Recovery Factor Model Study in the Niger Delta Oil

A Quarterly Publication of the Faculty of Science, Adeleke University, Ede, State of Osun, Nigeria www.jasra.adelekeuniversity.edu.ng - ISSN 2014 Edition No 1.

Recovery Factor Model Study in the Niger Delta Oil Reservoir for Water Drive Mechanism Oseh1, J. O and Omotara2, O. O Department of Chemical and Petroleum Engineering Petroleum Engineering Programme Afe Babalola University Ado- Ekiti, Ekiti State, Nigeria. E-mails: [email protected], [email protected] Phone: +234703 99106451, +23480341000822 *Corresponding author: Oseh, J. O. Department of Chemical and Petroleum Engineering Petroleum Engineering Programme Afe Babalola University Ado-Ekiti, Ekiti State, Nigeria. Email: [email protected] ABSTRACT Recovery Factor (R.F) can be expressed as the ratio of ultimate oil recovery to oil initially in place. In these work, the study of recovery factor for the water drive reservoir in the Niger Delta oil reservoir was analysed using a statistical correlation approach. A sensitivity analysis was performed on different parameters affecting recovery factor of water drive reservoir. The statistical correlation was based on data obtained from (5) reservoirs, with data based on actual production performance from oil producing reservoir. The material balance method was used to determine the oil in place and the drive indices. A statistical correlation package (SYSTAT) was used to correlate the rock and fluid properties to the Recovery Factor (R.F) obtained for the (5) reservoirs. Models were developed to determine the Recovery Factors; the two models tested were that of Guthrie and Green Berger Model, and the API correlation model. The results show that the proposed correlation is reliable in a full range of parameters but the compared simulated values of recovery factors obtained from these models was not in agreement with the obtained field data. These results confirmed that the recovery factor analysed only appeared to be conventional. Keywords: Recovery Factor; Oil Reservoir; Water Drive; Reservoir Drive Indices; Porosity; Permeability.

1. INTRODUCTION In the past, empirical correlations for prediction of recovery factor performance were investigated by statistical study of recovery factor performances. Guthrie and Greenberger studied oil recovery by water drive empirically to reservoir rock and fluid properties (Guthrie and Greenberger, 1955). They studied 73 sandstone reservoirs that had a water drive or that had solution gas drive combined with a water drive. The actual production data were available for these reservoirs. The oil recovery was related to the permeability, porosity, oil viscosity, formation thickness, connate water saturation, depth, oil reservoir volume factor, area, and well spacing. The correlation shown below fits so well that in 50 percent of the time the recovery factor was within 6.2 percent of the reported value, and in 75 percent of the time it was within 9.0 percent. ER = 0.2719log k + 0.25569 Swi – 0.1355log (

o)

– i.5380

- 0.00003488H + 0.11403 ……………… (1)

In this correlation, ER is the fractional recovery efficiency, k is the absolute permeability, Swi is the initial water saturation, ϕ is the porosity is the formation thickness and µo is the oil viscosity. This equation implies that the water drive recovery efficiency is lower in reservoirs of higher porosity. The API sub-committee on Recovery Efficiency, headed by J. J. Arps, presented a statiscal study of recovery efficiency (Arps et al., 1972) based on a statistical analysis of data from 312 reservoirs. They developed correlations for water drive recovery from sandstone and sand reservoirs, and for solution gas drive reservoirs from sandstones, sands, and carbonates. The water drive recovery, as a percentage of the original oil in place, is: 5


ER = 54.898

A

. [k.

] B. (Swi) C. (

) D ……………………………………(2)

