of 15
Energy Sources, Part A, 36:12341248, 2014
Copyright Taylor & Francis Group, LLC
ISSN: 1556-7036 print/1556-7230 online
DOI: 10.1080/15567036.2010.536829
The Optimization of Gas Allocation to a
Group of Wells in a Gas Lift Using anEfficient Ant Colony Algorithm (ACO)
M. Ghaedi,1 C. Ghotbi,1 and B. Aminshahidy2
1Chemical and Petroleum Department, Sharif University of Technology, Tehran, Iran2Institute of Petroleum Engineering, Tehran University, Tehran, Iran
When the reservoir energy is too low for the well to flow, or the production rate desired is greater than
the reservoir energy can deliver, using some kind of artificial lift method to provide the energy to bring
the fluid to the surface, seems to be necessary. Continuous flow gas lift is one of the most common
artificial lift methods widely used in the oil industry during which, at appropriate pressure, gas is
injected in a suitable depth into the tubing to gasify the oil column, and thus assist the production.
Each well has an optimal point at which it will produce the most oil. In ideal conditions, at which there
is no limitation in the total amount of available gas, a sufficient amount of gas could be injected into
each well to get the maximum amount of production. However, often the total amount of available gas
is insufficient to reach the maximum oil production for each well. Therefore, allocating an optimum
amount of gas to each well to obtain field maximum oil production rate is necessary. In this work,
a continuous ant colony optimization algorithm was used to allocate the optimum amount of gas to
a group of wells for three fields with a different number of wells. Based upon the total production
rates of the studied oil fields resulting from the gas allocation to the wells, the continuous ant colony
optimization algorithm shows better gas allocation to the wells in comparison with the previous works
with other optimization methods.
Keywords: ant colony algorithm, gas allocation, gas lift, genetic algorithm, production optimization
1. INTRODUCTION
When the reservoir energy is too low for the well to flow, or the production rate desired is greater
than the reservoir energy can deliver, it becomes necessary to use some kind of artificial lift
methods to provide the energy to bring the fluid to the surface. The gas lift is considered as
the most economical method for artificial lifting of oil (Ayatollahi et al., 2004; Nakashima andCamponogara, 2006).
In a gas lift, as the gas injection rate into the well increases, the oil production rate enhances
until a point called the optimal point, after which the oil rate declines with increasing the gas
injection rate. Having no concerns about the total amount of available gas, which is not often
Address correspondence to Prof. Cyrus Ghotbi, Chemical and Petroleum Engineering Department, Sharif University
of Technology, Azadi Ave., Tehran, Iran. E-mail: [email protected]
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ueso.
1234
OPTIMIZATION OF GAS ALLOCATION 1235
the case, sufficient gas could be injected into each well to get the maximum oil production rate.However, due to the limitation in available gas sources, it seems necessary to allocate an optimum
amount of gas to each well to obtain the field maximum oil production rate.
To allocate an optimum amount of gas to each well, gas lift performance curves (GLPC) are
used. The GLPC shows the injected gas rate versus oil production rate for each well. The GLPCcan be either measured in the field, or iteratively generated by computer simulations, by means
of nodal analysis (Alarcn et al., 2002).
Kanu et al. (1981) were the first to use the method of the equal slope allocation under both
limited and unlimited gas supply. Later, Nishikiori et al. (1995) presented an extension of theequal slope allocation method, based on the application of nonlinear optimization techniques of
the quasi-Newton type. Buitrago et al. (1996) reported a novel nonlinear methodology for the
optimal distribution of a given amount of gas to some set of wells.
Alarcn et al. (2002) improved upon Nishikiori et al.s (1995) method by replacing the quasi-Newton algorithmwith sequential quadratic programming (SQP). Fang and Lo (1996) reformulated
the problem as a linear-programming problem. Wang et al. (2002) suggested a mixed-integer
non-linear programming (MINLP) model to generalize the previous approaches. Camponogara
and Nakashima (2003) developed recursive algorithms for lift-gas allocation. Camponogara andConto (2005) proposed a piecewise-linear reformulation, thereby rendering a mixed-integer linear
programming problem. Ray and Sarker (2007) used genetic algorithm (GA) for gas lift allocation.
Zerafat et al. (2009) used both GA and ant colony optimization (ACO) to allocate gas lift to wells.
In this work, a continuous ant colony optimization (CACO) algorithm was used to allocateoptimum amount of gas to a group of wells for three fields with a different number of wells.
