The present paper proposes the use of a time dependent proxy model with the goal of efficient prediction of the future production performance of SAGD operations from a limited number of reservoir simulations. The proposed model is shown to provide powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. A SAGD case with 3 well pairs is used to illustrate the approach. The workflow is organized as follows:
The specified number of direct numerical simulations is run for the time horizon of ten years for the given reservoir. These simulations correspond to different combinations of the operational parameters sampled according to the Latin Hypercube Experimental Design (LHD).
The time series of the simulated production performance (particularly: entire field Oil Production Rate SCTR, and entire field SOR Cumulative SCTR) are used to build the time-dependent proxy model which represents production performance as an output function of the operational parameters and time. This paper uses and compares the following interpolators in N+1- dimensional space (operational parameters and time): a) anisotropic Ordinary Kriging, b) linear regression with regularization, c) Radial Basis Functions (RBF) Network method. Note that the extension of these methods to include time as the independent variable is one of the significant contributions of this paper.
The proxy model is then used to predict the production data for the given reservoir for any time period (even longer than 10 years) and any combinations of the operational parameters.
The predicted data are compared with the actual simulation results for the same time period and the same combinations of the operational parameters to evaluate the prediction quality. It is shown that all three proxy models can be used as a light version of simulator to get the production results for any combination of operational parameters and time horizon with much less computational efforts.