Where, A = 0.0422, B = 0.0770, C = -0.1903 and D = -0.2159 In this correlation, ER is the recovery factor, is the porosity, is the water viscosity, is the oil viscosity, k is the absolute permeability, Swi is the initial water saturation, Pi is the initial pressure, Pa is the pressure at depletion( abandonment pressure) and Boi is the oil formation volume factor. This correlation for water drive recovery is expressed as a logarithmic-type equation. The correlation coefficient for the equation is 0.958, which by its closeness to 1.000 shows a very good fit of the data. This correlation developed from a water drive reservoir performance data has limited usefulness for recovery factor utilizations. The usefulness of this type of correlation is generally limited to reservoirs in the particular geographical area being studied. In this study, two correlations are proposed for predicting recovery factor performance from a field data. Such correlations can be used for the validation and the estimation of the recovery factor from field data. 1.1 Objectives of the study The objective of this work include, but not limited to obtaining the Recovery Factor equation for the water drive reservoir in the Niger Delta oil reservoir which will be investigated by: • Reducing the material balance to a concept form, in this case using the technique of Havlena and Odeh in order to quantify reservoir performance • Using a statistical method to estimate Recovery Factor. 1.2 Geological Setting of the Niger Delta Niger Delta is a large arcuate Tertiary prograding sedimentary complex deposited under transitional marine, deltaic, and continental environments since Eocene in the North to Pliocene in the South. Located within the Cenozoic formation of Southern Nigeria in West Africa, it covers an area of about 75,000 Km (Arps et al., 1972) from the Calabar Flank and Abakaliki Trough in Eastern Nigeria to the Benin Flank in the West, and it opens to the Atlantic ocean in the South where it protrudes into the Gulf of Guinea as an extension from the Benue Trough and Anambra Basin provinces (Burke et al., 1972). The Niger Delta as a prograding sedimentary complex is characterized by a coarsening upward regressive sequences. The overall regressive sequence of clastic sediments was deposited in a series of offlap cycles that were interrupted by periods of sea level change (Etu-Efeotor, 1997). These periods resulted in episodes of erosion or marine transgression. Stratigraphically, the Tertiary Niger Delta is divided into three Formations, namely Akata Formation, Agbada Formation, and Benin Formation (Ekweozor & Daukoro, 1984). The Akata Formation at the base of the delta is predominantly undercompacted, overpressured sequence of thick marine shales, clays and siltstones (potential source rock) with turbidite sandstones (potential reservoirs in deep water). It is estimated that the formation is up to 7,000 meters thick (Bouvier et al, 1989). The Agbada Formation, the major petroleum-bearing unit about 3700m thick, is alternation sequence of paralic sandstones, clays and siltstone and it is reported to show a two-fold division (Doust and Omatsola, 1990). The upper Benin Formation overlying Agbada Formation consists of massive, unconsolidated continental sandstones. 1.3 Recovery Factor Reserves are the unproduced but recoverable oil or gas in a formation that has been produced by production. Oil reserves are the amount of technically and economically recoverable oil and Gas reserves are the amount of gas that can be technically and economically recoverable. The total estimated amount of oil in an oil reservoir, including both producible and non-producible oil is called oil in place (OIP). However, because of reservoir characteristics and limitations in petroleum extraction technologies, only a fraction of the oil can be brought to the surface, and it is only this producible fraction that is considered to be a reserves. A petroleum reservoir, or oil and gas reservoir, is a subsurface pool of hydrocarbons contained in porous or fractured rock formations containing producible hydrocarbons that has been confined in the subsurface by impermeable rocks and water barriers and is characterised by a single natural pressure system (Dake, 1978, Cole, 1969).

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Recovery Factor is the ratio of producible oil reserves to total oil on place for a given field. It can be expressed mathematically as the ratio of Np to N (Bradley, 1987). R.F = Np/N

…………………………………….(3)

