document preview

Summary

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.

Introduction

Four categories of errors commonly occur in reservoir production estimates: 1) Random measurements errors, 2) Systematic errors (bias), including lack of representativeness, 3) Upscaling errors, and 4) Model errors, In this work we shall concentrate on the first three error types.

As a basis for our discussion we shall assume the existence of a generic reservoir model consisting of rock and fluid parameters and a set of equations based on Darcy's law and conservation of mass. In order not to introduce too many complications we shall restrict the object of study to an isothermal black oil model consisting of two immiscible incompressible phases (water and oil) and incompressible rock.

Given an initial state of the reservoir where all the rock parameters and all the saturations are known in all points, for a given recovery strategy it is in principle possible to infer the state of the reservoir and the oil and water production rates at any time. However, all the information and all the computing power needed to operate in this model is not available.

For any piece of data that is introduced in a real world reservoir model there is uncertainty. While measurement precision (random errors) in most cases can be quantified, systematic errors can not be accounted for before they are known (- and when they are known they can usually be corrected!)

Reservoir description is the process of assigning parameter values to the reservoir model from the partial information that is available. Even if compliance with the measurements put restrictions on the model there is still a lot of ambiguity left. In reservoir uncertainty analysis one tries to quantify this ambiguity in order to assess the uncertainty in the predictions from the reservoir model (Fig. 1).