Damsleth, Eivind; Holden, Lars
Society of Petroleum Engineers
The main objective of reservoir characterization is to describe the features which influence the amount, position, accessibility, and flow of fluids through 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.
As a result of high costs in offshore areas like the North Sea, only a minimum number of exploration and appraisal wells can be justified before important field development decisions are made. The use of over-simplified geological models based on data from a limited number of widely spaced wells is probably one of the most important reasons for the failures in predicting field performance. Over-simplification and the use of unrealistic geological models is partly due to the paucity of well data, but is also a result of inappropriate use of the available data. Experience shows, for example, that linear interpolation of petrophysical characteristics between wells some kilometers apart will usually not give a realistic image of the heterogeneity required for the prediction of fluid flow. To be able to give a realistic description of the point to point variation, we resort to stochastic models and simulation.
The phenomena or variables that we normally seek to describe using stochastic models are those which influence the amount, the position, the accessibility, and the flow of fluids through reservoirs. Thus, stochastic modeling or simulation in this context usually refers to the generation of synthetic geological architecture and/or property fields in 1, 2, or 3 dimensions. The different realizations are conditioned to observations, and mimic the variety of possible reservoir-geological "images". The realizations are generated according to their probability of occurrence. Thus, all realizations can be regarded as equiprobable. These realizations can thus provide an improved base for recovery predictions. In addition, the uncertainty and risk associated with different development options can be better quantified.
To mimic reality, heterogeneity must be taken into account since it is one of the most important factors governing fluid flow. There are a number of different approaches to the stochastic modeling of heterogeneities. The choice of technique depends on: The objective and scale of the study, what input data are available, the theoretical skills of the people involved and finally, software availability.