Sensitivity analysis of water-alternating-CO2 flooding for enhanced oil recovery in high water cut oil reservoirs

Computers & Fluids 99 (2014) 93–103

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Computers & Fluids j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p fl u i d

Sensitivity analysis of water-alternating-CO2 flooding for enhanced oil recovery in high water cut oil reservoirs Zhaojie Song a,b,c, Zhiping Li a,c, Mingzhen Wei b,⇑, Fengpeng Lai a,c, Baojun Bai b a

School of Energy Resources, China University of Geosciences, 29# Xueyuan Road, Haidian District, 100083 Beijing, China Department of Geological Sciences and Engineering, Missouri University of Science and Technology, 1400 N. Bishop Avenue, Rolla, 65409 Missouri, United States c Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, 29# Xueyuan Road, Haidian District, 100083 Beijing, China b

a r t i c l e

i n f o

Article history: Received 10 December 2012 Received in revised form 28 February 2014 Accepted 20 March 2014 Available online 13 April 2014 Keywords: CO2 WAG flooding Enhanced oil recovery Orthogonal experimental design Operational scheme Net Present Value Technical and economic analyses

a b s t r a c t The objective of this work is to investigate the effect of operational schemes, reservoir types and development parameters on both the amount of incremental oil produced and CO2 stored in high water cut oil reservoirs during CO2 water-alternating-gas (WAG) flooding by running compositional numerical simulator. The method used is the orthogonal experimental design method to optimize operation parameters, including CO2 slug size, ratio of CO2 slug size to water slug size (WAG ratio), CO2 injection rate, and voidage replacement ratio. The Net Present Value (NPV) was used as an objective function for economic analysis. Various 3-D heterogeneous reservoir models were built to investigate the impact of reservoir types and development parameters on CO2 flooding efficiency and storage capacity. The results indicate that as compared to inverted nine-spot pattern and inverted seven-spot pattern, five-spot pattern is more suitable for CO2 WAG flooding. The earlier water injection is switched to CO2, the more benefit can be obtained. Compared with CO2 injection cost and tax credit per ton of CO2 stored, oil price is considered as the most influential economic parameter on CO2 WAG flooding. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Carbon dioxide flooding has been recognized as one of the most effective options for oil recovery enhancement in depleted or mature oil reservoirs [1–3]. The benefits of injecting CO2 include the expansion of oil volume and the reduction of oil viscosity [4,5]. CO2 is able to displace the residual oil that is immobilized by water flooding and therefore improve the microscopic displacement efficiency [6]. The CO2 EOR projects in Weyburn and the North Sea have also proved the great potentials of both oil production increment and CO2 sequestration [7,8]. However, if the gas source is located far from a target oil reservoir, considering the cost of CO2 capture, transportation, compression and injection, CO2 EOR projects may not be profitable without economic incentives from the government. Ghomian et al. [9] established the amounts and types of economic incentives for different reservoir types. They found that sandstone reservoirs had higher probability of need for economic incentives than carbonate reservoirs. Using the methodology of NPV, Jahangiri and Zhang [10]

⇑ Corresponding author. Tel.: +1 573 341 4657. E-mail address: [email protected] (M. Wei). http://dx.doi.org/10.1016/j.compfluid.2014.03.022 0045-7930/Ó 2014 Elsevier Ltd. All rights reserved.

determined that a minimum of $40/ton of carbon tax credit is required for immiscible CO2 flooding so as to obtain the same NPV as water flooding, while miscible CO2 flooding is more profitable than water flooding even without any economic incentives. Regarding the optimization of operational scheme, a number of studies have been conducted. Yang et al. [11] developed an integrated model to optimize the production-injection operation systems (PIOS). Taking the NPV as an objective function, the optimum production and injection parameters were achieved in a WAG miscible flooding reservoir. Kovscek and Cakici [12] defined an objective function that combines the ultimate oil recovery and the fraction of reservoir volume filled with CO2. The most effective injection and production scheme was determined which could cooptimize oil recovery and simultaneous CO2 sequestration. Chen et al. [13] developed a hybrid method that integrates orthogonal array and Tabu technique into a genetic algorithm. When conducting a sensitivity analysis on oil recovery and NPV, controlling variables were selected including injection rate, WAG ratio, injection time and bottomhole pressure for the producers. Studies revealed that WAG flooding recovers more oil than continuous injection flooding. That is because WAG flooding can reduce CO2 viscous fingering and provide better vertical sweep efficiency [14,15]. Additionally, the horizontal well impacts CO2 flooding greatly for the

