Eivind Damsleth

Achievements and challenges in petroleum geostatistics

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.

Errors and Uncertainties in Reservoir Performance Predictions

While the uncertainty related to mapping/quantification of hydrocarbons initially in place is well understood, there are open problems regarding the sources and propagation of errors/uncertainties in reservoir simulation. Based on measured data from only a small fraction of the total reservoir volume the challenge is to construct a reservoir model that utilizes the available data and minimizes errors in simulation results. Several studies have recently aimed at performing a total uncertainty analysis of reservoir simulation results. Underlying such work is usually a number of hypotheses/assumptions which are not always clearly expressed. In this paper we will discuss implications of some of the statistical methods that are commonly applied in uncertainty analysis and construction of a geological model. The Bayesian approach, where additional data can reduce uncertainties, is emphasized. Previous papers from Norsk Hydro and others have demonstrated the large variation in parameters obtained from routine and special core analysis on sample originating from the same geological building block (lithoface). This variation, which sometimes may be difficult to dissolve from uncertainty in the measurements, must be accounted for in models that describe small scale variation.

Sub-seismic Faults Can Seriously Affect Fluid Flow in the Njord Field off Western Norway - A Stochastic Fault Modeling Case Study

The Njord Field is heavily faulted. A stochastic fault modeling study has been performed on a sector of the field to quantify the potential impact of sub-seismic faulting on the production. Emphasis was given to the sensitivity of the results to the number of sub-seismic faults, the fault orientation, and the fault sealing properties. The main conclusions are: ○ Sub-seismic faults have neglectable effect on recovery, nor on the shape of the production profile, unless they are almost completely sealing. ○ The distribution of strike directions had no effects on the production. ○ Recovery decreases with increasing number of sub-seismic faults. ○ A large number of sealing sub-seismic faults will on average reduce the sector production with 20-25 %, compared to a base case model without sub-seismic faults. In some cases the reduction is much worse. ○ The production from individual wells is much more sensitive than the sector total to sub-seismic faults. Reductions up to 80 % have been observed in the simulations. The HAVANA software has been used for the sub-seismic faults modeling. Irap RMS has been used for visualization and quality control, and the effects of the sub-seismic faults on production have been investigated using the fluid flow simulator Eclipse. HAVANA has proved to be very useful for this kind of studies.

Geostatistical Approaches in Reservoir Evaluation

Reliable characterization of the reservoiris crucial for reservoir evaluation. According to the Preface in Ref. 1, Reservoir characterization is a process for quantitatively assigning reservoir properties, recognizing geological information and uncertainties in spatial variability. Geostatistics provides the tools to integrate the available information within a unified and consistent framework and to generate multiple realizations that can account for the uncertainty and spatial variability of the key reservoir parameters. The objective ofthis paper is to give our views on the use of geostatistics in reservoir evaluation, to illustrate some basic concepts and possibilities, and to increase (we hope) the readers interest in further investigation and application of geostatistical techniques.

Mixed Reservoir Characterization Methods

The main objective of reservoir characterization is to describe the features which influence the amount, position, accessibility, and flow of fluids though a reservoir. These features will be: the structural aspects (depth to the reservoir boundaries and inter-reservoir surfaces), faults (both seismically identifiable and sub-seismic faults), flow-units or facies bodies (position, orientation and size), and the spatial distribution of the relevant petrophysical parameters (permeability, porosity, saturations, ...) within each flow-unit. Although some hard data from seismic and wells will be available, there is a definite stochastic element in all these features. Stochastic techniques are thus required to model them properly. The paper reviews a number of techniques available for stochastic modeling of the above features: (marked point processes, Markov fields, truncated gaussian fields and indicator kriging for modeling discrete events (flow-units, faults, barriers); Gaussian fields and indicator kriging for modeling property values (depths, fault transmissibility, petrophysical variables)). The different techniques can be mixed or combined to give a complete stochastic model of every relevant aspect of the reservoir. Several examples from the North Sea will be presented.

The effect of stochastic relative permeabilities in reservoir simulation

Abstract During recent years Norsk Hydro has developed a 3D model for the simultaneous generation of stochastic absolute and relative permeabilities. By using a unique set of core data containing relative permeability curves measured on 85 core plugs from one single well in the North Sea, the authors have been able to model relative permeability curves (represented by endpoints and exponents) stochastically for four different depositional environments ranging from highly permeable mouthbar sands to low permeable tidal deposits. The authors will show that for all the four depositional environments represented here, the stochastic variation of the relative permeabilities have only marginal, if any, effect on the production characteristic, compared to keeping the relative permeabilities constant at their mean. Based on the fractional flow theory, for unit mobility ratio and ingnoring capillary forces, this paper presents both a theoretical and empirical statistical analysis of the correlation between the water shock front velocity and the absolute permeability for the different depositional environments. It is shown that in specific cases this correlation can serve as an indication of the potential effects of stochastically varying relative permeability curves. The main conclusion, which must be very comforting to practicing engineers, is that in within a wide range of depositional environments, stochastic modelling of the relative permeability curves is of minor importance. However, the choice of mean relative permeabilities may be crucial.

Scale Consistency From Cores to Geological Description

This paper describes a technique for conditioning stochastic simulation of permeability on a geologic description grid to the observed core-plug measurements. The technique handles the transition from core-plug to reservoir-description scale correctly and consistently, provided that some model assumptions are fulfilled. A North Sea case study is included for illustration.