Abstract
Stochastic simulations of sandstone deposits in hydrocarbon reservoirs should honour the available well data and geological knowledge about their setting. In this paper, the problem of conditioning the simulations on well data is considered. This is done in the case where a Boolean model is used to describe the spatial distribution of sandstone deposits in a reservoir (object-based modelling). It is argued that the conventional simulation algorithms generate sandstone deposits that do not possess the correct statistics for their size at the conditioning wells. The reason for this is closely related to the so-called waiting-time paradox. A statistically correct simulation approach is proposed for the problem of simulating random arcs on a circle, given that certain points on the circle are covered by arcs while other points remain uncovered. Intensity functions for the arc centres and probability distributions of an arc radius are derived for the conditional distribution of arcs on the circle. The results obtained for this problem might be partly used to solve the 2D and 3D conditional simulation problem.
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