Hierarchical Object-Based Geostatistical Modeling of Fluvial Reservoirs
Authors: Deutsch C.V. , Wang L. 
Published: December 2007

Abstract
This paper presents a novel approach to modeling braided stream fluvial reservoirs. The approach is based on a hierarchical set of coordinate transformations involving relative stratigraphic coordinates, translations, rotations, and straightening functions. The emphasis is placed on geologically-sound geometric concepts and realistically attainable conditioning statistics including areal and vertical facies proportions. The equations for the eight-fold coordinate transformation, a new analytical channel cross section shape, and a real example with 20 wells are presented.

Introduction
A characteristic feature of many fluvial reservoirs is the presence of sinuous sand-filled channels within a background of floodplain shale. Techniques for realistically modeling the spatial distribution of channels are necessary for reliable volumetrics connectivity assessment, and input to flow simulation. The approach presented here is applicable to stochastic modeling channel shapes and filling those shapes with porosity and permeability.
Modeling proceeds sequentially. Each major stratigraphic layer is modeled independently. The channel complex distribution, within a layer-specific stratigraphic coordinate system, is established first. Then, within each channel complex, the distribution of individual channels is simulated using appropriate transformed coordinate systems. This process is repeated down the hierarchy of geological units until the desired level of detail has been achieved. Finally, at the last coordinate system, petrophysical properties such as porosity and permeability are simulated with cell-based geostatistical algorithms within each facies.
This paper addresses the stochastic modeling of channel complexes and channels within a major reservoir layer. Multiple reservoir layers would be successively modeled and combined in a single reservoir model for volumetrics and flow simulation. At a higher level of iteration, multiple stochastic reservoir models could be constructed for assessing uncertainty.
An important feature of any approach to reservoir modeling is data conditioning. The data considered in this paper include lithofacies, porosity, and permeability data from wells, size and shape parameters of channel complexes, size and shape parameters of individual channels, vertical facies proportion curves, and areal facies proportion maps.
The approach presented in this paper has been inspired by the clear geometries observed at outcrops and as viewed from airplane windows in modern fluvial settings. There are similar object-based approaches documented in the literature. The approach adopted here is distinct from conventional object-based fluvial reservoir modeling in a number of ways,the use of an explicit reversable hierarchy of coordinate transformations that is keyed to sound sequence stratigraphic concepts,geologically-intuitive and accessible input data controlling channel sizes and shapes,explicit control over vertically varying and areally varying facies proportions,realistic asymmetric channel geometries,realistic non-undulating channel top surfaces, andintegrated porosity and permeability models where the main directions of continuity conform to channel geometries.
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