A Novel Response Surface Methodology Based on 'Amplitude Factor' Analysis forModeling Nonlinear Responses Caused by Both Reservoir and Controllable Factors

摘要

Response surfaces (RS) are proxies to reservoir simulators.rnThey relate responses, such as oil rate to key reservoir (I.e.,rngeological parameters) and/or controllable (I.e., wellsrnparameters) factors in simple analytical forms. These proxiesrncan then be used for uncertainty computation, instead of timernconsuming simulators.rnValidity and Efficiency of RS construction techniquesrndepend on the degree of non-linearity. Traditional design ofrnexperiments (DOE) coupled with regression methods generaternpolynomial-type RS. They work well for mildly non-linearrnproblems. However, the reconstructed RS can becomernsubstantially inaccurate, if RS exhibits stiff non-linearrnfeatures. Substituting interpolation methods for regressionrnoften improves a proxy's accuracy. However, they tend tornsmooth out non-linearity and are costly when the non-linearityrnis unevenly distributed in the parameters' space. Efficientrnexperimental space partitioning coupled with interpolation canrnfurther improve proxies' accuracy 1 . However, spacernpartitioning results in low computation efficiency.rnWe introduce a novel response surface methodologyrn(RSM), which accurately and efficiently handles non-linearrneffects without space partitioning. The basic idea is to modelrnnon-linear responses by:rn1. Identifying a kernel sub-space of the initial parametersrnspace which contains the factors causing highly non-linearrneffects on RS;rn2. Extracting the highly non-linear effects from RS byrn'amplitude factor' analysis;rn3. Treating all other effects by 'phase factor' analysis;rn4. Modeling all effects on the response with 'thin plate'rnspline interpolants.rnWe then test this method to generate RS of arbitrary shapesrnusing a synthetic model and a real reservoir model. Werngenerate RS for oil rate and water cut as functions of key parameters. We validate this method's accuracy for thernreconstructed RS and the data collection efficiency. We alsorncompare it with traditional RSM. We show that this novelrnmethodology outperforms other standard RSM when non-linearrneffects on RS are very strong in the parameter space.