Effectiveness and sensitivity analysis of solution gas re-injection in Baikouquan tight formation, Mahu sag for enhanced oil recovery

Journal Pre-proof Effectiveness and sensitivity analysis of solution gas re-injection in Baikouquan tight formation, Mahu sag for enhanced oil recovery Bing Wei, Tao Song, Yan Gao, Hua Xiang, Xingguang Xu, Valeriy Kadet, Jinlian Bai, Zhiwei Zhai PII:

S2405-6561(19)30164-6

DOI:

https://doi.org/10.1016/j.petlm.2019.10.001

Reference:

PETLM 283

To appear in:

Petroleum

Received Date: 28 August 2019 Revised Date:

21 September 2019

Accepted Date: 18 October 2019

Please cite this article as: B. Wei, T. Song, Y. Gao, H. Xiang, X. Xu, V. Kadet, J. Bai, Z. Zhai, Effectiveness and sensitivity analysis of solution gas re-injection in Baikouquan tight formation, Mahu sag for enhanced oil recovery, Petroleum (2019), doi: https://doi.org/10.1016/j.petlm.2019.10.001. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © [COPYRIGHT YEAR] Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. All rights reserved.

Effectiveness and sensitivity analysis of solution gas re-injection in Baikouquan tight formation, Mahu sag for enhanced oil recovery Bing Weia,∗, Tao Songa, Yan Gaob, , Hua Xiangc,* , Xingguang Xud, Valeriy Kadetc, Jinlian Baie, Zhiwei Zhaif a

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University,

Chengdu, Sichuan 610500, China b

XinJiang Oilfield, PetroChina, Karamay, Xinjiang 834000, China

c

Gubkin Russia State University of Oil and Gas, Moscow 119991, Russia

d

Energy Business Unit, The Commonwealth Scientific and Industrial Research Organization, 26 Dick Perry Avenue,

Kensington 6152, Perth, Australia e

Exploration and Development Research Institute of Qinghai Oilfield, PetroChina, Dunhuang, Gansu 736202,

China f

Department of Science, Technology and Industry, Shanxi Institute of Energy, Jinzhong, Shanxi 030600, China

ABSTRACT To address the fast productivity decline of the horizontal wells and low oil recovery during natural depletion in Baikouquan formation, the approach of solution gas re-injection was proposed with the primary objective of further developing this formation. Herein, a field-scale numerical compositional reservoir model was built up based on the formation properties and then the effects of permeability, fractures and formation stress on the production dynamics were thoroughly investigated. A sensitivity analysis, which can correlate the oil recovery with these parameters, was also performed. The results showed that the re-injection of solution gas could remarkably retard the production depletion of the horizontal wells thereby improving the oil production. The oil recovery rate increased with permeability, fracture half-length, fracture conductivity, and formation dip. With regard to the fracture distribution, it was found that the interlaced fracture outperformed the aligned fracture for the solution gas re-injection. The influence of the formation stress should be

∗ Corresponding author. Email address: [email protected] (B. Wei) and [email protected] (H. Xiang) 1

carefully considered in the production process. Sensitivity analysis indicated that the formation dip was the paramount parameter, and the permeability, fracture half-length, and fracture conductivity also played central roles. The results of this study supplement earlier observations and provide constructive envision for enhanced oil recovery of tight reservoirs. Keywords: Tight oil reservoir; Mahu sag; Solution gas re-injection; Numerical simulation; Fracturing; Sensitivity analysis. 1. Introduction With the increasing demand for oil production and the rapid depletion of conventional oils, unconventional tight resources with extremely low permeability (in-situ permeability: 0.01-0.1mD) have drawn worldwide attentions over the past decades. The enormous promise in tight oils has been demonstrated in the earlier studies [1-4]. It is estimated that 30 billion barrels of tight oil were held in 24 oil reservoirs globally [5]. As reported, the development of tight oil reservoirs has gained great success in the U.S.A., [6]. China is also rich in tight oil resources. The preliminary assessment suggests that the favorable tight oil exploration area in China is roughly 18×104 km2, and the total geological resources and recoverable resources are 74-80×108 and 13-14×108 t, respectively [7]. Therefore, technical developments for tight oil production are pressing to meet the energy demand and improve the energy security. The horizontal well coupled with multi-stage hydraulic fracture have been widely applied to stimulate the tight oil production. After fracturing, a large quantity of fractures will be created in the tight matrix, which accordingly enhances the flowability of fluids. Despite the potential effectiveness of this technique, the primary recovery remains low due to the tight nature of the target formation [8]. Rapid decline in the productivity always leads to the disagreeable abandonment of the production well, leaving a large fraction of oil unrecovered [9]. According to Yu et al., the fast decline is primarily due to the fast depletion occurring in the natural fractures and slow recharge from the rock matrix [10]. It has been widely recognized that the gas injection (CO2, natural gas, N2, etc.) was a promising technique in improving oil recovery especially for tight reservoirs [11-15]. In the last few years, the number of active CO2 flooding projects in USA has increased by more than 2

