Computers & Fluids 99 (2014) 93–103

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Computers & Fluids

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

http://dx.doi.org/10.1016/j.compfluid.2014.03.0220045-7930/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 573 341 4657.E-mail address: weim@mst.edu (M. Wei).

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, Chinab Department of Geological Sciences and Engineering, Missouri University of Science and Technology, 1400 N. Bishop Avenue, Rolla, 65409 Missouri, United Statesc Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, 29# Xueyuan Road, Haidian District, 100083 Beijing, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 December 2012Received in revised form 28 February 2014Accepted 20 March 2014Available online 13 April 2014

Keywords:CO2 WAG floodingEnhanced oil recoveryOrthogonal experimental designOperational schemeNet Present ValueTechnical and economic analyses

The objective of this work is to investigate the effect of operational schemes, reservoir types and devel-opment parameters on both the amount of incremental oil produced and CO2 stored in high water cut oilreservoirs during CO2 water-alternating-gas (WAG) flooding by running compositional numerical simu-lator.

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 voi-dage replacement ratio. The Net Present Value (NPV) was used as an objective function for economicanalysis. Various 3-D heterogeneous reservoir models were built to investigate the impact of reservoirtypes 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.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Carbon dioxide flooding has been recognized as one of the mosteffective options for oil recovery enhancement in depleted ormature oil reservoirs [1–3]. The benefits of injecting CO2 includethe expansion of oil volume and the reduction of oil viscosity[4,5]. CO2 is able to displace the residual oil that is immobilizedby water flooding and therefore improve the microscopic displace-ment efficiency [6]. The CO2 EOR projects in Weyburn and theNorth Sea have also proved the great potentials of both oil produc-tion increment and CO2 sequestration [7,8].

However, if the gas source is located far from a target oil reser-voir, considering the cost of CO2 capture, transportation, compres-sion and injection, CO2 EOR projects may not be profitable withouteconomic incentives from the government. Ghomian et al. [9]established the amounts and types of economic incentives for dif-ferent reservoir types. They found that sandstone reservoirs hadhigher probability of need for economic incentives than carbonatereservoirs. Using the methodology of NPV, Jahangiri and Zhang [10]

determined that a minimum of $40/ton of carbon tax credit isrequired for immiscible CO2 flooding so as to obtain the sameNPV as water flooding, while miscible CO2 flooding is more profit-able than water flooding even without any economic incentives.

Regarding the optimization of operational scheme, a number ofstudies have been conducted. Yang et al. [11] developed an inte-grated model to optimize the production-injection operation sys-tems (PIOS). Taking the NPV as an objective function, theoptimum production and injection parameters were achieved ina WAG miscible flooding reservoir. Kovscek and Cakici [12] definedan objective function that combines the ultimate oil recovery andthe fraction of reservoir volume filled with CO2. The most effectiveinjection and production scheme was determined which could co-optimize oil recovery and simultaneous CO2 sequestration. Chenet al. [13] developed a hybrid method that integrates orthogonalarray and Tabu technique into a genetic algorithm. When conduct-ing a sensitivity analysis on oil recovery and NPV, controlling vari-ables were selected including injection rate, WAG ratio, injectiontime and bottomhole pressure for the producers. Studies revealedthat WAG flooding recovers more oil than continuous injectionflooding. That is because WAG flooding can reduce CO2 viscous fin-gering and provide better vertical sweep efficiency [14,15]. Addi-tionally, the horizontal well impacts CO2 flooding greatly for the

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

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

reason that the displacement provides better sweep efficiencybased on both reservoir simulations and laboratory studies [16–18].

Despite the potentials of CO2 EOR, this technology is not suit-able for all types of hydrocarbon reservoirs [19,20]. Based on bothfield results and oil recovery mechanism study, Taber et al. [21]proposed the screening criteria for CO2 miscible and immiscibleflooding, respectively. Shaw and Bachu [22] presented a methodfor the screening and ranking of oil reservoirs suitable for CO2

EOR. Oil gravity, reservoir temperature and pressure, minimummiscibility pressure and remaining oil saturation were selectedas variables. However, most of studies on CO2 flooding describedabove have been conducted on undeveloped oil reservoirs, andvery few results from high water cut oil reservoirs are seen inthe literature.

