International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
© Research India Publications. http://www.ripublication.com
2586
Development of a Correlation to Predict Water-Flooding Performance of
Sandstone Reservoirs Based On Reservoir Fluid Properties
Dr. Saad Balhasan
American university of Ras Al khaimah, United Arab Emirates,
ORCID : 0000-0002-0830-133
Dr. Mohammad Jumaa
Kuwait Institute for scientific Research, Kuwait,
Eng. Ahmed Elbagir,
American university of Ras Al khaimah, United Arab Emirates
Abstract
A sensitivity analysis was performed to determine the effect
of temperature on oil recovery factor by water-flooding. In
this paper, several core flood experiments were conducted to
explain the mechanisms involved for oil recovery where the
water flooding temperatures are varied between 95°F and
149°F. The results from the relative permeability were applied
on a fives spot pattern to investigate the relationship between
the flooding temperature and oil recovery factor. As a result, a
significant improvement in oil recovery was achieved when a
five spot core flooding application was examined.
The recovery factor increased up to 48.8% at 194°F,
compared to 38% at 95°F when one pore volume was injected.
However, a statistical correlation was proposed for predicting
the water-flooding performance of sandstone reservoirs based
on the fluid properties. The results show that the proposed
correlation is reliable when compared with three sandstone
reservoirs in Libya and one sandstone reservoir in Kuwait.
INTRODUCTION
Water flooding is a secondary recovery method which is
applied through injecting water in one or more wells. A large
portion of the oil production (approximately 50%) is
recovered from the reservoirs under water flooding. Various
studies were conducted to illustrate the temperature effects on
relative permeability. Edmondson and his co-workers [1]
investigated the effect of temperature on the well
permeability. Their results showed that the residual oil
saturations decreased with increasing temperature and the
relative permeability ratio decreased with temperature at high
water saturations, but increased with temperature at low water
saturations. Weinbrandt et al. examined the relationship of
temperature and relative permeability on consolidated
sandstone cores. Oil relative permeability and water
saturations increased with increasing temperature. Besides,
the water relative permeability decreased with increasing
temperature. Moreover, the study found that the irreducible
water saturation increased with decreasing residual oil
saturation when the temperature increased [2].
In this research, a number of core flooding measurements
have studied the effect of temperature on two-phase relative
permeability of sandstone reservoirs. The objective of this
study was first to attempt to minimize both laboratory work
and theoretical calculations by deriving an empirical
correlation based on the temperature effects on relative
permeability to estimate the oil recovery factor. In order to
achieve the mentioned objectives, the lab work of a special
core analysis was done. The relative permeability of oil and
water has been estimated by using Corey correlation [3]. The
experiment was run at three different temperatures of 95°F,
122°F and 194°F. The results from the relative permeability
were applied on a fives spot pattern to estimate the recovery
factor. The results showed a significant improvement in oil
recovery, up to 48.8% at 194°F, compared to 95°F where the
recovery factor was 38%.
In the past, many statistical studies of water flooding
performances ended by an empirical correlation. Guthrie and
Greenberger studied oil recovery by water drive, empirically,
from reservoir rock and fluid properties [16]. Schauer
presented an empirical method for predicting the water-flood
behavior of Illinois Basin water flooding performance [4]. The
API correlation was derived by J. J. Arps, who developed a
correlation for water drive recovery from sandstone reservoirs
and carbonates for solution gas drive mechanism [5].
In this study, an empirical correlation was proposed for
predicting the recovery factor from water-flooding
performance based on laboratory data. The proposed
empirical correlation can be used for the screening and
ranking of unconsolidated sandstone reservoirs with medium
to high API gravity. The proposed correlation was applied on
several reservoirs and the results were reliable.
