Constraining Reservoir Facies Models to Dynamic Data - Impact of Spatial Distribution Uncertainty on Production Forecasts

This paper presents a new approach to constrain reservoir facies models to dynamic data. This approach is mainly based on the combination of an optimization method called the simplex method and parameterization techniques such as the gradual deformation method. This parameterization technique is well known for its efficiency in constraining geostatistical models to dynamic data. Originaly developped for continuous Gaussian models, the gradual deformation method was extended to facies models [12] and more recently to any kind of geostatistical model. However, the numerical behavior of the inversion can be strongly affected by discontinuities in the model changes in case of facies-based models. Our approach proposes a robust inversion method coupled with the gradual deformation method for the calibration of facies models. The methodology we present is directly inspired by the construction of a reservoir facies model. We start by generating a related Gaussian continuous geostatistical model. In a second phase this continuous model is transformed according to the number of facies and their proportions to obtain a consistent facies model. Since a direct parameterization of the facies model does not allow the preservation of the geological properties of the model, we perform the parameterization on the related continuous model and then we proceed to the model truncation. In this manner, we can optimize the deformation parameters involved in the parameterization using the simplex method to obtain an history match. The efficiency of this approach is illustrated by matching an interference test. The parameterization phase was performed using the gradual deformation method. Constrained facies models were thus obtained. A second phase of this study was devoted to quantifying the impact of uncertainty of spatial facies distribution on production forecasts. In an integrated process, we combine the simplex approach with experimental design theory and the joint modeling technique to achieve a probabilistic production forecast which takes into account the uncertainty on spatial facies distribution and classical reservoir parameters while preserving the history match. This application demonstrates the importance of the interference test matching in reducing the uncertainties on production forecasts. Introduction The quantification of uncertainties on production forecasts is a crucial goal for taking decision in a risk prone environment. Reservoir model characterization becomes one of the most important phase in a reservoir study. All available data should be integrated into the model to provide a more realistic description of the reservoir in order to reduce uncertainties and obtain reliable production forecasts. Geostatistical simulation is currently widely used to give a realistic reservoir description. Although geostatistics is clearly well suited to model geological information, it leads to an uncertain framework since the geostatistical model properties make it possible to produce not one geological model but a set of equiprobable realizations of the geological model. Use of geostatistical models leads then clearly to an important problematic: the integration of available dynamic data while quantifying the uncertainty on production forecasts due to this geostatistical modeling. The task of constraining reservoir facies models is a hard problem since it requires dealing with two main difficulties: to find an accurate optimization method that minimizes the objective function which represents the mismatch beetween the dynamic data and the simulated values of the pressure or of the production, to find an efficient parameterization method which allows to have a precise description of the facies model while keeping the number of involved parameters as small as possible to ensure a reasonable cost for the matching phase. SPE 71335 Constraining Reservoir Facies Models to Dynamic Data Impact of Spatial Distribution Uncertainty on Production Forecasts I. Zabalza-Mezghani, IFP, M. Mezghani, IFP, G. Blanc, IFP 2 I. ZABALZA-MEZGHANI, M. MEZGHANI, G. BLANC SPE 71335 This work presents a new approach for constraining reservoir facies model to dynamic data while quantifying the uncertainty on production forecasts. We suggest the use of the simplex method as an optimization technique since it is well suited to the particular form of the objective function, and the use of the gradual deformation method to parameterize the reservoir facies models. The quantification of uncertainty on production forecasts is performed using experimental design theory. More precisely, we illustrate our approach with a field case, where we decide to test a water injection scheme. In an integrated process which mixes gradual deformation, simplex method, experimental design and the joint modeling method, we show that the integration of interference test data on reservoir facies models is crucial since it allows an important dicrease of the uncertainties on the expected recovery factor. Constraining Reservoir Facies Models The objective here is to constrain a reservoir facies model to dynamic data. This consists in finding the model which best fits the dynamic data. To find this model, a classical procedure consists in building and then minimizing an objective function which quantifies the mismatch between the simulated results and the dynamic data. Thus, the reservoir facies model is updated until finding the one that satisfies the data. This update needs to be able to describe the reservoir facies model with a few set of parameters: it is the goal of the parameterization phase. Before presenting the parameterization we used: the gradual deformation method, we explain the main principle of a reservoir facies model simulation. Reservoir Facies Model Simulation. The simulation of a reservoir facies model relies on the simulation of a gaussian white noise. Thus, this white noise is transformed in categories or facies according to a given variogram, a number of facies, facies volume fractions, correlation lengths to obtain a reservoir facies model. Facies models can be obtained using either truncated Gaussian simulations [13] or sequential indicator simulation [14]. In both cases, the gradual deformation method must be performed on the Gaussian white noise, before the transformation. As an example, we illustrate on figure 1 the principle of the truncated Gaussian simulation. The parameterization:The Gradual Deformation Method. The basic principle of the gradual deformation [4][9][10] method is to generate a process of realizations which evolve smoothly at each step. This can be achieved by introducing a correlation between a new realization and the realization obtained at the previous step. To apply this principle to continuous geostatistical models, the gradual deformation method propose to generate new realizations as linear combinations of any number of independent initial realizations. Then, if we note {Z1, . , Zn} a set of n independent realizations of a Gaussian random field, a new realization can be expressed as follows: ∑