The main objective of this study is to investigate the effect ofoperational schemes, reservoir types and development parameterson WAG flooding in high water cut oil reservoirs by running com-positional simulations. By applying orthogonal experimentaldesign, the most effective operational scheme was determinedwhich could maximize the incremental oil produced by WAGflooding. Afterwards, various geological models were constructedby employing different reservoir parameters and developmentparameters. A technical analysis of five reservoir parameters andtwo development parameters was conducted. The NPV modelwas built for economic analysis. The effect of oil price, CO2 injec-tion 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 104fault block in Dagang Oilfield in China [23–28]. For the particularinterested area of 3.5 km2, the reservoir depth is from 2,650 m to2,750 m; the formation net thickness varies from 9.7 m to41.4 m; the average horizontal permeability varies from254.7 md to 425.7 md; the range of porosity is from 18% to 22%and the average porosity is 19.04%. The permeability variationcoefficient varies from 0.45 to 0.8. The sand body rhythms includenormal, reverse, compound normal and compound reverse. Five-spot patterns were initially applied and are still used in this reser-voir. This is a water-wet reservoir. The relative permeability endpoints are the critical water saturation of 0.478, the residual oil sat-uration of 0.227 for water–oil system, the connate gas saturation of0, and the maximum gas saturation of 0.522 for gas–liquid system.The relative permeability curves for water–oil system weredepicted in Fig. 1(a), while the relative permeability curves forgas–liquid system were shown in Fig. 1(b). The same set of relativepermeability curves was utilized in the simulations during waterflooding and CO2 WAG flooding.

In order to investigate the impact of operational schemes onCO2 flooding, a base reservoir model with impermeable boundarywas built based on the range of main parameters of that particularreservoir. The base reservoir model is 925 m, 925 m and 10 m inthe x, y and z dimensions, respectively. It consists of nine five-spotpatterns with a well spacing (i.e., the distance between two adja-cent producers) of 300 m; the locations of the 9 injectors and 16producers were shown in Fig. 2. These wells perforated in all fourlayers of the formation. The sand body is normal rhythmic, whichmeans the formation permeability increases downward. The basereservoir is water-wet, and the initial oil saturation is 0.522. Otherparameters in the base reservoir model were summarized inTable 1.

Slim-tube experiments were conducted to determine the mini-mum miscibility pressure (MMP) between the reservoir oil andCO2. The experiments were conducted under the temperature of108 �C. A slim tube with a length of 18 m and an inner radius of

3.175 mm was packed with sand of 200 mesh size. The pore vol-ume of the slim tube is 255.7 cm3. The slim tube was saturatedby 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 differ-ent displacement pressures. The color change and phase behaviorof the effluent were observed through the inspection window.The effluent was flashed in the separator connected with a flowmeter to measure gas flow. The oil was collected in a conical flaskand the density was measured using a densitometer. The cumula-tive oil recovery was recorded and the MMP was defined as thebreak in slope from the plot of oil recovery against displacementpressure [29]. As Fig. 3 depicts, the MMP was determined to be322.8 bars. The initial formation pressure is 272.1 bars that arelower than the MMP, which means CO2 immiscible flooding. Usingthe PVTi module in Eclipse software, the pseudo-components ofcrude oil were obtained as shown in Table 2. The light components(C2 � C6) just account for 10.1 mol%, and a large amount of heavycomponents leads to a high MMP between reservoir oil and CO2.

Eclipse Compositional Simulator was used. Initially, the reser-voir was water flooded; then RESTART function was used to con-duct WAG flooding. During WAG flooding, mass transfer betweenCO2 and oil was automatically considered in the compositionalsimulator.

3. Methodologies

3.1. Determination of operational scheme

In CO2 WAG flooding, the CO2 slug size, WAG ratio, CO2 injec-tion rate and voidage replacement ratio impact WAG flooding sig-nificantly [13,30]. A big CO2 slug size results in early gas

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

Table 1Basic parameters in the base reservoir model.

Parameter Value Parameter Value

Reservoir depth (m) 2700 Average horizontal permeability (md) 300Net thickness (m) 10 Permeability variation coefficient 0.5Porosity 0.1904 Ratio of vertical to horizontal

permeability0.1

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

Table 2Pseudo-components description of crude oil.

Component Mole fraction Molecular weight (kg/mole) Tc (K) Pc (bar)

CO2 0.00046 0.044010 304.2 72.9CH4 + N2 0.14012 0.016447 188.4 45.6C2H6 0.01524 0.030070 305.4 48.2C3–C4 0.03500 0.052477 401.1 39.6C5–C6 0.05062 0.078719 489.6 31.7C7–C10 0.17743 0.114980 589.4 27.2C11+ 0.58113 0.330300 847.2 10.2

Table 3Operation parameters for operational scheme study and their three levels ofuncertainty.

