Investigating the effect of heterogeneity on infill wells

Abstract

In recent years, improving oil recovery (IOR) has become an important subject for the petroleum industry. One IOR method is infill drilling, which improves hydrocarbon recovery from virgin zones of the reservoir. Determining the appropriate location for the infill wells is very challenging and greatly depends on different factors such as the reservoir heterogeneity. This study aims to investigate the effect of reservoir heterogeneity on the location of infill well. In order to characterize the effect of heterogeneity on infill well locations, some geostatistical methods, e.g., sequential gaussian simulation, have been applied to generate various heterogeneity models. In particular, different correlation ranges (R) were used to observe the effect of heterogeneity. Results revealed that an increase in correlation ranges will lead to (1) a higher field oil production total, and (2) a faster expansion of the drainage radius which consequently reduced the need for infill wells. The results of this study will help engineers to appropriately design infill drilling schemes.

http://crossmark.crossref.org/dialog/?doi=10.1007/s13202-015-0204-8&domain=pdf

Web End = http://crossmark.crossref.org/dialog/?doi=10.1007/s13202-015-0204-8&domain=pdf

Web End = J Petrol Explor Prod Technol (2016) 6:451463 DOI 10.1007/s13202-015-0204-8

ORIGINAL PAPER - PRODUCTION ENGINEERING

Investigating the effect of heterogeneity on inll wells

Mahmood Bagheri1 Mohsen Masihi2

Received: 19 November 2014 / Accepted: 17 October 2015 / Published online: 1 December 2015 The Author(s) 2015. This article is published with open access at Springerlink.com

Abstract In recent years, improving oil recovery (IOR) has become an important subject for the petroleum industry. One IOR method is inll drilling, which improves hydrocarbon recovery from virgin zones of the reservoir. Determining the appropriate location for the inll wells is very challenging and greatly depends on different factors such as the reservoir heterogeneity. This study aims to investigate the effect of reservoir heterogeneity on the location of inll well. In order to characterize the effect of heterogeneity on inll well locations, some geostatistical methods, e.g., sequential gaussian simulation, have been applied to generate various heterogeneity models. In particular, different correlation ranges (R) were used to observe the effect of heterogeneity. Results revealed that an increase in correlation ranges will lead to (1) a higher eld oil production total, and (2) a faster expansion of the drainage radius which consequently reduced the need for inll wells. The results of this study will help engineers to appropriately design inll drilling schemes.

Keywords IOR Inll wells Heterogeneity SGS

Correlation ranges Drainage radius

Introduction

Inll drilling technique plays an important role in reservoir development especially in tight reservoirs. Increasing oil price and limitations of new reserves make improving oil recovery methods inevitable. As the recovery ratio is controlled by many complicated factors, such as the level of reservoir heterogeneity, determining the location of inll wells seems to be a very challenging issue (Soto et al. 1999). Hence there is no homogeneous reservoir in reality, and it is widely believed that in heterogeneous reservoirs inll drilling plays an important role (Hou and Zhang 2007; Barber et al. 1983) and improves oil recovery by accelerating productions (Driscoll 1974; Gould and Munoz 1982; Gould and Sarem 1989; Sayyafzadeh and Pourafshari 2010). Moreover, if inll drilling is linked to water ooding, it becomes more effective and economical comparing to chemical injection or tertiary recovery (Holm et al. 1980; French et al. 1991; Thakur and Satter 1998). The existence of different rock types with various thicknesses between two wells in a reservoir may cause a complex ow behavior. One of the applications of inll wells is to reduce the distance between the wells which helps maintain layer continuity and enhances well connectivity (Wu et al. 1989; Malik et al. 1993).

Making a precise decision on the location and number of inll wells is critical to the economics of an inll drilling project. Feasibility of inll drilling potential, especially in marginal elds, must be reliably assessed both technically and economically (Cheng et al. 2008). Therefore, it is highly recommended to conduct a complete reservoir evaluation consisting of geological, geophysical, and petrophysical reservoir analysis and interpretations to determine inll drilling potential in a reservoir. While this is a very accurate method, this approach can be

& Mahmood Bagheri [email protected]

Mohsen Masihi [email protected]

1 Department of Petroleum Engineering, Science and ResearchBranch, Islamic Azad University, Tehran, Iran

2 Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

123

452 J Petrol Explor Prod Technol (2016) 6:451463

Table 1 Known permeability data in the reservoir model

Cell location (32, 47) (31, 26) (27, 90) (20, 12) (15, 86) (10, 32) (6, 2) (5, 30) (2, 80) (1, 5)