LABORATORY EXPERIMENTS BASED ON CORE
FLOODING UNIT:
To determine the relative permeability, the core, which is
under confining pressure, is flooded with a constant flow rate
mode. The data acquisition is used to monitor the confining
pressure and flow rates. The lab core flooding system is
shown in Figure 1 and a schematic diagram is presented in
figure 2.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
© Research India Publications. http://www.ripublication.com
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Figure 1. Core Flooding System
Figure 2. A schematic diagram of the core flooding
Core Sample Test
Step 1: The packed porous media (core) was saturated with
distilled water using a vacuum pump. The porosity of the core
was calculated by doing a material balance on the amount of
water left and knowing the exact value of the dead volume of
lines connected to the core. The absolute permeability of the
packed core was measured using an accurate pressure
transducer with an operational range of 0 - 3 bars.
Step 2: Place the Core inside the core holder, which can be
set at any desired temperature up to 500°F. End Caps of the
core holder were designed in such a way that the fluid could
be distributed evenly at the injection face. A beaker should be
placed at the end cap outlet line to collect the released fluids
[6].
Step 3: The next step, the oil was injected at a rate of 0.5
cc/min for calculating the initial water saturation (Swi). Oil
injection was continued at Swi to measure effective oil
permeability [6]. The baseline water permeability is
determined for core sample at different flow rates until the
correct laminar flow rate is achieved. With 1 cc/min,
approximately injected 3 pore volumes of oil to displace water
in place to reach initial water saturation. The produced
volumes of oil and water are calculated [6].
Step 4: After initializing the core, the separator was
connected and the imbibition’s process was initiated by
injecting water at a rate of 1 cc/min. During the water
injection phase, the oil production was recorded versus time,
and the pressure differential across the core was monitored as
well. The water injection was continued for almost 7 hours.
After the experiment, the separator was disconnected and held
at a temperature of 100°F for a few days in order for the
oil/water meniscus to be separated completely and any
possible adjustment to the final oil recovery. In the core
flooding test the following temperatures were used 95°F,
122°F and 194°F. The data shown in table 1 & 2 an example
of the log file at 122° F that appears on the software
connected to core flooding system [6].
Table 1. Log File Data for Core B-100
Temperature 122 °F
Length, cm 13.00
Diameter, cm 3.802
Vbulk, cm³ 147.59
Vpore, cm³ 28.90
Porosity 0.196
μw, cp 0.65
μo, cp 10
Swi 0.29
Table 2. Log File Data for Core B-100 by Time
Time(sec)
Upstream
Pressure(psi)
Confining
Pressure(psi)
0 3.184 1132.869
60 7.249 1109.676
120 9.373 1093.440
180 11.076 1076.839
240 12.553 1061.092
300 13.926 1043.880
360 15.488 1024.715
420 16.843 1013.545
480 18.150 1002.681
540 19.419 992.366
600 20.695 977.961
660 21.830 962.336
720 22.935 952.266
780 24.033 944.209
840 25.016 934.504
900 26.072 922.664
960 26.987 909.907
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
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METHODOLOGY
In order to be able to calculate for optimization of water-
flooding, reservoir information and special core analysis are
needed with its description. In this study Corey correlation
unsteady-state was used. The relative permeability
measurements usually include tabulated water saturations,
relative permeability to each fluid, fractional flow rate of each
fluid, and the calculated relative permeability ratio [7]. The
relative permeability is usually reported relative to the oil
permeability at the irreducible water saturation is also
reported. Tables 3 & 4 show an example of a log file which
includes core sample data and test description [6]... Note that
the absolute permeability to air and the porosity of a given
sample are known as the sample description. The type of
relative permeability test, the overburden pressure applied
during the test, and the temperature of the test should also be
reported [6].
Calculating Water Saturation
Part of the core sample test is a drainage test, which is
injecting oil to reach the point where only oil is produced
from the core [6]. This test is done to obtain the Swi, which is
the initial water saturation. The initial water saturation will
appear in the software linked to the core sample system [6].
The Corey correlation was used to estimate the relative
permeability curves from laboratory two-phase data (water
and oil) [3]; [7]. The equation implies that water-relative
permeability and water-oil capillary pressure in two-phase
systems are functions of water saturation alone, irrespective of
the relative saturations of oil. To be able to get the oil and
water relative permeability, the Sw* must be calculated [3].