Thus the oil in place and the water influx can be successfully analysed by the use of material balance equation and (Havlana and Odeh, 1963) approach respectively. Recovery factor vary greatly among oil fields. The recovery of any particular field may change over time based on operating history and in response to changes in technology and economies. The recovery factor may also rise over time if additional investment is made in Enhanced Oil Recovery techniques such as gas injection, surfactant injection, water flooding or microbial EOR. There are two main types of recovery factor which are: Technical recovery estimated from initial production till the time production becomes zero and Economic recovery estimated based on the production up to the time profitability of the production can no longer be achieved. Determining the Recovery factor of a given reservoir is the work of a reservoir engineer. In carrying out his job, he evaluates the nature and magnitude of the forces acting in the reservoir. He provides the operators (oil companies) with relevant information. Natural forces acting on and within a reservoir constitute the reservoir drive mechanism(s) in that reservoir. Reservoir drive mechanism could be defined as the energy that causes the fluid in the reservoir to flow into the well-bore and finally to the surface. A virgin reservoir may be under sufficient pressure to push hydrocarbons to surface. As the fluids are produced, the pressure will often decline, and production will falter. The reservoir may respond to the withdrawal of fluid in a way that tends to maintain the pressure. Additional drive mechanism such as water drive is necessary to maintain reservoir pressure. Water (usually salt) may be present below the hydrocarbons. Water, as liquids, is compressible to a small degree. As the hydrocarbons are depleted, the reduction in pressure in the reservoir allows the water to expand slightly. Although this unit expansion is minute, if the aquifer is large enough this will translate into a large increase in volume, which we push up on the hydrocarbons, maintaining pressure. With a water drive reservoir, the decline in reservoir pressure is very slight; in some cases the reservoir pressure may remain unchanged. The oil ratio also remains stable. The oil rate will remain fairly stable until water reaches the well. In time, the water cut will increase and the well will be watered out. (Havlena and Odeh, 1963) arranged the material balance equation algebraically in order to give an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful material balance equation should meet. Furthermore this algebraic arrangement attaches a dynamic meaning to the otherwise static material balance equation. The straight line method requires plotting of one variable group against another variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. 2. METHODOLOGY 2.1 Rock and Fluid Properties in Recovery Factor(s) Prediction of the reservoir rock is one of the factors Permeability variation: The relative permeability ratio controlling recovery factor. The more permeable a reservoir rock is higher the ultimate recovery, thus the recovery factor. Porosity variation: Highly porous materials (i.e. unconsolidated intergrannular material) affect recovery factor most favourably, while lowly porous materials tends to effect recoveries unfavourably. Connate water saturation: in water drive reservoir, low water saturation means a low surface area of the pores per unit space. Hence, for a larger and a more efficient displacement process by water, while on the solution gas drive reservoirs, low water saturation means more oil initially in place present in the pores. Oil gravity: The ultimate recovery increases with oil gravity. Thus higher oil gravity leads to higher recovery factor. Oil recoveries will be higher than those attainable by any other process that is in reservoirs where gravity is the predominant drive mechanisms. In this case, solution gas drive effects are negligible.

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Solution gas-oil ratio: The higher the solution gas-oil ratio, the lower the ultimate recovery, thus the lower the recovery factor. Viscosity: The lower the oil viscosity will lead to more improved recoveries, thus the higher the recovery factor and also the higher the water viscosity tends to high recovery. Reservoir thickness: The reservoir pay thickness does not have much effect on the recovery factor Formation volume factor: High formation volume factor results to high recovery, thus the higher the formation volume factor, the higher the recovery factor. The reservoir parameters, which control recovery process as described above, were collected for 5 producing reservoirs. Other data on reservoir parameter included are the reservoir pressure, cumulative oil production, cumulative gas production, cumulative water production, fluid and rock compressibility, reservoir radius and encroachment angle. These data were obtained from the Department of Petroleum Resources (DPR), and assumed that the data collected have accurate information on the reservoir rock and fluids. Drive Indices: From the general MBE, the MBE approach was used to determine the different drive indices in each of the reservoir from these relations: = 1.0

…………………(4)

The above MBE equation can be simplified to: ………………… (5) ………………… (6) ………………… (7) ………………… (8) ………………… (9) The value of the parameters obtained from the field was first plotted against time or pressure. Using the Havlena and Odeh’s approach, further MBE calculations on the oil initially in place, water influx and the contribution of water drive mechanism to recovery were thus determined (Havlena and Odeh, 1963, Van Everdingen et al., 1953, Woods and Muskat, 1945, Dake, 1978). 3. RESULTS AND DISCUSSION Using the Material Balance Method: The contribution of water drive to total recovery ranged between 0.31 to 0.60 (Table 1.0-5.0) Using the Havlena and Odeh Model: Fig. 1-Fig. 5 shows the simulated values for all data for each of the reservoir investigated. The investigated reservoirs show a linear relationship which is the square of the correlation coefficient for the various plots in the range of

to

. (Arps et al., 1967, API, 1984, Ertekin et al., 2001).

Correlation models for water drive reservoirs: From the correlation works carried out, the following models for water drive mechanism were arrived at for determining the recovery factor. Guthrie and Green Berger for water drive model resulted in a moderate R.F values ranging from and can be estimated from:

8

to


.

……………… (10)

API correlation model for water drive mechanism, the recovery factor provided a range from 0.5931 for water drive mechanism.

to

0

…….

