Geofluids
Volume 2018 (2018), Article ID 6293041, 6 pages
https://doi.org/10.1155/2018/6293041

Research Article

Study on Reasonable Energy Supplement Time of Tight Sandstone Oil Reservoirs with Rock Compressibility Stress Sensitivity

Tian Xiaofeng, Tan Xianhong, Tian Ji, Li Nan, Yuan Zhongchao, and Liang Bin

CNOOC Research Institute Ltd., Beijing 100028, China

Correspondence should be addressed to Tian Xiaofeng; txf5160@163.com

Received 20 May 2018; Revised 5 August 2018; Accepted 2 September 2018; Published 20 December 2018

Guest Editor: Emanuele Romano

Copyright © 2018 Tian Xiaofeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

A-HBR field is a tight sandstone oil reservoir with a threshold pressure gradient and a rock compressibility stress sensitivity. However, no existing approach could predict reasonable energy supplement time considering both of them. Therefore, in this paper, rock compressibility stress sensitivity experiments are conducted. Then, a new approach is presented. This approach considers the correlation of rock compressibility and formation pressure. And the formation pressure is different from the development time and distance to oil well. The study suggests that the energy supplement time is later when the original rock compressibility is larger. The energy supplement time is earlier when the rock compressibility is more severe. A-HBR field’s reasonable energy supplement time is 83 days when considering the effect of rock compressibility stress sensitivity. It is much earlier than that when not considering the effect of rock compressibility stress sensitivity.

1. Introduction

A-HBR field is an overpressured tight sandstone oil reservoir. The depth of the reservoir is 3760 m. The average porosity is 12%. The average permeability is 32 mD. The oil viscosity is 0.4 mPa·s. The original formation pressure is 50 MPa. Tight oil reservoirs have obvious threshold pressure gradient characters [1–3] and rock compressibility stress sensitivity characters [4–7]. The formation water is going to salt out and solution gas is going to get out from the oil if formation pressure decreases fast. As a result, oil production decreases [8–11]. Therefore, it is key to use natural energy as much as possible and replenish formation energy timely for A-HBR field.

Zhang [12] presented an approach to calculate energy supplement time considering the effect of threshold pressure gradient on drainage radius. However, this approach does not take the pressure distribution into account. Based on the Zhang’s approach, Chen et al. presented an approach considering the effect of threshold pressure gradient on pressure distribution [13]. Numerical simulation also could consider both of threshold pressure gradient and rock compressibility stress sensitivity [14–16]. However, numerical simulation takes longer time and is harder to conduct.

However, no existing approach could predict reasonable energy supplement time considering both threshold pressure gradient and rock compressibility stress sensitivity [12, 13, 17–19]. Therefore, this paper comes up with a new approach considering the effect of threshold pressure gradient and rock compressibility stress sensitivity.

2. Rock Compressibility Stress Sensitivity Experiment of A-HBR Field

The rock compressibility stress sensitivity experiments were conducted. The cores comes from A-HBR field, and the basic parameters are shown in Table 1. Experimental process is shown in Figure 1. The experimental method refers to the standard SY/T 5815-2008. The effective stress is designed to be 2.76, 5.52, 8.27, 10.34, 13.79, 20.68, 27.58, 34.47, and 55.16 MPa, respectively. The experimental results are shown in Figure 2. It is found that the rock compressibility stress sensitivity of A-HBR field is severe from Figure 2. The rock compressibility decreases by 90 percent when the effective stress increases from 2.76 MPa to 55.16 MPa. The correlation of rock compressibility and effective stress is obtained from the experimental results (1).

Table 1: Basic parameters of cores in rock compressibility stress sensitivity experiments.

Number
Depth (m)
(%)
(mD)
(×10⁻³ MPa⁻¹)

A
3773.72
12.6
37.6
7.8

B
3743.7
12.4
8.0
11

C
3727.36
11.5
35.2
7.6

D
3786.49
11.0
42.1
11

E
3775.76
10.6
40.3
7.4

Figure 1: Rock compressibility stress sensitivity experimental process.

