History Matching of Naturally Fractured Reservoirs Using Elastic Stress Simulation and Probability Perturbation Method
Authors: Suzuki Satomi , Daly Colin , Caers Jef Karel , Mueller Dietmar 
Published: March 2007

Summary
The application of elastic stress simulation for fracture modeling provides a more realistic description of fracture distribution than conventional statistical and geostatistical techniques, allowing the integration of geomechanical data and models into reservoir characterization. The geomechanical prediction of the fracture distribution accounts for the propagation of fracture caused by stress perturbation associated with faults. However, the challenge lies in estimating the past remote stress conditions which induced structural deformation and fracturing, the limited applicability of the elasticity assumption, and the latent uncertainty in the structural geometry of faults. The integration of historical production data and well-test permeability into geomechanical fracture modeling is a practical way to reduce such uncertainty. We propose to combine geostatistical algorithms for history matching with geomechanical elastic simulation models for developing an integrated yet efficient fracture modeling tool.
This paper presents an integrated approach to history matching of naturally fractured reservoirs which includes (1) fracture trend prediction through elastic stress simulation; (2) geostatistical population of fracture density based on a fracture trend model; (3) fracture permeability modeling integrating fracture density, matrix permeability and well-test permeability; and (4) numerical flow simulation and history matching. All of these implementations are incorporated into a single forward modeling process and iterated in the automatic history-matching scheme. To obtain a history match on a reservoir model, we jointly perturb the large-scale fracture trend and local-scale geostatistical fluctuations of fracture densities rather than perturbing permeability calibrated from fractures. This strategy enables us to preserve the geological/geomechanical consistency throughout the history-matching process. The geomechanically simulated fracture trend model is calibrated to both production data and the reservoir geological structure (faults and horizons) by searching for the optimum remote stress condition for elastic stress-field simulation. The latter is achieved by matching the actually observed structural deformation with the simulated one. The smaller-scale fluctuation of fracture density is simultaneously history matched through the probability perturbation method of Caers (Caers 2003; Hoffman and Caers 2005; Caers 2007). The methodology is presented on a synthetic reservoir application.

Introduction
The modeling of the density and pattern of fracture distributions can take different approaches depending on the origin and the type of fracture sets and on the ultimate reservoir engineering questions raised. In this paper, we focus on the modeling of shear fractures which are generated by structural deformation accompanied with fault slip. Recently, an application of the elastic stress simulation has been proposed for predicting the pattern of shear/tensile fractures or the pattern of secondary faults and shown promising results (Bourne and Willemse 2001; Maerten et al. 2002; Bourne et al. 2001). The elastic simulation numerically simulates the structural deformation of the reservoir by solving linear elasticity equations under given boundary conditions, and simultaneously calculates the corresponding stress/strain tensor fields (Bourne and Willemse 2001; Maerten et al. 2002; Bourne et al. 2001; Daly and Mueller 2004; Roxar FracPerm Reference Manual 2005). The boundary conditions consist of (1) location/geometry of fault surface, (2) stress conditions or displacement conditions on the fault surfaces, and (3) the remote loads applied to the structure at the time of structural deformation accompanied with fault slippage. First, satisfying boundary conditions and by minimizing strain energy, the linear elastic equations are solved to obtain a structural deformation field which is expressed by the displacement vector. Next, strain field is computed from the displacement gradient based on the definition of strain. Finally, under the assumption of elasticity, stress is calculated from strain by means of Hook's law.