(11)

Table 1.0: The Material Balance Output sheet for Reservoir, R1 Pi = 2763 psia Boi = 1.141 rb/stb Rsi = 380 scf/stb Bgi =0.00096 rb/scf So= 0.83 Co = 0.000013 (1/psi) H = 200 ft. Re = 4286 ft. k = 100 md w = 0.4 cp = 180° Dimensional radius initial input = 100 R.F given = 0.60 (fraction) Time (years) 1 2 3 4 5 6 7 8 9 10 Years 1 2 3 4 5 6 7 8 9 10

Reservoir Pressure (psia) 2701 2646 2597 2553 2516 2485 2460 2442 2429 2423

Np (mmstb)

Rp (scf/stb)

Bo (rb/stb)

Rs (scf/stb)

Bg (rb/scf)

Wp (bbls)

1.31 5.53 11.37 18.29 25.73 33.14 39.90 45.53 49.43 53.61

200.27 271.35 303.06 334.78 353.38 353.83 366.45 387.22 420.65 468.11

1.1396 1.1398 1.1397 1.1393 1.1389 1.1386 1.1384 1.1382 1.1381 1.1380

380.00 380.00 380.00 377.38 377.98 377.81 377.61 377.14 377.65 377.41

0.0009843 0.0010004 0.0010264 0.0010444 0.0010600 0.0010732 0.0010839 0.0010921 0.0010976 0.0011004

0.0003 0.0007 0.0395 0.1363 0.3827 0.8537 1.6243 2.7695 4.3630 6.4831

N (mmstb) 3823.585 2743.214 1335.272 1141.330 958.0178 935.3525 907.6772 815.089 726.744 564.551

We (mmbbl) 0.1435697 0.5259490 1.080317 1.773618 2.578547 3.470676 4.427297 5.325436 6.448888 7.473332

For an infinite radial aquifer system (Estimated output) N = 3823.585 mmstb We = 7.473332 mmstb WDI = 0.9884690 CDI = 0.11531013 URW = 2267.697mmstb N = 3823.585 mmstb 9

WDI Fraction 1.128422 0.912973 0.885716 0.875675 0.888706 0.923629 0.971030 1.003410 1.084881 1.110244


R.F given = 0.60 = 60% R.F W = 0.5930814 = 59.3% R.F O = 0.006918608 = 0.69%

Table 2.0: The material balance output sheet for Reservoir, R2. So = 0.82 Sw = 0.18 Co = 0.000011(1/psi) Cw = 0.000010 (1/psi) H = 140 ft. = 0.26 Re = 2610 ft. k = 2000 md w = 0.42 cp = 180° Dimensional radius initial input = 100 R.F given = 0.0018 (fraction) Time (years)

Np (mmstb)

Rp (scf/stb)

Bo (rb/stb)

Rs (scf/stb)

Bg (rb/scf)

Wp (bbls)

0 1 2 3 4 5 6

Reservoir Pressure (psia) 2678 2639 2601 2564 2528 2494 2461

0.38 1.66 3.55 5.96 8.77 11.88

200.27 258.23 303.06 334.78 353.38 358.85

1.166 1.162 1.158 1.154 1.150 1.146 1.142

383.10 373.97 365.20 356.82 348.79 341.13 333.82

0.000993 0.001010 0.001025 0.001040 0.001054 0.001037 0.001080

0.0116 0.0119 0.0158 0.2239 0.4488 0.7589

7 8 9 10

2430 2400 2370 2242

15.18 18.53 21.91 24.45

366.50 387.26 421.15 460.15

1.139 1.135 1.132 1.128

328.86 320.23 313.93 377.41

0.001097 0.001111 0.001124 0.001136

1.1506 1.6383 2.2244 3.0256

Years 0 1 2 3 4 5 6 7 8 9 10

N (mmstb) 7012.207 6037.310 5921.946 4711.120 3418.621 2121.761 1791.448 964.6400 881.8170 735.0570 377.7110

We (mmbbl) 0.3844922 0.0054946 0.0266876 0.0438721 0.0743372 0.1115519 0.1550042 0.2044710 0.2507636 0.3195181 0.3844922

For an infinite radial aquifer system (Estimated output) N = 7012.207 mmstb We = 0.3844922 mmbbls WDI = 0.9023997 10

