Petroleum Geoscience - Volume 7, Issue S, 2001

The current use of geostatistics in the petroleum industry is reviewed and the main issues that need to be tackled before the potential of geostatistics is fully realized are highlighted. The paper reviews and discusses three main topics: (1) geostatistics and geology; (2) multidisciplinary data integration; and (3) uncertainty quantification with multiple realizations. Our main message is that geostatistics has come a long way and reached maturity. In the years ahead, geostatisticians should focus less on the development of new algorithms and more on the training of geoscientists and the development of new work flows for decision support with geostatistics as the core.

An optimization method for incorporating dynamic data into reservoir modelling is presented. It integrates a very typical feature of the zonation approach that is based upon dividing the reservoir model into subregions. Solving the optimization problem consists of adjusting the subregion pattern so that the reservoir model duplicates the observed dynamic behaviour. Unlike the traditional approach, permeabilities in subregions are not constant, but show spatial variations. A variogram model that is the same for all the subregions describes this variability. The suggested method allows for optimization of permeability distributions within the subregions while preserving the second-order statistics for the whole reservoir model as well as the spatial continuity between subregions. It remains as flexible as the traditional zonation approach although it can handle complex structures.

The Upper Albian Namorado Sandstone is one of the reservoirs of the Albacora Field, located in the Campos Basin, deep-water offshore Brazil. It is a sand-rich turbidite system where the most important controls on permeability are calcite cementation, thin beds of non-reservoir lithologies and some north–south trending faults. A major multidisciplinary reservoir characterization project was conducted to improve the reservoir description using all available data. In this paper, we focus on how the effect of rock heterogeneities were represented in the fluid flow model and on the performance obtained from this model. The basic idea was to define a hierarchical model of facies established on the basis of three main work scales: porous systems (thin sections and core sample scale); composite facies (whole core and log scale); and seismic facies (interwell to field scale). An up-scaling technique, based on the geopseudo concept, was used to generate the effective petrophysical properties for the fluid-flow simulation model. A Markov–Bayes geostatistical simulation method was applied in facies stochastic modelling. The sophisticated model that was built allowed very fast history matching.

Recently, we proposed the gradual deformation approach for constraining stochastic models to dynamic data (well-tests and production history). In this paper, we review the basic gradual deformation algorithm and extend its application to different types of truncated Gaussian simulations (including non stationary truncated Gaussian and truncated pluri-Gaussian simulations). A case study on the calibration of a reservoir lithofacies model to well-test pressure data illustrates the efficiency of the gradual deformation approach.

Modelling faults from seismic data for a 3D depth model is a difficult task because of the multiple sources of uncertainty. The uncertainty may be attributed to migration velocities, picking of faults and organization of the fault network in 3D. Faults are generally not migrated from time to depth domain like horizons are, but modelled in the depth domain from the depth migrated horizons. For this reason, a new data structure has been designed that is targeted for fault modelling. Taking uncertainties into account, this structure allows for rapid modelling of faults from depth migrated horizons. The input data and the parameterization of the new data structure will be described. Following this, a way to incorporate uncertainties during the interpretation process is proposed and a description of different stochastic methods used to compute new shapes and locations inside a given uncertainty volume will be made. Finally, the method and the results obtained will be described while studying uncertainties on more complex fault networks. The influence of fault uncertainties on the reservoir volumetric estimates will be shown as one possible result of the simulation process.

