A Novel Response Surface Methodology Based on ‘‘Amplitude Factor’’ Analysis for Modeling Nonlinear Responses Caused by Both Reservoir and Controllable Factors

摘要

Response surfaces (RS) are proxies to reservoir simulators. They relate responses, such as oil rate to key reservoir (i.e., geological parameters) and/or controllable (i.e., wells parameters) factors in simple analytical forms. These proxies can then be used for uncertainty computation, instead of time consuming simulators. Validity and Efficiency of RS construction techniquesdepend on the degree of non-linearity. Traditional design of experiments (DOE) coupled with regression methods generate polynomial-type RS. They work well for mildly non-linear problems. However, the reconstructed RS can become substantially inaccurate, if RS exhibits stiff non-linear features. Substituting interpolation methods for regression often improves a proxy’s accuracy. However, they tend to smooth out non-linearity and are costly when the non-linearity is unevenly distributed in the parameters’ space. Efficient experimental space partitioning coupled with interpolation can further improve proxies’ a ccuracy. However, space partitioning results in low computation efficiency. We introduce a novel response surface methodology (RSM), which accurately and efficiently handles non-linear effects without space partitioning. The basic idea is to model non-linear responses by: 1. Identifying a kernel sub-space of the initial parameters space which contains the factors causing highly non- linear effects on RS; 2. Extracting the highly non-linear effects from RS by ‘amplitude factor’ analysis; 3. Treating all other effects by ‘phase factor’ analysis; 4. Modeling all effects on the response with ‘thin plate’ spline interpolants. We then test this method to generate RS of arbitrary shapes using a synthetic model and a real reservoir model. We generate RS for oil rate and water cut as functions of key parameters. We validate this method’s accuracy for the reconstructed RS and the data collection efficiency. We also compare it with traditional RSM. We show that this novel methodology outperforms other standard RSM when non- linear effects on RS are very strong in the parameter space.