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Research Papers: Petroleum Engineering

Smart Well Pattern Optimization Using Gradient Algorithm

[+] Author and Article Information
Liming Zhang, Jun Yao, Lixin Li

Petroleum Engineering Department,
China University of Petroleum,
66 Changjiang West Road,
Qingdao, Shandong 266555, China

Kai Zhang

Petroleum Engineering Department,
China University of Petroleum,
66 Changjiang West Road,
Qingdao, Shandong 266555, China
e-mail: reservoirs@163.com.

Yuxue Chen

Shandong Kerui Holding Group Co., Ltd.,
Dongying, Shandong 257000, China

Meng Li

Mechanical and Industrial Engineering Department,
Louisiana State University,
2508 Patrick Taylor Hall,
Baton Rouge, LA 70803

JungIn Lee

China University of Petroleum,
66 Changjiang West Road,
Qingdao, Shandong 266555, China

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received January 31, 2014; final manuscript received July 22, 2015; published online August 26, 2015. Assoc. Editor: Arash Dahi Taleghani.

J. Energy Resour. Technol 138(1), 012901 (Aug 26, 2015) (13 pages) Paper No: JERT-14-1033; doi: 10.1115/1.4031208 History: Received January 31, 2014; Revised July 22, 2015

For a long time, well pattern optimization mainly relies on human experience, numerical simulations are used to test different development plans and then a preferred program is chosen for field implementation. However, this kind of method cannot provide suitable optimal well pattern layout for different geological reservoirs. In recent years, more attentions have been paid to propose well placement theories combining optimization algorithm with reservoir simulation. But these theories are mostly applied in a situation with a small amount of wells. For numerous wells in a large-scale reservoir, it is of great importance to pursue the optimal well pattern in order to obtain maximum economic benefits. The idea in this paper is originated from the idea presented by Onwunalu and Durlofsky (2011, “A New Well-Pattern-Optimization Procedure for Large-Scale Field Development,” SPE J., 16(3), pp. 594-607), which focuses on well pattern optimization, and the innovations are as follows: (1) Combine well pattern variation with production control to get the optimal overall development plan. (2) Rechoose and simplify the optimization variables, deduce the new generation process of well pattern, and use perturbation gradient to solve mathematical model in order to ensure efficiency and accuracy of final results. (3) Constrain optimization variables by log-transformation method. (4) Boundary wells are reserved by shifting into boundary artificially to avoid abrupt change of objective function which leads to a nonoptimal result due to gradient discontinuity at reservoir edge. The method is illustrated by examples of homogeneous and heterogeneous reservoirs. For homogeneous reservoir, perturbation gradient algorithm yields a quite satisfied result. Meanwhile, heterogeneous reservoir tests realize optimization of various well patterns and indicate that gradient algorithm converges faster than particle swarm optimization (PSO).

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References

Figures

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Fig. 1

Geometric size description of the three inverted well patterns: (a) inverted five-spot, (b)inverted seven-spot, and (c) inverted nine-spot

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Fig. 2

Rotation transformation: (a) inverted five-spot and (b) inverted seven-spot

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Fig. 3

Shearing transformation: (a) inverted five-spot and (b) inverted seven-spot

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Fig. 4

Scaling transformation: (a) inverted five-spot and (b) inverted seven-spot

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Fig. 5

Shifting transformation: (a) inverted five-spot and (b) inverted seven-spot

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Fig. 6

Transformation on five-spot well pattern

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Fig. 7

The well placement representing optimized solution

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Fig. 8

Invalid perturbation for unit transformation

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Fig. 9

Treatment for exceeding well

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Fig. 10

Illustration for the searching direction of PSO algorithm

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Fig. 11

The disposal of boundary well in actual reservoir

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Fig. 12

The flow chart of well pattern optimization

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Fig. 13

The structure of well placement optimization

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Fig. 14

Well placement optimization using gradient algorithm in homogeneous reservoir: (a) initial well location, (b) well placement of the first iteration, (c) well placement of the sixth iteration, and (d) saturation distribution of the sixth iteration

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Fig. 15

Well placement optimization using PSO in homogeneous reservoir: (a) PSO-20, (b) PSO-40, and (c) PSO-60

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Fig. 16

NPV curve of gradient algorithm compared with PSO in homogeneous reservoir

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Fig. 17

Initial reservoir permeability in heterogeneous reservoir

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Fig. 18

Initial five-spot well placement and saturation distribution in heterogeneous reservoir

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Fig. 19

Final five-spot well placement and saturation distribution in heterogeneous reservoir

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Fig. 20

Initial seven-spot well placement and saturation distribution in heterogeneous reservoir

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Fig. 21

Final seven-spot well placement and saturation distribution in heterogeneous reservoir

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Fig. 22

Initial nine-spot well placement and saturation distribution in heterogeneous reservoir

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Fig. 23

Final nine-spot well placement and saturation distribution in heterogeneous reservoir

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Fig. 24

NPV curve for different well pattern in heterogeneous reservoir using gradient method

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Fig. 25

Oil saturation distribution

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Fig. 26

Oil saturation distribution and well location using PSO method with 20 particles

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Fig. 27

Oil saturation distribution and well location using PSO method with 40 particles

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Fig. 28

Oil saturation distribution and well location using PSO method with 60 particles

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Fig. 29

Oil saturation distribution and well location using gradient optimization method

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Fig. 30

NPV curve for different methods in heterogeneous reservoir with small well spacing

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Fig. 31

Oil saturation distribution and well location with inj–pro rate control

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Fig. 32

Oil saturation distribution and well location without inj–pro rate control

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Fig. 33

NPV curve with or without inj–pro rate control in heterogeneous reservoir

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