Figure 2: Rock compressibility stress sensitivity experimental results.

It is found that rock compressibility and effective stress show a good exponential relationship. Rock compressibility is the pore volume reduction per effective stress. When effective stress is small, pore volume is large and pore is easy to press. When effective stress increases, pore volume decreases and rock becomes tight. Thus, pore volume is harder to press and per effective stress results in less pore volume reduction. As a result, rock compressibility is less when effective stress increases [5, 20].

where is rock compressibility when the effective stress is , MPa⁻¹; is original rock compressibility, MPa⁻¹; is effective stress, , MPa; is overburden formation pressure, MPa; and is formation pressure, MPa.

3. Reservoir Engineering Approach to Predict Reasonable Energy Supplement Time

The rock compressibility of A-HBR field is stress sensitive. As a result, the location with different distances to oil well has different rock compressibilities (Figure 3). The elastic cumulative oil production, where the distance is from the oil well, is shown in (2) according to the matter balance principle.

where is the elastic cumulative oil production, m³; is the composite compressibility, , MPa⁻¹; is the porosity; is the oil compressibility, MPa⁻¹; is the rock compressibility, MPa⁻¹; is the drainage volume of the oil well, , m³; is the distance to the oil well, m; is the net pay, m; is original formation pressure, MPa; and is the formation pressure where the distance to the oil well is , MPa.

Figure 3: Rock compressibility distribution.

The threshold pressure gradient greatly affects the pressure distribution in tight sandstone oil reservoirs. The elastic cumulative oil production is the max in tight sandstone oil reservoirs when formation pressure gradient equals the threshold pressure gradient. The formation pressure distribution is shown in

where is the bottom hole pressure, MPa; is threshold pressure gradient, MPa/m; is the drainage radius, m; and is the well diameter, m.

At the same location, the formation pressure decreases in development. As a result, the rock compressibility decreases (Figure 3) because of the stress sensitivity. Integrating (2) with respect to formation pressure and distance yields the elastic cumulative oil production in drainage volume (4).

where is the well diameter, m, and the is drainage radius, m.

The controlled reserves per well is shown in (5) if the well space is .

where is the controlled reserves per well, m³; is the porosity; is the original oil saturation; and is the formation volume factor.

The oil production per well is shown in (6) if the oil recovery rate equals .

where is the oil production rate, m³/d; is the oil recovery rate; and is the production days per year, days.

Substituting (1) and (3) into (4) yields the elastic cumulative oil production. Substituting (5) into (6) yields the oil production rate. The reasonable energy supplement time is obtained when the elastic cumulative oil production divides the oil production rate:

where is the energy supplement time, days.

4. Verification

Numerical simulation could consider both threshold pressure gradient and rock compressibility stress sensitivity. Therefore, numerical simulation helps to verify the new approach, and commercial software Eclipse E100 is used. The numerical model is shown in Figure 4. The numerical model basic parameters are shown in Table 2. The threshold pressure gradient is shown in (8) [1]. Comparing to the formation pressure distribution of numerical model and the new approach, the new approach results have a great agreement with numerical model results (Figure 5). And the error of elastic oil recovery is less than 1% (Table 3).

where is the threshold pressure gradient, MPa/m, and is the permeability, mD.

Figure 4: Numerical model.

Table 2: Basic parameters of numerical model.

Parameters
Value

Grid number

Grid size

Porosity, %
10.6

Permeability, mD
20

Net pay, m
10

Original pressure, MPa
55

Drainage radius, m
1000

Fluid viscosity, mPa·s
0.4

Formation volume factor
1.6

Original rock compressibility, ×10⁻³ MPa⁻¹
8.9

Fluid compressibility, ×10⁻⁴ MPa⁻¹
4.5

Oil recovery rate, %
1

Figure 5: Verification of formation pressure distribution.