Based upon the fields oil total production rate resulting from the gas allocation to the wells, the
CACO algorithm shows better gas allocation to the wells in comparison with the previous workswith other methods.
2. MATHEMATICAL FORMULATION OF THE PROBLEM
Total oil production from n wells of a field is the summation of individual oil production of each
well and that is a function of gas injected into the wells:
maxQoT D
nXiD1
Qoi D
nXiD1
f .Qgi / D f .Qg1; Qg2; : : : ; Qgn/: (1)
QoT is the total oil production, which must be maximized. Instead of maximization, the problemcan define the minimization of 1=QoT . Thus, the gas lift optimization problem can be defined as:
min f .x/ D1
QoTD
1nX
iD1
Qoi
i D 1; 2; : : : ; n; (2)
nXiD1
Qoi total available gas, (3)
Qgi Qgi min i D 1; 2; : : : ; n; (4)
Qgi Qgi min i D 1; 2; : : : ; n: (5)
1236 M. GHAEDI ET AL.
Qgi min is a minimum amount of injection needed to start the oil production and Qgi max is thegas injection rate at which the well produces the maximum amount of oil and beyond this point
by increasing gas injection rate, oil production rate declines.
3. CACO TECHNIQUE
In recent decades, use of evolutionary algorithms, such as genetic algorithm, simulated annealing,and more recently, ant colony optimization (ACO), have been considered extensively. Ant colony
optimization technique was introduced in the early 1990s by Dorigo and Stutzle (2004). The
inspiring source of ant colony optimization is the foraging behavior of real ant colonies.
ACO has been applied successfully to solve various combinatorial optimization problems,especially discrete problems, such as the traveling salesman problem (Dorigo and Gambaredella,
1997). Optimization problems can be formulated as continuous optimization problems too. These
problems are characterized by the fact that the decision variables have continuous domains, in
contrast to the discrete domains of the variables in a combinatorial optimization problem. ACOhas been also applied to continuous domains (Jalalinejad et al., 2007; Jayaraman et al., 2000;
Razavi and Jalali-Farahani, 2008).
Optimization of gas lift allocation is considered as a continuous problem. In this article, theCACO algorithm introduced by Jalalinejad et al. (2007), Jayarman et al. (2007), and Razavi and
Jalali-farahani (2008) was used, and here by some modification applied it for gas lift allocation.
3.1. Data Structure for Continuous ACO Algorithm
In order to apply ACO algorithm in continuous domain a new data structure is needed. The data
structure, which has been used in this work, is shown in Figure 1. The two dimensional n mmatrices are the search area where n is the number of optimization variables and m is the numberof ants (i.e., regions in continuous domain), which are used to search with m n (Jalalinejad
FIGURE 1 CACO data structure.
OPTIMIZATION OF GAS ALLOCATION 1237
et al., 2007; Jayaraman et al., 2000; Razavi and Jalali-Farahani, 2008). fi and i are 1m vectorsrepresenting the ith region objective function and pheromone trail amount, respectively.
3.2. Steps of CACO Algorithm
The proposed CACO algorithm consists of four main steps. These steps are illustrated in the
following.
3.2.1. Initialization
In this stage, each region is randomly initialized for each variable in the feasible interval.Feasible interval is defined by the problem constraints. The equal amount of pheromone is also
placed in a pheromone trail vector.
3.2.2. Global Search
The global search consists of three operations: crossover, mutation, and trail diffusion. The
crossover operation is done as follows: select a parent randomly and set the first variable of
the childs position vector same as that of the first element of the parents positions vector. The
subsequent values of the variables of the child are set to the corresponding values of a randomlychosen parent with a probability equal to the crossover probability (CP). A crossover probability
equal to one means that each element of the childs position vector has a different parent, while a
CP of zero indicates that the child region has all the same elements as the chosen single parent.After the crossover step, mutation is carried out by randomly adding or subtracting a value to
each and every variable of the newly created region with a probability equal to a suitably defined
mutation probability (Jayaraman et al., 2000; Razavi and Jalali-Farahani, 2008).
In trail diffusion, two parents are selected at random from the parent regions. The variables ofthe childs position vector can have either (1) the value of the corresponding variable from the first
parent; (2) the corresponding value of the variable from the second parent, or (3) a combination
arrived from a weighted average of the above:
Newxi .j / D :xparent1.j /C .1 /:xparent2.j /; (6)
where is a uniform random number in the range [0, 1].The probability of selecting third option is set equal to the mutation probability while allotting
equal probability of selecting the first two steps (Jayaraman et al., 2000).