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reason that the displacement provides better sweep efficiency based on both reservoir simulations and laboratory studies [16– 18]. Despite the potentials of CO2 EOR, this technology is not suitable for all types of hydrocarbon reservoirs [19,20]. Based on both field results and oil recovery mechanism study, Taber et al. [21] proposed the screening criteria for CO2 miscible and immiscible flooding, respectively. Shaw and Bachu [22] presented a method for the screening and ranking of oil reservoirs suitable for CO2 EOR. Oil gravity, reservoir temperature and pressure, minimum miscibility pressure and remaining oil saturation were selected as variables. However, most of studies on CO2 flooding described above have been conducted on undeveloped oil reservoirs, and very few results from high water cut oil reservoirs are seen in the literature. The main objective of this study is to investigate the effect of operational schemes, reservoir types and development parameters on WAG flooding in high water cut oil reservoirs by running compositional simulations. By applying orthogonal experimental design, the most effective operational scheme was determined which could maximize the incremental oil produced by WAG flooding. Afterwards, various geological models were constructed by employing different reservoir parameters and development parameters. A technical analysis of five reservoir parameters and two development parameters was conducted. The NPV model was built for economic analysis. The effect of oil price, CO2 injection cost and tax credit on the NPV was investigated in the study. 2. Description of the base reservoir model This study was conducted based on a reservoir on Guan 104 fault block in Dagang Oilfield in China [23–28]. For the particular interested area of 3.5 km2, the reservoir depth is from 2,650 m to 2,750 m; the formation net thickness varies from 9.7 m to 41.4 m; the average horizontal permeability varies from 254.7 md to 425.7 md; the range of porosity is from 18% to 22% and the average porosity is 19.04%. The permeability variation coefficient varies from 0.45 to 0.8. The sand body rhythms include normal, reverse, compound normal and compound reverse. Fivespot patterns were initially applied and are still used in this reservoir. This is a water-wet reservoir. The relative permeability end points are the critical water saturation of 0.478, the residual oil saturation of 0.227 for water–oil system, the connate gas saturation of 0, and the maximum gas saturation of 0.522 for gas–liquid system. The relative permeability curves for water–oil system were depicted in Fig. 1(a), while the relative permeability curves for gas–liquid system were shown in Fig. 1(b). The same set of relative permeability curves was utilized in the simulations during water flooding and CO2 WAG flooding. In order to investigate the impact of operational schemes on CO2 flooding, a base reservoir model with impermeable boundary was built based on the range of main parameters of that particular reservoir. The base reservoir model is 925 m, 925 m and 10 m in the x, y and z dimensions, respectively. It consists of nine five-spot patterns with a well spacing (i.e., the distance between two adjacent producers) of 300 m; the locations of the 9 injectors and 16 producers were shown in Fig. 2. These wells perforated in all four layers of the formation. The sand body is normal rhythmic, which means the formation permeability increases downward. The base reservoir is water-wet, and the initial oil saturation is 0.522. Other parameters in the base reservoir model were summarized in Table 1. Slim-tube experiments were conducted to determine the minimum miscibility pressure (MMP) between the reservoir oil and CO2. The experiments were conducted under the temperature of 108 °C. A slim tube with a length of 18 m and an inner radius of

Fig. 1. Typical relative permeability curves for the target oil reservoir. (a) Relative permeability curves for water–oil system. (b) Relative permeability curves for gas– liquid system.

3.175 mm was packed with sand of 200 mesh size. The pore volume of the slim tube is 255.7 cm3. The slim tube was saturated by reconstituted oil that contains C1 + N2 (14.0 mol%), CO2 + C2  C10 (27.9 mol%) and C11+ (58.1 mol%). During the experiments, 1.2 PV CO2 was injected at the rate of 0.167 cm3/min at six different displacement pressures. The color change and phase behavior of the effluent were observed through the inspection window. The effluent was flashed in the separator connected with a flow meter to measure gas flow. The oil was collected in a conical flask and the density was measured using a densitometer. The cumulative oil recovery was recorded and the MMP was defined as the break in slope from the plot of oil recovery against displacement pressure [29]. As Fig. 3 depicts, the MMP was determined to be 322.8 bars. The initial formation pressure is 272.1 bars that are lower than the MMP, which means CO2 immiscible flooding. Using the PVTi module in Eclipse software, the pseudo-components of crude oil were obtained as shown in Table 2. The light components (C2  C6) just account for 10.1 mol%, and a large amount of heavy components leads to a high MMP between reservoir oil and CO2. Eclipse Compositional Simulator was used. Initially, the reservoir was water flooded; then RESTART function was used to conduct WAG flooding. During WAG flooding, mass transfer between CO2 and oil was automatically considered in the compositional simulator. 3. Methodologies 3.1. Determination of operational scheme In CO2 WAG flooding, the CO2 slug size, WAG ratio, CO2 injection rate and voidage replacement ratio impact WAG flooding significantly [13,30]. A big CO2 slug size results in early gas

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Fig. 2. Base reservoir model with well-spacing patterns and initial oil saturation distribution.

Table 1 Basic parameters in the base reservoir model. Parameter

Value

Parameter

Value

Reservoir depth (m) Net thickness (m) Porosity

2700 10 0.1904

Average horizontal permeability (md) Permeability variation coefficient Ratio of vertical to horizontal permeability

300 0.5 0.1

Fig. 3. Cumulative oil recovery at different displacement pressures in the slim-tube experiments.