NO. Operation parameter Low (�1) Median (0) High (1)

1 CO2 slug size (PV) 0.05 0.10 0.152 WAG ratio 2:1 1:1 1:23 CO2 injection rate (Sm3/d) 10,000 20,000 40,0004 Voidage replacement ratio 1:1 1:0.95 1:0.9

Z. Song et al. / Computers & Fluids 99 (2014) 93–103 95

breakthrough and high producing gas-oil ratio. While a small CO2

slug size increases the cycles of WAG and makes on-site operationscomplex. An appropriate WAG ratio is conducive to the control ofwater cut and the improvement of sweep efficiency. A high CO2

injection rate not only causes high producing gas-oil ratio but also

increases the requirements of CO2 compression and injectiondevices. Moreover, the bottomhole injection pressure may exceedthe formation fracturing pressure at high CO2 injection rates.Meanwhile the low CO2 injection rate narrows the miscible zoneand reduces CO2 flooding efficiency. It is required to achieve anoptimal injection rate to maximize the oil recovery improvement.An appropriate increase of voidage replacement ratio is beneficialin maintaining initial formation pressure and promoting masstransfer between CO2 and oil. However, an excessive voidagereplacement ratio leads to the injection pressure higher than for-mation fracturing pressure. Therefore, optimization study was con-ducted to achieve the optimal combination of these fourparameters.

Table 3 shows the four parameters discussed in the study andthe three levels of uncertainty considered for each parameter. Ifthe combinations of all parameters at all levels are studied (i.e.,full-factorial experiment), 34 runs will be required. Orthogonalexperimental design is the method that can be used to avoid thefull-factorial experiment implementation when multiple parame-ters are considered at multiple levels. As Table 4 depicts, only nineoperational schemes were required in orthogonal experimentaldesign, and all levels of all parameters were well distributed inthese schemes. The orthogonal experimental design significantlydecreases the number of simulation executions, therefore improvethe computational cost. In order to evaluate WAG flooding effi-ciency, two evaluating indices were defined: the improved recov-ery factor and gas replacing oil ratio. The former refers to theincreased oil recovery factor of WAG flooding as compared to thatof water flooding, and the latter refers to the amount of oil produc-tion 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 waterinjection rate of 70 m3/d for each injector. A fixed liquid productionrate was set for each producer to achieve a volumetric balance. Theultimate water flooding recovery factor is 43.56% when all the pro-

Table 4Scenario 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 0.05 2:1 10,000 1:1 0.05953 0.198F002 0.05 1:1 20,000 1:0.95 0.08391 0.349F003 0.05 1:2 40,000 1:0.9 0.17640 0.588F004 0.10 2:1 20,000 1:0.9 0.10790 0.366F005 0.10 1:1 40,000 1:1 0.09740 0.316F006 0.10 1:2 10,000 1:0.95 0.09412 0.393F007 0.15 2:1 40,000 1:0.95 0.09148 0.306F008 0.15 1:1 10,000 1:0.9 0.10850 0.302F009 0.15 1:2 20,000 1:1 0.09835 0.286

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

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

ducers reached the water cut of 98% to shut in. Fig. 5 presents theinformation for the primary production of the base reservoir. Dur-ing the first two years of water flooding, oil production ratedecreases from 611 m3/day to 115 m3/day, while water productionincreases from 0 m3/day to 500 m3/day. At the end of the primaryproduction, cumulative oil production is 194,653 m3, and recoveryfactor reaches 25.1%. The remaining oil saturation is 0.391. Theaverage formation pressure declines to 258.2 bars. The water cutreaches 81.2%, indicating the reservoir reaches high water cutstage. After the two years of water flooding, WAG flooding wasimplemented by applying RESTART function in the Eclipse Compo-sitional Simulator, and nine schemes shown in Table 4 were per-formed on the base reservoir model. The improved recoveryfactor and gas replacing oil ratio when all the producers reachedthe producing gas-oil ratio of 3,000 Sm3/m3 to shut in were sum-marized in Table 4.

Orthogonal experimental design is one type of designs of exper-iments. Applying this methodology enables us to obtain the meanvalues and range values of the two evaluating indices as shown inTable 5. The mean value refers to the average value of the evaluat-ing index of three schemes for each level of the parameter. The

Fig. 4. Flowchart of the

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

research procedure.

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

Operationparameters

Improved recovery factor Gas replacing oil ratio(m3/ton)

Meanvalue

Rangevalue

Meanvalue

Rangevalue

CO2 slug sizeLow (�1) 0.10661 0.00717 0.378 0.080Median (0) 0.09981 0.358High (1) 0.09944 0.298

WAG ratioLow (�1) 0.08630 0.03666 0.290 0.132Median (0) 0.09660 0.322High (1) 0.12296 0.422

CO2 injection rateLow (�1) 0.08738 0.03438 0.297 0.106Median (0) 0.09672 0.334High (1) 0.12176 0.403

Voidage replacement ratioLow (�1) 0.08509 0.04584 0.267 0.151Median (0) 0.08984 0.349High (1) 0.13093 0.418

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 ofproducing gas-oil ratio.

