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ScienceDirect Procedia Computer Science 102 (2016) 446 – 452

12th International Conference on Application of Fuzzy Systems and Soft Computing, ICAFS 2016, 29-30 August 2016, Vienna, Austria

Advanced well spacing system application in the development of oil and gas fields Gurbanov Rf.S.a *, Musayeva S.A.b, Gurbanov R.S.c , Ahmedov.Z.M.d a,d

Azerbaijan State Oil and Industrial University, bBaki Higher Oil School, cҰGeothecnological Problems of Oil and Gas, and ChemistryҰ Scientific-Research Institute

Abstract Selecting the spacing density of wells is very important issue of rational development of oil and gas fields. Wells spacing significantly affects to the key indicators of the field development such as the rate of liquid and gas recovery from the reservoir, completeness of oil sweep out from the producing formation, the hydrocarbons ultimate recovery factor, reservoir producing life and a number of other indicators of development. In view of applications in oilfield practice, in most cases technologically imperfect well patterns, particularly, in productive beds with geologically and physically complicated conditions (reservoir rock heterogeneity, low filtration properties of layers, high oil viscosity, low energy manifestations during reservoir development, and so on) leads to formation of "stagnant" oil and less drained areas undeveloped in the primary oil recovery method. The present scientific work is an attempt to prove that the right choice of wells spacing system can be excluded "stagnant" oil zone, left undrained zones during the primary field development method. © 2016 2016 The Elsevier B.V. This is an open access article under the CC BY-NC-ND license © The Authors. Authors.Published Publishedbyby Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility ofthe Organizing Committee of ICAFS 2016. Peer-review under responsibility of the Organizing Committee of ICAFS 2016 Keywords: well pattern; well spacing; well spacing density; well spacing system; uniform well spacing; non-uniform well spacing; oil recovery factor; stagnant oil; drainage zone; interference of wells.

1. Introduction Despite many theoretical and practical studies, the results of field experiments on individual oil fields, the question of rational spacing of operation wells in the productive area has not yet found its final decision. The new approach when selecting density of wells spacing, proposed by the authors of this research paper is based on the applying principles of fluid filtration hydrodynamics and takes into account the natural properties of reservoirs.

* Corresponding author, Tel.: +99 412 493 45 38 E mail address : [email protected]

1877-0509 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of ICAFS 2016 doi:10.1016/j.procs.2016.09.425

Rf.S. Gurbanov et al. / Procedia Computer Science 102 (2016) 446 – 452

2. Main results Well is the underground structure through which we have the access to the reservoir sources of hydrocarbons. Development of oil and gas fields is implemented by means of a spacing of wells. The aggregate operating and injection wells, located in a certain order on the productive formation are called well spacing. Productive formation is the part of oil-bearing formation, which stands apart in a sufficiently powerful oilbearing (gas bearing) horizon (reservoir) and is clearly seen on the area between the top and bottom of oil horizon. In oilfield practice, these oil and gas horizons stand out in performance objects (e.i. productive formation) if they are self-development of a special group wells (spacing system). The correct choice of well spacing density is a critical factor in justifying the development of a rational system of productive formation. In view of the fact that in the development of oil and gas fields in the largest part of capital investments spent on drilling, completion, operation and maintenance of wells, is inadmissible drilling more wells on productive formation than is required, i.e., excessive use of a well spacing density. At the same time providing the proper rate of oil and gas production and possible high ratio of ultimate hydrocarbon recovery factor, number of operation wells should be sufficient. Thus, the rationale for the selection of optimal well spacing in the development of oil and gas fields becomes topical, both technological and economic reasons, task. If we consider that a separate productive formation taken by geological and physical, and other features is characterized by heterogeneity of the vertical section and bedding, then for each productive formation must be selected appropriate well spacing. On the basis of the oilfield material accumulated during the exploration and early development of the field the average values of the operation performance that characterize the productive formation are determined. But it is because of the marked variability of the geological structure, the geological and physical characteristics of the productive formation, as a whole, remains poorly studied. In view of the above, the planning of oil and gas fields’ development is carried out a two stage drilling of productive formation. x In the first stage of placing the main well stock is located in the correct geometrical shape with regard to (1) the artificial stimulation, and (2) the density of wells is determined based on the average parameters of the productive formation set in the early periods of exploration and field development. x In the second stage is carried out sequentially drilling of reserve wells on the productive formation under a development project, which are 20-50% and sometimes the most of the main wells stock. The most important task in the planning of oil and gas fields’ development is the choice of the spacing of main wells stock. The variability of the geological and physical conditions of productive formations leads to the selection of the main wells in adequate ways. Therefore, in practice the selected spacing of the main wells stock differ from one another by the nature of the spacing, shape, distance between the wells and the density of the well pattern. Important indicators of the main spacing of wells should include (1) the density of the well spacing (distance between rows and wells in rows, and (2) as well as the specific area per one production well (ha/well). Well spacing and its density shall ensure the maximum allowable rate of development and the ultimate hydrocarbon recovery factor of the developed productive formation. And so the task justification the selection of well spacing and evaluation its density in development projects of the oil and gas fields in terms of the enhanced oil recovery should be improved with the serious way. At present, according to the adopted approach, drilling of a productive formation is performed on the basis of its geological features, a more or less uniform spacing and the well spacing, in its term, specified at the development process of the object. Selecting the spacing of wells and determining its density is based on old stereotypes and in the oil literature on this subject are often spoken contradictory opinions 1,2,3,4,5,6,7,8. Question of selection well spacing and its density, discussed in this paper is a very topical issue of the oil and gas industry must find its solution through the use of a fundamentally new way, radically different from the traditional one. Taking into consideration that the overwhelming majority of oil fields are composed of heterogeneous reservoir rocks are often weak drainage of productive layers during development leads to formation oil "stagnant" areas and too low ultimate recovery factor.

