Summary
Normally only approximately 30% of the oil in a reservoir is extracted
during primary production, but using secondary-production methods such as water
or gas injection, it is often possible to increase that percentage
significantly and maintain the production rate of a reservoir over a longer
period of time. In reservoirs under water or gas injection, additional gains
can be obtained through an efficient strategy for management of front movement
and reservoir sweep. The objective of reservoir production optimization is to
maximize an outcome such as sweep efficiency or net present value (NPV) through
the control of completion rates or pressures. Using optimization methods, it is
possible to compute control settings that result in increased oil production
and decreased water production compared with production from standard
practices. In this paper, we focus on optimization using sequential quadratic
programming (SQP) with an ensemble-based approach to estimate the gradient for
the optimization. Although uncertainty in reservoir properties is usually
important for the computation of optimal controls, here we use a single
realization of the reservoir to evaluate the efficiency of the optimization
algorithm.
The most expensive aspect of gradient-based optimization is usually the
computation of gradients. Most practical production-optimization problems
involve large-scale, highly complex reservoir models with thousands of
constraints, which makes numerical calculation of the gradient time consuming.
Here, we use an ensemble-based approach for finding gradients and use
localization to improve estimation of the gradient from a small number of
realizations. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used for
maximizing the objective function, with the Hessian estimated from a sequence
of estimates of the gradient. Improving the gradient approximation using
localization results in improvement to the Hessian approximation. A second
important aspect of the efficiency of the method is the identification of
active constraints. In this paper, we use a method for eliminating
nonnegativity constraints to decrease computation time and an updating
procedure to solve each iteration of SQP much faster than the base case. Both
the speed of the algorithm and the final NPV were increased significantly.
We evaluate the method by applying it to optimization of control settings in
the Brugge field. Brugge is a 3D synthetic model designed by TNO with 20
vertical producers and 10 vertical peripheral water injectors. All of the
producers and injectors are smart wells whose downhole chokes must be adjusted
to optimize NPV. The total number of completion flow rates to be controlled is
84 at each timestep, with 40 timesteps (every 6 months). There are 1,200
inequality constraints on total well liquid rates and 3,360 nonnegativity
constraints on completion liquid rates. There are also inequality constraints
on the bottomhole pressure (BHP) for wells at each time period.
© 2012. Society of Petroleum Engineers
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History
- Original manuscript received:
31 March 2011
- Meeting paper published:
22 February 2011
- Revised manuscript received:
7 October 2011
- Manuscript approved:
30 November 2011
- Published online:
23 August 2012
- Version of record:
12 September 2012
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