Z. Song et al. / Computers & Fluids 99 (2014) 93–103 97

effective scheme is regarded as the one with four optimal levels offour operation parameters. The range values are used for rankingthe four operation parameters. A bigger range value indicates thatthe parameter is more influential. For the purpose of maximizingthe improved recovery factor and gas replacing oil ratio, it wasdetermined from Table 5 that the most effective operationalscheme of WAG flooding was the one with a CO2 slug size of0.05 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 thiscase was improved 17.64% as compared to water flooding. Fromthe results, the most influential parameter is the voidage replace-ment ratio, WAG ratio, CO2 injection rate, and CO2 slug size, withdecreasing significance to those evaluating indices.

In order to conduct a sensitivity analysis of the most influentialoperation parameter, voidage replacement ratio, three WAG flood-ing schemes were designed. In these schemes, the CO2 slug size,WAG ratio, and CO2 injection rate were set to be the optimal valuesdiscussed above. The voidage replacement ratio was considered1:1, 1:0.95 and 1:0.9 in each of the three schemes, respectively. Ini-tially, a water flooding scheme was performed on the base modelfor comparison. A water injection rate of 70 m3/d was assumedfor each injector, while a fixed liquid production rate was set foreach producer to achieve a volumetric balance. After two years ofwater flooding, RESTART function was applied to conduct threeWAG flooding schemes.

Fig. 6 compares the formation pressure, oil production rate andproducing gas-oil ratio for these three WAG flooding schemes andthe water flooding scheme. Properly increasing the voidagereplacement ratio is beneficial in maintaining the current forma-tion pressure. In the WAG flooding scheme with a voidage replace-ment ratio of 1:0.9, the formation pressure almost maintains in theinitial condition of the reservoir before water flooding. When thevoidage replacement ratio is 1:1, 1:0.95 and 1:0.9, the ultimaterecovery factor of WAG flooding is 10.46%, 11.81% and 17.64% morethan that of water flooding, respectively. This indicates thatincreasing the voidage replacement ratio can improve sweep effi-ciency, and delay the breakthrough of CO2 as seen in Fig 6(c), soas to improve CO2 flooding efficiency. For these three WAG flood-ing schemes, the drastic increase in the producing gas-oil ratioafter gas breakthrough results in the substantial decrease in forma-tion pressure and oil production rate. After CO2 breakthrough, mostof the injected CO2 is produced directly by the producers, so the

wells should be shut in because of the decreasing benefit of WAGflooding. In the WAG flooding scheme with a voidage replacementratio of 1:0.9, the average oil production rate is 289.45 m3 which isabout 2.5 times as much as that of water flooding. Further increas-ing the voidage replacement ratio will lead to the formation pres-sure higher than the formation fracturing pressure, which has beenproved 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 pro-posed above was used to perform numerical simulations for tech-nical and economic analyses. The injectors were set at constantCO2 and water injection rates, while the producers were set at afixed liquid rate according to the voidage replacement ratio of1:0.9.

Five reservoir parameters and two development parameterswere taken into account to investigate their effect on WAG flood-ing. The average horizontal permeability, the permeability varia-tion coefficient, the ratio of vertical to horizontal permeability,the rhythm of sand body and the net thickness of formation werediscussed as reservoir parameters; while the well-spacing patternand the percentage of recoverable reserves by water flooding werestudied as development parameters. As Table 6 depicts, four levels

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

Level Sensitivity parameter

Average horizontalpermeability (md)

Permeabilityvariationcoefficient

Ratio of vertical tohorizontalpermeability

Net thicknessof formation(m)

Rhythm ofsand body

Well-spacing pattern Percentage of recoverablereserves by water flooding

1 200 0.5 0.1 10 Normal Five-spot pattern with a wellspacing of 300 m

01020

2 300 0.6 0.2 20 Reverse Five-spot pattern with a wellspacing of 200 m

304050

3 400 0.7 0.3 30 Compoundnormal

Inverted nine-spot patternwith a well spacing of 300 m

607080

4 500 0.8 0.4 40 Compoundreverse

Inverted seven-spot patternwith a well spacing of 300 m

90100

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

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

of uncertainty were considered for each of the first six parameters.The last parameter, percentage of recoverable reserves by waterflooding, indicates what percentage of maximum water floodingrecoverable reserves have been already extracted before CO2