3.2.3. Local Search
Local ants search in a smaller region around the potential solution to improve the objective
function. Different methods, such as simulated annealing, could be used for a local search. The
probability of selecting a region i by a local ant is given by the same formula as before:
Pi Di .t/
mXiD1
i .t/
: (7)
In this work, complex algorithm introduced by Box (1965) has been used as the local search
procedure.
1238 M. GHAEDI ET AL.
3.2.4. Pheromone Update
Trail evaporation is used in order to ensure that the search during the next generation is not
biased by the proceeding iteration. The pheromone trail is updated after each iteration, as follows:
.tC1/i D
8 pc then(1). Newxi .j / D xR1.j /
iv. Endif
(d). End for
(e). Accept new created regions and replace weakest regions, if it is feasible and its
fitness is improved.(Mutation operation)
(f). For j D 1; : : : ; n, doi. Let r a random number in (0, 1)ii. If r pc then (1). Randomly add or subtract a value to each and every
variable of the new region i .iii. Endif
(g). End for(h). Accept new created regions and replace weakest regions, if it is feasible and its
fitness is improved.
(Trail diffusion)
(i). For j D 1; : : : ; n doi. Let r a random number in (0, 1)ii. If r pm then
(1). Newxi .j / D :xparent1.j /C.1/:xparent2.j /, where a random numberin (0, 1).
iii. If pm r .1 pm=2/ then(2). Newxi .j / D xparent1.j /
iv. If .1 pm=2/ r 1 then(3). Newxi .j / D xparent2.j /
v. Endif
(j). End for
(k). Accept new created regions and replace weakest regions, if it is feasible and its
fitness is improved.3. End for
1240 M. GHAEDI ET AL.
Algorithm 3. The procedure of local search
1. For i D 1; : : : ; L, do(a). Select region i for local search, with probability of Eq. (7).(b). Apply a local search procedure to the region i .(d). Accept new created regions and replace weakest regions, if it is feasible and its
fitness is improved.
3. End for
Algorithm 4. The procedure of pheromone update
1. For i D 1; : : : ; L, do(a). If fitness of region i improved then
i. .tC1/i D .1 /
ti C
ti
(b). If fitness of region i did not improve then
i. .tC1/i D .1 /
ti
(c). Endif
2. End for
4.1. The Set of Six Wells
Total available gas for this set of six wells is 4,600 Mscf/day. Table 1 shows CACO algorithm
parameters for this set of six wells. Figure 2 represents the best and average values for each
generation and Table 2 shows the comparison between the obtained results for the proposed
CACO algorithm and the results of previous works. As it can be seen from this table, the resultsof the proposed CACO algorithm are better than those obtained from the previous works. CACO
algorithm obtained 9.3 STB/day more in the total field production rate than the best of previous
works did.
4.2. The Set of 56 Wells
Total available gas for this set of 56 wells is 22,500 Mscf/day. CACO algorithm parameters for
this set of 56 wells are shown in Table 3. Figure 3 represents the best and average values for
each generation and Table 4 shows the comparison between the obtained results for the proposed
CACO algorithm and the obtained results of previous works. From this table, the results of theproposed CACO algorithm appear to be better than the previous works. The total production rate
evaluated by the CACO algorithm is 25,374.71 STB/day, while the best previous result, which is
TABLE 1
CACO Algorithm Parameters for the Set of Six Wells
Ants
Crossover
Probability
Mutation
Probability
Evaporation
Rate
% Local
Ants
Maximum
Iteration
20 0.6 0.4 0.9 40 40
OPTIMIZATION OF GAS ALLOCATION 1241
FIGURE 2 Best and average value of fitness at each generation for the set of six wells with CACO algorithm.