Table 3: Error of the new approach.

Method
Elastic cumulative oil production (m³)
Elastic oil recovery (%)
Energy supplement time (d)
Average formation pressure (MPa)

Numerical model
5111
0.25
81
53.0

New approach
5136
0.25
81
53.3

Error (%)
0.48
0.43
0.39
0.59

5. Sensitivity Analysis

5.1. Original Rock Compressibility

Original rock compressibility ranges from 0.0074 MPa⁻¹ to approximately 0.011 MPa⁻¹ (Table 1). Therefore, the effect of original rock compressibility on energy supplement time is studied. The basic parameters in the new approach is shown in Table 2. It is found that the original rock compressibility and energy supplement time have a good linear relationship (Figure 6). The average rock compressibility is larger in elastic development when the original rock compressibility is larger. As a result, formation pressure decreases slower and energy supplement time is later.

Figure 6: Energy supplement time vs original rock compressibility.

5.2. Rock Compressibility Reduction

The rock compressibility reduction is different, although the effective stress is the same (Figure 2). Therefore, the effect of rock compressibility reduction on energy supplement time is studied. The basic parameters in the new approach is shown in Table 2. It is found that rock compressibility reduction and energy supplement time have a good logarithmic relationship (Figure 7). The average rock compressibility is larger in elastic development when the rock compressibility reduction is less. As a result, formation pressure decreases slower and energy supplement time is later.

Figure 7: Energy supplement time vs rock compressibility reduction.

6. Application

Existing approach and this new approach are used to predict energy supplement time of A-HBR field. Basic data of the field is shown in Table 4. From Table 4, it is found that formation pressure decreases faster considering rock compressibility stress sensitivity (Figure 8). In order to avoid gas degassing from oil and oil rate decreasing, energy supplement time should be 86% earlier than not taking the effect of rock compressibility stress sensitivity into account.

Table 4: Basic data of A-HBR field.

Field
(m)
(%)
(mD)
(mPa·s)

(MPa)
(×10⁻³ MPa⁻¹)
Energy supplement time (d)

Existing approach (2)
The new approach

A-HBR
13
12
33
0.4
1.6
20
8.9
589
83

Figure 8: Formation pressure comparison of the existing approach and the new approach.

7. Conclusions

(1)From experimental results, it is found that A-HBR field has obvious rock compressibility stress sensitivity. The rock compressibility and effective stress have a good power relationship(2)A new approach is presented to predict energy supplement time of tight sandstone oil reservoirs. This new approach takes threshold pressure gradient and rock compressibility stress sensitivity into account(3)The formation pressure decreases more slowly, and elastic recovery is larger if the original rock compressibility is larger. As a result, the energy supplement time is later. The formation pressure decreases faster and elastic recovery is smaller if the rock compressibility reduction is larger. As a result, the energy supplement time is earlier(4)The energy supplement time of A-HBR is 83 days considering the effect of rock compressibility stress sensitivity. It is 86% earlier than the energy supplement time of not taking the effect of rock compressibility stress sensitivity into account

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References

B. Q. Zeng, L. S. Cheng, and F. Hao, “Experiment and mechanism analysis on threshold pressure gradient with different fluids,” in Nigeria Annual International Conference and Exhibition, Tinapa-Calabar, Nigeria, August 2010.

R. Gao, X. Wang, M. Che, C. Bo, and H. Chunming, “The fractures optimization method with the threshold pressure of multistage fracturing in tight oil reservoir,” in SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, Abu Dhabi, UAE, May 2017.

Y. L. Zhao, L. H. Zhang, Z. X. He, and B. N. Zhang, “Productivity for horizontal wells in low-permeability reservoir with oil/water two-phase flow,” Mathematical Problems in Engineering, vol. 2014, Article ID 364678, 9 pages, 2014.

