Formulating the history matching problem with consistent error statistics

Abstract It is common to formulate the history-matching problem using Bayes’ theorem. From Bayes’, conditional probability density function (pdf) of uncertain model parameters proportional prior pdf parameters, multiplied by likelihood measurements. The static are random variables characterizing reservoir while observations include, e.g., historical rates oil, gas, and water produced from wells. prediction assumed perfect, there no errors besides those in parameters. However, this formulation flawed. rate data only approximately represent real production contain errors. History-matching methods usually take these into account conditioning but neglect them when forcing simulation observed during integration. Thus, depends on some same used conditioning. paper presents a theorem that considers dependency model. In new formulation, one must update both poorly known rate-data result an improved posterior ensemble models better cover with more substantial realistic uncertainty. implementation accounts correctly for correlated measurement demonstrates critical role correlations reducing update’s magnitude. also shows consistency subspace inversion scheme Evensen (Ocean Dyn. 54 , 539–560 2004) case its accuracy “larger” perturbations error covariance matrix.