WDI Fraction 0.902399 1.362275 1.088266 1.025336 0.995595 0.993059 1.010809 1.033164 1.010417 1.056607 1.099009


CDI = 0.09760031 URW = 2974.072 mmstb R.F Given = 0.47 = 47% R.F W = 0.4241279 = 42% R.F O = 0.045872141 = 4.6%

Table 3.0: The material balance output sheet for Reservoir, R3. So = 0.74 Sw = 0.26 Co = 0.000013 (1/psi) Cw = 0.000003 (1/psi) Sf = 0.000004 (1/psi) H = 44 ft. = 0.25 Re = 3162 ft. k = 220 md w = 0.39 cp = 360° Dimensional radius initial input = 16 R.F given = 0.38 (fraction) Aquifer Constant = 0.0008 Time (years)

Np (mmstb)

Rp (scf/stb)

Bo (rb/stb)

Rs (scf/stb)

Bg (rb/scf)

Wp (bbls)

0 1 2 3 4 5 6


0.42 1.60 2.58 4.89 7.78 10.68

207.27 278.23 313.06 344.78 350.48 358.85

1.203 1.160 1.154 1.150 1.145 1.140 1.138

544.70 393.97 385.20 366.42 358.44 348.15 338.82

0.000882 0.000997 0.001015 0.001020 0.001033 0.001037 0.001080

0.0127 0.0139 0.0158 0.2245 0.4498 0.7689

7 8 9 10

3428 3403 3367 3245

14.38 17.33 20.81 24.15

362.50 383.26 418.10 458.25

1.137 1.134 1.131 1.127

330.86 324.73 319.33 307.41

0.001095 0.001101 0.001114 0.001128

1.1616 1.6453 2.2346 3.1256

Years 0 1 2 3 4 5 6 7 8 9 10

N (mmstb) 738.5580 688.3102 592.9462 481.1203 361.6218 282.7616 212.4482 184.6408 125.8178 87.05780 32.71130

We (mmbbl) 0.0700266 0.0549462 0.0566676 0.0588721 0.0592272 0.0616519 0.0640042 0.0664710 0.0680768 0.0698518 0.0700266

For an infinite radial aquifer system (Estimated output) N = 738.5580mmstb 11

WDI Fraction 0.8347482 1.3523751 1.0382662 1.0253366 0.9955957 0.9830519 1.0108084 1.0381645 1.0104276 1.0566323 1.0871063


We = 0.0700266mmbbls WDI = 0.8347482 CDI = 0.1652518 URW = 234.2738mmstb R.F given = 0.38= 38% R.F W = 0.3172043 = 31.7% R.F O = 0.06279568 = 6.27% Table 4.0: The material balance output sheet for Reservoir, R4. So = 0.25 Sw = 0.75 Co = 0.000013 (1/psi) Cw = 0.000003 (1/psi) Sf = 0.000004 (1/psi) H = 20 ft. = 0.26 Re = 5000 ft. k = 300 md w = 0.43 cp = 180° Dimensional radius initial input = 8 R.F given = 0.60 (fraction) Aquifer Constant = 0.0005 Time (years)

Np (mmstb)

Rp (scf/stb)

Bo (rb/stb)

Rs (scf/stb)

Bg (rb/scf)

Wp (bbls)

0 1 2 3 4 5 6


0.67 1.26 2.48 4.92 7.58 9.88

148.22 154.86 160.06 164.78 170.48 178.85

1.288 1.285 1.282 1.280 1.274 1.270 1.264

736.4 725.4 713.6 700.42 688.44 665.13 638.62

0.000585 0.000594 0.000604 0.000622 0.000644 0.000692 0.000715

0.037 0.045 0.055 0.065 0.078 0.089

7 8 9 10

3728 3693 3637 3545

12.78 15.39 18.72 22.80

182.50 188.26 191.20 198.40

1.262 1.256 1.251 1.245

610.00 594.73 582.33 577.49

0.000725 0.000743 0.000774 0.000798

1.096 1.103 1.234 1.325

Years N (mmstb) We (mmbbl) 0 873.790 0.1364245 1 640.976 0.0001599 2 552.946 0.0004667 3 471.120 0.0008487 4 321.621 0.0034337 5 232.761 0.0086519 6 198.448 0.0159004 7 164.640 0.1184718 8 105.817 0.1247687 9 64.0574 0.1307689 10 12.7110 0.1364245 For an infinite radial aquifer system (Estimated output) N = 873.7983 mmstb We = 0.1364245 mmbbls WDI = 0.92107 12