TABLE 2
Comparison between the Results of Proposed CACO Algorithm and Previous Works for the Set of Six Wells
Total Available Gas D 4,600 MSCF/Day
Kanu et al. (1981)
(Equal Slope)
Buitrago et al. (1996)
(Ex-In)
Ray and Sarker (2007)
(GA) CACO
Well
Qg ,
MSCF/day
Qo,
STB/day
Qg ,
MSCF/day
Qo,
STB/day
Qg ,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
1 186.7 316.1 364.8 351.9 475.525 365.053 482.25 366.72
2 479.2 703.2 836.8 761.6 743.4451 755.421 768.52 758.05
3 708 1,039 1,237.1 1,137.6 1,350.922 1,146.155 1,132.41 1,132.38
4 589.9 585.6 611 589 827.7491quad 622.693 898.75 631.32
5 742.6 697.4 1,378 788.9 1,199.585 774.668 1,285.87 784.86
6 1,667.3 168.9 0 0 0.212049 0 32.2 0.0003
Total 4,373.7 3,510.2 4,427.7 3,629 4,597.438 3,663.99 4,600 3,673.33
Qg=Qo 1.25 1.22 1.22 1.25
TABLE 3
CACO Algorithm Parameters for the Set of 56 Wells
Ants
Crossover
Probability
Mutation
Probability
Evaporation
Rate
% Local
Ants
Maximum
Iteration
400 0.8 0.4 0.9 40 50
TABLE4
ComparisonbetweentheResultsofProposedCACO
Algorithm
andPreviousWorksfortheSetof56Wells
TotalGasAvailableD
22,500MSCF/day
Kanuetal.(1981)
(EqualSlope)
Buitragoetal.(1996)
(Ex-In)
Wangetal.(2002)
(MILP)
RayandSarker(2007)
(GA)
CACO
Well
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
1225
290
504.9
357.1
672
386
812.3447
389.2922
614.258
381.109
20
487
234.6
583
450
626
447.2224
621.576
537.250
637.447
360
481
725.7
626.6
521
605
150.8009
521.0045
404.258
586.311
40
280
478.8
304.2
0280
25.72567
279.6338
42.147
284.011
50
281
54.3
287.1
0281
2.681695
279.3014
510.985
305.840
60
287
363.9
356.6
157
333
428.4005
360.2759
418.321
361.708
70
790
221
833.6
235
836
443.1134
861.4855
510.721
870.224
858
209
333.5
279.6
268
276
550.4224
296.3572
506.214
300.202
91,295
1,568
431.7
813.2
1,295
1,568
1,431.407
1,567.67
1,069.475
1,477.112
10
0233
365
206.7
0233
9.943476
231.1562
330.252
259.210
11
201
727
591.6
871.4
1,048
957
1,186.703
968.2653
646.258
889.307
12
617
459
2,435.4
657.9
800
510
1,797.354
644.1792
709.872
487.768
13
0108
194.9
118.3
0108
0.292891
105.0039
104.698
116.961
14
128
277
184.2
301.2
186
302
381.3879
330.8143
367.258
331.386
15
153
493
649.6
655.2
598
648
855.1724
683.0084
413.258
603.203
16
69
198
228.8
295.3
460
361
966.7526
381.7123
702.522
566.769
17
0892
188.4
918.9
0892
572.052
964.1574
125.268
908.563
18
01,151
428.8
1,234.3
282
1,213
835.341
1,275.154
236.147
1,204.862
19
0310
644.7
340.7
0310
53.06131
311.4512
117.258
319.259
20
215
213
929.5
383.1
975
391
1,417.769
435.0734
534.214
314.906
21
189
251
542.3
384.6
772
455
674.1595
434.5178
717.253
446.680
22
270
195
385.8
214.9
370
214
260.7425
190.4233
447.147
222.757
23
0944
44.5
945.6
0944
0.062342
941.0026
79.254
946.991
24
399
1,420
1,713.9
1,752.6
1,030
1,680
738.5139
1,580.227
832.140
1,617.447
25
0487
805.4
546.6
0487
142.1995
502.8872
368.125
527.245
26
082
591.6
127.2
120
105
3.961657
79.96662
184.258
111.793
27
0353
247.8
355.9
0353
1.579943
350.0281
110.247
355.021
28
01,044
140.2
1,052.7
01,044
180.759
1,051.767
654.214
1,061.503
29
0184
268.5
196.4
0184
25.61667
182.767
89.124
188.848
(continued)
1242
TABLE4
(Continued)
TotalGasAvailableD
22,500MSCF/day
Kanuetal.(1981)
(EqualSlope)
Buitragoetal.(1996)
(Ex-In)
Wangetal.(2002)
(MILP)
RayandSarker(2007)
(GA)
CACO
Well
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
Qg,
MSCF/day
Qo,
STB/day
30
0308
68.7
309.2
0308
2.85942
304.0543
69.214
309.228
31
0354
1.5
354
0354
2.491896
354
0.000
354.000
32
0618
451.8
681.2
131
654
175.8315