K (md) 208.812 107.974 32.9067 73.5827 262.615 198.433 176.104 91.4402 73.5827 151.29

Cell location (93, 55) (85, 47) (81, 31) (64, 44) (62, 95) (59, 29) (51, 1) (43, 22) (39, 79) (36, 67)

K (md) 187.548 262.615 228.224 91.4402 151.29 123.366 278.007 270.444 54.1704 151.29

Table 2 Model parameters

Property Explanation

Number of permeability data points 20

Reservoir dimensions 2500 9 2500 9 30 ft

Number of grids 100 9 100 9 1

Variogram type Isotropic spherical

Uniform interval 625 ft

Minimum permeability 0 md

Maximum permeability 300 md

Number of simulation runs 100 times

prohibitively time consuming and expensive for hydro-carbon elds.

Methods of investigating inll well potential are divided into two main categories: (1) statistical methods and (2) optimization methods.

Statistical methods

A statistical view is the rst approach in reservoir evaluation. The most common method in statistical approaches is the moving window technique. This method can use a minimum amount of reservoir geological description to determine the inll potential (Fuller et al. 1992). There have been a multitude of empirical and statistical analysis developments in the moving window method (Hudson et al. 2000, 2001). McCain et al. (1993) particularly used the statistical moving window approach to determine inll potential in a complex, low-permeability gas reservoir (McCain et al. 1993). Later, Voneiff and Cipolla (1996) developed the moving window technique and applied it for rapid assessment of inll and recompletion potential in the eld (Voneiff and Cipolla 1996).

The other approach to nd inll candidate wells is rapid inversion. In this technique, which was introduced and developed by Gao and McVay (2004), reservoir simulation is combined with automatic history matching (Gao and McVay 2004). In rapid inversion, a reservoir simulator serves as the formal method to calculate well production responses from reservoir description data. Then sensitivity coefcients are calculated internally and are used in the estimated permeability eld and forward model. Lastly, the expected performances of potential inll wells can be determined (Guan et al. 2005).

Optimization method

Disseminating the locations of well is one critical issue in exploration and development of oil and gas elds. The process of determining the optimal well location is an optimization problem.

Shook and Mitchell (2009) used time-of-ight to extend the derivation of classical measures of heterogeneity to three-dimensional models. They proposed application of ow-capacity/storage-capacity F-; diagram, Lorenz coef

cient. Moyner et al. (2014) used ow diagnostics for reservoir management. They used Lorenz coefcient as the popular measure of heterogeneity in the context of streamline. Based on their work, the coefcient perfectly correlated with oil recovery predicted by a multiphase ow simulation. Also they used Lorenz coefcient as an objective function for optimization process (Moyner et al. 2014).

Although the Lorenz coefcient correlates well with recovery, it will generally give multiple local minimums and using from global optimization method will be necessary.

Several new methods are suggested by researchers, and only a few studies have presented a careful comparison of their performance with more popular genetic algorithm-based and gradient-based optimization techniques. (Onswnulu and Durlofski 2010; Nasrabadi et al. 2012).

Genetic algorithm

This method is one of the most popular methods in the well placement optimization. The idea of a genetic algorithm is rst introduced by Holland in 1975 (Ariadji et al. 2014).

The genetic algorithm is a stochastic and heuristic search technique (Abukhamsin 2009). A genetic algorithm,

123

J Petrol Explor Prod Technol (2016) 6:451463 453

Fig. 1 Variogram models for different realizations

123

454 J Petrol Explor Prod Technol (2016) 6:451463

Table 3 Variogram model parameters

No. Variogram type Range (ft) Sill Nugget

1 Spherical 250 5000 10.0

2 Spherical 375 5000 10.0

3 Spherical 500 5000 10.0

4 Spherical 625 5000 10.0

5 Spherical 750 5000 10.0

in its purest form, will try to replicate the concepts of natural evolution, in a controlled and mathematical environment. In a well placement optimization problem, the different individuals in a generation are replaced with well location data, and their cumulative production or NPV is a measure of their chance of survival (Nasrabadi et al. 2012).

The rst step in optimization of well placement by genetic algorithm is to generate an initial population (randomly selected well locations). The next step will be to evaluate each well and rate their individual performance by calling a reservoir objective function.

Gradient method

Gradient-based method is an important class of optimization methods. This method provides an improved objective function; each iteration results in a better well placement scenario, close to the original selection within a few iterations (Nasrabadi et al. 2012).