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Dependence on oil well spacing in general has been proposed and justified axiomatic by M. Muscat according to this principle with infill drilling oil recovery increased up to a certain limit, then reduced the rate of increase and, finally, a further increase in well spacing does not affect the recovery factor, which remains constant. At high well spacing densities, the wells’ drilling and operation costs increase so that the development of the productive formation is become economically unprofitable. Hence the conclusion: the well spacing, appropriate to "Muscat principle" can be adopted optimal well spacing limit on productive formation. Well-known researches M.F. Mirchink and V.N. Shelkachev in different periods, regardless of the intensity of the bed water stimulation, held the idea of using a dense spacing of wells. In practice, the application of triangular well spacing the distance between wells is taken to be 125-340 meters. At that time, on the proposal of M.F. Mirchink the transition from a triangular pattern to the linear arrangement of wells considered positive phenomenon. Research works in the vast majority on the analysis of the practice of development of oil fields, mainly consisted of search spacing density wells. Posing the question in this aspect was justified by heterogeneity of oil reservoir rocks. In the oilfield practice, there are different views on the subject to choose the shape and density of well spacing. However, the most scientific and reasonable position on this issue until today belongs to M. Muscat. It should be noted that, regardless of the position of M. Muscat in this issue different researchers in different periods held discussions on the choice of the well spacing in different forms and at different levels. According to the authors of this scientific paper well spacing should be chosen so that is inadmissible leaving of "stagnant" oil zones in the development of oil fields between the operating wells and the formation of these "zones" is allowed only in areas of "draining" wells. Only in this way it will be possible to effectively address the issue of the recovery of oil reserves of "dead zones" in areas "drainage" wells. In our opinion, the issue of improving the selection spacing of wells can be resolved taking into account the satisfaction of the following two conditions: x The first condition: to be determined well spacing, providing economic efficiency in development of reservoirs with the highest possible recovery factor. x The second condition is adopted well spacing prevents the formation of "stagnant oil zones" in developed productive formations. From a technological point of view the most effective spacing well density is the one that minimizes the formation of "stagnant oil zones" in the reservoirs. In this case, "dead zones" are located virtually in the wells "drainage" zones. It is possible to recover oil from the "dead space" by affecting the buttonhole zone of wells in various ways. In this case, there is no need to find a relationship between the oil recovery factor and well spacing. Our fundamental analysis allows taking the following positions: 1. Regardless of the geological and physical features and reservoir drive, shape and well spacing density for a particular reservoir is selected and then, with a view to ensuring the maximum possible ultimate oil recovery factor, refined more precisely during the development of productive formation. 2. The shape and density of the well spacing pattern for reservoir must be chosen such that the entire area of the oil was in the drainage area of the wells could prevent the emergence of "stagnant" oil zones. 3. "Stagnant" zones should be located only in areas of "drainage" wells. 4. Develop and implement measures for the production of oil from the areas of "draining" wells. 5. How was proposed by M.F. Mirchink triangular shape of the well spacing should be replaced by a linear spacing of wells. 6. In the process of drilling defined geological and physical properties of the producing formation (oil-bearing area of the reservoir, porosity, permeability, formation oil-, gas-, and water-bearing factors thickness, oil density, viscosity, reservoir oil and gas saturation etc.), and in the course of well completion using pressurebuild-up curves (PBUC) the radius of drainage area is determined, and then oil reserves of the drainage area are counted. 7. The distance between the operation wells in the linear range should be less than the sum of the radii of neighboring wells drainage zone, i.e. drainage areas of adjacent wells have partially overlapped . Here R 1 and R 2 are radii of neibouring wells, m; L is distance between operation wells. In connection with the above provisions for the shape and density of wells spacing offers two options:

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• The T first option - a well placed d inside a squaree whose sides arre equal to 10000 m. The oil areea in the squaree will be S= =1000x1000=10 06 m2=100 ha. In nside the squaree is placed as much m as four weells, two integerrs, consisting off four half-w wells, and one whole w wells con nsisting of four 1/4 1 holes. (Figu ure 1).