657.6575
398.214
655.833
33
184
185
358.8
220
280
211
500.2639
240.9669
467.254
239.341
34
0209
459
215.6
0209
1.078196
207.0639
82.619
209.959
35
0179
772.3
265.6
195
216
211.7989
216.4891
208.147
217.946
36
064
198.5
216.3
108
204
0.031785
176.0157
396.145
231.477
37
0270
170.5
73.2
064
1.727461
61.10487
99.472
70.626
38
112
174
668.2
325
157
282
242.6654
292.9252
358.214
311.640
39
168
0235.1
190.6
301
207
313.905
206.4406
667.721
236.547
40
0372
114.9
27.9
98
27
13.69307
5.077453
381.217
31.792
41
0372
315.1
373.4
0372
329.8575
371.1076
429.214
373.409
42
0200
33.7
201.2
0200
0.099835
198.0036
105.269
203.454
43
00
1,284
404.9
797
337
1,199.252
390.0909
702.150
313.846
44
047
95.6
404.7
0397
34.83983
398.9659
174.125
407.958
45
0397
33.2
83.4
083
59.72461
81.55598
64.214
83.677
46
083
289.3
65.8
14
50
2.538431
45.06269
481.257
158.918
47
3,042
441
00
3,042
441
1.812014
082.125
0.000
48
1,633
197
00
2,466
483
2572.13
459.3049
59.300
0.000
49
1,418
232
00
1,418
232
0.075651
1.015529
427.932
2,479.870
50
1,301
146
00
00
0.044171
0139.245
0.000
51
2,224
223
00
00
0.37171
02,741.210
461.404
52
2,830
317
00
00
5.910134
10.72841
510.250
585.219
53
1,304
186
00
1,484
267
11.68654
0115.241
0.000
54
2,594
278
00
00
16.88857
34.24514
545.842
599.316
55
2,317
152
00
00
5.103219
0121.249
0.000
56
1,655
403
00
1,770
452
2,274.167
501.3664
278.147
154.807
Total
22,508
21,265
20,453.9
21,789.9
22,500
22,632
22,376.39
22,033.4
22,487.38
25,374.71
Qg=Q
o1.059
0.939
0.994
1.016
0.886
1243
1244 M. GHAEDI ET AL.
FIGURE 3 Best and average value of fitness at each generation for the set of 56 wells with CACO algorithm.
obtained by mixed integer linear programming (Wang et al., 2002) method, is 22,376.39 STB/day.CACO algorithm resulted in 2,742.7 STB/day more in the field total oil production rate than the
best result of previous works.
4.3. The Set of Nine Wells
This set of nine wells belongs to an Iranian southern west field. Wells 1 through 6 have been
completed in the Asmari reservoir, while wells 7 through 9 produce from the Bangestan section.
Tables 5 and 6 show the reservoir data and the production data of these nine wells respectively.
GLPCs of these wells were calculated with VFPi module of Eclipse commercial software. Withoutany gas lift operation in this field, total oil production rate of the field is 6,502 STB/day. If there
is not any limitation in the amount of available gas, and gas is optimally injected into each well
to reach the maximum oil production rate as well, the total oil production rate of the field would
be 23,344.88 STB/day. Table 7 shows the optimum gas injection rate as well as the oil productionrate of each well.
It is supposed that only 100 MMscf/day of gas is available and this amount of gas optimally
distributed among the wells. CACO algorithm parameters for this set of nine wells are shown in
Table 8. Figure 4 represents the best and average values for each generation. Table 9 shows thegas injection rate along with oil production rate of each well.
5. CONCLUSIONS
1. A CACO algorithm for optimization of gas allocation to a group of wells in gas lift was
introduced.
2. The applied CACO technique seems to be an efficient optimization method for optimizingthe gas lift allocation (improvement of 9.3 STB/day relative to the best previous results of
previous works for a field with 6 wells and of 2,742.7 STB/day relative to the best previous
results of previous works for a field with 56 wells, confirms this fact).
