Methodology to Incorporate Geological Knowledge in Variogram Modeling

Abstract

Geological knowledge is an important ingredient in a successful reservoir characterization process. Geoscientists and engineers have used variogram extensively as the tool to quantify the spatial relationship of various attributes, e.g., facies/rock type, porosity, and permeability. Proper variogram modeling is a key factor to obtain a geologically-sound reservoir characterization model. This paper discusses the difficulty that is commonly encountered by many practitioners in modeling the variogram and proposes a way to incorporate geological knowledge as the soft information to improve variogram model. Common difficulty in variogram modeling is the calculation of horizontal variogram. The averaging technique that uses combination of geological knowledge and analogy in geophysical literature about frequency data analysis is implemented to solve the difficulty in calculating horizontal variogram. This technique has produced results that are agreeable with geology of the reservoir. The art of incorporating the geological knowledge in variogram modeling lies in the fact that geological knowledge is a qualitative measure whereas variogram is a quantitative measure. The methodology to combine these two measures presented in this paper is as follows. First, interpreting various geological aspects of the reservoir in detail. These include, but not limited to, the interpretations of geological environment, sequence stratigraphy, pore-space characteristics, iso-chores, iso-porosity and iso-permeability maps. From these interpretations, a summary table, that includes the major continuity direction, lateral extension and anisotropy index of each attribute, is prepared. Second, calculating experimental variogram using the Averaging Technique. Third, modeling the experimental variogram considering the information obtained from the first step. The procedure presented above has been implemented as a routine procedure in several reservoir characterization studies for both carbonate and sandstone reservoirs in the Middle East and in the USA. For illustration purposes, comparison of the realization results, taken from carbonate field study, between the model with variogram derived purely from the hard data, i.e., well log data, and the variogram derived from both hard and soft data, i.e., geological knowledge, is presented. It is concluded that the incorporation of geological knowledge has improved the confidence level of the results and should always be part of any reservoir characterization study. Introduction Geoscience data sets are distinguished from other types of data sets in one important aspect: they exhibit spatial relationship.1 In simple terms, neighboring values are related to each other. This relationship gets stronger as the distance between two neighbors becomes smaller. In most instances, beyond a certain distance the neighboring values become uncorrelated. This type of qualitative information needs to be defined in a suitable form so that it can be used to estimate values at unsampled locations. The most common statistics used to describe spatial relationship is variogram. It is the most widely used tool to investigate and model spatial variability of various reservoir attributes.2 The success in modeling the spatial relation, via the variogram, will provide higher chance of a successful reservoir characterization study. The main role of variogram is to reflect our understanding of the geometry and continuity of reservoir properties, which can have an important effect on the predicted flow behavior and reservoir management decisions. It is the measure of "geological variability" versus distance; it increases, as samples become more dissimilar. Therefore, it is clear that geological knowledge in reservoir charactersization is incorporated through variogram model. Therefore, thorough interpretation of geological knowledge should be done prior to modeling the variogram relationship. The interpretation that is of interest to the variogram modeling is anything that can lead to the information of lateral extent and major/minor continuity directions.

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