300% [16]. However, most of the oil reservoirs in China are characterized by high viscosity and high reservoir temperature, which thus leads to undesirable miscibility pressure between crude oil and CO2 under reservoir conditions [17]. A few pilot tests of CO2-EOR have been conducted in China and the injected CO2 was mainly sourced from natural sources or chemical plants via lorry tank transportations. However, these pilot tests were usually performed at small scale because of the limited CO2 supply [18-20]. In addition, the technical issues including the facility corrosion, scaling and asphaltene deposition might restrict its future application especially in tight reservoirs. Recent studies have shown that CH4 is more favorable than CO2 for EOR because of its compressibility and availability [21,22]. In comparison with CO2, CH4 is readily available in reserves, and the solution gas can achieve miscibility under relatively low pressure due to its higher compatibility with in-situ hydrocarbons [9]. For example, Zanganeh et al. investigated the effects of CH4, N2 and CO2 on asphaltene precipitation and concluded that the precipitated asphaltenes induced by CO2 was much more notable than that of other two gases [23]. Shayegi et al. reported laboratory investigations on cyclic gas injection using CH4, N2 and the mixtures of these gases with CO2 under immiscible condition in consolidated models. It was found that CH4 flooding almost recovered as much oil as CO2 flooding did after the water flooding [24]. Sanchez-Rivera et al. evaluated the re-injection of produced hydrocarbon gases along with CO2 as an alternative to the natural gas flaring. They claimed that the separator gas (approximately 50 mol. % CO2 and 50 mol. % produced gas) was more efficient in improving oil recovery than CO2 alone [22]. Considering its unique technical merits including ready-miscibility, high-solubility, easy-operation, and abundant supply, the re-injection of solution gas can be a promising replacement of the currently used CO2 and N2 injections especially for high gas-oil ratio (GOR) oil reservoirs. Therefore, it is worthy evaluating its feasibility in the high GOR oil reservoir, for example, the Baikouquan reservoir in China [25]. Stress-dependent deformation is another key parameter influencing the accumulative production of the tight oil reservoirs [26]. Previous studies have concluded that stress affected the matrix permeability and fracture conductivity[27-29]. Cao et al. examined the stress-dependent permeability hysteresis of 3

tight reservoirs during pressure loading-unloading process using tight rocks, which confirmed the significance of stress-dependent hysteresis in tight reservoirs [30]. In this paper, a field-scale numerical model was designed and used to simulate the approach of solution gas re-injections in Baikouquan formation, Mahu sag, based on the real reservoir and fluid properties. Solution gas used in this work is originally sourced from this formation during primary production, named solution gas re-injection. The reservoir model with multi-stage fractured horizontal wells was built-up using local grid refinement (LGR) approach in the CMG simulator. Based on fluid phase matching, six sensitive factors of this process were comprehensively analyzed using CMG simulator. Eventually, a response surface model was established to correlate the oil recovery factor with these variables. This study provides a quantitative assessment of the effect of reservoir properties and hydraulic fracturing on the EOR performance of solution gas re-injection in Baikouquan formation. 2. Reservoir simulation To evaluate the EOR performance of solution gas re-injection in the target formation, a two horizontal wells component model with multi-stage fracturing was built up using CMG-GEM based on the realistic geological and fluid properties. 2.1. Reservoir fluids The live-oil and solution gas components were categized into nine pseudo components, i.e., N2, CO2, CH4, C2-C4, C5, C6, C7-C10, C11-C22, C23-C35, and the molar fraction is listed in Table 1. The oil properties are calculated using CMG-Winprop based on these components with the input data for the Peng-Robinson equation-of-state (EOS) (Table 2) and the binary coefficient for flash calculation (Table 3) [31]. These parameters are consistent with the measured values. The results of constant component expansion and gas injection expansion experiments were matched to obtain the EOS parameters representing the real reservoir fluids. Fig.1 shows the matching results. The parameters used for simulation based on the properties of oil in this formation are listed in Table 4.

