Summary
Field-scale rate optimization problems often involve highly complex
reservoir models, production-and-facilities related constraints, and a large
number of unknowns. These factors make optimal reservoir management through
rate- and flood-front control difficult without efficient optimization tools.
Some aspects of the optimization problem have been studied before mainly using
an optimal control theory. However, the applications to date have been rather
limited to small problems because of the computation time and the complexities
associated with the formulation and solution of adjoint equations. Field-scale
rate optimization for maximizing waterflood sweep efficiency under realistic
field conditions has remained largely unexplored.
This paper proposes a practical and efficient approach for computing optimal
injection and production rates, thereby managing the waterflood front to
maximize sweep efficiency and delaying the arrival time to minimize water
cycling. Our work relies on equalizing the arrival times of the waterflood
front at all producers within selected subregions of a waterflood project. The
arrival-time optimization has favorable quasilinear properties, and the
optimization proceeds smoothly even if our initial conditions are far from the
solution. Furthermore, the sensitivity of the arrival time with respect to
injection and production rates can be calculated analytically using a
single-flow simulation. This makes our approach computationally efficient and
suitable for large-scale field applications. The arrival time optimization
ensures appropriate rate allocation and flood-front management by delaying the
water breakthrough at the producing wells.
Several examples are presented to support the robustness and efficiency of
the proposed optimization scheme. These include several 2D-synthetic examples
for validation purposes and a 3D field application. In addition, we demonstrate
the potential of the approach to optimize the flow profile along
injection/production segments of horizontal-smart wells.
Introduction
Waterflooding is by far the most commonly used method to improve oil
recovery after primary depletion. In spite of its many favorable
characteristics, reservoir heterogeneity—particularly permeability contrast—can
have an adverse impact on the performance of waterflooding. The presence of
high-permeability streaks can severely reduce the sweep efficiency, leading to
an early water arrival at the producers and bypassed oil. Also, an increased
cost is associated with water recycling and handling. One approach to
counteract the impact of heterogeneity and improve waterflood sweep efficiency
is optimal rate allocation to the injectors and producers (Asheim 1988;
Sudaryanto and Yortsos 2001; Brouwer et al. 2001; Brouwer and Jansen 2004;
Grinestaff 1999; Grinestaff and Caffrey 2000). Through optimal rate control, we
can manage the propagation of the flood front, delay water breakthrough at the
producers, and also increase the recovery efficiency.
Previous efforts to optimize waterflooding relied on optimal control theorem
to allocate injection/production rates for fixed well configurations. Asheim
(1988) investigated the optimization of waterflood based on maximizing net
present value (NPV) for multiple vertical injectors and one producer where the
rate profiles change throughout the optimization time. Sudaryanto and Yortsos
(2001) used maximizing the displacement efficiency at water breakthrough as the
objective for the optimization with two injectors and one producer. The optimal
injection policy was found to be bang bang type. That is, the injectors were
operated only at their extreme values—either at the maximum allowable injection
rate or fully shut. The optimization then involved finding the switch time
between the two injectors to ensure simultaneous water arrival at the producing
well. Brouwer et al. (2001) studied the static optimization of waterflooding
with two horizontal smart wells containing permanent downhole well-control
valves and measurement equipment. The static optimization implies that the flow
rates of the inflow-control valves (ICVs) along the well segments were kept
constant during the waterflooding process until the water arrived at the
producer. Various heuristic algorithms were utilized to minimize the impact of
high-permeability streaks on the waterflood performance through rate control.
The results indicated that the optimal rate allocation can be obtained by
reducing the distribution of water-arrival times at various segments along the
producer. Subsequently, Brouwer and Jansen (2004) extended their work to
dynamic optimization of waterflooding with smart wells using the optimal
control theory. The optimization was performed on one horizontal producer and
one horizontal injector. Each well is equipped with 45 ICVs. The objective was
to maximize the NPV, and it was achieved through changing the rate profile
along the well segments throughout the optimization period. Both
rate-constrained and bottomhole-pressure-constrained well conditions were
studied.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
28 June 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
3 May 2007
- Manuscript approved:
9 June 2007
- Version of record:
20 October 2007
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