What in the Reservoir is Geostatistics Good For?
Authors: Deutsch C.V. 
Published: March 2010

Geostatistics provokes strong reactions. There are champions who believe the application of geostatistics adds value in almost any reservoir modelling situation. There are skeptics who do not think that a geostatistical model will have a meaningful impact on reservoir management decisions. The majority of engineers and geoscientists, however, are seeing an increasing use of geostatistics and are not sure when geostatistics should be used and how the results affect reservoir decisions.

There are three specific cases where geostatistics can provide valuable support for decision-making:calculating maps of uncertainty over large areas to support resource calculations and well placement;reconciling well and seismic data into high resolution reservoir models; and,constructing representative models of heterogeneity to provide input to flow simulation and support reservoir forecasting.

These three cases are developed without excessive theoretical detail. Realistic examples are presented without getting lost in the details of a particular reservoir. Limitations and pitfalls are discussed.

Framework of Geostatistics

Geostatistics refers to the theory of regionalized variables and the related techniques that are used to predict variables such as rock properties at unsampled locations. Matheron formalized this theory in the early 1960s(1). Geostatistics was not developed as a theory in search of practical problems. On the contrary, development was driven by engineers and geologists faced with real problems. They were searching for a consistent set of numerical tools that would help them address real problems such as ore reserve estimation, reservoir performance forecasting, and environmental site characterization. Reasons for seeking such comprehensive technology included:an increasing number of data to deal with;a greater diversity of available data at different scales and levels of precision;a need to address problems with consistent and reproducible methods;a belief that improved numerical models should be possible by exploiting computational and mathematical developments in related scientific disciplines; and,a belief that more responsible decisions would be made with improved numerical models.

These reasons explain the continued expansion of the theory and practice of geostatistics. Problems in mining, such as unbiased estimation of recoverable reserves, initially drove the development of geostatistics. Problems in petroleum, such as realistic heterogeneity models for unbiased flow predictions, were dominant from the mid 1980s through the late 1990s. More recently, the problems of realistic geologic modelling and reliable uncertainty quantification are driving development.

The main focus of geostatistics is constructing high-resolution 3D models of categorical variables, such as facies, and continuous variables, such as porosity and permeability. It is necessary to have hard truth measurements at some volumetric scale. All other data types including geophysical data are considered soft data and must be calibrated to the hard data. It is neither possible nor optimal to construct models at the resolution of the hard data. Models are generated at some intermediate geological modelling scale, and then scaled to an even coarser resolution for resource calculation or flow simulation.