The technique of variance simulation is introduced here as an adjunct or an alternative to Monte-Carlo simulation for the practical evaluation of outcome distributions in petroleum engineering as a consequence of uncertain inputs. Both methods allow one to establish the probability of a desired function falling within a range of extremes, by establishing the output distribution. However, not only is the method by which the output distribution is attained different in each of the two cases, but the variance simulation also supplies the component variance for each of the uncertain inputs. In other words, it provides a measure of simultaneous sensitivity of the output to the combined effect of all the uncertainties, and the rate at which the sensitivity changes with increasing uncertainty in the data. This extra information is a key to deteπnining the relative value gained per unit expenditure on data to improve the quality of the input variables. It can be applied equally to economic or technical evaluations.
As variance simulation requires the evaluation of second order system moments, the object function must be continuous so that numerical derivatives can be calculated. The method is demonstrated by illustrating the effect on payout and economic limit of decline data containing quantifiable uncertainty. The uncertain data affect the values of the well operating cost, the hyperbolic constant, the initial decline and oil rate in the case of a hyperbolic decline. The uncertainty is defined as a normal or log-normal distribution about a mean value with a defined coefficient of variance. The moment output distribution is compared to an equivalent Monte-Carlo analysis of the same data, and the component variance is tabulated. The results show that variance simulation can be used to examine mean estimates, the total variance and the probability of success or failure, and can be used as an alternative to Monte-Carlo simulation, while providing additional information for decision making in the form of component variance and bias.