Unbiased Resource Evaluations with Kriging and Stochastic Models of Heterogeneous Rock Properties

摘要

This paper revisits the computation of product combinations for quantification of resources (e.g., pore volume for hydrocarbon reservoir formations). The explanations have been simplified by considering the exhaustive numerical model for properties that are multiplied first and then added or averaged for evaluation. The analysis starts without any probabilistic considerations. Abbreviated (up-scaled) computations in the sum of multiplications are proposed by substituting the individual values by averages for each rock property in the coarser cell resolution model. A result found is that averaged properties can be utilized for estimation at non-sampled locations, instead of individual values; however, covariances and cumulants must also be included in the abbreviated computations. The smoothing effect of kriging is found to be irrelevant if the kriging variance is also included in the up-scaled abbreviated pore volume computations. Thus, the equivalence between computation of resource volumes from kriging estimates and conditional stochastic simulations is established, with the condition that numerical estimation must incorporate the complete covariance and cumulant information as well. An example shows pore volume prediction from a kriging model matches the unbiased result from stochastic simulations.