TABLE5
AsmariandBangestanReservoirData
ofOneoftheIranianSouthern
WestFields
Asm
ariReservoir
BangestanReservoir
Well1
Well2
Well3
Well4
Well5
Well6
Well7
Well8
Well9
Welldepth
(ft)
7,910
7,635
7,720
7,825
7,865
7,900
10,250
10,200
10,265
Reservoirpressure
(psia)
3,738
3,738
3,738
3,738
3,738
3,738
5,304
5,304
5,304
Bubblepointpressure(psia)
2,925
2,925
2,925
2,925
2,925
2,925
2,995
2,995
2,995
Form
ationgas
liquid
ratio(scf/STB)
853
853
853
853
853
853
940
940
940
APIoilgravity(API)
30.2
30.2
30.2
30.2
30.2
30.2
28.4
28.4
28.4
Water
cut(%
)0
00
00
00
00
Bottom
holetemperature
(F)
190
190
190
190
190
190
238
238
238
Wellheadtemperature
(F)
100
100
100
100
100
100
100
100
100
TubingI.D.(in.)
551/2
55
55
41/2
45
CasingI.D.(in.)
795/8
77
77
55
7
PI(STB/day/psi)
1.56
2.2
1.7
1.82
1.9
2.15
1.41
1.59
1.7
Wellheadflowingpressure
880
970
810
805
945
935
1,720
1,710
1,690
Specificgravityofproducedwater
1.16
1.16
1.16
1.16
1.16
1.16
1.14
1.14
1.14
Specificgravityofgas
0.751
0.751
0.751
0.751
0.751
0.751
0.65
0.65
0.65
Welldeviation
Straight
VogelsequationforIPRbelowbubblepointpressure
1245
1246 M. GHAEDI ET AL.
TABLE 6
Production Data of One of the Iranian Southern Field Wells
Rate,
BPD
FWHP,
psia
FBHP,
psia
P.I.,
bbl/dayay/psi
Drawdown,
psi
AOF,
BPD
Well 1 502 880 3,415 1.56 322 3,366
Well 2 1,020 970 3,275 2.2 463 4,842
Well 3 650 810 3,355 1.7 383 3,693
Well 4 720 805 3,340 1.82 398 3,943
Well 5 930 945 3,250 1.9 488 4,200
Well 6 1,060 935 3,245 2.15 493 4,743
Well 7 480 1,720 4,965 1.41 339 4,295
Well 8 540 1,710 4,960 1.59 339 4,830
Well 9 600 1,690 4,950 1.7 354 5,150
TABLE 7
Optimum Gas Injection Rate and Oil Production Rate of Each Well,
for the Set of Nine Wells with CACO
Total Available Gas D Unlimited
Well
Qg ,
MSCF/day
Qo,
STB/day
1 41,769.5 2,211.167
2 54,678.3 3,383.803
3 41,342.3 2,344.323
4 41,206.2 2,551.114
5 42,305.9 3,005.679
6 43,867.9 3,252.963
7 45,812.2 2,066.432
8 46,256.8 2,187.667
9 45,926.1 2,341.732
Total 403,165.2 23,344.88
TABLE 8
CACO Algorithm Parameters for the Set of Nine Wells
Ants
Crossover
Probability
Mutation
Probability
Evaporation
Rate
% Local
Ants
Maximum
Iteration
200 0.8 0.4 0.9 40 50
3. It is recommended to use stochastic optimization methods like the CACO algorithm in the
case of dealing with a large number of wells (as in the mentioned problem with 56 wells).4. The effect of optimum gas allocation was very well shown by the studied three practical
cases.
5. This work shows very well the effect of gas lift on increasing the field production rate. For
instance, in the last studied case (Iranian field), a 280.6% increase in the field productionrate could be reached by optimally allocating only 100 MMSCF/day of gas to the wells
(from 6,502 STB/day to 18,249.69 STB/day).
OPTIMIZATION OF GAS ALLOCATION 1247
FIGURE 4 Best and average value of fitness at each generation for the set of nine wells with CACO algorithm.
TABLE 9
Gas Injection Rate and Oil Production Rate for the Set of Nine Wells
with CACO Algorithm When the Amount of Available Gas is Limited
Total Available Gas D 100,000 MSCF
Well
Qg ,
MSCF/day
Qo,
STB/day
1 8,621.677 1,644.183
2 10,806.63 2,755.742
3 17,082.79 1,942.741
4 11,480.12 1,986.983
5 8,440.89 2,488.846
6 7,946.661 2,610.393
7 10,548.68 1,478.036
8 12,037.9 1,587.696
9 13,034.65 1,755.076
Total 100,000 18,249.69
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