multivariate production systems optimization - Stanford University

• Nonlinear optimization may be used to optimize well conditions over a
span of time. This is best described by considering an example: for a tenyear
time span, nonlinear optimization will determine the optimal tubing
diameter to use each year--simply add ten decision variables, one for each
tubing size each year. As another example, if only three tubing changes
are allowed over the ten-year span, nonlinear optimization will determine
when the changes should be made and what size the tubing should be.
Attempting this with exhaustive iteration is ill-advised.
• Nonlinear optimization avoids the trial and error procedure of exhaustive
iteration. Nonlinear optimization based on Newton’s technique will
achieve quadratic convergence to the optimal solution.
This study investigated several different nonlinear optimization methods. The
significant findings are
• Unmodified Newton’s Method is not viable for optimization. This
technique is highly sensitive to the initial guess.
• The performance of Newton’s Method can be greatly improved by
including a line search procedure and a modification to ensure a direction
of descent.
• For nonsmooth functions, the polytope heuristic provides an effective
alternative to a derivative-based method.
• For nonsmooth functions, the finite difference approximations are greatly
affected by the size of the finite difference interval. This study found a
finite difference interval of one-tenth of the size of the variable to be
advisable.
8.2 Suggestions for Future Work
One idea that was flirted with briefly but is not included in this report is to revise the
implementation of classical nodal analysis. Current practitioners of nodal analysis use
exhaustive iteration to solve the system of equations that represents the well. Why not
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