History Matching of Object-Based Stochastic Reservoir Models

Object-based models can be regarded as arrangements of a population of geometrical objects in space. In reservoir modeling, these models are often used for describing meandering channel systems, fracture networks etc., where geological objects can be clearly identified. Unlike pixelbased models, object-based models can provide geologically realistic representations of reservoir heterogeneities even at the appraisal stage with few well data. Although an extensive literature on object-based models is available, little has been done for constraining these models to dynamic data (history matching). This is however of great importance for their application in reservoir engineering. This paper first reviews the basic concepts of the widely used object-based Boolean model. Then, we present a methodology for calibrating Boolean simulations to dynamic production data. This methodology is based on a generalization of the gradual deformation method that was initially developed for calibrating pixel-based Gaussianrelated reservoir models to dynamic data. Finally, a simple synthetic example is presented and the results show the validity of the above methodology. In particular, this methodology is potentially applicable to history matching of fractured reservoir models. Introduction In the last two decades, different stochastic models have been developed for describing reservoir heterogeneities of different depositional environments and at different scales. These models can be classified in three types: pixel-based models (e.g., Gaussian-related stochastic models), object-based models (e.g., Boolean models) and process-based models. Pixel-based models are relatively easy to be constrained by quantitative data but they are often unable to describe complex geological features, particularly at the field appraisal stage with few well data. On the contrary, process-based models can reproduce complex geological features but they are highly difficult to be constrained by quantitative data. In the case where geological objects can be clearly identified (fractures, faults, channels, vacuoles etc.), object-based models can be a good compromise between pixel-based and process-based models. There are many examples of geological modeling of fluvial-deltaic reservoirs using the object-based approach. For fractured reservoirs, Cacas et al. developed a specific object-based model to represent fracture swarms and subseismic faults (Fig.1). However, little has been done for constraining these models to dynamic production data. This is however of great importance for their application in reservoir engineering. Constraining object-based models to production data requires the development of algorithms for the consistent deformation and migration of geometric/geological objects. In recent years, the gradual deformation method was developed for constraining pixel-based Gaussian-related stochastic models to production data. This method consists in iteratively optimizing combinations of independent realizations of a multi-Gaussian stochastic model until the constraints are satisfied. This method was successfully applied to several cases with data from synthetic and real oil fields. In this paper, we first review the basic concepts of the most widely used object-based Boolean model. Then, based on a generalization of the gradual deformation method to nonGaussian stochastic models, we develop algorithms for the gradual deformation of Boolean simulations, including nonstationary and conditional Boolean simulations. These algorithms are integrated in an inverse procedure for calibrating Boolean models to production data. Finally, a simple synthetic example is used to illustrate the applicability of this procedure. Object-Based Reservoir Models An object-based reservoir model can be regarded as an arrangement of a population of geological objects in the reservoir field. The spatial distribution of these objects is defined accounting for their interactions (attraction, repulsion, clustering etc.). A basic object-based model is the Boolean model that can be intuitively defined as the union of objects of identical natures. Object locations of the Boolean model are defined according to a Poisson point pattern with a constant intensity. Object shapes and sizes are independent from their locations. This model can be generalized by combining objects of different natures or/and by using a regionalized Poisson intensity. In addition, an algorithm was developed for conditioning Boolean simulations to well data. We review in SPE 81503 History Matching of Object-Based Stochastic Reservoir Models Lin Y. Hu, Institut Français du Pétrole