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Global/local optimization strategies combined for waterflooding problems

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

In oil Reservoir Engineering application, a problem of great interest is the dynamic optimization of waterflooding management. In this work, the net present value (NPV) is taken as the function to be maximized, in which the allocated rates of wells are considered as design variables. Alternatively, the switching times of the control cycles can also be considered as design variables. This assumption increases flexibility to the management. Despite this, the formulation of this problem leads to a highly nonlinear, multimodal objective function. Therefore, to conduct the management, a hybrid optimization strategy is proposed here considering surrogate models. The hybrid strategy combines different methods at two different stages, a global and local. In this sense, the global search is driven by the genetic algorithm (GA) and the local search is driven by the sequential approximation optimization (SAO) method. The proposed methodology was successful in identifying wells that should be late started or shut-in before the end of the concession period and in handling different kinds of production strategies. It was also verified that an increasing on operation flexibility results in NPV improvement. Cycle duration variables proved to be useful in decreasing the number of design variables while maintaining recovery efficiency.

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Abbreviations

A :

Coefficient matrix of constraints

b :

Right-hand side of constraints

c w :

Cost of produced water

c wi :

Cost of injected water

f :

Objective function

\( \hat{f} \) :

Kriging model (surrogate function for objective function)

F :

Fitness function

g :

Inequality constraints

\( \hat{g} \) :

Kriging model (surrogate function for inequality constraints)

h :

Equality constraints

\( \hat{h} \) :

Kriging model (surrogate function for equality constraints)

I :

Injection wells

k :

Permeability

n t :

Number of control cycles

n w :

Number of wells

p :

Pressure

P :

Producer well

q :

Well rates

Q :

Maximum rate allowed for well set of the field

r :

Oil price

t :

Time step

T :

Concession period

v :

Violation of the constraints

x :

Design variables

Z :

Gaussian function

α :

Ration between maximum production and injection rates

β :

Unknown constant (for Kriging model)

γ :

Penalty parameter

δ :

Over injection parameter

Δ:

Size of the trust region

Δτ :

Time size of control cycles

λ :

Activation parameter

σ 2 :

Variance

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Acknowledgments

The authors acknowledge the financial support for this research given by PRH-26, from ANP (National Petroleum Agency—Brazil), PETROBRAS, Foundations CMG, CNPq (National Research Council—Brazil), FACEPE (Support Foundation of Science and Technology of Pernambuco), and UFPE.

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Authors and Affiliations

  1. Civil Engineering Department, Federal University of Pernambuco, Recife, PE, 50670-901, Brazil

    Leonardo Correia de Oliveira, Silvana M. B. Afonso & Bernardo Horowitz

Authors
  1. Leonardo Correia de Oliveira
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  2. Silvana M. B. Afonso
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  3. Bernardo Horowitz
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Correspondence to Leonardo Correia de Oliveira.

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Technical Editor: Celso Kazuyuki Morooka.

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de Oliveira, L.C., Afonso, S.M.B. & Horowitz, B. Global/local optimization strategies combined for waterflooding problems. J Braz. Soc. Mech. Sci. Eng. 38, 2051–2062 (2016). https://doi.org/10.1007/s40430-015-0461-y

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