In the characterization of petroleum reservoirs, three types of uncertainty typically arise: (1) the uncertainty about the value of a petrophysical attribute at an unsampled location (local uncertainty); (2) the joint uncertainty about attribute values at several locations taken together (spatial uncertainty); and (3) the uncertainty about production forecasts, such as time to recover a given proportion of the oil (response uncertainty). In each case, the probabilistic way to assess the uncertainty consists of determining the distribution or set of possible outcomes (e.g., local permeability value, permeability grid, or production parameters), which is referred to as the space of uncertainty.

This chapter reviews the major geostatistical algorithms available to model both local and spatial uncertainties of continuous attributes. Goodness criteria are introduced for each type of space of uncertainty, and the impacts of the following parameters are discussed: stochastic-simulation algorithm, number of realizations, and ergodic fluctuations. Conclusions are drawn on the relations between the different spaces of uncertainty. The discussion is illustrated using an exhaustive set of 102 102 permeability values.