As the optimal location for a new well depends on how it is to be operated, Isebor et al. (2014) considered well location and well control optimization problems simultaneously as a joint problem and applied gradient approach in addition to several other methods to solve the optimization problem. They believed that exclusive gradient method may get trapped in relatively poor local optima (Isebor et al. 2014).

Current optimization methods do not include both reliability and efciency features simultaneously. Although gradient-based methods are very efcient, they are highly dependent on the initial guess and cannot guarantee nding a global optimum. However, more reliable methods, such

Fig. 2 Permeability model generated using the variogram of Fig. 1

123

J Petrol Explor Prod Technol (2016) 6:451463 455

Fig. 3 5-spot well pattern and the selected inll wells between them

as genetic algorithm, need an excessive number of reservoir simulation which makes their eld application very expensive (in terms of required CPU time or computational hardware).

In order to solve such problems, there are new and advanced methods. However, it should not cause neglecting basic methods. Although more advanced optimization-based techniques have been presented for well placement, this is a basic research attempting to nd a relation between correlation lengths in permeable/impermeable region with

well spacing within inll drilling decision. We used geo-statistical method to investigate the effect of heterogeneity on inll wells.

Model set-up and procedure

The starting point in system behavior recognition is generating a static reservoir model. Generally, in simulation and modeling, the number of known parameters is less than

123

456 J Petrol Explor Prod Technol (2016) 6:451463

A B

Correla on range :250

Correla on range :375

3760000

1550 1650 1750 1850 1950

3800000

1550 1650 1750 1850 1950

3740000

3720000

Final produc on(FTP-STB)

Final produc on(FTP-STB)

3750000

3700000

3700000

3680000

3650000

3660000

3640000

3600000

3620000

3550000

3600000

3580000

3500000

3560000

3450000

3540000

Average Well Spacing ( )

Average Well Spacing ( )

Correla on range : 500

correla on range : 625

C

D

3760000

1550 1650 1750 1850 1950

3760000

1550 1650 1750 1850 1950

3750000

3750000

Final produc on(FTP-STB)

3740000

3740000

3730000

Final produ on(FTP-STB)

3730000

3720000

3720000

3710000

3710000

3700000

3700000

Average Well Spacing ( )

Average Well Spacing ( )

E

Correla on range:750

3760000

1550 1650 1750 1850 1950

3755000

Final produc on (FTP-STB)

3750000

3745000

3740000

3735000

3730000

3725000

3720000

3715000

3710000

Average Well Spacing ( )

Fig. 4 Final production versus average well spacing for each correlation ranges (from diagram ae): 250, 375, 500, 625, and 750 (ft)

that of the unknown ones. Therefore, applying a suitable estimation method for solving the problem is essential. In addition to all estimation techniques, simulations based on geostatistical methods, such as Sequential Gaussian simulation (SGS), seem to be very efcient. In the SGS method, different realizations can be produced from a data series with the same probability. This method is an appropriate technique for generating data with constant

spatial variability of statistical parameters. In this study, after generating the heterogeneity factors with the SGS method, a 5-spot standard model has been applied for the basic wells arrangement. Then heterogeneities in ve different correlation ranges (drawn from the SGS model results) were applied in the basic model.

In particular, 20 permeability data points were used to generate the permeability model using geostatistical

123

J Petrol Explor Prod Technol (2016) 6:451463 457

Table 4 The reservoir characteristics

Reservoir characteristics Explanation

Reservoir dimensions 2500 9 2500 9 30 ft3

Reservoir depth 18,000 ft

Grid numbers 100 9 100 9 1

Grid dimensions 25 9 25 9 30 ft3

Porosity 20 %

Reservoir rock type Sandstone

Reservoir rock compressibility 1.2E-6 (1/psi)

Reference pressure 4100 psi

Initial reservoir pressure 3000 psi

Initial water saturation 20 %

Residual oil saturation 15 %

Oil density 37.457 lb/ft3

Water density 62.366 lb/ft3

Oil viscosity 1.174 (Cp)

Water viscosity 0.9 (Cp)

Table 5 Well characteristics

Well characteristics Explanation

Water injection pressure 3000 psi

Production type Constant rate

Production rate 2000 STB/day

Water cut limit 90 %

Simulation start day 30 Jan 2013

Simulation time 30 years

methods (Table 1). Therefore, in order to show the heterogeneity effect, ve different correlation ranges of 250, 375, 500, 625, and 750 ft were applied in the variogram model construction. By means of SGS, 25 different realizations were produced to calculate the error of each correlation range. However, it should be noted that some assumptions were taken into account before generating the permeability models. For this research, a one-layer reservoir with 2500 ft 9 2500 ft 9 30 ft dimensions which consists of 100 9 100 9 1 grids in the x, y, and z directions was applied. The reservoir rock type was normal sandstone

with a constant porosity of 20 %, and the initial pressure of the reservoir rock was 2000 psi (Table 2).