The Sw* is irreducible water saturation. Below this saturation,
water cannot flow due to the forces between fluid-rock and
fluid-fluid (surface tension and interfacial tension). To
calculate it, the following equation is used.
𝐒𝐰∗ = 𝐒𝐰 − 𝐒𝐰𝐢
𝟏 − 𝐒𝐰𝐢 − 𝐒𝐨𝐫𝐰
… … … … (𝟏)
Where:
Sw* = Irreducible water saturation, %
Sw = water saturation
Swi = initial water saturation, %
Sorw= residual oil saturation
Calculating relative Permeability
Relative permeability is the ratio of the effective permeability
for a particular fluid to a reference or base permeability of the
rock [4]. Firstly, calculate the relative permeability of both oil
and water and the following equations are used [7].
Oil Relative Permeability:
𝐊𝐫𝐨 = (𝟏 − 𝐒𝐰∗)𝟐 … … … … (𝟐)
𝐊𝐫𝐨@𝟗𝟓𝐅 = 𝐊𝐫𝐨 ∗ 𝐊𝐫𝐨(𝐬𝐰𝐢) … … … (𝟑)
Where:
Kro = oil relative permeability
𝐒𝐰∗ = irreducible water saturation, %
Water Relative Permeability:
𝐊𝐫𝐰 = 𝐒𝐰∗𝟐… … … (𝟒)
𝐊𝐫𝐰@𝟗𝟓𝐅 = 𝐊𝐫𝐰 ∗ 𝐊𝐫𝐰(𝐬𝐨𝐫) … … … (𝟓)
Where:
Krw = water relative permeability
Based on the core sample analysis results, Kro and Krw are
illustrated in the description which is used to find the oil and
water relative permeability based on the case being used [6].
Here, Corey correlation is used, the graph in figure 3 shows
the relative permeability curve which is a plot relationship
between relative permeability (Kro/Krw) vs. Water saturation
(Sw) [8].
Fractional Flow
The fractional flow of water or any displacing fluid is defined
as the water flow rate divided by the total flow rate [7]. For
the simplest case of horizontal flow with negligible capillary
pressure, the expression reduces to:
𝐟𝐰 = (𝟏
(𝟏 + 𝐊𝐫𝐨
𝐊𝐫𝐰∗
µ𝐰
µ𝐨)) … … … (𝟔)
Where;
fw = fractional flow (Producing water cut)
Kro = oil relative permeability
Krw = water relative permeability
µo = oil viscosity, cp
µw= water viscosity, cp
Relative permeability data is obtained from laboratory studies
or from available correlation, as in this study Corey
correlation is used to calculate relative permeability of water
and oil. Alternately, fractional flow curves can be generated
by noting the following relationship between the relative
permeability ratio and water saturation [7]:
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
© Research India Publications. http://www.ripublication.com
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(𝐊𝐫𝐨
𝐊𝐫𝐰
)𝐬𝐰 = (𝐚𝐞−𝐬𝐰𝐛) … … … (𝟕)
Where, the coefficient a = constant in log (Kro/Krw) versus Sw
plot, and b= slop of log (Kro/Krw) versus Sw plot. Hence, the
equation of the fractional flow of water and its derivative can
be written as in the following [4]:
𝒅𝒇𝒘
𝒅𝒔𝒘
= (𝒃 ∗ 𝒇𝒘 ∗ (𝟏 − 𝒇𝒘)) … … … (𝟖)
3.4 Determining Water injection (PVwi %)
To determine the percentage of water injection (pore volume),
Eq. 9 is used as follows:
𝑷𝑽𝒘𝒊 = (𝟏
𝒅𝒇𝒘
𝒅𝒔𝒘
) … … … (𝟗)
Average Water Saturation
The average water saturation in the reservoir at breakthrough
is found by extending the tangent to the fw= 1. The average
water saturation is estimated by using the tangents of the
fractional flow vs. water saturation after the breakthrough
portion.