WDI Fraction 0.92107 0.08051 0.03826 1.02533 0.95595 0.98305 1.01080 1.02816 1.03042 1.05663 1.09710


CDI = 0.047911 URW = 508.143 mmstb R.F given = 0.60= 60% R.F W = 0.5526475= 55.3% R.F O = 0.04735246 = 4.74% Table 5.0: The material balance output sheet for Reservoir, R5. So = 0.95 Sw = 0.05 Co = 0.0000004 (1/psi) Cw = 0.000003 (1/psi) Sf = 0.000004 (1/psi) H = 100ft = 0.25 Re = 9200 ft. k = 200 md w = 0.55cp = 60° Dimensional radius initial input = 2.8 R.F given = 0.60 (fraction) Aquifer constant = 0.001657 Time (years)

Np (mmstb)

Rp (scf/stb)

Bo (rb/stb)

Rs (scf/stb)

Bg (rb/scf)

Wp (bbls)

0 1 2 3 4 5 6


7.88 11.26 17.44 24.90 37.55 49.84

760 812 845 897 923 945

1.404 1.400 1.382 1.370 1.364 1.360 1.354

650 592 523 487 421 362 302

0.00093 0.00098 0.00100 0.00102 0.00104 0.00109 0.00115

0.005 0.008 0.105 0.108 0.109

7 8 9 10

1428 1343 1237 984

52.70 65.56 78.55 82.32

977 999 1129 1428

1.352 1.350 1.349 1.345

265 217 175 131

0.00118 0.00121 0.00125 0.00132

1.116 1.118 1.120 1.122

Years 0 1 2 3 4 5 6 7 8 9 10

N (mmstb) 199.3773 198.6415 197.9462 196.1203 195.6219 194.7616 193.4486 192.6409 190.8179 188.0574 179.7115

We (mmbbl) 0.4933761 0.0065029 0.0084660 0.0098481 0.0104337 0.0126519 0.0169002 0.2084714 0.2407682 0.3585184 0.4933761

For a bounded reservoir radial aquifer system (Estimated output) N = 199.3773 mmstb We = 0.4933761 mmbbls 13

WDI Fraction 1.000015 0.427164 0.999998 1.125312 1.055942 1.183093 1.010815 1.038151 1.080406 2.016628 2.037134


WDI = 1.000015 CDI = 0.0179115 URW = 168.143 mmstb R.F given = 0.60= 60% R.F W = 0.6000087= 60% R.F O = 0.0000214 = 0.002% negligible Table 6.0: Data used for correlation works in water drive mechanism (Guthrie and Green Berger) Reservoir R.F W Log k Sw H Log R1 R2 R3 R4 R5

0.4881 0.5936 0.4055 0.5574 0.3177

3.000 3.3010 2.3541 2.4771 2.3010

0.17 0.18 0.26 0.75 0.05

0.114 0.114 0.114 0.114 0.114

200 140 44 20 100

0.26 0.26 0.25 0.26 0.25

Table 7.0: Data used for correlation works in water drive mechanism (API correlation model) Reservoir

Sw K( wi/ w) R1 0.5931 0.1892 125.00 0.17 R2 0.3854 0.1759 82.49 0.18 R3 0.4186 0.1822 833.42 0.26 R4 0.3369 0.2007 51.60 0.75 R5 0.5854 0.1605 196.29 0.05 Table 8: Values obtained from the different reservoirs investigated R1 F/Eo 9684.1 10359.1 10649.8 10923.7 11155.7 12497.7 13122.4

