Multiscale gradient computation for flow in heterogeneous porous media

Multiscale gradient computation for flow in heterogeneous porous media

Jesus de Moraes, R. (TU Delft Reservoir Engineering)
Rodrigues, José R P (Petrobras)
Hajibeygi, H. (TU Delft Reservoir Engineering)
Jansen, J.D. (TU Delft Civil Engineering & Geosciences; TU Delft Geoscience and Engineering)

Civil Engineering & Geosciences

Geoscience and Engineering

2017-05-01

An efficient multiscale (MS) gradient computation method for subsurface flow management and optimization is introduced. The general, algebraic framework allows for the calculation of gradients using both the Direct and Adjoint derivative methods. The framework also allows for the utilization of any MS formulation that can be algebraically expressed in terms of a restriction and a prolongation operator. This is achieved via an implicit differentiation formulation. The approach favors algorithms for multiplying the sensitivity matrix and its transpose with arbitrary vectors. This provides a flexible way of computing gradients in a form suitable for any given gradient-based optimization algorithm. No assumption w.r.t. the nature of the problem or specific optimization parameters is made. Therefore, the framework can be applied to any gradient-based study. In the implementation, extra partial derivative information required by the gradient computation is computed via automatic differentiation. A detailed utilization of the framework using the MS Finite Volume (MSFV) simulation technique is presented. Numerical experiments are performed to demonstrate the accuracy of the method compared to a fine-scale simulator. In addition, an asymptotic analysis is presented to provide an estimate of its computational complexity. The investigations show that the presented method casts an accurate and efficient MS gradient computation strategy that can be successfully utilized in next-generation reservoir management studies.

Adjoint method
Automatic differentiation
Direct method
Gradient-based optimization
Multiscale methods

http://resolver.tudelft.nl/uuid:ace246d6-efa7-47e8-9942-14d4d75ef04c

https://doi.org/10.1016/j.jcp.2017.02.024

2017-08-14

0021-9991

Journal of Computational Physics, 336, 644-663

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2017 R. Jesus de Moraes, José R P Rodrigues, H. Hajibeygi, J.D. Jansen