In the last few years, finding sufficient oil and gas volumes to supply the increasing worldwide demand has been a challenge for the industry. Resources are generally deeper and exploration is progressively becoming more expensive and more complex. In this context, state-of-the-art technologies are essential for efficient decision-making. Geostatistics is part of this needed technology as it offers the sound technology required to achieve the expected level of confidence in reservoir models while rating the risks attached to them.
What Is Geostatistics? The basis of geostatistics is the study of the spatial correlation of data measured at various points in 3D space and their integration into subsequent mapping or simulation approaches. The fundamental technique is called kriging, in recognition of the work carried out by DG Krige on gold and uranium deposits in South Africa in the late 1940s and early 1950s. Geostatistics was originally used to estimate the potential of ore deposits from sp rse data as accurately as possible. The petroleum industry became interested in geostatistics in the late 1980s, in part to improve the modelling of the geometry of oil reservoirs when using sparse data sets with more detailed 3D seismic surveys.
Geostatistics is primarily applied to interpolate or simulate isolated data into a continuous space. Given that the estimation is subject to error, geostatistics can also be used to assess how much confidence can be placed in the produced map. The system offers a compelling set of tools for modelling spatial data in an accurate and intelligent way. It guarantees a level of precision and reliability of results unlike any other methodology. Furthermore, it provides an efficient venue for data quality control and data analysis, mapping, volume estimation, resource estimation and risk assessment. Most importantly, perhaps, it provides the means to quantitatively assess the confidence in mathematical static models. In the oil and gas industry, geostatistical metho ologies are mainly applied to seismic data processing and quality control, time-to-depth conversion, facies modelling, petrophysical property modelling and uncertainty quantification by volumetrics. Dubrule1 and Yarus2 provide an exhaustive overview of these applications.
A Brief History of Geostatistics Geostatistics has its origins in the mining industry in the 1950s. Krige and HS Sichel, a statistician, developed a new estimation method when ‘classic’ statistics was found unsuitable for estimating disseminated ore reserves.
Subsequently, French engineer Georges Matheron pioneered and developed the use of geostatistics in the early 1960s at the Centre de Géostatistique of the École des Mines de Paris. He formalised these innovative concepts with his publication entitled The Theory of Regionalized Variables and Its Applications.
At about the same time, for the first time quantitative reservoir description techniques were applied on the giant Hassi Messaoud field in Algeria. he distribution of sand lenses and shale breaks was modelled in a vertical cross-section with the goal of understanding its effect on effective permeability.5 However, it was not until the mid- to late 1980s that the petroleum industry started to use geostatistical techniques for reservoir characterisation. Geostatistics was essentially based on variogram-based modelling applications with ‘deterministic’ geostatistics (the term deterministic refers to the fact that the result comprised a single model).
Since the 1990s, geostatistics has quickly become established in the petroleum industry. Geostatistics was first used by reservoir engineers, followed by geologists, who realised its potential for geological modelling. 3D simulation-based ‘stochastic’ reservoir modelling was developed to generate 3D heterogeneous reservoir models. Applying geostatistics to quantify uncertainties came soon after.