WAG flooding is implemented in the target oil reservoir. Elevenlevels (0 at the initial reservoir condition, 10, 20, 30, 40, 50, 60,70, 80, 90, and 100 when maximum water flooding recoverablereserves are produced) were considered for this parameter to opti-mize WAG injection timing in a water flooding reservoir. Percent-age of recoverable reserves by water flooding was defined asfollows

Percentage of recoverable reserves by water flooding

¼ Cumulative oil production during water floodingWater flooding recoverable reservesjwater cut¼98%

When one parameter was under investigation, various geologi-cal reservoir models were built by employing different values ofthis parameter. The other parameters were the same as those inthe base reservoir model. The five-spot pattern with a well spacingof 300 m was arranged in the reservoir. Initially, water floodingwas performed on the reservoir models. The maximum waterflooding recovery factor can be obtained when all the producersreached the water cut of 98% to shut in. By applying RESART func-tion in the compositional simulator, water injection was switchedto CO2 when different percentages (for sensitivity analysis of per-centage of recoverable reserves by water flooding) or 80% (for sen-sitivity analysis of other parameters in Table 6) of recoverablereserves by water flooding were achieved.

By performing numerical simulations on these reservoir mod-els, the WAG flooding recovery factor (i.e., the ultimate oil recoveryat the end of WAG flooding), the amount of CO2 injected and theimproved recovery factor can be determined when all the produc-ers reach the producing gas-oil ratio of 3,000 Sm3/m3 to shut in.These three dependent variables and water flooding recovery fac-tor were considered as technical objective functions to conduct atechnical analysis.

For the purpose of implementing an economic analysis, thedetailed production data of these reservoir models were used tocalculate the NPV of WAG flooding. The economic objective func-tion of NPV was computed as

NPV ¼XN

t¼0

ðCI� COÞtð1þ icÞt

where t is the the time of the cash flow, a; (CI � CO)t the the netcash 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,

a and ic the annual discount rate, which is set at the common valueof 12% in petroleum engineering.

The cash inflow includes the revenue of produced oil and thetax credit per ton of CO2 stored. Combining the local financial dataat the target reservoirs and international price for gas and oilindustry, the price of oil was considered $80/bbl for the entire pro-duction 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 costof $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. Thenet cash flow at time t is the difference between the cash inflowand outflow.

4. Results and discussion

4.1. Sensitivity analysis of reservoir parameters

Fig. 7 shows the recovery factor of water flooding and WAGflooding, the improved recovery factor, the amount of CO2 injected,and the NPV of WAG flooding at different levels of the average hor-izontal permeability. With higher reservoir permeability, the waterflooding oil recovery increases, while WAG flooding oil recoverydecreases. This behavior was also observed in previous study onan undeveloped oil reservoir [31], and this is because more perme-able reservoirs have better water flooding sweep efficiency. At thesame producing gas-oil ratio limit of 3,000 Sm3/m3, the totalamount of CO2 injected decreases when the average horizontal

Table 7Average gas saturation in different formation layers and WAG injection duration.

Reservoir parameter Average gas saturation after 720 days of WAG injection WAG injection duration (day)

The first (top) layer The second layer The third layer The fourth (bottom) layer Overall

Average horizontal permeability (md)200 0.150 0.067 0.030 0.009 0.064 948300 0.202 0.068 0.023 0.005 0.075 894400 0.249 0.062 0.015 0.004 0.083 815500 0.288 0.057 0.010 0.002 0.089 777

Permeability variation coefficient0.5 0.202 0.068 0.023 0.005 0.075 8940.6 0.162 0.090 0.018 0.003 0.068 9780.7 0.137 0.084 0.030 0.004 0.064 10500.8 0.119 0.086 0.043 0.005 0.063 1096

Ratio of vertical to horizontal permeability0.1 0.202 0.068 0.023 0.005 0.075 8940.2 0.312 0.061 0.008 0.002 0.096 7700.3 0.346 0.079 0.007 0.002 0.109 7390.4 0.364 0.093 0.012 0.002 0.118 735

Rhythm of sand bodyNormal 0.202 0.068 0.023 0.005 0.075 894Reverse – – – – – 293Compound normal 0.240 0.060 0.016 0.007 0.081 822Compound reverse 0.266 0.086 0.027 0.001 0.095 775

Net thickness of formation (m)10 0.202 0.068 0.023 0.005 0.075 89420 0.121 0.073 0.039 0.013 0.062 97130 0.081 0.077 0.060 0.023 0.060 101440 0.061 0.077 0.072 0.034 0.061 996