Figure 1 illustrates the applied variograms in the reservoir modeling. The assumptions for the variogram model construction are given in Table 3.

An example of a permeability map generated using the variogram shown in Fig. 1 is plotted in Fig. 2.

In order to generate the permeability map, a 5-spot pattern is applied as the basic scenario on the reservoir which consists of four production wells and one injection well in the middle of the reservoir. Then, two inll

123

458 J Petrol Explor Prod Technol (2016) 6:451463

Table6Maximumproductionofeveryrealizationindifferentcorrelationranges

Rx(ft)1streal_FOPT(STB)2ndreal_FOPT(STB)3rdreal_FOPT(STB)4threal_FOPT(STB)5threal_FOPT(STB)6threal_FOPT(STB)7threal_FOPT(STB)

2503,743,0683,715,5563,730,9863,664,1123,693,2703,630,9823,715,710

3753,700,7143,729,5453,739,5083,684,8353,682,2283,739,7413,648,883

5003,734,6763,750,0743,736,3263,739,8863,736,8533,739,6703,745,588

6253,751,1683,747,1223,734,0643,748,3863,741,4713,739,9543,739,617

7503,735,8123,742,1373,751,1623,751,7903,739,4183,741,7443,737,803

Rx(ft)8threal_FOPT(STB)9threal_FOPT(STB)10threal_FOPT(STB)11threal_FOPT(STB)12threal_FOPT(STB)13threal_FOPT(STB)14threal_FOPT(STB)

2503,704,3603,701,8103,652,3143,682,5233,682,1383,637,7323,746,240

3753,692,3303,734,2103,714,1333,621,8973,735,0343,717,1813,737,894

5003,746,3183,742,5793,738,5663,723,5303,728,3303,741,2623,742,706

6253,733,8293,745,9743,733,0793,745,8153,757,2063,747,9963,732,520

7503,736,8083,737,3703,736,1583,747,0253,748,2633,745,8523,756,550

Rx(ft)15threal_FOPT(STB)16threal_FOPT(STB)17threal_FOPT(STB)18threal_FOPT(STB)19threal_FOPT(STB)20threal_FOPT(STB)21streal_FOPT(STB)

2503,735,6703,701,4363,681,5223,672,8713,592,8983,704,7513,751,390

3753,615,7323,667,5663,688,3773,691,2963,702,7663,639,5633,686,172

5003,744,0413,731,9943,733,8033,742,5673,742,1033,736,8403,740,203

6253,747,6223,743,3663,741,3883,752,3073,740,9143,744,7013,740,489

7503,752,7983,730,5483,742,9673,750,2693,740,6883,742,5893,745,083

Rx(ft)22ndreal_FOPT(STB)23rdreal_FOPT(STB)24threal_FOPT(STB)25threal_FOPT(STB)av.

2503,696,1033,727,9883,711,5073,526,6293,688,143

3753,597,7213,650,7383,715,5823,730,5243,690,567

5003,738,5213,742,3183,755,5993,740,7033,739,802

6253,743,0503,746,3923,744,8783,742,3003,743,424

7503,737,6313,750,2223,738,8683,751,7953,743,654

123

J Petrol Explor Prod Technol (2016) 6:451463 459

3800000

150 250 350 450 550 650 750 850

Final produc on(FTP-STB)

3700000

3650000

3600000

potentials were placed in the basic model at six different locations (Fig. 3). Each production well produces with the constant rate of 2000 bbl./day and the injection pressure is 3000 psi. The simulation was applied to this reservoir to predict the reservoir behavior for 40 years of production. Thereafter, 100 realization simulations took place for each well conguration, and the average of these 100 simulations was considered for each correlation range. Finally, total production of each case was compared to the average well spacing for each inll pattern as shown in Fig. 4. Also, characterization of production reservoir mentioned in Tables 4, 5.

