Application of Automatic Differentiation to Reservoir Design Models

Abstract

Automatic differentiation is a technique for computing derivatives accurately and efficiently with minimal human effort. The calculation of derivatives of numerical models is necessary for gradient-based op­ timization of reservoir systems to determine optimal sizes for reservoirs. The writers report on the use of automatic differentiation and divided difference approaches for computing derivatives for a single- and multiple­ reservoir yield model. In the experiments, the AD1FOR (Automatic Differentiation of Fortran) tool is employed. The results show that, for both the single- and the multiple-reservoir model, automatic differentiation computes derivatives exactly and more efficiently than the divided difference implementation. Postoptimization of the ADIFOR-generated derivative code by exploiting the model structure is also discussed. The writers observe that the availability of exact derivatives significantly benefits the convergence of the optimization algorithm: the solution of the muItireservoir problem, which took 10.5 hours with divided difference derivatives, is decreased to less than two hours with ADIFOR out of the box derivatives, and to less than an hour using the postop­ timized ADIFOR derivative code.