Table 2 Pseudo-components description of crude oil. Component

Mole fraction

Molecular weight (kg/mole)

Tc (K)

Pc (bar)

CO2 CH4 + N2 C2H6 C3–C4 C5–C6 C7–C10 C11+

0.00046 0.14012 0.01524 0.03500 0.05062 0.17743 0.58113

0.044010 0.016447 0.030070 0.052477 0.078719 0.114980 0.330300

304.2 188.4 305.4 401.1 489.6 589.4 847.2

72.9 45.6 48.2 39.6 31.7 27.2 10.2

increases the requirements of CO2 compression and injection devices. Moreover, the bottomhole injection pressure may exceed the formation fracturing pressure at high CO2 injection rates. Meanwhile the low CO2 injection rate narrows the miscible zone and reduces CO2 flooding efficiency. It is required to achieve an optimal injection rate to maximize the oil recovery improvement. An appropriate increase of voidage replacement ratio is beneficial in maintaining initial formation pressure and promoting mass transfer between CO2 and oil. However, an excessive voidage replacement ratio leads to the injection pressure higher than formation fracturing pressure. Therefore, optimization study was conducted to achieve the optimal combination of these four parameters. Table 3 shows the four parameters discussed in the study and the three levels of uncertainty considered for each parameter. If the combinations of all parameters at all levels are studied (i.e., full-factorial experiment), 34 runs will be required. Orthogonal experimental design is the method that can be used to avoid the full-factorial experiment implementation when multiple parameters are considered at multiple levels. As Table 4 depicts, only nine operational schemes were required in orthogonal experimental design, and all levels of all parameters were well distributed in these schemes. The orthogonal experimental design significantly decreases the number of simulation executions, therefore improve the computational cost. In order to evaluate WAG flooding efficiency, two evaluating indices were defined: the improved recovery factor and gas replacing oil ratio. The former refers to the increased oil recovery factor of WAG flooding as compared to that of water flooding, and the latter refers to the amount of oil production increased in m3 when one ton of CO2 is stored. The flowchart of the research procedure was provided in Fig. 4. Initially, a water flooding simulation was performed with a water injection rate of 70 m3/d for each injector. A fixed liquid production rate was set for each producer to achieve a volumetric balance. The ultimate water flooding recovery factor is 43.56% when all the proTable 3 Operation parameters for operational scheme study and their three levels of uncertainty.

breakthrough and high producing gas-oil ratio. While a small CO2 slug size increases the cycles of WAG and makes on-site operations complex. An appropriate WAG ratio is conducive to the control of water cut and the improvement of sweep efficiency. A high CO2 injection rate not only causes high producing gas-oil ratio but also

NO.

Operation parameter

Low (1)

Median (0)

High (1)

1 2 3 4

CO2 slug size (PV) WAG ratio CO2 injection rate (Sm3/d) Voidage replacement ratio

0.05 2:1 10,000 1:1

0.10 1:1 20,000 1:0.95

0.15 1:2 40,000 1:0.9

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Table 4 Scenario design for operational scheme study and results of two evaluating indices. Scheme

CO2 slug size (PV)

WAG ratio

CO2 injection rate (Sm3/d)

Voidage replacement ratio

Improved recovery factor

Gas replacing oil ratio (m3/ton)

F001 F002 F003 F004 F005 F006 F007 F008 F009

0.05 0.05 0.05 0.10 0.10 0.10 0.15 0.15 0.15

2:1 1:1 1:2 2:1 1:1 1:2 2:1 1:1 1:2

10,000 20,000 40,000 20,000 40,000 10,000 40,000 10,000 20,000

1:1 1:0.95 1:0.9 1:0.9 1:1 1:0.95 1:0.95 1:0.9 1:1

0.05953 0.08391 0.17640 0.10790 0.09740 0.09412 0.09148 0.10850 0.09835

0.198 0.349 0.588 0.366 0.316 0.393 0.306 0.302 0.286

ducers reached the water cut of 98% to shut in. Fig. 5 presents the information for the primary production of the base reservoir. During the first two years of water flooding, oil production rate decreases from 611 m3/day to 115 m3/day, while water production increases from 0 m3/day to 500 m3/day. At the end of the primary production, cumulative oil production is 194,653 m3, and recovery factor reaches 25.1%. The remaining oil saturation is 0.391. The average formation pressure declines to 258.2 bars. The water cut reaches 81.2%, indicating the reservoir reaches high water cut stage. After the two years of water flooding, WAG flooding was implemented by applying RESTART function in the Eclipse Compositional Simulator, and nine schemes shown in Table 4 were performed on the base reservoir model. The improved recovery factor and gas replacing oil ratio when all the producers reached the producing gas-oil ratio of 3,000 Sm3/m3 to shut in were summarized in Table 4. Orthogonal experimental design is one type of designs of experiments. Applying this methodology enables us to obtain the mean values and range values of the two evaluating indices as shown in Table 5. The mean value refers to the average value of the evaluating index of three schemes for each level of the parameter. The

Fig. 5. Production profiles during the first two years of water flooding in the base reservoir model.

range value is the difference between the maximum and minimum mean values for each parameter. The mean values are used to determine which level is optimal for each parameter. The most

Fig. 4. Flowchart of the research procedure.

