SPE Journal
Volume 17, Number 2, June 2012, pp. 402-417

Summary

In history matching, one of the challenges in the use of gradient-based Newton algorithms (e.g., Gauss-Newton and Levenberg-Marquardt) in solving the inverse problem is the huge cost associated with the computation of the sensitivity matrix. Although the Newton type of algorithm gives faster convergence than most other gradient-based inverse solution algorithms, its use is limited to small- and medium-scale problems in which the sensitivity coefficients are easily and quickly computed. Modelers often use less-efficient algorithms (e.g., conjugate-gradient and quasi-Newton) to model large-scale problems because these algorithms avoid the direct computation of sensitivity coefficients. To find a direction of descent, such algorithms often use less-precise curvature information that would be contained in the gradient of the objective function. Using a sensitivity matrix gives more-complete information about the curvature of the function; however, this comes with a significant computational cost for large-scale problems.

An improved adjoint-sensitivity computation is presented for time-dependent partial-differential equations describing multiphase flow in hydrocarbon reservoirs. The method combines the wavelet parameterization of data space with adjoint-sensitivity formulation to reduce the cost of computing sensitivities. This reduction in cost is achieved by reducing the size of the linear system of equations that are typically solved to obtain the sensitivities. This cost-saving technique makes solving an inverse problem with algorithms (e.g., Levenberg-Marquardt and Gauss-Newton) viable for large multiphase-flow history-matching problems. The effectiveness of this approach is demonstrated for two numerical examples involving multiphase flow in a reservoir with several production and injection wells.

© 2012. Society of Petroleum Engineers

View full textPDF ( 6,040 KB )

History

• Original manuscript received: 12 June 2010
• Meeting paper published: 20 September 2010
• Revised manuscript received: 4 July 2011
• Manuscript approved: 19 July 2011
• Published online: 8 February 2012
• Version of record: 11 June 2012