Recovery Factor Determination
Recovery factor is defined as the ratio of recoverable oil or
gas to estimated oil or gas in place in reservoir [7]. The
recovery factor is expressed in the following equation by
using water saturations:
𝐑𝐅 = (𝐒𝐰𝐚𝐯𝐞𝐫𝐚𝐠𝐞 − 𝐒𝐰𝐢
𝟏 − 𝐒𝐰𝐢) … … … (𝟏𝟎)
RESULTS AND DISCUSSIONS
Relative Permeability Curves at different Temperatures
The unsteady-state displacement experiments were performed
to investigate the effect of reservoir temperature on water-oil
relative permeability and the ultimate oil recovery. Figure 2
shows the relative permeability curves, which explain the
situation of water and oil during the test, as shown initial
water saturation is increasing and the residual oil saturation
(ROS) is decreasing. From the figure we can obtain the water
relative permeability at residual oil saturation (Krw at Sor) and
the oil relative permeability at initial water saturation (Kro at
Swi).
As the flooding temperature increased from 95°F to 122°F the
residual oil saturation decreased, and the recovery factor
increased from 0.39 to 0.38, and 38.1% to 44%, respectively.
Also, when the temperature increased from 122°F to 195°F,
the residual oil saturation decreased and the recovery factor
increased from 0.38 to 0.37, and 44% to 48.8%, respectively.
This is because the oil viscosity decreased as the reservoir
temperature increased, leading to improvement of the oil flow.
Figure 3. Water-oil relative permeability curves under
different temperatures
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.00 0.20 0.40 0.60 0.80
Kro
/Krw
Swi
Kro(@ 95°F)
Krw(@ 95 °F)
Kro(@ 122°F)
Krw(@ 122 °F)
Kro(@194 °F)
Krw (@194°F)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
© Research India Publications. http://www.ripublication.com
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Table 3. Water Saturation and Relative Permeability Data of Core Sample B-100 at 95 °F
Sw Sw* Kro Krw Kro (95°F)
Krw
(95 °F)
0.30 0.0429 0.9161 0.0018 0.7329 0.0002
0.31 0.0729 0.8596 0.0053 0.6877 0.0005
0.32 0.1029 0.8049 0.0106 0.6439 0.0010
0.33 0.1329 0.7519 0.0177 0.6015 0.0017
0.34 0.1629 0.7008 0.0265 0.5606 0.0026
0.35 0.1929 0.6515 0.0372 0.5212 0.0037
0.36 0.2229 0.6040 0.0497 0.4832 0.0049
0.37 0.2529 0.5582 0.0639 0.4466 0.0063
0.38 0.2829 0.5143 0.0800 0.4114 0.0079
0.39 0.3129 0.4722 0.0979 0.3777 0.0096
0.40 0.3429 0.4318 0.1176 0.3455 0.0116
0.41 0.3729 0.3933 0.1390 0.3146 0.0137
0.42 0.4029 0.3566 0.1623 0.2853 0.0160
0.43 0.4329 0.3217 0.1874 0.2573 0.0184
0.44 0.4629 0.2885 0.2142 0.2308 0.0211
0.45 0.4929 0.2572 0.2429 0.2058 0.0239
0.46 0.5229 0.2277 0.2734 0.1821 0.0269
0.47 0.5529 0.1999 0.3057 0.1599 0.0301
0.48 0.5829 0.1740 0.3397 0.1392 0.0334
0.49 0.6129 0.1499 0.3756 0.1199 0.0370