Fig 1. Square well patteern.

Zo ones drainage wells w overlap witth each other, i.e. at the site of the formation "stagnation zonee" cannot be forrmed. "Stag gnation zones" may m be formed in areas of draainage wells. Wells, W in this casse, are placed in n the form of linear seriess. Inside the squuare pattern are placed p as much h as eight wells. Well spacing iss 100:4 = 25 ha//well. It is possible to co over productive formation pllacing the prop per geometric standards (weells pattern) around hboring local geometric standarrds (simple wellls pattern). neigh For ex xample, if we place p 8 operation n wells around simple square shape geometricc well standard consisting c 9 wells, it will cover c a large areea of productivee formation with h filtration process. • The T second optiion - 109 wells are located insside the circle with w a diameter of 3500 m. Th he area of a circcle in this case is 38,46x10 02 hectares. Welll spacing densitty is 35.3 hectarres/well (Figuree 2). m an economic an nd technologicaal point of view the first option n is considered m most acceptable. From

Fig 2. Circullar shape of linear well w pattern.

Co onsider the com mparison of mod dern widely app plied well spacin ng form with thhe proposed form m of the latest w wells spacin ng. To this end we choose a ho omogeneous resservoir square section side a=1000 m. The areea of oil-bearingg part is: A= = 1000x1000 = 106 m2. Thick kness oil-saturatted part of the productive form mation is h= 50 0 m; porosity ffactor m=0.2 25 and a residuaal water contentt of formation S=0.15. S On this square area oil reserves will bee:

V

Ahm (1  S ), m3

Th he volume of oill produced from m each well is: ~

V1 ~

~2

S hm (1  S ) R1 , ~2

V 1 S hm (1  S ) R 2 . Total volume of the two t neighboring g production weells is equal to:

((1)

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~

¦V

§

~ 1

~2

~2

·

S hm (1  S ) ¨ R1 R 2 ¸

 V2

©

(2)

¹

Comparison of existing wells spacing form with the proposed form of the latest wells spacing allowed to express the volume of oil produced during the period of development or recovery factor of relationship (2). Recovery factor is calculated by the following relationship § ~2 ~2· S hm (1  S ) ¨ R1 R 2 ¸ ~ © ¹ ˜n K 2 Ahm (1  S ) or § ~2

~

~2

·

S ¨ R1 R 2 ¸ ©

K

2A

¹ ˜n .

(3)

By calculating the recovery ratio for the recovery of the two systems - the existing well pattern form and of the proposed form of the latest wells using relationship (3) we could compare the results. ~

~

For the latest forms of relationship between the drainage areas of two neighboring wells ( R1  R 2 ). The mathematical relationship between these parameters is described by the following formula: ~

~

R1  R 2

~

L.

(4)

If the wells interfere with the each other (Figure 1,a) the relationship (4) for them is written as ~

~

~

R1  R 2 > L .

(5)

It should be noted that in dependence ~

~

~

R1  R 2 < L ,

(6) ~

~

~

between two adjacent zones drainage wells ( R1  R ) and the distance between two adjacent wells L contributes to the origin of "stagnant" areas between the adjacent oil production wells (Figure 1,b), which may not be effective both from the technological and economic point of view. Perform calculations for choosing the most profitable number and the distance between production wells for the perfect system of wells spacing density. ~

~

~

~

In this problem the value of parameters R1 , R 2 , L and K are approximately in the real oil and gas fields conditions. Therefore, it is reasonable applying the fuzzy-logic theory, which is the effective tool. ~

~

~

~

Taking into consideration this case we select the R1 , R 2 , L and K as the fuzzy parameters. By using fuzzy nonlinear programming model optimal solution for this problem is defined. For example, if well ~

~

~

number n=50, R1 =50 m, R 2 =50 m and L =100 m. Graphical representation of solution for fuzzy nonlinear programming problem is given in the Figure 3. ~

~

~

Example 1. Data given: R1 = 50 m, R 2 = 50 m, L =100 m and number of wells n =50. With these data, study area reservoir oil recovery factor will be:

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Rf.S. Gurbanov et al. / Procedia Computer Science 102 (2016) 446 – 452 ~

~

K

~

3,14 (0, 25 0, 25) ˜104 ˜˜ 50 2 ˜106

~

0,395.

~

Fig 3. Fuzzy value of the oil recovery factor ~

K.

