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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:Random measurements errors,Systematic errors (bias), including lack of representativeness,Upscaling errors, andModel 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).

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Copyrig ht 1996 . Stee rirq Committee of th e Europea n IOR -Symposium. This peper was pt esented at the 8th. Eueopeen IO R -Symposium in Vbnna, AueMa , May 1 6 -17 . 1 99 6 This paper was aebcted tor presenta tion by the Stee rinp Comm~, following re view of infortn a tion conte in ed in an abstraet submitted by the authortsl. The pepar, as precented hes not been reviewed by t h e Steerinp C ommittee. ABSTRACTCapillary pressure is frequently omitted from large stele reservoir simulation , rationalized by arguments that may not always be valid . A number of papers have shown that correct modelling of capillary pressure may be as important for the simulation result as properly accounting for relativa permeabilities . Especially in strongly heterogeneous modale it is important to study the sensitivity to all petrophysical parameters before simplifications are introduced in the simulation model . In a previous paper from Norsk Hydro [1]. it was demonstrated and explained why stochastic oil / water relativa permeabilities (varying from cell to cell) in many cases can be replaced with one pair of "average" relativa permeabilities without significantly changing the simulation results. Our current study indicates that a similar procedure is not always valid for capillary pressure .A number of simulations exemplifies the effects of stochastic capillary pressure in various displacement regimes in a realistic geostatistical reservoir model : -Gravity dominated water/oil displacement -Viscous dominated water / oil displacement Varying water/oil mobility ratios -Including/excluding capillary pressur e -Stochastic vs . constant capillary pressure -Grid sensitivities Even if the simulation results can be explained by well understood physical theory , our study emphasizes that the net effect of capillary pressure on the oil production curve is in general difficult to predict without numerical simulation on a fine grid : Front smearing lende to give earlier water breakthrough while suppressing of channelling / fingering will have the opposite effect . These true physical effects c an be obscured by the numerical diffusion introduced by the finite difference schema applied in the reservoir simulator . INTRODUCTIO N

During the last couple of years Norsk Hydro has developed a 3D model for simultaneous generation of stochastic absolute and relative permeabilities. By using core data containing relative permeability curves measured on a large number of core plugs from one single well in the North Sea, we 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.We show that for all the depositional environments, 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 fractional flow theory, this paper summarizes the results from a theoretical and empirical statistical analysis of the correlation between the water shock front velocity and the absolute permeability for the different depositional environments, and we show 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 some situations stochastic modeling of the relative permeability curves is of minor importance, However, the choice of mean relative permeabilities may be crucial.