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Table 5 Mean values and range values of two evaluating indices at different levels of operation parameters. Operation parameters

Improved recovery factor

Gas replacing oil ratio (m3/ton)

Mean value

Range value

Mean value

Range value

CO2 slug size Low (1) Median (0) High (1)

0.10661 0.09981 0.09944

0.00717

0.378 0.358 0.298

0.080

WAG ratio Low (1) Median (0) High (1)

0.08630 0.09660 0.12296

0.03666

0.290 0.322 0.422

0.132

CO2 injection rate Low (1) Median (0) High (1)

0.08738 0.09672 0.12176

0.03438

0.297 0.334 0.403

0.106

0.04584

0.267 0.349 0.418

0.151

Voidage replacement ratio Low (1) 0.08509 Median (0) 0.08984 High (1) 0.13093

effective scheme is regarded as the one with four optimal levels of four operation parameters. The range values are used for ranking the four operation parameters. A bigger range value indicates that the parameter is more influential. For the purpose of maximizing the improved recovery factor and gas replacing oil ratio, it was determined from Table 5 that the most effective operational scheme of WAG flooding was the one with a CO2 slug size of 0.05 PV, a WAG ratio of 1:2, a CO2 injection rate of 40,000 Sm3/d, and a voidage replacement ratio of 1:0.9. The oil recovery in this case was improved 17.64% as compared to water flooding. From the results, the most influential parameter is the voidage replacement ratio, WAG ratio, CO2 injection rate, and CO2 slug size, with decreasing significance to those evaluating indices. In order to conduct a sensitivity analysis of the most influential operation parameter, voidage replacement ratio, three WAG flooding schemes were designed. In these schemes, the CO2 slug size, WAG ratio, and CO2 injection rate were set to be the optimal values discussed above. The voidage replacement ratio was considered 1:1, 1:0.95 and 1:0.9 in each of the three schemes, respectively. Initially, a water flooding scheme was performed on the base model for comparison. A water injection rate of 70 m3/d was assumed for each injector, while a fixed liquid production rate was set for each producer to achieve a volumetric balance. After two years of water flooding, RESTART function was applied to conduct three WAG flooding schemes. Fig. 6 compares the formation pressure, oil production rate and producing gas-oil ratio for these three WAG flooding schemes and the water flooding scheme. Properly increasing the voidage replacement ratio is beneficial in maintaining the current formation pressure. In the WAG flooding scheme with a voidage replacement ratio of 1:0.9, the formation pressure almost maintains in the initial condition of the reservoir before water flooding. When the voidage replacement ratio is 1:1, 1:0.95 and 1:0.9, the ultimate recovery factor of WAG flooding is 10.46%, 11.81% and 17.64% more than that of water flooding, respectively. This indicates that increasing the voidage replacement ratio can improve sweep efficiency, and delay the breakthrough of CO2 as seen in Fig 6(c), so as to improve CO2 flooding efficiency. For these three WAG flooding schemes, the drastic increase in the producing gas-oil ratio after gas breakthrough results in the substantial decrease in formation pressure and oil production rate. After CO2 breakthrough, most of the injected CO2 is produced directly by the producers, so the

Fig. 6. Effect of voidage replacement ratio (VRR) on CO2 WAG flooding efficiency. (a) Profiles of formation pressure. (b) Profiles of oil production rate. (c) Profiles of producing gas-oil ratio.

wells should be shut in because of the decreasing benefit of WAG flooding. In the WAG flooding scheme with a voidage replacement ratio of 1:0.9, the average oil production rate is 289.45 m3 which is about 2.5 times as much as that of water flooding. Further increasing the voidage replacement ratio will lead to the formation pressure higher than the formation fracturing pressure, which has been proved through simulations. Therefore, in the range of this study, the optimal voidage replacement ratio was determined to be 1:0.9.

3.2. Technical and economic analyses As Fig. 4 presents, the most effective operational scheme proposed above was used to perform numerical simulations for technical and economic analyses. The injectors were set at constant CO2 and water injection rates, while the producers were set at a fixed liquid rate according to the voidage replacement ratio of 1:0.9. Five reservoir parameters and two development parameters were taken into account to investigate their effect on WAG flooding. The average horizontal permeability, the permeability variation coefficient, the ratio of vertical to horizontal permeability, the rhythm of sand body and the net thickness of formation were discussed as reservoir parameters; while the well-spacing pattern and the percentage of recoverable reserves by water flooding were studied as development parameters. As Table 6 depicts, four levels

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Table 6 Sensitivity parameters and their levels of uncertainty for technical and economic analyses. Level