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

permeability is higher than 300 md. Table 7 summarizes the gassaturation distribution in four layers after 720 days of WAG injec-tion, and correspondingly WAG injection durations at differentaverage horizontal permeabilities. Because formation pressure ishigher than oil saturation pressure, no solution gas comes out inthe reservoir in the process of production, and the free gas in thereservoir is CO2. Due to the gravity difference between oil andCO2, gas saturation is higher on the top. As average horizontal per-meability increases, the average gas saturation increases in the toplayer and WAG injection duration reduces. It can be concludedhigher permeability increases CO2 gravity overriding and acceler-ates gas production, and thus the sweep efficiency of WAG floodingis reduced. Therefore, the technical and economic advantage ofWAG flooding as compared to water flooding decreases as theaverage horizontal permeability increases.

Fig. 8 summarizes the technical and economic objective func-tions at different permeability variation coefficients. As the perme-ability variation coefficient increases, the recovery factor of WAGflooding improves, while that of water flooding declines. This

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

result is different from those of undeveloped reservoirs [32]. Thereason is the upper part of the formation becomes less permeable,while the lower part becomes more permeable as heterogeneityincreases in the normal rhythmic reservoir. Therefore, as Table 7presents, with the increase of permeability variation coefficient,gas saturation in the top layer reduces and the effect of CO2 gravityoverriding decreases. The sweep efficiency of WAG floodingimproves, and meanwhile that of water flooding worsens. MoreCO2 was injected when the permeability variation coefficient isgreater than 0.6. This indicates the higher permeability variationcoefficient delays gas production; therefore, WAG flooding recov-ery factor improves with more injected CO2 displacing more oilfrom the reservoir. But sometimes a slight improvement in oilrecovery cannot offset the cost of increased CO2 injection. In thisstudy, the NPV reaches its maximum value when the permeabilityvariation coefficient equals 0.6.

When the average horizontal permeability was constant, theratio of vertical to horizontal permeability represents the verticalpermeability of the formation. As shown in Table 7, gas saturationin the top layer increases and WAG injection duration reduces asthe ratio of vertical to horizontal permeability increase. This meanslower vertical permeability can lessen CO2 gravity overriding anddelay gas production. Hence, as Fig. 9 indicates, the most CO2

was injected when the ratio of vertical to horizontal permeabilityis 0.1. However, lower vertical permeability does not favor waterflooding. As the vertical permeability improves, WAG floodingrecovery factor decreases, but water flooding recovery factorincreases, which is in agreement with previous study [31]. Fig. 9shows the trends of the improved recovery factor and the NPV ofWAG flooding. It is clear that the technical and economic efficiencyof WAG flooding worsens as the ratio of vertical to horizontal per-meability increases.

Fig. 10 plots the technical and economic objective functions atdifferent sand body rhythms. In the reverse rhythmic model, thereservoir permeability increases upward by layers. As Table 7depicts, WAG injection only lasted 293 days in the reverse rhyth-mic model. After 180 days of WAG injection, the average gas

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

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

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

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

saturation in the top layer is 0.012, which is much higher than theaverage gas saturation in the top layer of the normal rhythmicmodel. This reveals that CO2 gravity overriding was aggravated inthe reverse rhythmic model. In the reverse rhythmic reservoir, just0.1 PV CO2 was finally injected when all the producers reached theproducing gas-oil ratio of 3,000 Sm3/m3. The recovery factor ofWAG flooding almost equals that of water flooding, so it is not suit-able to implement WAG flooding in the reverse rhythmic reser-voirs. The compound normal rhythmic model means normalrhythmic sand bodies overlap each other, while the compoundreverse rhythmic model means reverse rhythmic sand bodies over-lap each other. The compound reverse rhythmic model achievesthe highest NPV for WAG flooding. This is because, as comparedto the normal rhythmic model, the substantial reduction of CO2

injection cost is more beneficial to the NPV than the slight reduc-tion of oil revenue.

Fig. 11(a) presents the recovery factors for WAG flooding andwater flooding, the improved recovery factor and the amount ofCO2 injected at different levels of net thickness of formation. Previ-ous study has shown that an increase in net thickness would aggra-vate CO2 gravity overriding and accelerate CO2 production [33].This study observed that the recovery factor of WAG floodingimproves as the net thickness increases, and the recovery factorbegins to decline when the net thickness exceeds 30 m. Moreover,the maximum amount of CO2 was injected when the net thicknessis 30 m. It can be seen from Table 7 that an increase of net thick-ness would not increase gas saturation in the top layer and aggra-vate CO2 gravity overriding, which is our new observationcompared with previous study [33]. Because the layers are toothick when net thickness is 40 m, which increases the internalgas overriding in each layer, CO2 is relatively well-distributed in

