3-D Stochastic Reservoir Modeling: A Non Stationary Approach Guided by Seismic Data
Authors: Johann P. , Fournier F. , Souza O. , Doligez B. 
Published: December 2007

Abstract
A new methodology for 3-D stochastic reservoir modeling with a non stationary approach guided by seismic data is applied to a pilot area, the Namorado 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 construction of the 3-D proportion matrix is done by two approaches: by zone or by cell. In the reservoir zonation approach the 3-D proportion matrix is defined by zone from a seismic pattern recognition technique (seismic facies). The approach by cell uses a 3-D proportion matrix defined by cells from a lithotype proportions prediction method. This prediction use a statistical calibration technique of seismic attributes in terms of vertical lithotype proportion curves from typical wells selected for a training data set. Whatever type of seismic derived constraints - seismic facies or lithotype proportions - their incorporation in the reservoir modeling led to a major improvement of reservoir heterogeneities representation and a reduction in the uncertainties of the reservoir model.

Introduction
The integration of 3-D seismic data in reservoir stochastic models provide a more realistic 3-D reservoir image associated with risk assessment through an improved uncertainty representation. 3-D seismic data offer a dense coverage from the interwell areas; however, their integration in reservoir stochastic models is still a challenge. The difficulties for this integration include different measurement scales and domains of measurements for seismic and well information, and also the often complex and non-unique relationship between the useful reservoir properties and the acoustic or elastic attributes. The methodology described in this paper allows to overcome these difficulties of scale, domain and indirect relationship between seismic data and reservoir properties for simulation (Figure 1). The problem of integration 3-D seismic data in stochastic reservoir modeling is break in two steps:the seismic information is turned into average geological information, directly related to the modeling process;this information is accounted as global and soft constraints in the modeling.

Principles of the methodology
The non stationary approach guided by seismic facies. Tridimensional seismic data offer a dense coverage from the interwell. areas, however, the integration of seismic information in terms of reservoir properties is a complex task. In this paper the seismic facies analysis allows the extraction of zonation of reservoir properties. This zonation is used for the regionalization of lithotype vertical proportion curves for each reservoir stratigraphic unit. The general idea is to analyze the morphology of seismic trace after seismic stratigraphic inversion and interpretation at reservoir level for each stratigraphic unit of reservoir (Figure 2). This morphology is analyzed in connection with the main geological variations. This is done using statistical seismic pattern recognition techniques. The methodology of statistical seismic pattern recognition involves:the characterization of the portions of traces under analysis by a set of seismic attributes;multivariate statistical techniques to cluster the traces in the attribute space.
These groups of traces correspond to different seismic facies. Conversely to standard attribute studies, this approach is multivariate. In this methodology two approaches were used: unsupervised and supervised. The unsupervised approach uses the statistically common characteristics of underlying seismic trace attributes at each stratigraphic unit. This approach is interesting to detect seismic facies related to reservoir behavior in horizons not yet drilled, or seismic facies not related to the geological variations within the reservoir (e.g. variations in overburden, or even to seismic acquisition or processing artifacts). Non supervised facies analysis is also still possible with very limited well control.