Sensitivity parameter Average horizontal permeability (md)

Permeability variation coefficient

Ratio of vertical to horizontal permeability

Net thickness of formation (m)

Rhythm of sand body

Well-spacing pattern

Percentage of recoverable reserves by water flooding

1

200

0.5

0.1

10

Normal

Five-spot pattern with a well spacing of 300 m

2

300

0.6

0.2

20

Reverse

Five-spot pattern with a well spacing of 200 m

3

400

0.7

0.3

30

Compound normal

Inverted nine-spot pattern with a well spacing of 300 m

4

500

0.8

0.4

40

Compound reverse

Inverted seven-spot pattern with a well spacing of 300 m

0 10 20 30 40 50 60 70 80 90 100

of uncertainty were considered for each of the first six parameters. The last parameter, percentage of recoverable reserves by water flooding, indicates what percentage of maximum water flooding recoverable reserves have been already extracted before CO2 WAG flooding is implemented in the target oil reservoir. Eleven levels (0 at the initial reservoir condition, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 when maximum water flooding recoverable reserves are produced) were considered for this parameter to optimize WAG injection timing in a water flooding reservoir. Percentage of recoverable reserves by water flooding was defined as follows

Percentage of recoverable reserves by water flooding ¼

Cumulative oil production during water flooding Water flooding recoverable reservesjwater cut¼98%

When one parameter was under investigation, various geological reservoir models were built by employing different values of this parameter. The other parameters were the same as those in the base reservoir model. The five-spot pattern with a well spacing of 300 m was arranged in the reservoir. Initially, water flooding was performed on the reservoir models. The maximum water flooding recovery factor can be obtained when all the producers reached the water cut of 98% to shut in. By applying RESART function in the compositional simulator, water injection was switched to CO2 when different percentages (for sensitivity analysis of percentage of recoverable reserves by water flooding) or 80% (for sensitivity analysis of other parameters in Table 6) of recoverable reserves by water flooding were achieved. By performing numerical simulations on these reservoir models, the WAG flooding recovery factor (i.e., the ultimate oil recovery at the end of WAG flooding), the amount of CO2 injected and the improved recovery factor can be determined when all the producers reach the producing gas-oil ratio of 3,000 Sm3/m3 to shut in. These three dependent variables and water flooding recovery factor were considered as technical objective functions to conduct a technical analysis. For the purpose of implementing an economic analysis, the detailed production data of these reservoir models were used to calculate the NPV of WAG flooding. The economic objective function of NPV was computed as

NPV ¼

N X ðCI  COÞ t¼0

ð1 þ ic Þ

a and ic the annual discount rate, which is set at the common value of 12% in petroleum engineering. The cash inflow includes the revenue of produced oil and the tax credit per ton of CO2 stored. Combining the local financial data at the target reservoirs and international price for gas and oil industry, the price of oil was considered $80/bbl for the entire production period, while the tax credit was set as $0 per ton of CO2 stored. The effect of the tax credit on the NPV will be discussed. The cash outflow includes the well construction cost of 1.6 $mm/ well, the CO2 injection cost of $60/ton (including the cost of CO2 capture, transportation and compression), the water injection cost of $0.25/bbl, the water disposal cost of $1.5/bbl, the oil lift cost of $0.5/bbl and the fixed operational cost of 0.03 $mm/month. The net cash flow at time t is the difference between the cash inflow and outflow.

4. Results and discussion 4.1. Sensitivity analysis of reservoir parameters Fig. 7 shows the recovery factor of water flooding and WAG flooding, the improved recovery factor, the amount of CO2 injected, and the NPV of WAG flooding at different levels of the average horizontal permeability. With higher reservoir permeability, the water flooding oil recovery increases, while WAG flooding oil recovery decreases. This behavior was also observed in previous study on an undeveloped oil reservoir [31], and this is because more permeable reservoirs have better water flooding sweep efficiency. At the same producing gas-oil ratio limit of 3,000 Sm3/m3, the total amount of CO2 injected decreases when the average horizontal

t

t

where t is the the time of the cash flow, a; (CI  CO)t the the net cash flow at time t, $; (CI)t the the cash inflow at time t, $; (CO)t the cash outflow at time t, $; N the cumulative production period,

Fig. 7. Effect of average horizontal permeability on technical and economic objective functions.

