Integrated Stochastic Modeling in Reservoir Evaluation for Project Evaluation and Risk Assessment
Authors: Tyler K. , Sandsdalen C. , Maeland L. , Aasen J.O. , Siring E. , Barbieri M. 
Published: December 2007

Abstract
This paper gives an integrated method for estimating uncertainty in static hydrocbrbon volumes and production profiles. The study described provides a method for integrating the uncertainties from the relevant petroleum technical disciplines into consistent estinates for production potential for 3 individual fields in a project. Aggregation of the uncertainties in the profiles for the fields resulted in risked profiles for the unitized development project and were linked to Net Present Value for use with other project uncertainties in project risk management. The resulting risked profiles have also been used for commercial evaluation and gas contract issues within corporate management, and facilities design and investment issues within project management.
The method described includes the use of object-based stochastic modeling of reservoir heterogeneities to generate 99 realizations of the 3D geological model. These realizations were ranked and 3 realizations chosen to be combined with other reservoir and production uncertainties. A select number of the many possible scenarios combining the various uncertainties were used as input to reservoir simulation. Regression analysis combined with Monte Carlo simulation of the regression results provided the basis of the risked production profiles for each of the fields.

Introduction
As oil and gas operators are faced with a larger number of more complex projects, there is a strong need for more consistent analyses of project uncertainties as basis for corporate and project risk management. The purpose is to identify, analyze and describe relevant uncertainties and potential consequences of these, and to prioritize and take actions to improve robustness. Risk management is a continuous activity within the project management, carried out in close cooperation with all relevant disciplines of the project.
The methods have been applied to the Aasgard Unit located in the Norwegian Sea on the Halten Terrace. The Aasgard Unit is comprised of three discoveries, the Midgard, Smorbukk, and Smorbukk Fields, and is one of Norway's largest and most complex offshore projects.
The Midgard Field is a high quality sandstone containing a lean gas condensate. Smorbukk contains volatile oil and rich gas condensate in a heterogeneous and fairly low quality sandstone. Smorbukk Sor contains volatile oil and rich gas condensate in a severely faulted dome structure.
Uncertainties in the Hydrocarbon Pore Volume Uncertainty analyses of the Hydrocarbon Pore Volume (HCPV) for the three fields were performed combining geostatistical and Monte Carlo simulation methods. The results were aggregated for the Aasgard Unit.
Geostatistical Modeling of GRV. For the structural modeling of the Smorbukk and Smorbukk Sor Fields, a commercial geostatistical modeling package (HORIZON) was used. The purpose of this modeling was to quantily the laterally varying uncertainties in the horizons within the reservoir. 500 maps of each of the horizons were simulated, all conditioned to well data.
The Base Cretaceous Unconformity was the starting point of the simulations, and the deeper horizons were simulated sequentially as gaussian random fields to achieve the full layered model. Time-, velocity- and isochore maps from the deterministic model were used as trends. The uncertainties in these maps were modeled as residuals according to a geostatistical model consisting of spherical variograms and standard deviation maps which were used to quantify the laterally varying uncertainties.
Figure 1 shows the standard deviation map for the depth of the Top Ile formation of the Smorbukk Field. This map shows that the uncertainty in the proximity of the wells is nearly negligible, and the uncertainty near the outer flanks of the reservoir being the largest. A simulated depth map is shown in Figure 2. The simulated maps are less smooth than the base case model. The smoothness of these maps is controlled by the input variogram and its correlation range.