Because of the multiscaled character of fracture networks and their high degree of heterogeneity, characterization and modelling of fractured reservoirs requires different techniques to the well-established geostatistical methods derived for modelling rock heterogeneity. We have developed a method to improve the geological model used as an input of fractured reservoir fluid flow simulators, either in single or dual permeability simulations, as well as new specific procedures. The method is based on three nested models. The first, the ‘global geo-cellular fracture model’, considers fracture average property distribution at the scale of the reservoir. Location of the major faults as well as properties, such as horizon curvature, are taken into account. ‘The global discrete model’ considers the fault system at the same scale and algorithms generate realistic synthetic fault patterns using an object-orientated approach. The third model, the ‘local discrete model’, creates realistic synthetic fracture patterns at the decametre scale with another object-orientated procedure. These models are all constrained by hard data acquired from seismic, well imaging and logs. They can be constrained by output from deterministic approaches like structural evolution analyses and geomechanical modelling. Interrelationships between these models enable account to be taken of the complex interrelationships between fractures at different scales and rock material heterogeneity. Finally, this modelling approach makes the geological model used as an input of fractured reservoir fluid flow simulators more satisfying than conventional approaches.

This study concerns the modelling of complex tidal heterogeneities found in the Lower Jurassic Tilje Formation offshore mid-Norway. The Tilje Formation is characterized by tidal channels, tidal bars (shoals), tidal flats and deltaic deposits. The lithofacies associations have been modelled as large-scale objects with a wide range of shapes (channels, sheets and lobes). In addition small-scale models of the internal bedding structure have been generated in order to calculate effective permeability values at appropriate modelling scales.

In order to assess the influence of the static input factors on recovery predictions, several production response variables were recorded for each of the 120 realizations generated. These include: streamline densities, breakthrough time measured in movable pore volume injected, pore volume tracer injected at 50% and 95% tracer fraction in the producer, and recovery factor of movable pore water at 95% tracer fraction in the producer. For this purpose we used a streamline reservoir simulator (Frontsim) with a tracer option (single-phase flow simulations).

By using analysis of variance, we identified the following parameters which have the largest influence on single-phase fluid flow: (1) dimension of large-scale bar objects; (2) effective permeabilities of marginal (background) facies; and (3) interaction effects between bar objects and background permeabilities. In addition, the effective permeability values of the marginal facies are highly controlled by certain thresholds in mud content.

The problem of mapping reservoir properties, such as porosity and permeability, and of assessing the uncertainty in the mapping has been largely approached probabilistically, i.e. uncertainty is estimated based on the properties of an ensemble of random realizations of the reservoir properties all of which satisfy constraints provided by data and prior geological knowledge. When the constraints include observations of production characteristics, the problem of generating a representative ensemble of realizations can be quite difficult partly because the connection between a measurement of water-cut or GOR at a well and the permeability at some other location is by no means obvious. In this paper, the progress towards incorporation of production data and remaining challenges are reviewed.

This paper presents a comparison study in which several partners have applied methods to quantify uncertainty on production forecasts for reservoir models conditioned to both static and dynamic well data. A synthetic case study was set up, based on a real field case. All partners received well porosity/permeability data and ‘historic’ production data. Noise was added to both data types. A geological description was given to guide the parameterization of the reservoir model. Partners were asked to condition their reservoir models to these data and estimate the probability distribution of total field production at the end of the forecast period. The various approaches taken by the partners were categorized. Results showed that for a significant number of approaches the truth case was outside the predicted range. The choice of parameterization and initial reservoir models gave the largest influence on the prediction range, whereas the choice of reservoir simulator introduced a bias in the predicted range.

In this paper a brief introduction to the theory of stochastic vector and tensor fields is given. Necessary and sufficient conditions for isotropic vector random fields are reviewed and necessary conditions for second order tensors are developed. These models increase the flexibility of the usual geostatistical models but at the cost of increased complexity. This complexity can be reduced to a manageable level for a class of tensor fields that are associated with strain. The potential for modelling fractures using strain models is briefly discussed.

In this paper we apply scaling laws from percolation theory to the problem of estimating the time for a fluid injected into an oil field to breakthrough into a production well. The main contribution is to show that, when these previously published results are used on realistic data, they are in good agreement with results calculated in a more conventional way but they can be obtained significantly more quickly. As a result they may be used in practical engineering circumstances and aid decision-making for real field problems.