3750000

3550000

3500000

Correla on range( )

Fig. 5 Final production of reservoir versus correlation range

Fig. 6 Drainage radius after the rst 10 days for the model (with correlation range of 625 ft)

123

460 J Petrol Explor Prod Technol (2016) 6:451463

Fig. 7 Drainage radius after the rst 10 days for the model (with correlation range of 500 ft)

Table 7 Drainage radius in every correlation range

Rx 250 Rx 375 Rx 500 Rx 625 Rx 750

Day 1 443.807 443.425 425.268 450.115 456.804

Day 2 705.275 715.596 721.33 791.284 1026.38

Day 4 850.057 920.298 1014.91 1204.13 1384.75

Day 6 951.835 1192.66 1324.54 1390.48 1390.48

Day 8 1069.38 1364.68 1376.15 1390.48 1390.48

Day 10 1189.79 1384.75 1384.75 1390.48 1390.48

Day 12 1227.06 1384.75 1384.75 1390.48 1390.48

Day 14 1235.67 1384.75 1384.75 1390.48 1390.48

Day 16 1390.48 1390.48 1390.48 1390.48 1390.48

Day 18 1390.48 1390.48 1390.48 1390.48 1390.48

123

J Petrol Explor Prod Technol (2016) 6:451463 461

Fig. 8 Changes of average drainage radius in different correlation ranges versus time

1550

Average of drainage radius( )

1350

Rx=250 ( )

Rx=375 ( )

Rx=500 ( )

Rx=625 ( )

Rx=750 ( )

1150

950

750

550

350 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Day

According to Fig. 4, reducing the average well spacing in an inll drilling scenario causes an increase in total production. However, if this average distance becomes less than 1500 ft, it will have a reverse effect and the total production will decrease. It should be mentioned that for higher correlation ranges more production in the reservoir occurs with less average well spacing. Moreover, changes in correlation ranges also may affect production values. The maximum production value in each realization and at each correlation range is summarized in Table 6.

Figure 5 illustrates that while the correlation range increases, hydrocarbon production will increase as well. Also, in lower correlation ranges, there are more scattered data than those observed at higher correlation ranges. This may be caused by higher correlation ranges leading to a greater effective radius in the simulation outcomes. Therefore, the reservoir will be more homogeneous, and, as a result, the production rate from the reservoir will increase.

In order to observe the changes in the well drainage radius, the pressures of each cell were calculated, and the isobar surfaces were plotted at different time steps. The graphs reveal that the pressure diminished through the production period (Figs. 6, 7; Table 7).

It can be concluded from the graphs seen in Fig. 8 that it takes more time for the drainage radius to reach its

maximum level in lower correlation ranges. This means that by increasing the correlation ranges, the heterogeneous reservoir can be assumed to be a homogeneous one (see Fig. 9).

Conclusions

In this research, the effect of reservoir heterogeneities generated by geostatistical methods applied to inll drilling scenarios has been discussed. The following can be concluded from this study:

1. Inll drilling is an appropriate method in developing hydrocarbon reservoirs and producing more oils.

2. Increasing the correlation range may cause an increase in the production of the reservoir. The production increased almost 5961 % in the rst 10 years and 1115 % at the end of the simulation. In addition, the maximum drainage radius increased as well.

3. In inll drilling, reducing the average distance between wells to a certain limit resulted in an increase in the total production rate of the reservoir, but while the average distance between wells became less than 1500 ft, the nal production decreased.

123

462 J Petrol Explor Prod Technol (2016) 6:451463

Fig. 9 Final oil saturation distribution after 40 years (end of simulation) for each correlation range

123

J Petrol Explor Prod Technol (2016) 6:451463 463

The results of this study can help engineers to better design appropriate inll drilling schemes.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http:// http://creativecommons.org/licenses/by/4.0/

Web End =creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

References

Abukhamsin A (2009) Optimization of well design and location in real eld. A report submitted to the department of energy resources engineering. Thesis of the Stanford University

Ariadji T et al (2014) A novel tool for designing well placements by combination of modied genetic algorithm and articial neural networks. Petrol Sci Eng 122:6982

Barber AH, George CJ, Stiles LH, Thompson BB (1983) Inll drilling to increase reservesactual experience in nine elds in Texas, Oklahoma, and Illinois. SPE 11023

Cheng Y, McVay DA, Wang J, Ayers WB (2008) Simulation-based technology for rapid assessment of redevelopment potential in marginal gas elds-technology advances and validation in garden plains eld, Western Canada sedimentary basin. SPE 100583:521534

Driscoll VJ (1974) Recovery optimization through inll drilling concepts, analysis, and eld results. In: Paper SPE 4977 presented at the 49th annual meeting of the society of petroleum engineers of AIME, Houston, Texas, 69 October