4

40

Measured Simulated

35

Saturation pressure (MPa)

Relative volume

2.5

2.0

1.5

30

1.5

Measured saturation pressure Simulated saturation pressure Measured oil swelling factor Simulated oil swelling factor

1.4 1.3

25

1.2

20

1.1

15

Oil swelling factor

3.0

1.0

1.0

b

a 0

5

10

15

20

25

30

35

10

40

0

Pressure (MPa)

10

20

30

40

0.9 50

Mole fraction of solution gas (%)

(1) Constant component expansion

(2) Gas injection expansion

Figure 1. Matching of the reservoir fluid phase 2.2. Reservoir model In the model, two horizontal wells of 1201.7 m in length with 6 stages of hydraulic fractures and 4 clusters for each stage were built up using CMG compositional simulator GEM as shown in Fig. 2 (a). The dimensions of the model were 1598.2 m × 817.4 m × 12 m, which corresponded to length, width and thickness, respectively. The number of grid blocks was set to 262×134×1 in I, J and K directions, respectively. The hydraulic fracture was set up using local grid refinement (LGR) method as shown in Fig. 2 (b) and the LGR for each grid with fracture was set as 5×3×1 to reduce the numerical dispersion. Baikouquan formation has an initial reservoir pressure of 37 MPa and temperature of 89 oC. The fracture half-length was 80 m and the fracture conductivity was 50 mD·m in order to achieve the comparable transport performance of real fractures. Table 5 summarized the parameters used for simulation based on the properties of this formation. The relative permeability curves, as shown in Fig. 3, were obtained by history matching (not provided in this work). This formation was assumed to be homogeneous and the fractures had stress-independent porosity and permeability. The bottomhole pressure of 33 MPa was used for reservoir simulation constraint to respect the real production conditions.

5

Table 1. Pseudo components of the model Component

Live oil (mol. %)

Solution gas (mol. %)

N2

2.88

5.07

CO2

0.10

0.18

CH4

46.15

81.21

C2-C4

7.64

13.45

C5

1.64

0.09

C6

4.39

0

C7-C10

13.43

0

C11-C22

16.92

0

C23-C35

6.85

0

Table 2. Basic properties of pseudo components after regression

Critical temperature Component

Critical volume

Critical pressure (MPa)

Molar weight Acentric factor

(K)

(L/mol)

Parachor (g/gmol)