the top three layers. However, the overall average gas saturationincreases and WAG injection duration reduces when net thicknessexceeds 30 m. Therefore, the conclusion can be reached that anincrease of net thickness would increase the technical efficiencyof WAG flooding when net thickness is less than 30 m; but it wouldcounter CO2 displacing oil when net thickness exceeds 30 m.Fig. 11(b) indicates that the NPV of WAG flooding increases drasti-cally as the net thickness increases. This occurs because the origi-nal oil in place (OOIP) increases with thicker formations, andcumulative produced oil is enhanced greatly, even though therecovery factor of WAG flooding only slightly changes as the netthickness increases.

4.2. Sensitivity analysis of development parameters

In order to study the impact of well-spacing pattern, four reser-voir models were constructed with nine five-spot patterns with awell spacing of 300 m, nine five-spot patterns with a well spacingof 200 m, nine inverted nine-spot patterns with a well spacing of300 m, and seven inverted seven-spot patterns with a well spacingof 300 m, respectively. In these study cases, the reservoir sizes andOOIP are different and other properties keep the same.

Fig. 12 summarizes the effect of different well-spacing patternson water flooding and WAG flooding. Four well-spacing patternsunder investigation are represented by A, B, C, and D, where Arefers to the five-spot pattern with a well spacing of 300 m; Brefers to the five-spot pattern with a well spacing of 200 m; Crefers to the inverted nine-spot pattern with a well spacing of300 m; and D refers to the inverted seven-spot pattern with a wellspacing of 300 m. Two five-spot patterns with well spacing of200 m and 300 m were investigated to analyse the effect of wellspacing.

As shown in Fig. 12(a), the inverted nine-spot pattern achievesthe highest recovery factor from water flooding, while the five-spotpattern achieves the highest recovery factor from WAG flooding,which is consistent with previous study [34]. In terms of the eco-

Fig. 12. Effect of well-spacing pattern on technical and economic objectivefunctions. (a) Technical objective functions. (b) Economic objective functions. Fig. 13. Effect of percentage of recoverable reserves by water flooding on technical

and economic objective functions. (a) Technical objective functions. (b) Economicobjective function.

Z. Song et al. / Computers & Fluids 99 (2014) 93–103 101

nomic analysis, the NPV of the inverted nine-spot pattern is muchhigher than those of the other well-spacing patterns, as presentedin Fig. 12(b). This is mainly because the reservoir with invertednine-spot patterns has the largest OOIP, while the reservoirs withfive-spot patterns have the smallest OOIP. And much more oilwas produced in the reservoir with inverted nine-spot pattern thanin the reservoirs with other well-spacing patterns. Therefore, sen-sitivity analysis that takes total NPV as the economic objection isnot reasonable for an oil reservoir with a fixed area and OOIP.The NPV per unit area is a much clear NPV indicator at differentwell-spacing patterns, as shown in Fig. 12(b). The NPV per unitarea of five-spot pattern with a well spacing of 300 m is about1.3 times that of other well-spacing patterns. The five-spot patternwith a well spacing of 300 m has a higher NPV per unit area thanthe five-spot pattern with a well spacing of 200 m, even thoughthe latter has a slightly higher recovery factor of WAG flooding.Expanding well spacing appropriately is recommended for WAGflooding.

The five-spot pattern is the most favorable well-spacing patternfor WAG flooding and is also mostly used in the target oilfield.Therefore, the five-spot pattern with a well spacing of 300 m waschosen to analyse the impact of WAG injection timing. A seriesof simulations were conducted under different percentages ofrecoverable reserves by water flooding. At percentages of recover-able reserves by water flooding of 10, 20, 30, 40, 50, 60, 70, 80, 90and 100, the remaining oil saturation in the reservoir model wouldbe 0.497, 0.479, 0.451, 0.432, 0.406, 0.384, 0.362, 0.340, 0.317 and0.295, respectively, which serve as the starting points of CO2 WAGflooding. And simulations ended when all the producers reachedthe producing gas-oil ratio of 3,000 Sm3/m3. Fig. 13(a) comparesthe technical objective functions at different percentage of recover-able reserves by water flooding. The recovery factor of WAG flood-ing and the improved recovery factor decline slightly as the waterflooding was switched to WAG flooding at later stage of develop-ment. The results mean that different values of percentage of