French RL, Brimhall RM, Wu CH (1991) A statistical and economic analysis of incremental waterood inll drilling recoveries in West Texas carbonate reservoirs. In: SPE 22624 presented at the SPE annual technical conference and exhibition, Dallas, 69 October

Fuller SM, Sarem AM, Gould TL (1992) Screening wateroods for inll drilling opportunities. In: SPE 22333 presented at the SPE international meeting on petroleum engineering held in Beijing, China, 2427 March

Gao H, McVay DA (2004) Gas inll well selection using rapid inversion methods. In: Paper SPE 55563, presented at the SPE annual technical conference and exhibition held in Houston, TX, 2629 September

Gould TL, Munoz MA (1982) An analysis of inll drilling. In: SPE

11021, presented at the 57th annual fall technical conference and exhibition of the society of petroleum engineers of AIME, New Orleans, Louisiana, pp 2629Gould TL, Sarem AM (1989) Inll drilling for incremental recovery.

SPE 18941:229237Guan L, Du Y, Wang Z (2005) Petroleum lessons in past 20 years,

World Petroleum Congress, WPC-18-0885Holm LW et al (1980) Inll drilling vs. tertiary oil recovery vs. more imports. In: SPE 9094, presented at the SPE annual technical conference, Union Oil Co. of California

Hou J, Zhang SH (2007) A streamlinebased model for potentially prediction of enhance oil recovery, SPE 105246

Hudson JW, Jochen JE, Jochen VA (2000) Practical technique to identify inll potential in low-permeability gas reservoirs applied to the milk river formation in Canada. In: SPE 59779, presented at the SPE/CERI gas symposium, Calgary, 35 April

Hudson JW, Jochen JE, Spivey JP (2001) Practical methods to high-grade inll opportunities applied to the mesaverde, morrow, and cotton valley formations. In: SPE 68598 presented at the SPE hydrocarbon economics and evaluation symposium, Dallas, 23 April

Isebor O, Durlofsky L, Ciaurri DE (2014) A derivativefree methodology with local and global search for the constrained joint optimization of well locations and controls. Comput Geosci 18:463482

Malik ZA, Silva BA, Brimhall RM, Wu CH (1993) An integrated approach to characterize low permeability reservoirs connectivity to optimize waterood inll drilling. In: SPE 25853 presented at the joint rocky mountain regional and low permeability reservoirs symposium, Denver, April 2628

McCain WD Jr., Voneiff GW, Hunt ER, Semmelbeck ME (1993) A tight gas eld study: Carthage (Cotton Valley) eld. In: Paper SPE 26141 presented at the SPE gas technology symposium, Calgary, 2830 June

Moyner O, Krogstad S, Lie K (2014) The application of ow diagnostics for reservoir management. SPE 171557, pp 306323

Nasrabadi H et al (2012) Well placement optimization: a survey with special focus on application for gas/gas-condensate reservoirs. In: Presented at natural gas science and engineering, pp 616

Onswnulu JE, Durlofski LJ (2010) Application of particle swarm optimization algorithm for determining optimum well location and type. Comput Geosci 140:183198

Sayyafzadeh M, Pourafshari P (2010) Increasing ultimate oil recovery by inll drilling and converting weak production wells to injection wells using streamline simulation. In: SPE132125-MS, Presented as conference paper in international oil and gas conference and exhibition in China, 810 June, Beijing, China

Shook G, Mitchell K (2009) A robust measure of heterogeneity for ranking earth models: the F-Phi curve and dynamic Lorenz coefcient. In: SPE annual technical conference and exhibition

Soto BR, Wu CH, Buleba AM (1999) Inll drilling recovery models for carbonate reservoirsa multiple statistical, non-parametric regression, and neural network approach. In: SPE 57458, presented at the SPE eastern regional conference and exhibition, Charleston, West Virginia

Thakur GC, Satter A (1998) Integrated waterood asset management.

Tulsa, Okla, PennWell BookVoneiff GW, Cipolla CA (1996) New approach to large-scale inll evaluations applied to the Ozona (Canyon) gas eld. In: SPE 35203, presented at the SPE Permian oil and gas recovery conference. Midland, TexasWu CH et al (1989) An evaluation of waterood inll drilling in west texas Clearfork and San Andres carbonate reserves. In: SPE 19783, presented at the SPE annual technical conference and exhibition, San Antonio, 811 October

123