N2

3.350

126.200

0.0895

0.040

28.013

41.000

CO2

7.280

304.200

0.094

0.225

44.010

78.000

CH4

4.540

190.600

0.099

0.008

16.043

77.000

6

C2-C4

4.519

339.124

0.175

0.068

37.183

128.750

C5

3.340

460.400

0.306

0.227

72.151

225.000

C6

3.246

507.500

0.344

0.275

86.000

250.109

C7-C10

3.011

584.095

0.445

0.326

136.690

327.643

C11-C22

1.774

722.108

0.791

0.853

253.030

566.841

C23-C35

1.392

871.639

1.398

1.289

469.960

909.489

Table 3. Binary interaction parameters for oil components Component

N2

CO2

CH4

C2-C4

C5

C6

C7-C10

C11-C22

C23-C35

N2

0.0000

0.0000

0.0250

0.0431

0.1000

0.1100

0.1100

0.1100

0.1100

CO2

0.0000

0.0000

0.1050

0.1272

0.1150

0.1150

0.1150

0.1150

0.1150

CH4

0.0250

0.1050

0.0000

0.0054

0.0209

0.0253

0.0366

0.0682

0.1071

C2-C4

0.0430

0.1270

0.0054

0.0000

0.0052

0.0076

0.0144

0.0369

0.0682

C5

0.1000

0.1150

0.0209

0.0052

0.0000

0.0002

0.0023

0.0149

0.0373

C6

0.1100

0.1150

0.0253

0.0076

0.0002

0.0000

0.0011

0.0115

0.0320

C7-C10

0.1100

0.1150

0.0366

0.0144

0.0023

0.0011

0.0000

0.0055

0.0214

C11-C22

0.1100

0.1150

0.0681

0.0369

0.0149

0.0115

0.0930

0.0000

0.0054

C23-C35

0.1100

0.1150

0.1071

0.0682

0.0373

0.0320

0.0930

0.0054

0.0000

7

Table 4. The matching result of characteristic of fluid phase state Parameters

Measured value

Simulated value

Error (%)

Saturation pressure (MPa)

22.00

21.37

2.86

Solution gas-oil ratio (m /m )

117.56

117.33

0.20

Volume factor

1.46

1.39

4.79

Crude oil density (kg/m )

636.90

627.10

1.54

Crude oil viscosity (mPa·s)

1.08

1.06

1.85

3

3

3

(a) A 3D model containing two horizontal wells

(

(b) Enlarged zone with LGR used to model hydraulic fracture 8

Figure 2. A schematic of 3D reservoir model with two horizontal wells and multiple hydraulic fractures In a typical simulation, the time scale of 5 years in total was set up. Prior to solution gas re-injection, a natural depletion production was performed in the first 2 years, after which the horizontal wells were drilled. The injection rate of solution gas was set as 6000 m3/day. At the end of gas injection (Huff phase), the wells were usually shut-in for soaking for one month and then re-opened for production (Puff phase). Table 5. Reservoir and fractures properties used for the basic reservoir model Parameter

Value

Units

Model dimension (I×J×K)

1598.2×817.4×12

m

Number of grid blocks (I×J×K)

262×134×1

Reservoir temperature

89

Initial oil saturation

0.65

Reservoir porosity

9%

C

_ _ -7

1/kPa

Total compressibility

1.5×10

Reservoir permeability

0.1

mD

Well spacing

305

m

Horizontal length

1201.7

m

Number of stage

6

_

Per stage spacing

24.4

m

Fracture half-length

80

m

Fracture conductivity

50

mD·m

1.0

1.0

Krw Krow

0.8

Relative permeability

Relative permeability

_ o

0.6

0.4

0.2

0.0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.6

0.4

0.2

0.0 0.0

1.0

Water saturation, Sw

krg krog

0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Gas saturation, Sg

(a) Water-oil relative permeability curves

(b) Liquid-gas relative permeability curve

Figure 3. Relative permeability curves used in this study 9

3. Results and discussion To elucidate the effects of some key parameters on the oil production using this approach, a series of simulations were designed and conducted in this section. The reservoir permeability, fracture half-length, fracture conductivity, formation dip, fracture distribution, and formation stress were thoroughly assessed as discussed below. 3.1. Reservoir permeability In this subsection, three different reservoir permeabilities ranging from 0.001 mD to 0.1 mD were investigated while keeping the other parameters constant in the model. Fig. 4 plots the oil recovery factor over production time for these three scenarios with and without solution gas injection treatment. As depicted in Fig. 4, for the natural depletion (black curves), the oil production quickly increased in the first two 2 years and then tended to level off, implying the fast decline of the well productivity. The oil recovery was found to heavily depend on reservoir permeability. The injection of solution gas was able to significantly improve the oil production on the basis of natural depletion as observed from Fig. 4 (red curves). Under the identical conditions, the oil recovery factor was increased by 0.27%, 0.32% and 0.44% at the end of production (5 years) for the permeabilities of 0.001 mD, 0.01 mD, and 0.1 mD, respectively. As widely accepted, the tight formation cannot provide adequate flow channels for the injected gas entering the matrix, which thus led to restricted contact between the injected gas and the oil in place, although it had high residual oil saturation after natural depletion. Figure 5 presents the change of reservoir matrix pressure during the primary recovery and solution gas injection processes. These curves confirmed that the conductivity of pressure in the matrix was largely determined by reservoir permeability. The injection of solution gas hardly pressurized the reservoir in the case of 0.001 mD permeability due to the low matrix conductivity, whereas for the 0.01 mD permeability reservoir the pressurization was delayed. Note that pressure drop is the driving force for oil production; therefore, low reservoir permeability would decrease the EOR efficiency of this approach.