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Z. Song et al. / Computers & Fluids 99 (2014) 93–103 Table 7 Average gas saturation in different formation layers and WAG injection duration. Reservoir parameter

Average gas saturation after 720 days of WAG injection The first (top) layer

WAG injection duration (day)

The second layer

The third layer

The fourth (bottom) layer

Overall

Average horizontal permeability (md) 200 0.150 300 0.202 400 0.249 500 0.288

0.067 0.068 0.062 0.057

0.030 0.023 0.015 0.010

0.009 0.005 0.004 0.002

0.064 0.075 0.083 0.089

948 894 815 777

Permeability variation coefficient 0.5 0.202 0.6 0.162 0.7 0.137 0.8 0.119

0.068 0.090 0.084 0.086

0.023 0.018 0.030 0.043

0.005 0.003 0.004 0.005

0.075 0.068 0.064 0.063

894 978 1050 1096

Ratio of vertical to horizontal permeability 0.1 0.202 0.2 0.312 0.3 0.346 0.4 0.364

0.068 0.061 0.079 0.093

0.023 0.008 0.007 0.012

0.005 0.002 0.002 0.002

0.075 0.096 0.109 0.118

894 770 739 735

Rhythm of sand body Normal Reverse Compound normal Compound reverse

0.202 – 0.240 0.266

0.068 – 0.060 0.086

0.023 – 0.016 0.027

0.005 – 0.007 0.001

0.075 – 0.081 0.095

894 293 822 775

Net thickness of formation (m) 10 0.202 20 0.121 30 0.081 40 0.061

0.068 0.073 0.077 0.077

0.023 0.039 0.060 0.072

0.005 0.013 0.023 0.034

0.075 0.062 0.060 0.061

894 971 1014 996

permeability is higher than 300 md. Table 7 summarizes the gas saturation distribution in four layers after 720 days of WAG injection, and correspondingly WAG injection durations at different average horizontal permeabilities. Because formation pressure is higher than oil saturation pressure, no solution gas comes out in the reservoir in the process of production, and the free gas in the reservoir is CO2. Due to the gravity difference between oil and CO2, gas saturation is higher on the top. As average horizontal permeability increases, the average gas saturation increases in the top layer and WAG injection duration reduces. It can be concluded higher permeability increases CO2 gravity overriding and accelerates gas production, and thus the sweep efficiency of WAG flooding is reduced. Therefore, the technical and economic advantage of WAG flooding as compared to water flooding decreases as the average horizontal permeability increases. Fig. 8 summarizes the technical and economic objective functions at different permeability variation coefficients. As the permeability variation coefficient increases, the recovery factor of WAG flooding improves, while that of water flooding declines. This

Fig. 8. Effect of permeability variation coefficient on technical and economic objective functions.

result is different from those of undeveloped reservoirs [32]. The reason is the upper part of the formation becomes less permeable, while the lower part becomes more permeable as heterogeneity increases in the normal rhythmic reservoir. Therefore, as Table 7 presents, with the increase of permeability variation coefficient, gas saturation in the top layer reduces and the effect of CO2 gravity overriding decreases. The sweep efficiency of WAG flooding improves, and meanwhile that of water flooding worsens. More CO2 was injected when the permeability variation coefficient is greater than 0.6. This indicates the higher permeability variation coefficient delays gas production; therefore, WAG flooding recovery factor improves with more injected CO2 displacing more oil from the reservoir. But sometimes a slight improvement in oil recovery cannot offset the cost of increased CO2 injection. In this study, the NPV reaches its maximum value when the permeability variation coefficient equals 0.6. When the average horizontal permeability was constant, the ratio of vertical to horizontal permeability represents the vertical permeability of the formation. As shown in Table 7, gas saturation in the top layer increases and WAG injection duration reduces as the ratio of vertical to horizontal permeability increase. This means lower vertical permeability can lessen CO2 gravity overriding and delay gas production. Hence, as Fig. 9 indicates, the most CO2 was injected when the ratio of vertical to horizontal permeability is 0.1. However, lower vertical permeability does not favor water flooding. As the vertical permeability improves, WAG flooding recovery factor decreases, but water flooding recovery factor increases, which is in agreement with previous study [31]. Fig. 9 shows the trends of the improved recovery factor and the NPV of WAG flooding. It is clear that the technical and economic efficiency of WAG flooding worsens as the ratio of vertical to horizontal permeability increases. Fig. 10 plots the technical and economic objective functions at different sand body rhythms. In the reverse rhythmic model, the reservoir permeability increases upward by layers. As Table 7 depicts, WAG injection only lasted 293 days in the reverse rhythmic model. After 180 days of WAG injection, the average gas

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Fig. 9. Effect of ratio of vertical to horizontal permeability on technical and economic objective functions.

Fig. 11. Effect of net thickness of formation on technical and economic objective functions. (a) Technical objective functions. (b) Economic objective function.

