A robust Kriging model for predicting accumulative outflow from a mature reservoir considering a new horizontal well

The objective of this research is to build a response surface based on Kriging method to predict accumulative outflow from a mature reservoir as a function of location, direction and length of a new horizontal well over a planning horizon. Investigating the impacts of horizontal well parameters on the outflow using repetitive runs of reservoir flow simulation would involve enormous computation time for evaluating possible well placement scenarios. Instead, we construct a Kriging model to build a good approximation of accumulated outflow from a reservoir when a new horizontal well is to be drilled. Kriging method is a geostatistical approach in which the spatial correlation of samples can be estimated via a variogram or a covariance matrix. The objective of this research is to find a more accurate estimate of the covariance matrix used in the construction of Kriging model. The method includes an optimization model to smoothen the noisy experimental covariance matrix which in turn leads to enhancing the fitting process. We have observed a very good fit of the resulting Kriging model in a case study on a mature oil reservoir in Iran for which a dynamic simulation model was set up previously. However, it is necessary to add the nugget effect to the model in order to yield better predictions.

► We developed a robust estimation model for extraction of a robust covariance matrix given the experimental covariances.
► The resulting problem becomes a semi-definite optimization problem.
► The resulting solution is a positive semi-definite covariance matrix that leads to a significant noise reduction.
► We have observed a very good fit of the resulting Kriging model from a mature oil reservoir in Iran.
► We find it very useful and necessary to add the nugget effect to the Kriging model and to use covariance tapering.