R. Smith, K. Bard, and R. Colmenares, “Non-linear rock compressibility in the Naricual and Los Jabillos formations, El Furrial Field, Venezuela,” in SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, March 2001.

G. P. da Silva Jr., D. R. Franco, G. C. Stael et al., “Petrophysical studies of North American carbonate rock samples and evaluation of pore-volume compressibility models,” Journal of Applied Geophysics, vol. 123, pp. 256–266, 2015.

D. Davudov and R. G. Moghanloo, “Impact of pore compressibility and connectivity loss on shale permeability,” International Journal of Coal Geology, vol. 187, pp. 98–113, 2018.

H. X. Wang, Y. Song, H. F. Fang, Y. J. Li, and Y. X. Xie, “Transforming laws of rock compressibility,” Journal of Oil and Gas Technology, vol. 29, no. 1, pp. 42–44, 2007.

Z. Y. Wu, K. Li, and T. C. Li, “Water injection development and stable production technology in Ansai extra low permeability oilfield,” in International Oil and Gas Conference and Exhibition in China, Beijing, China, November 2000.

D. Denney, “Characterization of water injection in low-permeability rock using sandstone micromodels,” Journal of Petroleum Technology, vol. 56, no. 5, pp. 71-72, 2004.

L. M. Surguchev, N. H. Giske, and L. Kollbotn, “Cyclic water injection improves oil production in carbonate reservoir,” in Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE, November 2008.

B. Haynes, A. Abdemawla, and S. G. L. Stromberg, “Impact of pore volume compressibility on recovery from depletion drive and miscible gas injection in South Oman,” in SPE Annual Technical Conference and Exhibition, Denver, CO, USA, September 2008.

X. L. Zhang, “Calculation of natural depletion oil recovery for low permeability reservoirs,” Journal of Liaoning Technical University (Natural Science), vol. 33, no. 5, pp. 633–636, 2014.

M. F. Chen, M. Zhao, M. Wang, G. Jian, and S. Jianhu, “Study on reasonable energy supplement timing for low permeability and high saturation reservoirs,” Fault-Block Oil & Gas Field, vol. 21, no. 4, pp. 463–466, 2014.

J. Akande and J. P. Spivey, “Considerations for pore volume stress effects in over-pressured shale gas under controlled drawdown well management strategy,” in SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, October 2012.

H. Pu, G. F. Wang, and Y. X. Li, “Reservoir simulation study on improvement of waterflooding effect for a naturally fractured low permeability field in Daqing, China: a successful case,” in SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, March 2009.

A. Graue, R. Moe, and B. A. Baldwin, “Comparison of numerical simulations and laboratory waterfloods with in-situ saturation imaging of fractured blocks of reservoir rocks at different wettabilities,” in SPE International Petroleum Conference and Exhibition in Mexico, Villahermosa, Mexico, February 2000.

X. Q. Xie, H. Q. Jiang, Q. Z. Wang, T. Liu, and W. Zhang, “Discussion on pressure-sensitivity effect and water-flooding timing in low-permeability reservoir,” Acta Petrolei Sinica, vol. 30, no. 4, pp. 574–577, 2009.

X. L. Zhang and J. Q. Zhang, “Calculation method of natural depletion oil recovery for micro-fractured low permeability reservoirs,” Xinjiang Petroleum Geology, vol. 32, no. 4, pp. 409–411, 2011.

X. L. Zhang, X. P. Li, Y. Zhao, and D. Luo, “Calculation of elastic recovery for abnormal high pressure and low permeability reservoir,” Rerservoir Evaluation and Development, vol. 3, no. 2, pp. 34–37, 2011.

G. L. P. D. Oliveira, M. A. R. Ceia, R. M. Missagia et al., “Pore volume compressibilities of sandstones and carbonates from helium porosimetry measurements,” Journal of Petroleum Science and Engineering, vol. 137, pp. 185–201, 2016.