Turbidite reservoir characterization : object-based stochastic simulation meandering channels
Authors: Viseur Sophie 
Published: June 2005

Abstract
Stochastic imaging has become an important tool for risk assessment and has successfully been applied to oil field management. This procedure aims at generating several possible and equiprobable 3D models of subsurface structures that enhance the available data set. Among these stochastic simulation techniques, object-based approaches consist of defining and distributing objects reproducing underground geobodies.
A technical challenge still remains in object-based simulation. Due to advances in deep water drilling technology, new hydrocarbon exploration has been opened along the Atlantic margins. In these turbidite oil fields, segments of meandering channels can be observed on high-resolution seismic horizons. However, no present object-based simulation technique can reproduce exactly such known segments of channel. An improved object-based approach is proposed to simulate meandering turbidite channels conditioned on well observations and such seismic data.
The only approaches dealing with meandering channels are process-based as opposed to structure-imitating. They are based on the reproduction of continental river evolution through time. Unfortunately, such process-based approaches cannot be used for stochastic imaging as they are based on equations reflecting meandering river processes and not turbiditic phenomena. Moreover, they incoporate neither shape constraints (such as channel dimensions and sinuosity) nor location constraints, such as well data. Last, these methods generally require hydraulic parameters that are not available from oil field study.
The proposed approach aims at stochastically generating meandering channels with specified geometry that can be constrained to pass through well-observations. The method relies on the definition of geometrical parameters that characterize the shape of the expected channels such as dimensions, directions and sinuosity. The meandering channel object is modelled via a flexible parametric shape. The object is defined by a polygonal center-line (called backbone) that supports several sections. Channel sinuosity and local channel profiles are controlled by the backbone and, respectively the sections. Channel generation is performed within a 2D domain, D representing the channel-belt area.
The proposed approach proceeds in two main steps. The first step consists in generating a channel center-line (C) defined by an equation v=Z(u) within the domain D. The geometry of this line is simulated using a geostatistical simulation technique that allows the generation of controlled but irregular center-lines conditioned on data points.
During the second step, a vector field enabling the curve (C) to be transformed into a meandering curve (C’) is estimated. This vector field acts as a transform that specifies the third degree of channel sinuosity, in other words, the meandering parts of the loops. This field is parameterized by geometrical parameters such as curvature and tangent vectors along the curve (C) and the a priori maximum amplitude of the meander loops of the curve (C’). To make channel objects pass through conditioning points, adjustment vectors are computed at these locations and are interpolated along the curves.
Synthetic datasets have been built to check if a priori parameters such as tortuosity are reproduced, and if the simulations are equiprobable. From this dataset, hundred simulations have been generated and enable one to verify that these two conditions are satisfied. Equiprobability is however not always satisfied from data points that are very close and located in a multivalued part of a meander : preferential orientation of the loops may indeed be observed. Solving this issue will be the focus of future works. Nevertheless, the results presented in this paper show that the approach provides satisfying simulations in any other configurations. This approach is moreover well-suited for petroleum reservoir characterization because it only needs specification of geometrical parameters such as dimension and sinuosity that can be inferred from the channel parts seen on seismic horizons or analogues.