Geostatistical Reservoir Modeling Accounting for Precision and Scale of Seismic Data
Authors: Deutsch C.V. , Srinivasan S. , Mo Y. 
Published: December 2007

Abstract
An approach to model the detailed 3-D distribution of lithofacies and porosity constrained to seismic data is presented. The simulated annealing-based approach explicitly honors the relatively coarse vertical resolution, from a reservoir modeling perspective, and the less than perfect correlation of seismic with lithofacies proportions and effective porosity. Conventional geostatistical procedures such as co-located cokriging or the Markov-Bayes model assume that the seismic attribute has the same volumetric support as the geological modeling cells. The conventional techniques are reviewed, details of the proposed methodology are presented, and a reservoir case study is shown.

Introduction
Due to geological complications and inherent limitations in seismic data acquisition, seismic inexactly measures lithofacies proportions and average porosity. Typically, the seismic-derived lithofacies proportion and porosity may be correlated with the true values with a correlation of 0.5 to 0.7. The specific seismic attribute and degree of correlation must be calibrated for each reservoir. Geostatistical techniques to integrate seismic data must account for this precision.
Another consideration, when using seismic data, is that seismic-derived proportions and porosity represent a volume significantly larger than the typical geological modeling cell. The areal resolution is often comparable. The vertical resolution; however, is 10 to 100 times the resolution of the geological modeling cells. Current geostatistical models are built at a vertical resolution of 1-3 feet and current seismic data informs a 30-100 foot vertical average. The detailed resolution of geostatistical models is considered necessary to transfer the effect of heterogeneities into flow simulators.
There is a need for geostatistical modeling tools to explicitly account for the precision and scale of seismic data. Most conventional geostatistical techniques account for the precision of the seismic data by treating it as soft or secondary data. At times, the seismic data is considered to represent an arithmetic volume average of the lithofacies indicator or the porosity. A review of conventional geostatistical techniques will show that they do not simultaneously handle the precision and scale of seismic data.
An approach will be proposed based on an extension of the simulated-annealing approach to geostatistical model construction. An objective function is constructed that constrains the model to the seismic data accounting for both the predefined precision and scale of the seismic data.
An example from a West Texas Permian Basin reservoir is developed to demonstrate the practical applicability of the proposed approach. The 3-D distribution of porosity is constrained to a seismic attribute representing an imprecise (= 0.5) 50-foot vertical average.
In an increasing number of cases, seismic data or hand-drawn geological trend maps are available and we want to build them into detailed 3-D geostatistical models. The methodology proposed in this paper is suited to those situations.
The importance of simultaneously accounting for the precision and scale of seismic data could only be assessed by a number of comparative reservoir case studies. These comparative studies are considered important but are not included in this paper. For the time being we must argue that better reservoir models are obtained when they are constrained to the maximum amount of data properly accounting for the precision and scale of each data source.
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