R.F W

We/Eo 4310.9 4690.6 5226.7 5481.5 6560.3 7417.8 8510.1

Ø(1-Swc)/Boi

R2 F/Eo 74.1 172.1 260.4 349.6 428.3 494.9 558.1

We/Eo 184.8 349.8 490.3 614.9 735.6 848.0 959.7

R3 F/Eo 153.3 249.2 349.1 455.5 566.6 617.5 688.2

We/Eo 328.3 662.4 993.2 1370.4 1820.1 2053.9 2421.2

R4 F/Eo 32.9 35.2 37.3 39.1 40.5 42.0 45.4

Pi/Pa

Krg/kro

9.2 8.7 9.8 8.9 9.6

52.79 34.72 28.44 9.18 12.18

We/Eo 109.6 117.4 131.5 146.6 168.5 188.2 212.8

R5 F/Eo 451.7 536.4 541.1 552.2 562.3 573.4 581.2

Table 9: Recovery Factors obtained for simulated data from different reservoirs Reservoir Field MBE API

G-GB

R1 R2 R3 R4 R5

0.49 0.60 0.40 0.56 0.32

0.60 0.47 0.38 0.60 0.60

0.59 0.42 0.32 0.55 0.60

14

0.59 0.38 0.42 0.34 0.59

o

38.98 25.72 22.50 38.98 22.00

We/ Eo 253.3 413.9 439.3 457.4 477.2 498.6 521.3


14000 12000 y = 0.7735x + 6535.8 R² = 0.9593

X/Eo

10000 8000 6000 4000 2000 0 0

2000

4000 6000 We/Eo

8000

10000

Fig. 1: Simulated output values for all data in Reservoir, R1



15




Fig. 6: Comparing the recovery factors obtained for simulated data from different reservoirs

16


4. CONCLUSION The main conclusions of this study are: • The reservoir and rock properties that affect the recovery factor in water drive reservoir are oil in place, oil mobility, connate water saturation, the pressure ratio (initial pressure to abandonment pressure), relative permeability ratio and the oil gravity. • From the Guthrie and Green models and API correlation model for water drive reservoir, different recovery factors models used obtained different values of recovery factor for the same water drive reservoir. The obtained simulated values of recovery factor from these models were not in agreement with the values obtained experimentally. • It would be of great need to develop a consistent recovery factor model for water drive reservoir in Niger delta that will be a match to the field data. 5. RECOMMENDATIONS The main recommendations of this study are: • Further work should be carried out on this study to determine the best recovery factor model in the Niger delta oil reservoir due to the fact that as more production occur pressure data becomes more available. There is need for frequent updating on production data. • It is important to establish a constant recovery factor model for water drive reservoirs due to the availability of obtained production data.

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REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Arps, J. J., & Ertekin, T. (1967). “Statistical Analysis of Crude Oil Recovery and Recovery Efficiency," Bulletin D14, American Petroleum Institute, Washington D.C. Arps, J. J., & Ertekin, T. (1967). “Statistical Analysis of Crude Oil Recovery and Recovery Efficiency," Bulletin D14, American Petroleum Institute, Washington D.C. Bouvier, J. D., Kaars-Sijpesteijn, C. H., Kluener, D. F., & Onyejekwe, C. C. (1989). “Threedimensional Seismic Interpretation and Fault sealing Investigations”. Nun River Field, Nigeria. AAPG Bulletin 73(11): 1397-1414. Bradley. (1987). Handbook of Petroleum Engineering for water drive equation, 44-48 Burke, R. C., Desauvagie, T .F. J., & Whiteman, A. J. (1972). Geological History of the Benue Valley and adjacent areas. University press: Ibadan. Cole, F.W. (1969). Reservoir Engineering Manual. Houston, Texas: Gulf Publishing Co. Dake, L. P. (1978). Fundamentals of Reservoir Engineering. Amsterdam: Elsevier Scientific Publishing Co. Dake, L. P. (1978). The Practice of Reservoir Engineering. Amsterdam: Elsevier Scientific Publishing Co. Doust, H., & Omatsola, E. (1990). Niger Delta. “Divergent/passive Margin Basins”. AAPG Memoir 48: 239-248. Ekweozor, C. M., & Daukoro, E. M. (1984). Petroleum source bed evaluation of Tertiary Niger Deltareply: American Association of Petroleum Geologists Bulletin, v. 68, 390-394. Ertekin, T., & Arps, J. J. (2001). Basic Reservoir Simulation (2001), page 5 for summary of regression based recovery equations. Etu-Efeotor, J. O. (1997). Fundamentals of Petroleum Geology. Paragraphics: Port Harcourt, PH. Guthrie, R. K., & Greenberger, M. H. (1955). The Use of Multiple-Correlation Analyses for Interpreting Petroleum Engineering Data. Drilling and Production Practices, API 130-137. Guthrie, R. K., & Greenberger, M. H. (1955). The Use of Multiple-Correlation Analyses for Interpreting Petroleum Engineering Data. Drilling and Production Practices, API 130-137. Havlena, D., & Odeh, A. S. (1963). The Material Balance as an Equation of a Straight Line. J. Pet. Technology 15 (8): 896–900. SPE-559-PA. http://dx.doi.org/10.2118/559-PA Statistical Analysis of Crude Oil Recovery and Recovery Efficiency, American Petroleum Institute, Dallas, (April 1984). Van Everdingen, A. F., Timmerman, E. H., & McMahon, J. J. (1953). Application of the Material Balance Equation to a Partial Water-Drive Reservoir. Trans., AIME 198: 51. Woods, R. W. & Muskat, M. M. (1945). An Analysis of Material-Balance Calculations. Trans., AIME 160: 124.

