Development of reservoir models using economic loss functions

As oil and gas supply decrease, it becomes more important to quantify the uncertainty associated with reservoir models and implementation of field development decisions. Various geostatistical methods have assisted in the development of field scale models of reservoir heterogeneity. Sequential simulation algorithms in geostatistic require an assessment of local uncertainty in an attribute value at a location followed by random sampling from the uncertainty distribution to retrieve the simulation value. Instead of random sampling of an outcome from the uncertainty distrubution, the retrieval of an optimal simulated value at each location by considering an economic loss function is demonstrated in this thesis. By applying a loss function that depicts the economic impact of an over or underestimation at a location and retrieving the optimal simulated value that minimizes the expected loss, a map of simulated values can be generated that accounts for the impact of permeability as it relates to economic loss. Both an asymmetric linear loss function and a parabolic loss function models are investigated. The end result of this procedure will be a reservoir realization that exhibits the correct spatial characteristics (i.e. variogram reproduction) while, at the same time, exhibiting the minimum expected loss in terms of the parameters used to construct the loss function. The process detailed in this thesis provides an effective alternative whereby realizations in the middle of the uncertainty distribution can be directly retrieved by application of suitable loss functions. An extension of this method is to alter the loss function (so as to emphasize either under or over estimation), other realizations at the extremes of the global uncertainty distribution can also be retrieved, thereby eliminating the necessity for the generation of a large suite of realizations to locate the global extremes of the uncertainty distribution.