3-D Stochastic Reservoir Modeling Constrained by Well and Seismic Data on a Turbidite Field
Authors: Johann P. , Fournier F. , Souza O. , Eschard R. , Beucher H. 
Published: December 2007

P. Johann,^ Petrobras S.A.; F. Fournier, SPE, Institut Francais du Petrole; O. Souza Jr., Petrobras S.A.; R. Eschard, Institut Francais du Petrole; H. Beucher, Centre de Geostatistique de l'Ecole Nationale Superieure des Mines de Paris.

Abstract
A new methodology for 3-D stochastic reservoir modeling constrained by well and seismic data is applied to a pilot area, the Namorado turbidite giant oil field in the Campos basin. The stochastic modeling is based on a truncated Gaussian approach, with a non stationary algorithm using a 3-D matrix of lithotype proportions. The proportion matrix can he constrained by qualitative or quantitative seismic derived information. Qualitative information corresponds to vertical proportion curves, predicted at the trace locations, from seismic facies analysis. Quantitative information are estimates of lithotype thicknesses, over all the reservoir section, derived from calibration of seismic attributes. Whatever type of seismic constraints -qualitative or quantitative- their incorporation in the reservoir modeling led to a major improvement of reservoir heterogeneity representation, in the case of the Namorado field. The methodology is thus promising for other fields, particularly in turbidite environment.

Introduction
Reservoir stochastic modeling provides a good frame for integrating data of different sources and qualities. It leads to a more realistic 3-D reservoir image associated with risk assessment through an improved uncertainty representation. Well logs and core data provide detailed information about vertical variations of many reservoirs properties but they are restricted to regions adjacent to the borehole. Conversely, 3-D seismic data offer a dense coverage of the interwell areas and therefore should play a key role in describing reservoir heterogeneities. However, the integration of seismic data in reservoir stochastic models is still a challenge. Most of the time, the reservoir is described as a high resolution 3-D model of lithotypes and/or petrophysical properties, in which seismic information has to be incorporated. The difficulties for this incorporation are due to very different measurement scale for seismic and well information, and to often complex and non unique relationship between the useful reservoir properties and the acoustic or elastic parameters. Therefore, a direct incorporation of seismic information (amplitudes, acoustic impedances…) in the stochastic modeling is possible only in a limited number of cases, corresponding to simple (homogeneous) reservoirs. Unfortunately, it is not the frame of nearly homogeneous reservoirs for which seismic data is so crucial for bringing extra information between wells, since very small geological variations are expected in this case. In this paper, a conservative approach for integration of seismic in 3-D stochastic modeling is proposed. The key point is to break the problem in two steps. Firstly, the seismic information is turned into average geological information, directly related to the modeling process. Secondly, this information is accounted as global and soft constraints in the modeling. This approach allows to overcome both difficulties of scale and indirect relationship between seismic data and reservoir properties to simulate.
Two possibilities are proposed for extracting the soft geological information contained in the seismic data. The first one, based on seismic facies analysis, provides a qualitative interpretation of the reservoir interval in terms of geological behavior. The second one uses statistical calibration techniques to derive estimates on average reservoir properties (quantitative information). Both kind of information -qualitative and quantitative- are integrated in the 3-D modeling of lithotypes using a non stationary truncated Gaussian approach (Figure 1). P. 51