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APPENDIX Nomenclature Pi Initial reservoir pressure Pa Abandonment pressure Boi Initial Oil formation volume factor Bo Oil formation volume factor Bt Two phase formation volume factor Bgi Initial gas formation volume factor Bg Gas formation volume factor Bw Water formation volume factor Rsi Initial solution gas to oil ratio Rs Solution gas to oil ratio So Oil saturation Sw Water saturation Swc Connate water saturation Co Oil compressibility Cw Water compressibility Sf Fluid saturation H Formation thickness Porosity Re Reservoir radius K Formation permeability Kro Relative oil permeability Krg Relative gas permeability Initial water viscosity wi w

Water viscosity

Formation angle N Oil initially in place Np Cumulative oil produced Wp Cumulative water produced Rp Cumulative gas to oil produced We Cumulative water influx WDI Water Drive Index CDI Gas Cap Drive Index SDI Solution gas Drive Index DDI Depletion Drive Index URW Ultimate Water Recovery R.F Recovery Factor ER Percent recovery from bubble point to abandonment R.F W Recovery factor due to water drive R.F O Recovery factor due to other drives Oil gravity o X Net underground withdrawal Eo Expansion of oil and its dissolved gas R Correlation coefficient MBE Material Balance Equation API American Petroleum Institute G-GB Guthrie-Green Berger

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AUTHOR’S BIOGRAPHY MR. OSEH JEFFREY ONUOMA is a Lecturer ll at the Department of Chemical and Petroleum Engineering (Petroleum Engineering Programme), Afe Babalola University, Ado-Ekiti (ABUAD), Ekiti State, Nigeria. I obtained a B.Eng. Chemical Engineering at the Nnamdi Azikiwe University, Awka, Anambra State, Nigeria in 2005. I was awarded a Master of Science Degree in Petroleum Engineering at the University of Ibadan, Ibadan, Oyo State, Nigeria in 2012. I am an active registered corporate member of Nigerian Society of Engineers (CMNSE) and a professional member of Society of Petroleum Engineers (SPE). I am the corresponding author for the manuscript “: RECOVERY FACTOR MODEL STUDY IN THE NIGER DELTA OIL RESERVOIR FOR WATER DRIVE MECHANISM” and was co-authored with MR. OMOTARA OLUWAGBENGA OLAWALE. My research is focused on reservoir fluid characterization, Drilling process optimization and Petroleum production processes. I can be reached on +2347039110645 and through E-mail: [email protected]. MR. OMOTARA OLUWAGBENGA OLAWALE is an Assistant Lecturer at the Department of Chemical and Petroleum Engineering (Petroleum Engineering Programme), Afe Babalola University, Ado-Ekiti (ABUAD), Ekiti State, Nigeria. He obtained a B.Eng. Petroleum Engineering at the University of Benin, Benin-City, Edo State, Nigeria in 2010. He is a professional member of Society of Petroleum Engineers (SPE). He co-authored the work “RECOVERY FACTOR MODEL STUDY IN THE NIGER DELTA OIL RESERVOIR FOR WATER DRIVE MECHANISM” with MR. OSEH JEFFREY ONUOMA. His research is focused on Subsea Engineering, Reservoir Modeling, and Natural Gas process optimization. He can be reached on +234803410008 and through E-mail: [email protected]

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