0.50 0.6429 0.1276 0.4133 0.1020 0.0407
0.51 0.6729 0.1070 0.4527 0.0856 0.0446
0.52 0.7029 0.0883 0.4940 0.0706 0.0486
0.53 0.7329 0.0714 0.5371 0.0571 0.0529
0.54 0.7629 0.0562 0.5820 0.0450 0.0573
0.55 0.7929 0.0429 0.6286 0.0343 0.0619
0.56 0.8229 0.0314 0.6771 0.0251 0.0666
0.57 0.8529 0.0217 0.7274 0.0173 0.0716
0.58 0.8829 0.0137 0.7794 0.0110 0.0767
0.59 0.9129 0.0076 0.8333 0.0061 0.0820
0.60 0.9429 0.0033 0.8890 0.0026 0.0875
0.61 0.9729 0.0007 0.9465 0.0006 0.0931
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Table 4. Water Saturation and Relative Permeability Data of Core Sample B-100 at 122 °F
Sw Sw* Kro Krw Kro (122°F)
Krw
(122 °F)
0.30 0.0400 0.9216 0.0016 0.7373 0.0001
0.31 0.0680 0.8686 0.0046 0.6949 0.0004
0.32 0.0960 0.8172 0.0092 0.6538 0.0008
0.33 0.1240 0.7674 0.0154 0.6139 0.0013
0.34 0.1520 0.7191 0.0231 0.5753 0.0019
0.35 0.1800 0.6724 0.0324 0.5379 0.0027
0.36 0.2080 0.6273 0.0433 0.5018 0.0036
0.37 0.2360 0.5837 0.0557 0.4670 0.0047
0.38 0.2640 0.5417 0.0697 0.4334 0.0059
0.39 0.2920 0.5013 0.0853 0.4010 0.0072
0.40 0.3200 0.4624 0.1024 0.3699 0.0086
0.41 0.3480 0.4251 0.1211 0.3401 0.0102
0.42 0.3760 0.3894 0.1414 0.3115 0.0119
0.43 0.4040 0.3552 0.1632 0.2842 0.0137
0.44 0.4320 0.3226 0.1866 0.2581 0.0157
0.45 0.4600 0.2916 0.2116 0.2333 0.0178
0.46 0.4880 0.2621 0.2381 0.2097 0.0200
0.47 0.5160 0.2343 0.2663 0.1874 0.0224
0.48 0.5440 0.2079 0.2959 0.1663 0.0249
0.49 0.5720 0.1832 0.3272 0.1465 0.0275
0.50 0.6000 0.1600 0.3600 0.1280 0.0302
0.51 0.6280 0.1384 0.3944 0.1107 0.0331
0.52 0.6560 0.1183 0.4303 0.0947 0.0361
0.53 0.6840 0.0999 0.4679 0.0799 0.0393
0.54 0.7120 0.0829 0.5069 0.0664 0.0426
0.55 0.7400 0.0676 0.5476 0.0541 0.0460
0.56 0.7680 0.0538 0.5898 0.0431 0.0495
0.57 0.7960 0.0416 0.6336 0.0333 0.0532
0.58 0.8240 0.0310 0.6790 0.0248 0.0570
0.59 0.8520 0.0219 0.7259 0.0175 0.0610
0.60 0.8800 0.0144 0.7744 0.0115 0.0650
0.61 0.9080 0.0085 0.8245 0.0068 0.0693
0.62 0.9360 0.0041 0.8761 0.0033 0.0736
0.63 0.9640 0.0013 0.9293 0.0010 0.0781
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Table 5. Water Saturation and Relative Permeability Data of Core Sample B-100 at 194 °F
Sw Sw* Kro Krw
Kro
(194 °F) Krw (194°F)
0.30 0.0375 0.9264 0.0014 0.7411 0.0001
0.31 0.0638 0.8766 0.0041 0.7013 0.0003
0.32 0.0900 0.8281 0.0081 0.6625 0.0006
0.33 0.1163 0.7810 0.0135 0.6248 0.0010
0.34 0.1425 0.7353 0.0203 0.5882 0.0015
0.35 0.1688 0.6910 0.0285 0.5528 0.0021
0.36 0.1950 0.6480 0.0380 0.5184 0.0028
0.37 0.2213 0.6065 0.0490 0.4852 0.0036
0.38 0.2475 0.5663 0.0613 0.4530 0.0045
0.39 0.2738 0.5274 0.0749 0.4220 0.0056
0.40 0.3000 0.4900 0.0900 0.3920 0.0067
0.41 0.3263 0.4539 0.1064 0.3632 0.0079
0.42 0.3525 0.4193 0.1243 0.3354 0.0092
0.43 0.3788 0.3860 0.1435 0.3088 0.0106