Fig. 10. Effect of sand body rhythm on technical and economic objective functions.

saturation in the top layer is 0.012, which is much higher than the average gas saturation in the top layer of the normal rhythmic model. This reveals that CO2 gravity overriding was aggravated in the reverse rhythmic model. In the reverse rhythmic reservoir, just 0.1 PV CO2 was finally injected when all the producers reached the producing gas-oil ratio of 3,000 Sm3/m3. The recovery factor of WAG flooding almost equals that of water flooding, so it is not suitable to implement WAG flooding in the reverse rhythmic reservoirs. The compound normal rhythmic model means normal rhythmic sand bodies overlap each other, while the compound reverse rhythmic model means reverse rhythmic sand bodies overlap each other. The compound reverse rhythmic model achieves the highest NPV for WAG flooding. This is because, as compared to the normal rhythmic model, the substantial reduction of CO2 injection cost is more beneficial to the NPV than the slight reduction of oil revenue. Fig. 11(a) presents the recovery factors for WAG flooding and water flooding, the improved recovery factor and the amount of CO2 injected at different levels of net thickness of formation. Previous study has shown that an increase in net thickness would aggravate CO2 gravity overriding and accelerate CO2 production [33]. This study observed that the recovery factor of WAG flooding improves as the net thickness increases, and the recovery factor begins to decline when the net thickness exceeds 30 m. Moreover, the maximum amount of CO2 was injected when the net thickness is 30 m. It can be seen from Table 7 that an increase of net thickness would not increase gas saturation in the top layer and aggravate CO2 gravity overriding, which is our new observation compared with previous study [33]. Because the layers are too thick when net thickness is 40 m, which increases the internal gas overriding in each layer, CO2 is relatively well-distributed in

the top three layers. However, the overall average gas saturation increases and WAG injection duration reduces when net thickness exceeds 30 m. Therefore, the conclusion can be reached that an increase of net thickness would increase the technical efficiency of WAG flooding when net thickness is less than 30 m; but it would counter CO2 displacing oil when net thickness exceeds 30 m. Fig. 11(b) indicates that the NPV of WAG flooding increases drastically as the net thickness increases. This occurs because the original oil in place (OOIP) increases with thicker formations, and cumulative produced oil is enhanced greatly, even though the recovery factor of WAG flooding only slightly changes as the net thickness increases. 4.2. Sensitivity analysis of development parameters In order to study the impact of well-spacing pattern, four reservoir models were constructed with nine five-spot patterns with a well spacing of 300 m, nine five-spot patterns with a well spacing of 200 m, nine inverted nine-spot patterns with a well spacing of 300 m, and seven inverted seven-spot patterns with a well spacing of 300 m, respectively. In these study cases, the reservoir sizes and OOIP are different and other properties keep the same. Fig. 12 summarizes the effect of different well-spacing patterns on water flooding and WAG flooding. Four well-spacing patterns under investigation are represented by A, B, C, and D, where A refers to the five-spot pattern with a well spacing of 300 m; B refers to the five-spot pattern with a well spacing of 200 m; C refers to the inverted nine-spot pattern with a well spacing of 300 m; and D refers to the inverted seven-spot pattern with a well spacing of 300 m. Two five-spot patterns with well spacing of 200 m and 300 m were investigated to analyse the effect of well spacing. As shown in Fig. 12(a), the inverted nine-spot pattern achieves the highest recovery factor from water flooding, while the five-spot pattern achieves the highest recovery factor from WAG flooding, which is consistent with previous study [34]. In terms of the eco-

Z. Song et al. / Computers & Fluids 99 (2014) 93–103

Fig. 12. Effect of well-spacing pattern on technical and economic objective functions. (a) Technical objective functions. (b) Economic objective functions.

nomic analysis, the NPV of the inverted nine-spot pattern is much higher than those of the other well-spacing patterns, as presented in Fig. 12(b). This is mainly because the reservoir with inverted nine-spot patterns has the largest OOIP, while the reservoirs with five-spot patterns have the smallest OOIP. And much more oil was produced in the reservoir with inverted nine-spot pattern than in the reservoirs with other well-spacing patterns. Therefore, sensitivity analysis that takes total NPV as the economic objection is not reasonable for an oil reservoir with a fixed area and OOIP. The NPV per unit area is a much clear NPV indicator at different well-spacing patterns, as shown in Fig. 12(b). The NPV per unit area of five-spot pattern with a well spacing of 300 m is about 1.3 times that of other well-spacing patterns. The five-spot pattern with a well spacing of 300 m has a higher NPV per unit area than the five-spot pattern with a well spacing of 200 m, even though the latter has a slightly higher recovery factor of WAG flooding. Expanding well spacing appropriately is recommended for WAG flooding. The five-spot pattern is the most favorable well-spacing pattern for WAG flooding and is also mostly used in the target oilfield. Therefore, the five-spot pattern with a well spacing of 300 m was chosen to analyse the impact of WAG injection timing. A series of simulations were conducted under different percentages of recoverable reserves by water flooding. At percentages of recoverable reserves by water flooding of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100, the remaining oil saturation in the reservoir model would be 0.497, 0.479, 0.451, 0.432, 0.406, 0.384, 0.362, 0.340, 0.317 and 0.295, respectively, which serve as the starting points of CO2 WAG flooding. And simulations ended when all the producers reached the producing gas-oil ratio of 3,000 Sm3/m3. Fig. 13(a) compares the technical objective functions at different percentage of recoverable reserves by water flooding. The recovery factor of WAG flooding and the improved recovery factor decline slightly as the water flooding was switched to WAG flooding at later stage of development. The results mean that different values of percentage of