10

With solution gas injection Without solution gas injection

Oil recovery factor (%)

1.2 1.0

0.1 mD

0.8 0.6 0.01 mD

0.4 0.001 mD

0.2 0.0 0

1

2

3

4

Time (years)

Figure 4. The oil recovery factor as a function of reservoir permeability with and without solution gas injection

Figure 5. Reservoir matrix pressure during primary recovery and solution gas huff-n-puff process 3.2. Fracture half-length Fracture half-length is considered to be one of the critical parameters for hydraulic fracturing and determines the productivity of the wells. Hence, the effect of fracture half-length ranging from 70 m to 130 m on the production of this approach was investigated while keeping the other parameters constant. Figure 6 plots the oil recovery factor over time with different facture half-length. As indicated, the oil production was improved with the increase in facture half-length because the drainage area was proportional with the fracture half-length. The dependence of oil recovery on facture half-length was plotted in Fig. 7. We 11

found that oil recovery factor could be linearly correlated with fracture half-length. However, when the fracture half-length exceeded 100m, the increases rate of oil recovery tended to become slow. This was presumably caused by the relatively slow flow of oil in the long fractures, which subsequently lowered the oil recovery rate. Figure 8 shows the pressure distribution in the reservoir after gas injection (Left: 70 m; Right: 130 m). The pressurizing effect of the injected gas mainly occurred in the proximity of fractures and the area in the central matrix (red dotted line) was hardly affected as indicated in Fig. 8(a). Conversely, the conductivity of pressure increased fracture half-length, which finally led the pressure to spread into the deeper reservoir matrix and favored oil production, as shown in Fig. 8(b).

Oil recovery of factor (%)

1.4 Fracture half-length 70m Fracture half-length 80m Fracture half-length 90m Fracture half-length 100m Fracture half-length 110m Fracture half-length 120m Fracture half-length 130m

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

1

2

3

4

5

Time (years)

Oil recovery of factor (%)

Figure 6. Oil recovery factor curves over time under different fracture half-length

1.28

1.26

1.24

1.22

1.20 70

80

90

100

110

120

130

Fracture half-length (m)

Figure 7. The dependence of oil recovery factor on fracture half-length 12

(a) Fracture half-length: 70 m

(b) Fracture half-length: 130 m

Figure 8. Pressure distribution after solution gas injection for different fracture half-length 3.3. Fracture conductivity Hydraulic fracturing creates a large contact surface area within reservoirs and maintains adequate fracture conductivity during long-term production [32]. In the process of hydraulic fracturing, fracture conductivity largely determines the fracturing effectiveness and the EOR performance. Therefore, fracture conductivity is closely associated with the economic production of unconventional reservoirs [33]. In this subsection, the effect of fracture conductivity ranging from 30 mD·m to 130 mD·m on the oil production during natural depletion and gas injection was examined. Figure 9 presents the oil recovery factor curves over production time. It is clear that the oil production increased with the fracture conductivity. The dependence of oil production on fracture conductivity was plotted in Fig. 10, in which the change of oil recovery factor could be readily identified. Consistent with the tendency of fracture half-length, the increase rate of oil recovery became slow after the conductivity of 90 mD·m. Therefore, considering the oil recovery and economy, the conductivity of 80 mD·m was suggested to be optimal based on this result.

13

Oil recovery of factor (%)

30 mD·m 50 mD·m 70 mD·m 90 mD·m 110 mD·m 130 mD·m

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0

1

2

3

4

5

Time (years)

Figure 9. Oil recovery factor curves over time under different fracture conductivity

Oil recovery of factor (%)

1.245 1.240 1.235 1.230 1.225 1.220 1.215 20

40

60

80

100

120

140

Fracture conductivity (mD·m)

