Risk Assessment of Oil Fields Using Proxy Models: A Case Study
Authors: Risso F.V.A. , Risso F.F. , Schiozer D.J. 
Published: March 2010

Abstract
Reservoir studies commonly consider many scenarios, cases and realizations. However, reservoir simulation can be expensive. Statistical design has been used in reservoir engineering applications, including performance prediction, uncertainty modelling, sensitivity studies, upscaling, history matching and development optimization. If reservoir simulation studies are conducted with a statistical design, response surface models can estimate how the variation of input factors affects reservoir behaviour with a relatively small number of reservoir simulation models. In petroleum exploration and production, a decision has to consider the risk involved in the process which can be obtained by quantifying the impact of uncertainties on the performance of the petroleum field in question. The process is even more critical because most of the investments are realized during the phase in which the uncertainties are greater. The statistical design is efficient to quantify the impact of the uncertainties of the reservoirs in the production forecast and to reduce the number of simulations to obtain the risk curve. The main objective of this work is the application of the statistical design: Box-Behnken and Central Composite Design using different attributes ranges. To compare the precision of the results, different techniques are used. These are the Derivative Tree Technique by simulation flow, the Monte Carlo Technique and the Response Surface Methodology.

Introduction
In petroleum exploration and production, a decision has to consider the risk involved in the process(1). Decision and risk analysis can be integrated with a wide variety of engineering and economic applications in the oil and gas industry, including economic evaluation of oil and gas reserves, reservoir modelling and simulation, seismic interpretation, petrophysical analysis and others(2).
Decision analysis applied to petroleum field development plans are always strongly related to risk due to the uncertainties present in the process. There are many uncertainties that can influence the success of an E&P project. The most common uncertainties are due to the geological model, the recovery factor and the economic model(3).
Quantification of uncertainty in reservoir performance is an important part of proper economic evaluation. The uncertainty in our understanding of a given reservoir performance arises from the uncertainty in the information we have about the attributes that control reservoir performance (permeability, oil water contact, etc.).
In a risk methodology, it is possible to combine the geological uncertainties by using the Monte Carlo technique to estimate the range of uncertainty of some objective functions. These values can be obtained through numerical simulation flow or proxy models.
The statistical theory, and especially the statistical (experimental) design approach, is well-suited to determine the most uncertain parameters to evaluate the impact of uncertainty on production forecasts, and to help making decisions during the reservoir's development(4).
If reservoir simulation studies are conducted with a statistical design, response surface models can estimate how the variation of input attributes affects reservoir behaviour with a relatively small number of reservoir simulation models. Response surface models can test the relative importance of the attributes statistically(5). Because response surfaces are accurate and simple to evaluate, they are efficient proxies for reservoir simulators.