is able to integrate local data from well-bore imaging and field scale data derived from seismic attributes, fault-related-strain-field, structural information (curvature), etc. These geological (static) models of fracture networks can now be turned into flow models for well-test simulation or full-field simulation, through practical upscaling solutions [3, 4]. Constraining these models to hydrodynamic data from well-tests and production history is the natural next step in the development of an effective modeling methodology for fractured reservoirs. Natural fracturing is a typical multi-scale phenomenon. Considering the impact of fractures on fluid flow, reservoir engineers generally classify fractures of different scales into two major classes: large-scale fractures cross-cutting the reservoir and small-scale fractures preferentially located in given reservoir layers. Small-scale fractures can be homogenized into a geo-cellular model while large-scale fractures must be directly taken into account in flow simulations. This paper focuses on large-scale fractures. On the basis of existing methods for geological modeling [2], fluid flow simulation [5] and deformation of object-based stochastic model [6], we propose an integrated methodology for history matching of stochastic models of large-scale fracture networks to production data. This methodology is applied to a North Africa Field and the results are presented. 1 GEOLOGICAL MODELING OF LARGE-SCALE FRACTURES The methodology for geological modeling of fracture networks is extensively described by Cacas et al. [2] and Bourbiaux et al. [7]. Large-scale fractures include faults above seismic resolution, sub-seismic faults or clustered joints of large vertical extent, called fracture swarms. These fractures are split into different sets according to specified geometrical properties such as orientation or spacing, in relation with past tectonic episodes. All fracture sets are described separately and then merged into a global model that incorporates: – a deterministic description of large-scale faults above seismic resolution, – a stochastic description of other faults and fractures under seismic resolution, namely sub-seismic faults or fracture swarms. We consider stochastic vertical fractures that cross the entire reservoir. The information for constraining each stochastic fracture set consists of: – an orientation map based on seismic fault information and well data. This map allows to model spatial variation of fracture orientation; – statistical parameters related to the distribution function of fracture lengths, which is inferred from fault analysis; – fracture density map (or probability map of fracture occurrence) derived from geological, geomecanical and seismic information known over the entire field (seismic attributes, fault-related strain field, structural information such as curvature intensity map etc). The methodology for building such a map can be found, for instance, in Gauthier et al. [8]. This map controls both the location and the extension of stochastic fractures. Fractures of a given fracture set are generated sequentially in three steps. For each fracture, – first we randomly generate its location (fracture seed) according to a Poisson point pattern (process) with a regionalized intensity [9], which is proportional to the fracture density map; – second, its length is drawn from the fracture length distribution; 266 stochastic fractures in the reservoir field while preserving their consistency with static constraints (location of seismic fractures, fracture density and orientation maps), whereby different realizations of the stochastic fracture network can be obtained. All these elements are integrated in an inverse procedure for calibrating stochastic models of large-scale fracture networks to hydrodynamic two-phase flow data. The above methodology is applied to an actual fractured reservoir. We build a field-scale fracture network constrained to the fracture density map and the orientations of the two fracture sets. Then we perform history matching of water-cut data in four zones of the field. Different calibration procedures are tested: global optimization that allows a general improvement of the model calibration to production data, and local calibration that further improves the match of each well. The results show the validity of the proposed methodology. S Jenni et al. / History Matching of a Stochastic Model of Field-Scale Fractures: Methodology and Case Study – third, we propagate the fracture, from the seed, under geological constraints. A fracture growth process conditioned to the fracture orientation map governs the incremental propagation of a broken line away from the fracture seed. The growth process is continued until the fracture length is reached. The fracture propagation is also constrained to the fracture density map. Once a fracture is generated, the density map is updated in the neighborhood of the fracture to account for fracture interactions (repulsive behavior of large faults, clustering, etc.). Following the above algorithm, we can build realistic stochastic fracture networks constrained to geological (static) data. Figure 1 shows an example of such network. There are two independent fracture sets, one oriented around N120-130 and the other around N170. They are constrained by the fracture density map shown in the same figure. The next step is to calibrate such stochastic fracture network to production history. 2 FLUID FLOW SIMULATION History matching applications need an accurate representation of fracture networks in fluid flow simulation models. For instance, a small difference of fracture locations can result in connecting or disconnecting flow paths between the wells and thus highly affecting the hydrodynamic behavior of the reservoir model. In the present methodology for history matching, we use a conventional dual porosity simulator with an upscaling procedure that does not mixture large-scale fractures with the matrix medium and the small-scale fractures (smaller than the cell size of the fluid flow simulation grid). This approach for fluid flow simulation was successfully applied to a giant Middle East oil field with large-scale fractures [5]. 267 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0