Prediction Of Uncertainty In Reservoir Performance Forecast
Authors: Ballin P.R. , Journel A.G. , Aziz K. 
Published: March 2010

Abstract
Geostatistical models are used to provide equally probable reservoir descriptions that honour available data of a given reservoir. The differences between these descriptions provide an indication of reservoir uncertainty due to lack of information. Transferring this uncertainty into the reservoir performance forecast would require flow simulation of a large number of these equally probable descriptions. The spread in the response derived from the flow simulation measures its uncertainty. However, this approach is not a viable option in most cases because it would require excessive amounts of computer time.
A new approach for transferring geological uncertainty is presented. Each reservoir description is first ranked using a Fast Simulator (FS) rather than the Comprehensive flow Simulation (CS). A few selected descriptions are then processed through the CS to generate an approximate probability distribution of tile reservoir production response. This approach yields a considerable saving in the computer time over the use of the CS alone.
This approach is tested using a waterflood example in a quarter of a five-spot. A standard black-oil type simulator is used as the CS and a tracer model is used as the FS. Approximate probability distribution of production parameters (water breakthrough rime, cumulative oil recovery and cumulative water-oil ratio) are generated by selecting just five reservoir descriptions among 100, and processing them through the CS. The approximation is tested by running the CS on all 100 cases to generate the reference probability distributions. The tracer concentration at the producer provided very good results with a 90% reduction in computer time over the use of the CS for all 100 descriptions.

Introduction
Many complex geological processes, such as sedimentation, erosion, migration, compaction and diagenesis produce complex spatial distributions of reservoir properties. Rock type, porosity, permeability, fault occurrence, degree of cementation, and hydrocarbon saturation are some of these properties. However, the exact conditions that result from these complex geological processes are never known e.xacrly. This spatia [distribution of reservoir properties generally presems some degree of Variability, often shared with a complex geological architecture. Moreover, in practice, samples obtained represem only a very small fraction of [he whole reservoir volume, resulting in incomplete knowledge about the reservoir structure at all scales. For all these reasons, it is not advisable to consider only one single reservoir description or image and describe the spatial distribution of reservoir properties in a purely deterministic manner. Rather, a statistic.a1 treatment of the variables involved is desirable one that recognizes the lack of knowledge or uncertainty associated with any description selected.
The geological uncertainty can be determined through the differences between many equally probable reservoir descriptions generated using a geostatistical technique known as slochastic simulation(l,2). Each of the images reproduces a prior measure of spatial continuity (covariances) and may be conditioned to honour available data, such as, core and log data, well test, geophysical and geological interpretation, etc. The variables that should mostly be described using probablistic techniques are those that influence the amount, position, accessibility and flow of fluids through the reservoir (e.g. lithofacies or flow unit distributions, porosity, permeability, and fault occurrences).