0.44 0.4050 0.3540 0.1640 0.2832 0.0122
0.45 0.4313 0.3235 0.1860 0.2588 0.0138
0.46 0.4575 0.2943 0.2093 0.2354 0.0155
0.47 0.4838 0.2665 0.2340 0.2132 0.0174
0.48 0.5100 0.2401 0.2601 0.1921 0.0193
0.49 0.5363 0.2151 0.2876 0.1721 0.0213
0.50 0.5625 0.1914 0.3164 0.1531 0.0235
0.51 0.5888 0.1691 0.3466 0.1353 0.0257
0.52 0.6150 0.1482 0.3782 0.1186 0.0281
0.53 0.6413 0.1287 0.4112 0.1030 0.0305
0.54 0.6675 0.1106 0.4456 0.0884 0.0331
0.55 0.6938 0.0938 0.4813 0.0750 0.0357
0.56 0.7200 0.0784 0.5184 0.0627 0.0385
0.57 0.7463 0.0644 0.5569 0.0515 0.0413
0.58 0.7725 0.0518 0.5968 0.0414 0.0443
0.59 0.7988 0.0405 0.6380 0.0324 0.0473
0.60 0.8250 0.0306 0.6806 0.0245 0.0505
0.61 0.8513 0.0221 0.7246 0.0177 0.0538
0.62 0.8775 0.0150 0.7700 0.0120 0.0571
0.63 0.9038 0.0093 0.8168 0.0074 0.0606
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Recovery Factor
A five spot pattern of vertical wells of a sandstone oil
reservoir under a fixed model of production rate and water
injection rate has been selected to apply the results of the
water-oil relative permeability curves under different
temperatures 95°F, 122°F, 194°F. The economic limit point is
determined at 1 pore volume injected. The five spot pattern
data is given in Table 8.
Table 6. The five spot pattern data
The calculation of oil recovery factors at the different
temperatures 95°F, 122°F, and 194°F showed an increase in
the recovery factor when the flooding temperature increases.
When the flooding temperature increased from 95°F to 122°F
the recovery factor increased 6%. Moreover, the recovery
factor increased by 4.8% when the temperature is increased
from 122°F to 194°F. Tables 7, 8, and 9 showed the recovery
factor calculation under different temperatures 95°F, 122°F,
and 194°F.
Table 7. The Recovery Factor Estimation at Temperature 95°F, μo 18 cp, and μw 0.8 cp.
Sw
fw
(95°F)
Sw
(Ave.) ROS
R.F
(95°F)
Wi,
Vp
0.450 0.735 0.510 0.490 0.314 0.198
0.455 0.747 0.514 0.486 0.320 0.203
0.460 0.769 0.518 0.482 0.325 0.216
0.465 0.789 0.522 0.478 0.331 0.231
0.470 0.809 0.526 0.474 0.336 0.249
0.475 0.827 0.530 0.470 0.342 0.269
0.480 0.844 0.534 0.466 0.348 0.292
0.485 0.860 0.536 0.464 0.350 0.319
0.490 0.874 0.540 0.460 0.356 0.349
0.495 0.887 0.542 0.458 0.359 0.385
0.500 0.900 0.544 0.456 0.362 0.426
0.505 0.911 0.546 0.454 0.364 0.474
0.510 0.921 0.548 0.452 0.367 0.531
0.515 0.931 0.550 0.450 0.370 0.597
0.520 0.939 0.552 0.448 0.373 0.675
0.525 0.947 0.554 0.446 0.376 0.768
0.530 0.954 0.556 0.444 0.378 0.880
0.535 0.961 0.558 0.442 0.381 1.015
Variable Value
N, STB 1.07E+07
Area, acre 380
H, ft 32
Swi 0.29
Boi, bbl/stb 1.26
Porosity 0.2
Production and Inj. Rate, stb/day 10000
