Surface prediction using rejection sampling to handle non-linear relationships

We demonstrate accurate surface predictions by imposing consistent physical and stochastic relationships between surfaces. The accuracy is improved by using all relevant information collected in wells: well markers, zone logs in horizontal sections, and gas/fluid content along wells. The conditioned surfaces are used to provide estimates of gross rock volumes of oil and gas reservoirs. In particular, we show how spill point and zone log information affect trapped volumes. We apply plain rejection sampling techniques to deal with the highly non-linear relationships between a surface and its spill point. For well path conditioning we build upon an extension of kriging to treat inequality constraints, based on an efficient rejection sampling from a high dimensional truncated multivariate Gaussian distribution. A fast approximate approach to simulating surfaces is presented and successfully applied to estimate volumes. The impact on gross rock volume distributions from different assumptions and data types is demonstrated by several examples and the uncertainties in all the involved data types are consistently handled and quantified.