Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

Korounis, D.
Durlofsky, L.J.
Jansen, J.D.
Aziz, K.

Civil Engineering and Geosciences

Geoscience and Engineering

2014-04-01

An adjoint formulation for the gradient-based optimization of oil-gas compositional reservoir simulation problems is presented. The method is implemented within an automatic differentiation-based compositional flow simulator (Stanford's AD-GPRS). The development of adjoint procedures for general compositional problems is much more challenging than for oil-water problems due to the increased complexity of the code and the underlying physics. The treatment of nonlinear constraints, an example of which is a maximum gas rate specification in injection or production wells, when the control variables are well bottom-hole pressures, poses a particular challenge. Two approaches for handling these constraints are presented -- a formal treatment within the optimizer, and a simpler heuristic treatment in the forward model. The relationship between discrete and continuous adjoint formulations is also elucidated. Results for four example cases of increasing complexity are presented. Improvements in the objective function (cumulative oil produced) relative to reference solutions range from 4.2% to 11.6%. The heuristic treatment of nonlinear constraints is shown to offer a cost-effective means for obtaining feasible solutions, which are in some cases better than those obtained using the formal constraint handling procedure.

adjoint formulation
gradient-based optimization
production optimization
recovery optimization
compositional reservoir simulation
discrete adjoint
continuous adjoint
automatic differentiation
nonlinear constraints
general constraints

http://resolver.tudelft.nl/uuid:d8b575bb-7fc4-48e2-90bf-7293352f14eb

https://doi.org/10.1007/s10596-013-9385-8

Springer

2015-04-01

1420-0597

http://link.springer.com/article/10.1007/s10596-013-9385-8

Computational Geosciences, 18 (2), 2014; Manuscript (author version)

Institutional Repository

journal article

(c) 2014 The Author(s)