Experimental design method is an alternative to traditional sensitivity analysis. The basic idea behind this methodology is to vary multiple parameters at the same time so that maximum inference can be attained with minimum cost. Once the appropriate design is established and the corresponding experiments (simulations) are performed, the results can be investigated by fitting them to a response surface. This surface is usually an analytical or a simple numerical function which is cheap to sample. Therefore it can be used as a proxy to reservoir simulation to quantify the uncertainties.

Designing an efficient sensitivity study poses two main issues:

  • Designing a parameter space sampling strategy and carrying out experiments.

  • Analyzing the results of the experiments. (Response surface generation)

In this paper we investigate these steps by testing various experimental designs and response surface methodologies on synthetic and real reservoir models.

We compared conventional designs such as Plackett-Burman, central composite and D-optimal designs and a space filling design technique that aim at optimizing the coverage of the parameter space. We analyzed these experiments using linear, second order polynomials and more complex response surfaces such as kriging, splines and neural networks. We compared these response surfaces in terms of their capability to estimate the statistics of the uncertainty (i.e., P10, P50 and P90 values), their estimation accuracy and their capability to estimate the influential parameters (heavy-hitters). Comparison with our exhaustive simulations showed that experiments generated by the space filling design and analyzed with kriging, splines and quadratic polynomials gave the greatest accuracy while traditional designs and the associated response surfaces performed poorly for some of the cases we studied. We also found good agreement between polynomials and complex response surfaces in terms of estimating the effect of each parameter on the response surface.

You can access this article if you purchase or spend a download.