Figure 10. The dependence of oil recovery on fracture conductivity 3.4. Formation dip The target formation is located in the slope area of Mahu sag; thus, it is essential to investigate the effect of formation dip on the oil production. The formation dip considered in this paper was ranged from 0° to 15° and the other parameters were kept constant. Fig. 11 illustrates a 3D image of the model at formation dip of 15°. Fig. 12 shows the oil recovery curves of different formation dip. These curves clearly indicated that the oil production dip was of great significance for this approach. Fig. 13 depicts the reservoir pressure distribution in details after natural depletion. It was confirmed that the increase of formation dip led to more significant pressure depletion at the well heel than that of well toe. After solution gas re-injection, the reservoir was substantially pressurized as illustrated in Fig. 14. 14

Figure 11. A 3D image of the model at formation dip of 15° 1.6

Formation dip 0° Formation dip 5° Formation dip 10° Formation dip 15°

Oil recovery of factor (%)

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

1

2

3

4

5

Time (years) Figure 12. Oil recovery factor curves over time under different formation dip

(a) 0°

(b) 5o

15

(c) 10°

(d) 15°

Figure 13. Reservoir pressure distribution after natural depletion under different formation dip

(a) 0°

(b) 5o

(c) 10°

(d) 15°

Figure 14. Reservoir pressure distribution after solution gas re-injection under different formation dip 3.5. Fracture distribution To assess the effect of fracture distribution on the oil production, two fracturing cases were created in the model, interlaced fracture (Fig.15 (a)) and aligned fracture (Fig.15 (b)). Note that the difference between these two cases was only the relative position of fractures and the other parameters of the fractures were the same as the base model. Based on these models, the primary recovery and gas injection processes were simulated. The results indicated that the oil recovery factor of these two cases were 1.227% (interlaced fracture) and 1.221% (aligned fracture), respectively, after 5 years production. Since the molar composition of CH4 in the solution gas was 81%, the spreading of the injected gas can 16

be roughly understood by the distribution of CH4 species. Fig. 16 presents the global fraction distribution of CH4 in the model. It was observed that the injection capacity of solution gas was approximately the same in these two modes. Fig. 17 shows the pressure distribution after gas injection. As could be seen, for the interlaced fracture (see Fig. 16(a)), the high pressure zones and low pressure zones were staggered, which consequently generated a larger pressure drop between fracture and rock matrix than that of aligned fracture (see Fig. 16(b)). This result accelerated the spreading of the injected gas in the rock matrix and led to an improved oil production as discussed earlier. Meanwhile, the interlaced fracture mode could mitigate gas breakthrough because of the distance between the neighboring fractures of injectors and producers [34].

(a) Interlaced fracture

(b) Aligned fracture

Figure 15. Schematics of the fracture distribution

(a) Interlaced fracture

(b) Aligned fracture 17

Figure 16. The fraction distribution of CH4 in the model after solution gas injection under different fracture distribution modes

(a) Interlaced fracture

(b) Aligned fracture

Figure 17. Pressure distribution after solution gas injection under different fracture distribution modes 3.6. Formation stress The decrease of formation pressure during production would lead to an increase in the effective stress posed on the porous media and subsequent elastoplastic deformation, rock permeability decrease, and productivity reduction [30]. Thus, the effect of formation stress on the primary recovery and EOR efficiency of this approach in this formation was also investigated. To consider the formation stress effect, a stress-dependent correlation was applied with linear-elastic constitutive model as shown in Fig. 18. Fig. 19 compares the oil production with and without formation stress. In the target formation, the oil recovery factor was decreased due to the effect of formation stress especially at the gas injection stage. Fig. 20 depicts the change of effective permeabilities of fractures (a) and rock matrix (b) during 5 years. As a result of formation stress, the effective permeability of either fracture or matrix was increased during gas injection and then slowly dropped in the puff phase. This change seemed to be more evident for the rock matrix.

