development of a correlation to predict water-flooding ... of a correlation to predict...

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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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.

mailto:[email protected]

http://orcid.org/0000-0002-0830-133X



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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

https://www.google.ae/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiC2IuWnZPTAhVBvhQKHccfBwcQjhwIBQ&url=https%3A%2F%2Fwww.researchgate.net%2Ffigure%2F271021603_fig4_Figure-1-A-schematic-diagram-of-the-core-flooding-apparatus-Color-figure-can-be-viewed&psig=AFQjCNEaiYLtPTXpE9SFscTFbS4N4VNf6g&ust=1491684393846736



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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]:



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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)



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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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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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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



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


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


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


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)



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

REFERENCES

[1] Edmondson, T., 1965, "Effect of temperature on

waterflooding". J. of Canadian Petroleum

Technology, 4(04): p. 236-242.

[2] Weinbrandt, R., H. Ramey Jr, and F. Casse,

1975, "The effect of temperature on relative and

absolute permeability of sandstones". Society of

Petroleum Engineers Journal, 15(05): p. 376-384.

[3] Corey, A.T., 1954, "The interrelation between

gas and oil relative permeabilities. Producers

monthly", 19(1): p. 38-41.

[4] Schauer Jr, P. 1957, "Application of Empirical

Data in Forecasting Water Flood Behavior. in

Fall Meeting of the Society of Petroleum

Engineers of AIME", Society of Petroleum

Engineers.

[5] Oseh, J.O. and O.O. Omotara, 2014, "Recovery

Factor Model Study in the Niger Delta Oil

Reservoir for Water Drive Mechanism. Recovery

Factor Model Study in the Niger Delta Oil

Reservoir for Water Drive Mechanism", 1: p. 1-

20.

[6] Hawkins F. M., Benjamin C. C., 1959. “Applied

petroleum reservoir engineering Prentice-Hall

chemical engineering series”. 2nd Ed. Louisiana

State University, USA, Prentice-Hall.

[7] Tarik A., 1946, “Reservoir Engineering



2597

Handbook”. 4th Ed., the Boulevard, Langford

Lane, Kidlington, Oxford, OX5 1GB, UK.

[8] Mohammad A.J, “Special Core Analysis”,

Kuwait Institute for Scientific Research.

[9] Abdus S., 2008. “Practical Enhanced Reservoir

Engineering”. 1st ed. Tulsa, Oklahoma: PennWell

Corporation.

[10] Waterflood Recovery - Zargon Oil & Gas Ltd...

2015. Waterflood Recovery - Zargon Oil & Gas

Ltd., Available at: http://zargon.ca/operations/oil-

exploitation/waterflood-recovery. [Accessed 20

September 2015].

[11] Technology: Enhanced Oil Recovery |

Technology | Chevron. 2015. Technology:

Enhanced Oil Recovery | Technology | Chevron,

Available

at:http://www.chevron.com/technology/eor/.

[Accessed 20 September 2015].

[12] Waterflooding Optimization for Improved

Reservoir Management | Masoud Asadollahi -

Academia.edu. 2015. Waterflooding

Optimization for Improved Reservoir

Management | Masoud Asadollahi -

Academia.edu. Available at:

https://www.academia.edu/1502655/Waterfloodi

ng_Optimization_for_Improved_Reservoir_Man

agement [Accessed 7 October 2015].

[13] Recovery rates, enhanced oil recovery and

technological limits | Philosophical Transactions

of the Royal Society of London A: Mathematical,

Physical and Engineering Sciences.

2015. Recovery rates, enhanced oil recovery and

technological limits | Philosophical Transactions

of the Royal Society of London A: Mathematical,

Physical and Engineering Sciences. Available at:

http://rsta.royalsocietypublishing.org/content/372

/2006/20120320. [Accessed 12 October 2015].

[14] TRAINING| How Does Water Injection Work? |

Rigzone. 2015. Available at:

http://www.rigzone.com/training/insight.asp?i_id

=341. [Accessed 12 October 2015].

[15] Corey, A.T1954, "The Interrelation between Gas

and Oil Relative Permeabilities". Production

Monthly.

[16] Guthrie, R. K., and Greenberger, M. H., “The

Use of Multiple-Correlation Analyses for

Interpreting Petroleum-engineering Data,” Drill.

& Prod. Prac., API (1955)

http://zargon.ca/operations/oil-exploitation/waterflood-recovery

http://zargon.ca/operations/oil-exploitation/waterflood-recovery

http://www.chevron.com/technology/eor/

https://www.academia.edu/1502655/Waterflooding_Optimization_for_Improved_Reservoir_Management



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