~

~

Example 2. Data given R1 = 60 m, R 2 = 60 m, L = 120 m and number of wells n =50. With these data, study area reservoir oil recovery factor will be: ~

~

K

~

3,14 (0,36 0,36) ˜104 ˜˜ 50 2 ˜106

~

0,560. ~

~

~

Example 3. Data given R 2 = 50 is given L =100 m and number of wells n =40. R1 determine from the condition ~

~

~

~

(5). Hence, R1 > L  R 2 =50 m. Considering the limitation in the expression (5), take R1 = 60 m. With these data, study area reservoir oil recovery factor will be: ~

~

K

~

3,14 (0,36 0, 25) ˜104 ˜n 2 ˜106 ~

In this example, when the number of oil production wells is n =40 oil recovery factor will be K =0.383. At n =50 ~

oil recovery factor will be K =0.409. ~

~

~

Example 4. Data given R 2 =60 m, L = 120 m and number of wells n=42. R1 determine from the condition ~

~

~

~

~

~

~

R1  R 2 > L (5). Hence,. R1 > L  R 2 =60 m. Considering the limitation in the expression (5), take R1 = 70 m. With these data, study area reservoir oil recovery factor will be: ~

~

K

~

3,14 (0, 49 0,36) ˜104 ˜n 2 ˜106

3,14 ˜ 0,85 n ˜ n 1,3345 2 ˜100 100 ~

At = 40 the oil recovery rate is: K = 0,560. ~

At = 50 the recovery rate is: K = 0,667. Table 1. The results of numerical solutions of the examples listed below in the table 1

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Rf.S. Gurbanov et al. / Procedia Computer Science 102 (2016) 446 – 452

Example

Condition

Drainage radii, m

Distance between the wells, m

Number of wells

Recovery factor

Note

~

-

number

R1  R 2

1

L

2

R1  R 2 > L

3

4

R1

R2

~

~

~

50

50

100

~

~

~

60

60

120

~

~

~

60

50

100

~

~

~

70

60

120

50

0,395 ~

50

-

0,560 ~

40

42

~

0,383

0,409

~

~

0,560

0, 667

Note: Case of equal number of wells n Examples 1 and 2.

Table 1 shows that in Examples 1 and 3 values oil recovery factor are very close and, accordingly, equal to ~

~

0.395 and 0.383 , respectively This can be explained by fewer wells in the area (sometimes 20%). ~

In the second and fourth examples values oil recovery factor are equal 0.560. However, in Example 4 the number of wells is 16% less. It should be noted that in order to make the right decision which should be applied, the results of these studies should be economically justified. Increasing the number of wells increases the cost of drilling and operating of wells. Increased oil, in some cases, cannot cover these unwarranted costs and the company can operate at a loss. 3. Conclusion ~

~

~

1. Inequality R1  R 2 < L , contributes to the origin of "stagnant" areas between the adjacent oil production wells. 2. In developing the productive formation should be provided wells interference making up well spacing. 3. Areas "dead" zones should be kept to a minimum. For this purpose, well spacing system is specified in the subsequent phases of the development of the productive formation. 4. It should be developed methods for optimizing the process of flooding, increasing the permeability and widening fissures in the rock, creating of physical fields in the formation, contributing to increase the mobility of the oil, separation of oil-water emulsion, reduce oil viscosity, etc. 5. Select one of the forms of wells spacing systems - square, triangular or hexagonal - to be placed on the area determined by the sequence of drilling and bringing-in wells into production. 6. The radii of drainage wells zones should be set based on the pressure-build-up curves (PBUC). 7. There should be calculated oil reserves, are defined rate of recovery and ultimate oil recovery factor in drainage areas of wells and reservoirs geometric standard areas. 8. In order to increase oil recovery on the geometric standard zones in the central wells should be implemented stimulation of formation with different impulsive physical fields. References 1. Abasov MT, Zakirov S. Affect of wells spacing density on an oil production factory. Azerbaijan Oil Industry 2005; 9. 2. Dongbo H, Ailin J, Chengye J, et al,. Well Spacing Optimization for Tight Sandstone Gas Reservoir 2010, SPE 131862-MS. 3. Gimatudinov ShK. Physics of oil and gas reservoir. Moscow: Nedra; 1971. 4. Jian-guo Z, Yong W, Fang A. Rational Well Spacing Optimization of Low Permeability Gas Reservoir. Physics and Chemistry. Published Online December;2012. 5. Muscat M. Physical bases of oil production technoloji. Moscow:Gostoptexizdat; 1953. 6. Shelkachev VN, Development of oil-water reservoirs at water-elastic drive. Moscow: Gostoptexizdat; 1959. 7. Shelkachev VN, Oil production modern state analysis and oil fields development. Moscow: GOSINTI; 1963. 8. Zakirov SN, Analysis problem:Wells spacing density-oil recovery factor. Moscow; Graal; 2002.