Simple procedures for imposing constraints for nonlinear least squares optimization

Conference · Sun Dec 31 04:00:00 EST 1995

OSTI ID:170086

Carvalho, R ^[1]; Thompson, L G; Redner, R; Reynolds, A C ^[2]

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1. Petrobras, Rio de Janeiro (Brazil)
2. Univ. of Tulsa, OK (United States)

Nonlinear regression method (least squares, least absolute value, etc.) have gained acceptance as practical technology for analyzing well-test pressure data. Even for relatively simple problems, however, commonly used algorithms sometimes converge to nonfeasible parameter estimates (e.g., negative permeabilities) resulting in a failure of the method. The primary objective of this work is to present a new method for imaging the objective function across all boundaries imposed to satisfy physical constraints on the parameters. The algorithm is extremely simple and reliable. The method uses an equivalent unconstrained objective function to impose the physical constraints required in the original problem. Thus, it can be used with standard unconstrained least squares software without reprogramming and provides a viable alternative to penalty functions for imposing constraints when estimating well and reservoir parameters from pressure transient data. In this work, the authors also present two methods of implementing the penalty function approach for imposing parameter constraints in a general unconstrained least squares algorithm. Based on their experience, the new imaging method always converges to a feasible solution in less time than the penalty function methods.

• OSTI ID: 170086
• Report Number(s): CONF-950331--
• Country of Publication: United States
• Language: English

Related Subjects

03 NATURAL GAS
ALGORITHMS
FLOW MODELS
FLUID FLOW
MATHEMATICAL MODELS
MEASURING METHODS
NATURAL GAS WELLS
WELL PRESSURE