recoverable reserves by water flooding and corresponding remain-ing oil saturation have limited effect on WAG flooding oil recovery.The amount of CO2 injected does not change at different WAGinjection timing. This indicates the stage of water flooding doesnot affect CO2 production in the specified reservoir. The effect ofWAG injection timing on WAG flooding can also be analysed bymeans of NPV. Fig. 13(b) shows that the earlier water injection isswitched to CO2, the higher NPV of WAG flooding can be obtained.When the percentage of recoverable reserves by water floodingequals 0 (i.e., WAG flooding is performed directly in the undevel-oped oil reservoir), the NPV achieves its maximum value. It isbecause that WAG flooding provides higher oil production ratebefore gas breakthrough than water flooding, thus shorten the pro-duction cycle and improve the NPV. More importantly, at differentWAG injection timing, the NPVs of WAG flooding are always higherthan that of water flooding even without any tax credit. This meansit is much economically advantageous to switch water injection toWAG injection in a water flooding reservoir.

4.3. Sensitivity analysis of economic parameters

In addition to the sensitivity analysis of five reservoir parame-ters and two development parameters, three economic parameterswere considered including oil price, CO2 injection cost and taxcredit per ton of CO2 stored to investigate their effect on theNPV. When one economic parameter was under investigation,the other economic parameters were set as follows. The oil priceis $80/bbl. The CO2 injection cost is $60/ton. The tax credit is $20per ton of CO2 stored. Same with above analyses, water floodingwas initially performed on the base reservoir model, and thenwater injection was switched to CO2 when 80% of recoverablereserves by water flooding were achieved. Table 8 shows the fivelevels of uncertainty for these three economic parameters andthe corresponding NPV results. As Fig. 14 presents, the relative

Table 8Net Present Value of CO2 WAG flooding at different levels of economic parameters.

Oil price($/bbl)

NPV(108 $)

CO2 injectioncost ($/ton)

NPV(108 $)

Tax credit($/ton)

NPV(108 $)

40 0.2293 30 1.1343 10 1.083160 0.6603 45 1.1128 15 1.087280 1.0913 60 1.0913 20 1.0913

100 1.5223 75 1.0698 25 1.0954120 1.9533 90 1.0483 30 1.0995

Fig. 14. Effect of relative change of oil price, gas injection cost, tax credit on relativechange of NPV.

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

change of NPV as the relative change of three economic parametersclearly indicates that the NPV of WAG flooding changes signifi-cantly as oil price varies. Therefore, oil price is considered as themost influential economic parameter on the NPV. CO2 injectioncost has the second highest effect, but the effect of CO2 injectioncost and tax credit is much smaller than that of oil price.

5. Conclusions

This paper presented a numerical study on WAG performancewith water flooded reservoirs. Orthogonal experimental designwas applied to optimize operation parameters of CO2 WAG flood-ing in a water flooding reservoir. Significant work was done on sen-sitivity analysis aiming to evaluate the suitable reservoirconditions and development parameters. The following conclu-sions were achieved.

� The optimal scheme was determined with a CO2 slug size of0.05 PV, a WAG ratio of 1:2, a CO2 injection rate of40,000 Sm3/d, and a voidage replacement ratio of 1:0.9. Therecovery factor can be increased 17.64% as compared to waterflooding. The voidage replacement ratio is recognized as themost influential operation parameter.� The technical and economic efficiency of WAG flooding worsen

as the average horizontal permeability and the ratio of verticalto horizontal permeability increase. This is attributed to thequicker production of CO2 in the higher permeability reservoir.Even though WAG flooding recovery factor and the improvedrecovery factor increase as the permeability variation coeffi-cient increase, the highest NPV is achieved when permeabilityvariation coefficient equals 0.6.� WAG flooding offers no technical advantage over water flooding

in reverse rhythmic reservoirs, and compound reverse rhythmicreservoirs could benefit the most economically from WAGflooding. The technical efficiency of WAG flooding improves ini-tially as the net thickness of formation increases, and then

worsens when it exceeds 30 m. However, the NPV increases sig-nificantly as the formation becomes thicker because of the sub-stantial oil production increase.� As compared to inverted nine-spot pattern and inverted seven-

spot pattern, five-spot pattern is more suitable for WAG flood-ing. Appropriately expanding well spacing improves the eco-nomic efficiency, even though the recovery factor decreasesslightly. The analysis of WAG injection timing reveals that theearlier water injection is switched to CO2 in a water floodingreservoir, 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 thatimpacts the economic efficiency of WAG flooding moresignificantly.

Acknowledgements

We would like to gratefully acknowledge support from theNational Natural Science Foundation Program of China(51174178), the National Science and Technology Major Projectof China (2011ZX05016-006), the Fundamental Research Fundsfor the Central Universities (2-9-2011-206) and China ScholarshipCouncil.

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