In this paper we present four methods of estimating the effective vertical permeability of a reservoir containing stochastic shales in both two and three dimensions. The methods vary in their accuracy, speed and range of applicability. The first is based on numerical simulation, the second is an analytical method, the third and fourth are based on calculating approximate streamline lengths. The methods give consistent results for similar models and are used to show that the effective vertical permeability is strongly dependent on the shale dimensions, shale fraction and layer thickness. It is also shown that the results of the two-dimensional models are inappropriate even when the megascopic flow is unidirectional.

Characterization of heterogeneous reservoirs for simulation studies by use of a statistical component to the reservoir description combined with calculation of effective permeabilities is discussed through a case study of a fluvial reservoir. Inspection of whole core and logs from the Sherwood reservoir revealed that it is extremely heterogeneous, containing short shales embedded in a mixture of sands and silts. A statistical approach was used to quantify the distribution of core-plug porosity and permeability measurements to discriminate between significantly different rock types. A successive rescaling procedure was then adopted in which we first calculated effective values for each rock type from the core-plug data. These results were combined with statistics on the spatial distribution of the rock types to calculate effective values for the nonshale part of each layer. Finally, the effect of the shales on the vertical permeability was incorporated. The resulting anisotropy ratios, on the order of 10-3 , were used successfully in black-oil model studies, a good match between the simulator predictions and observed production data being achieved with minimal fine tuning of the model parameters.

The normal rule for choosing between alternatives in a decision situation is to select the one with the maximum estimated value. Due to uncertainty in the estimates (prediction errors), the mere fact of choosing the maximum induces a systematic bias that guarantees that, over repeated decisions, less than the estimated expected value will be realized. Although some "proof-of-concept" instances of this behaviour (variously termed Post-decision Surprise, the Optimizer's Curse, Inevitable Disappointment) have been reported, it is not well-publicised in the O&G world and its importance/relevance in realistic O&G decision situations has not been thoroughly assessed.This paper places the effect in a more-widely applicable theoretical context and reports a systematic study that explores its impact on typical O&G decisions, using NPV as the value measure. Three typical situations, with different characteristics, are identified for investigation: intra-project alternative selection, using a Max[NPV] decision criterion; project "go"/"no go" decisions, using an NPV > 0 decision criterion; constrained portfolio selection, using a Max[NPV/I] criterion, subject to a budget limit. Sensitivity analysis of the magnitude of the effect is carried out in each case.We conclude that, whilst the effect is real and its magnitude may be large in some situations, it was of order 2% and 10% respectively, for the project and portfolio cases we analyzed. Further, the real prediction error, defined as expected difference between the true values of the selected alternative and the genuinely best alternative, was about half the above values. Given the range of other sources of prediction errors, plus the fact that its impact may be reduced due to corrective decisions as a project is executed, it may not, in practice, be as significant as previously suggested.

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