18

1.0

Porosity Mulitiplier Permeability Multiplier

Porosity Mulitiplier

0.998

0.8

0.996 0.6 0.994 0.4 0.992

Permeability Multiplier

1.000

0.2

0.990 0.988 15

20

25

30

35

0.0 40

Presure (MPa)

Figure 18. Porosity and permeability multiplier curves for this model

Figure 19. Oil recovery factor over production time with and without formation stress

(a) Fractures

(b) Rock matrix

Figure 20. Reservoir pressure and effective permeability during primary recovery and solution gas injection

19

3.7. Sensitivity analysis To comprehensively assess the effects of four uncertain parameters on the oil production in this formation, the reservoir numerical simulation software CMG- CMOST module was used for multifactor regression and experimental design. Meanwhile, response surface methodology (RSM) were used to perform sensitivity analysis [35,36]. RSM explores the relationships between input variables (parameters) and responses (objective functions). The main idea of RSM is to use a set of designed experiments to build a proxy (approximation) model to represent the original complicated reservoir simulation model [37]. The minimum and maximum values of these uncertain parameters are listed in Table 6. According to four parameters, 14 case were created based on the approach of D-optimal design, which was originated from the optimal theory [34,38], as summarized in Table 7. Table 6. Four uncertain parameters with a reasonable range considered in this study Parameter

Units

default

Minimum

Maximum

Formation dip

°

5

0

10

Fracture half-length

m

80

60

100

Fracture conductivity

mD·m

50

37.5

62.5

Reservoir permeability

mD

0.1

0.075

0.125

Table 7. 14 cases generated based on the D-optimal design and the corresponding oil recovery factor for solution gas injection Reservoir

Oil recovery factor

half-length (m)

Fracture conductivity (mD·m)

permeability (mD)

(%)

5

80

50.0

0.100

1.2997

2

4

72

55.0

0.100

1.2711

3

0

76

45.0

0.085

1.1723

4

6

88

47.5

0.105

1.3474

5

8

72

50.0

0.090

1.2969

6

7

64

42.5

0.125

1.3496

7

3

68

40.0

0.125

1.3054

8

9

80

37.5

0.090

1.3247

9

10

84

57.5

0.115

1.4261

10

5

64

52.5

0.110

1.2904

11

4

68

62.5

0.095

1.2521

12

10

76

62.5

0.080

1.3155

Formation

Fracture

dip (°)

1

Case

20

13

2

60

42.5

0.075

1.1258

14

8

86

60.9

0.078

1.3004

The “linear + quadratic” model was selected to establish the response surface model. The proxy model fitted to the response surface of oil recovery factor (Eq. 1). Figure 21 presents the plots of proxy predicted and simulated for 14 cases. The results indicated that there was a reliable matching between the generated response values and the actual model response values. The sobol method was widely used in quantifying the relative importance of input factors as well as their interaction [37,39], as shown in Fig. 22. The dependence of the oil recovery on the parameters was in the order of formation dip (41.87%), reservoir permeability (39.81%), fracture half-length (17.70%) and fracture conductivity (0.62%). 2 Oil recovery factor = − 2.4201×10−5 Lh + 0.571484454+0.0143507F d + 0.00631122Lh + 0.000411147F c + 2.79986K r (1)

where Fd is formation dip (°), Lh is fracture half-length (m), Fc is fracture conductivity (mD·m) and Kr is reservoir permeability (mD).

Figure 21. The proxy model accuracy verification plot of the oil recovery factor

21

Parameter

Formation dip

41.87

Reservoir permeability

39.8125

Fracture half-length

17.7015

Fracture permeability 0.616

0

10

20

30

40

Effects (%)

Figure 22. Sobol analysis of uncertain parameters affecting the oil recovery factor 4. Conclusions In the present work, a field-scale numerical model was built up to investigate the effects of reservoir properties and hydraulic fracturing on EOR performance of solution gas re-injection in Baikouquan formation. A series of simulations were designed and conducted using the CMG. The experiment design and RSM were applied to perform sensitivity analysis and correlate the uncertain parameters with the oil recovery. Based on the data, the following conclusions can be generally drawn: (1) Fracture half-length and conductivity improved the EOR efficiency of solution gas injection process in this formation, which thus should be fully considered in the hydraulic fracturing design to optimize the production. (2) The interlaced fracture outperformed aligned fracture for this process. (3) Formation stress noticeably affected the production of this formation especially at the solution gas injection phase. This parameter should be considered for the performance prediction. (4) Based on sensitivity analysis, the dependence of the oil recovery on the uncertain parameters followed the order of formation dip, reservoir permeability, fracture half-length and fracture conductivity for this approach. Acknowledgements The authors gratefully acknowledge the financial support of the National Natural Science 22

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The authors declare no competing conflict of interest.