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Fig. 13. Effect of percentage of recoverable reserves by water flooding on technical and economic objective functions. (a) Technical objective functions. (b) Economic objective function.

recoverable reserves by water flooding and corresponding remaining oil saturation have limited effect on WAG flooding oil recovery. The amount of CO2 injected does not change at different WAG injection timing. This indicates the stage of water flooding does not affect CO2 production in the specified reservoir. The effect of WAG injection timing on WAG flooding can also be analysed by means of NPV. Fig. 13(b) shows that the earlier water injection is switched to CO2, the higher NPV of WAG flooding can be obtained. When the percentage of recoverable reserves by water flooding equals 0 (i.e., WAG flooding is performed directly in the undeveloped oil reservoir), the NPV achieves its maximum value. It is because that WAG flooding provides higher oil production rate before gas breakthrough than water flooding, thus shorten the production cycle and improve the NPV. More importantly, at different WAG injection timing, the NPVs of WAG flooding are always higher than that of water flooding even without any tax credit. This means it is much economically advantageous to switch water injection to WAG injection in a water flooding reservoir. 4.3. Sensitivity analysis of economic parameters In addition to the sensitivity analysis of five reservoir parameters and two development parameters, three economic parameters were considered including oil price, CO2 injection cost and tax credit per ton of CO2 stored to investigate their effect on the NPV. When one economic parameter was under investigation, the other economic parameters were set as follows. The oil price is $80/bbl. The CO2 injection cost is $60/ton. The tax credit is $20 per ton of CO2 stored. Same with above analyses, water flooding was initially performed on the base reservoir model, and then water injection was switched to CO2 when 80% of recoverable reserves by water flooding were achieved. Table 8 shows the five levels of uncertainty for these three economic parameters and the corresponding NPV results. As Fig. 14 presents, the relative

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Z. Song et al. / Computers & Fluids 99 (2014) 93–103

Table 8 Net Present Value of CO2 WAG flooding at different levels of economic parameters. Oil price ($/bbl)

NPV (108 $)

CO2 injection cost ($/ton)

NPV (108 $)

Tax credit ($/ton)

NPV (108 $)

40 60 80 100 120

0.2293 0.6603 1.0913 1.5223 1.9533

30 45 60 75 90

1.1343 1.1128 1.0913 1.0698 1.0483

10 15 20 25 30

1.0831 1.0872 1.0913 1.0954 1.0995

worsens when it exceeds 30 m. However, the NPV increases significantly as the formation becomes thicker because of the substantial oil production increase.  As compared to inverted nine-spot pattern and inverted sevenspot pattern, five-spot pattern is more suitable for WAG flooding. Appropriately expanding well spacing improves the economic efficiency, even though the recovery factor decreases slightly. The analysis of WAG injection timing reveals that the earlier water injection is switched to CO2 in a water flooding reservoir, the more benefit can be obtained.  Additionally, oil price, rather than CO2 injection cost and tax credit per ton of CO2 stored, is considered as the parameter that impacts the economic efficiency of WAG flooding more significantly.

Acknowledgements We would like to gratefully acknowledge support from the National Natural Science Foundation Program of China (51174178), the National Science and Technology Major Project of China (2011ZX05016-006), the Fundamental Research Funds for the Central Universities (2-9-2011-206) and China Scholarship Council. Fig. 14. Effect of relative change of oil price, gas injection cost, tax credit on relative change of NPV.

change of NPV as the relative change of three economic parameters clearly indicates that the NPV of WAG flooding changes significantly as oil price varies. Therefore, oil price is considered as the most influential economic parameter on the NPV. CO2 injection cost has the second highest effect, but the effect of CO2 injection cost and tax credit is much smaller than that of oil price. 5. Conclusions This paper presented a numerical study on WAG performance with water flooded reservoirs. Orthogonal experimental design was applied to optimize operation parameters of CO2 WAG flooding in a water flooding reservoir. Significant work was done on sensitivity analysis aiming to evaluate the suitable reservoir conditions and development parameters. The following conclusions were achieved.  The optimal scheme was determined with a CO2 slug size of 0.05 PV, a WAG ratio of 1:2, a CO2 injection rate of 40,000 Sm3/d, and a voidage replacement ratio of 1:0.9. The recovery factor can be increased 17.64% as compared to water flooding. The voidage replacement ratio is recognized as the most influential operation parameter.  The technical and economic efficiency of WAG flooding worsen as the average horizontal permeability and the ratio of vertical to horizontal permeability increase. This is attributed to the quicker production of CO2 in the higher permeability reservoir. Even though WAG flooding recovery factor and the improved recovery factor increase as the permeability variation coefficient increase, the highest NPV is achieved when permeability variation coefficient equals 0.6.  WAG flooding offers no technical advantage over water flooding in reverse rhythmic reservoirs, and compound reverse rhythmic reservoirs could benefit the most economically from WAG flooding. The technical efficiency of WAG flooding improves initially as the net thickness of formation increases, and then

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