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Table 8. The Recovery Factor Estimation at Temperature 122°F, μo 10 cp, and μw 0.65 cp
Sw
fw
(122°F)
Sw
(Ave.) ROS
R.F
(122°F)
Wi,
Vp
0.500 0.784 0.554 0.446 0.376 0.227
0.505 0.803 0.556 0.444 0.378 0.244
0.510 0.822 0.558 0.442 0.381 0.262
0.515 0.839 0.562 0.438 0.387 0.284
0.520 0.855 0.566 0.434 0.392 0.309
0.525 0.869 0.568 0.432 0.395 0.339
0.530 0.883 0.574 0.426 0.404 0.373
0.535 0.896 0.576 0.424 0.406 0.413
0.540 0.908 0.580 0.420 0.412 0.461
0.545 0.919 0.586 0.414 0.420 0.517
0.550 0.929 0.590 0.410 0.426 0.583
0.555 0.938 0.592 0.408 0.429 0.663
0.560 0.947 0.594 0.406 0.432 0.760
0.565 0.954 0.598 0.402 0.437 0.878
0.570 0.961 0.600 0.400 0.440 1.024
Table 9. The Estimated Recovery Factor at Water Temperatures 194°F, μo 4 cp, and μw 0.4 cp
Sw
fw
(194°F)
Sw
(Ave.) ROS
R.F
(194°F)
Wi,
Vp
0.550 0.843 0.580 0.420 0.412 0.329
0.555 0.859 0.590 0.410 0.426 0.360
0.560 0.874 0.602 0.398 0.443 0.395
0.565 0.888 0.606 0.394 0.448 0.437
0.570 0.901 0.610 0.390 0.454 0.487
0.575 0.913 0.614 0.386 0.460 0.546
0.580 0.924 0.620 0.380 0.468 0.617
0.585 0.934 0.625 0.375 0.475 0.703
0.590 0.943 0.628 0.372 0.479 0.809
0.595 0.951 0.630 0.370 0.482 0.939
0.600 0.959 0.634 0.366 0.488 1.010
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
© Research India Publications. http://www.ripublication.com
2595
Table 10. The Estimated Recovery Factor and ROS at
Different Temperatures and 1 Pvwi
Temp, F Oil Vis,
cp
Water
Vis, cp
ROS RF Pv(wi)
95 18 0.8 0.442 0.381 1.015
122 10 0.65 0.400 0.440 1.024
194 4 0.4 0.366 0.488 1.010
Figure 4. Recovery Factor Sensitivity as a function of 1 Pore
Volume of Water Injection at Different Temperatures
EMPIRICAL CORRELATION
A correlation, based on the five parameters mentioned below,
is proposed for the estimation of the recovery factor of water-
flooding in core scale under constant water injection rate. The
coefficients and powers of parameters were determined using
a non-linear regression. The correlation mainly depends on the
dimensionless temperatures and fluid properties as defined
below:
𝐑𝐅 = [(𝟎. 𝟏𝟔𝟓 𝐋𝐍 (𝑻𝒓
𝑻𝒔)
𝟎.𝟖𝟖
) + (𝟎. 𝟎𝟎𝟔𝟔 𝑳𝑵 (𝝁𝒐
𝝁𝒘
))
+ (𝟎. 𝟐𝟖𝟎 𝑳𝑵 (𝟏
𝜸𝒐
)𝟏.𝟓𝟓
)] + 𝟎. 𝟐𝟔𝟒
In this correlation, RF is the recovery factor, %, 𝐓𝐫 is the
reservoir temperature, °F, 𝐓𝐬 is the surface temperature, °F,
μo is the oil viscosity, cp, μw is the water viscosity, cp, 𝛄𝐨 is
the oil specific gravity.
Validations and Testing
Validation and testing the empirical correlation are shown in
Figure 5. The outputs of correlation were compared with the
results of the experimental recovery factor. Figure 5 shows the
results from the three methods listed above. As observed, both
curves were matched.
Figure 5. The outputs of correlation were compared with the
results of the experimental recovery factor.
