Summary
Determination of the operating conditions of a field under a set of physical
system constraints (e.g., compressor limits) and engineering preferences (e.g.,
voidage replacement) is a primary concern for petroleum engineers. Rule-based
systems have been proposed for this, but the process is most suitably defined
as an optimization problem. An optimization procedure that uses mixed-integer
linear programming (MILP) is discussed in this study. Well rates that honor
system and engineering constraints are handled simultaneously while the maximum
for an objective is calculated (e.g., field oil rate or cash revenue). Optimal
rates for the current conditions of the field are determined. Note that this
results in instantaneous optimization and, thus, cannot account for recurrent
events such as water breakthrough. Nevertheless, an efficient and robust
instantaneous optimizer is useful within a grander optimization scheme, short
forecast periods and, also, in real-time allocation situations. The approach is
able to efficiently handle the nonlinearities in the system by way of piecewise
linear functions. Also, as a result of the formulation, the exact optimal
solution of the problem is guaranteed. Another property of the approach is
that, in cases in which it is not possible to honor all the targets and limits
of the system simultaneously, a scheme is introduced that enables the engineer
to prioritize the constraints. This prioritization scheme proves to be of great
practical significance because most real cases have conflicting targets and
limits that result in optimization systems with no feasible solutions. Also, a
heuristic is used that ensures realistic results by elimination of mathematical
artifacts (rate oscillations in time) that often arise when the reservoir
contains wells with similar properties [e.g., water/oil ratio (WOR) and gas/oil
ratio (GOR)]. The optimization system is applied to synthetic cases and two
real-field cases. The real-field cases pose problems that cannot be handled by
conventional rule-based systems.
Introduction
Production and injection allocation with the objective of maximizing profits
while simultaneously honoring all facilities limits, contractual targets, and
engineering preferences, is a process that can best be addressed as an
optimization problem. Optimization techniques have been applied to a variety of
oil-field-development problems. Early approaches used linear programming (LP)
techniques to solve rate-allocation problems with linear constraints, a linear
objective, and continuous parameters (Brown et al. 1998; Bohannon 1970; Lang
and Horne 1983; Lo et al. 1995). MILP methods, however, enable optimization on
discrete and continuous variables in which discrete variables are commonly used
to model decisions or approximate nonlinear functions. For example, Saif et al.
(1987) were interested in determining production allocation when considering
several reservoirs and used discrete variables to model selection of a
production profile from a set of predefined profiles for each reservoir. The
profiles were generated by use of aggregate production from all wells in the
reservoir, which simplied well performance and interaction. Fang and Lo (1996)
demonstrated how separable programming techniques can be used to optimize oil
production during artificial lift with gas injection; for each well, flow
performance vs. amount of lift gas was represented as a piecewise linear curve,
and the optimizer determined the best allocation of gas lift under various
facility constraints. For wells not under gas lift, the wellbore performance
was represented with a simple linear relationship between the phase flowing
rates that assumed equal scaling of phase flow rates. This approach is similar
to that presented by Wang et al. (2002a) in which piecewise linear curves were
used to model the well performance for all wells, not just those on gas lift.
Nonlinear optimization methods, such as sequential quadratic programming, have
also been used to optimize coupled reservoir-facility models in systems in
which the gathering system has significant impact on individual well
performance (Wang et al. 2002b; Davidson and Beckner 2003). These methods are
capable of incorporating pipe and facility devices in the formulation and
capturing gathering system impact of individual well performance. However, they
lose the ability to incorporate discrete variables representing common
well-management actions such as producing at a minimum flow rate or shutting in
the well.
Optimization is still not widely used and accepted as a best-practice
approach for rate allocation in the reservoir-engineering community. Sequential
rule-based heuristic systems are still the most common form of well-management
systems (Wijesinghe et al. 1983). Apart from the engineer’s familiarity with
rule-based systems, one reason for their persistence might be that, although
these systems often deliver suboptimal results, they are robust. The systems
hardly fail in delivering a solution no matter how suboptimal it may be. Here,
we present a similarly robust and easy-to-use allocation-optimization framework
that is advantageous when compared to rule-based systems in several ways:
- Ability to define an objective to be maximized: This also brings in the
ability to penalize the production of certain phases or components.
- Ability to handle all operating constraints simultaneously: Rule-based
systems often deliver suboptimal solutions because they fail to capture the
dependencies among the operating constraints as a result of their sequential
nature.
- Ease of use: Removes the complexity of finding the correct allocation
scheme, which, in rule-based systems, might involve defining convoluted logic
with dependence among the allocation steps and iterations.
The approach presented here focuses on optimization of allocation at a point
in time rather than over time. The allocation is conducted in real time in the
sense that the future behavior is not taken into consideration while allocating
the rates for the current time. While this is a limitation, a robust
instantaneous optimization framework works in many situations:
- Replace sequential rule-based allocation logic to deliver optimal
allocation: The use of rule-based allocation systems is currently the common
practice in the reservoir-engineering community.
- Use with a reactive operating strategy. This might be the case when we have
confidence in our numerical models to represent the current or near-future
situation in the reservoir but we may not have the same level of confidence in
the models predictions. For instance, we might not want to proactively shut
wells before we observe any water breakthrough despite the model’s predictions
indicating this would be beneficial over time.
- Use for real-time production optimization. This point is related to the
previous one.
- Use as the inner loop in grander optimization schemes.
As compared to previous allocation-optimization approaches, (Wang et al.
2002a; Davidson et al. 2003) we present a prioritization scheme that enables
the prioritization of the operating conditions to deliver the desired
allocation in the case of conflicting targets and limits. Additionally,
techniques are developed that avoid unrealistic operating scenarios that result
from continually solving for the optimal solution.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
5 December 2006
- Meeting paper published:
26 February 2007
- Revised manuscript received:
7 April 2008
- Manuscript approved:
5 May 2008
- Version of record:
15 November 2008
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