The empirical correlation was tested on four oil reservoirs,
one in Kuwait and three reservoirs in Libya. The four
reservoirs have a good reservoir quality. The porosity and
permeability were ranged between 0.15 to 0.2 and 150 md to
500 md, respectively. Moreover, the API gravity ranged from
26 to 38. As shown in Tables 11, 12, 13, and 14, the estimated
error of the empirical correlation was estimated and found
between 1.93% and 12.61%.
Table 11: Comparing the Empirical correlation with the
estimated RF of Libya EE Reservoir
Tem
p, F
Oil
Vis,
cp
Water
Vis, cp
Oil Speci.
Gravity
Estimat
ed RF
RF
(Empiric
al)
Erro
r, %
235 0.43 0.4 0.82 0.47 0.493 4.68
Table 12: Comparing the Empirical correlation with the
estimated RF of Libya MM Reservoir
Tem
p, F
Oil
Vis,
cp
Water
Vis, cp
Oil Speci.
Gravity
Estimat
ed RF
RF
(Empiric
al)
Erro
r, %
210 0.717 0.45 0.83 0.45 0.478 5.78
Table 13: Comparing the Empirical correlation with the
estimated RF of Kuwait KK Reservoir
Tem
p, F
Oil
Vis,
cp
Water
Vis, cp
Oil Speci.
Gravity
Estimat
ed RF
RF
(Empiric
al)
Erro
r, %
177 1.3 0.58 0.86 0.435 0.444 1.93
Table 14: Comparing the Empirical correlation with the
estimated RF of Libya SS Reservoir
Tem Oil Water Oil Speci. Estimat RF Erro
0.000
0.100
0.200
0.300
0.400
0.500
0.600
-0.100 0.400 0.900 1.400
RF
Pv(wi)
R.F @ 95°F
R.F @ 122°F
R.F @ 194°F
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0 100 200 300
RF
Temperature, F
RF (Experimental)
RF (Empirical)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 10 (2017) pp. 2586-2597
© Research India Publications. http://www.ripublication.com
2596
p, F Vis,
cp
Vis, cp Gravity ed RF (Empiric
al)
r, %
210 0.75 0.33 0.832 0.54 0.479 12.6
1
CONCLUSION
Based on the results obtained from a core flooding at three
different temperatures, the ultimate oil recovery factor
increases to about 10% from 0.381 to 0.488, when the
temperature is increased form 95°F to 194°F. Three
relationships were developed to correlate the oil recovery
factor at three different temperatures 95°F, 122°F, and 194°F.
The empirical correlation was applied on four different
reservoirs to estimate the oil recovery factor. The new
empirical correlation will require the reservoir fluid properties
for oil and water and the reservoir temperature to use for
estimating the oil recovery factor.
As expected, the correlation had an acceptable level of error.
The lowest error for the empirical correlation is 1.93%, while
the highest error is 12.61%. The new empirical correlation
will provide to the user, a very fast and practical method to
estimate the oil recovery factor.
NOMENCLATURE
Boi Formation volume factor of oil at initial reservoir
conditions, bbl/STB
Bw Formation volume factor of water, bbl/STB
K Absolute permeability, md
Soi Initial oil saturation, %
RF Recovery Factor, %
ROS Remaining average oil saturation after one pore
volume injected, %
Sw Water saturation, %
Vp Pore volume, cc
µo Oil Viscosity, cp
WI Cumulative injected water volume, bbl
PV Pore volume, cc
STB Stock tank barrels of oil
So Oil saturation, %
Swc Connate water saturation, %
Kro Oil relative permeability
Krw water relative permeability
Swi initial water saturation, %
Sorw residual oil saturation to water, %
Co Corey oil exponent
Cw Corey water exponent
Dfw/dsw fractional flow derivative
K rw (Sorw) water relative perm at residual oil
K rw (Swmax) water relative perm at maximum water saturation
K ro(Swmin) oil relative perm at minimum water
saturation
Sw-average Average water saturation, %
Symbols
Ø Porosity
µw Viscosity of water
Σ Sum of (specify)
µo Viscosity of oil
°F Degrees Fahrenheit
°C Degrees Celsius
Δ Delta
℮ Exponential
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