Available online at http://ijcpe.uobaghdad.edu.iq and www.iasj.net 

Iraqi Journal of Chemical and Petroleum 
 Engineering  

Vol.23 No.4 (December 2022) 71 – 80 
EISSN: 2618-0707, PISSN: 1997-4884 

 

Corresponding Authors:  Name: Ahmed Radhi Wattan, Email: a.watten1308d@coeng.uobaghdad.edu.iq, Name: Mohammed Salih Aljwad, Email: 

mjawad@coeng.uobaghdad.edu.iq  

IJCPE is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. 

 

Normalize and De-Normalize of Relative Permeability Data for 

Mishrif Formation in WQ1: An Experimental Work 

 
Ahmed Radhi Wattan and Mohammed Salih Aljwad 

 
Petroleum Engineering Department – College of Engineering – University of Baghdad 

 

Abstract 

 
   In many oil-recovery systems, relative permeabilities (kr) are essential flow factors that affect fluid dispersion and output from 

petroleum resources. Traditionally, taking rock samples from the reservoir and performing suitable laboratory studies is required to 

get these crucial reservoir properties. Despite the fact that kr is a function of fluid saturation, it is now well established that pore 

shape and distribution, absolute permeability, wettability, interfacial tension (IFT), and saturation history all influence kr values. 

These rock/fluid characteristics vary greatly from one reservoir region to the next, and it would be impossible to make kr 

measurements in all of them. The unsteady-state approach was used to calculate the relative permeability of five carbonate for core 

plugs from the Mishrif formation of WQ1. The relative permeability calculated by using Johnson, Bossler and Naumann (JBN) 

Correlation, which is, consider one of the unsteady-state approach where it found that the core plugs are water wet. A normalizing 

approach has been used to remove the effect of irreducible water and residual saturations, which would vary according on the 

environment. Based on their own irreducible water and trapped saturations, the relative permeabilities can subsequently be de-

normalized and assigned to distinct sections (rock types) of the reservoir. The goal of this research is to normalize the relative 

permeability that was determined through water flooding.    

      
Keywords: relative permeability, absolute permeability normalization, de-normalization. 
 
Received on 06/07/2022, Accepted on 31/08/2022, Published on 30/12/2022 

 

https://doi.org/10.31699/IJCPE.2022.4.9  

 
1- Introduction 
 

   In the laboratory, relative permeability (kr) is assessed 

using one of two methods: steady state or unsteady-state 

studies. The unsteady-state approach takes less time than 

the steady-state method, but it has a smaller range of 

saturation change. Measuring kr in mixed-wet rocks with 

low-IFT fluids is very difficult and necessitates 

specialized equipment [1]. 

   A petroleum reservoir is a porous subsurface substance 

that traps oil, gas, or both structurally and 

stratigraphically. Fluid movement in such a porous media 

is a very difficult phenomenon to understand. The 

physical parameters of reservoir fluids must be learned in 

order to understand and forecast the volumetric behavior 

of oil and gas reservoirs as a function of pressure. 

Laboratory investigations on samples of actual reservoir 

fluids are frequently used to determine these fluid 

properties [2]. 

   Studying and analyzing a reservoir's performance 

necessitates a knowledge of the rock's physical properties 

as well as the existing interaction between the 

hydrocarbon system and the formation. 

Laboratory investigations of cores from the reservoir to be 

examined are used to determine rock attributes. The cores 

are taken out of the reservoir, causing changes in the core 

bulk volume, pore volume, reservoir fluid saturations, 

and, in some cases, formation wettability [2]. 

One of the key sources of data available to aid the 

reservoir engineer in appraising the economic viability of 

a hydrocarbon accumulation is special core analysis 

(SCAL) [1]. 

   Special Core Analysis tries to extrapolate information 

from routine measurements to settings that are more 

indicative of reservoir conditions. In order to acquire a 

better knowledge of individual well and overall reservoir 

performance, SCAL data is used in conjunction with log 

and well test data. SCAL measurements, on the other 

hand, are more expensive and are often only performed on 

a small number of samples or when a challenging 

strategic reservoir management choice needs to be made 

(e.g. to gas flood, or not to gas flood). On intact core, tests 

are performed to determine fluid distribution, electrical 

properties, and fluid flow characteristics in two and 

occasionally three phase situations. Fig. 1 shows a 

schematic diagram of common SCAL measurements [1]. 

   In general, relative permeability is defined as the ratio 

of a continuous phase's conductance in a linked passage 

occupied by that phase to the overall conductance of the 

porous material. As a result, relative permeability of one 

phase denotes the contribution of that phase's flow to the 

overall flow. However, some elements of existing phases 

are not mobile in most displacement processes, and thus 

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A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

72 

 

do not contribute to flow until they join a continuous-

flowing channel [2]. 

   As a result, there are two types of saturations in any 

phase distribution: mobile and immobile saturations, with 

only the mobile fluids contributing to flow and 

production. Rock absolute permeability, wettability, IFT, 

and hysteresis are significant characteristics that affect 

relative permeability because they control fluid dispersion 

inside porous media. The immobile fluids in the pore 

space of the rock limit the path available for mobile fluids 

to move [3]. 

 

 
Fig. 1. Schematic Diagram of Common SCAL Measurements 

 

   As a result, immobile-fluid saturation is an important 

factor to consider when determining relative permeability. 

The immobile saturation of any fluid is given as a 

function of other fluid saturations, rock absolute 

permeability, wettability, IFF, and hysteresis behavior as 

shown in Equation 1: 

 

Simmobile=Simmobile (S, K, wettability, IFT, hysteresis)              (1) 

 

   To account for the influence of irreducible water and 

trapped saturations, which would vary depending on the 

conditions, normalization procedures have been proposed 

to described the classic normalization procedure as 

follows [4]: 

 

Si normalize= (Si-Sir)/ (1-Swr-Sor-Sgr)                                     (2) 

 

i=oil, gas, water 

   Where Sin represents the normalized saturation for 

phase i, Si represents the phase saturation at any moment, 

and Sir represents the residual (immobile) saturation for 

each phase obtained at the end of displacement. 

   We presume that the kr under new conditions may be 

approximated from previous kr under different situations 

using the normalized saturation and the applicable 

irreducible and residual saturations. 

   We use relative permeability (Kr) normalization 

techniques on the experimental water-oil relative 

permeabilities in this paper. 

   In the world of petroleum technology, core analysis is a 

relatively new development. The first studies on this topic 

were conducted in the context of analyzing and planning 

secondary oil recovery via water flooding. The current 

examination of flush field sands necessitates new and 

independent interpretations of cored material data. 

The development of quick, conventional methods for 

analyzing physical properties of sandstone, such as 

permeability, porosity, and grain size, and the fluid 

content of the sand, is a priority [5]. 

   SCAL data, particularly capillary pressure (Pc) and 

relative permeability (Kr), are critical inputs to the 

reservoir simulation model, whose predictions are used to 

orient exploration and production decisions toward 

optimum productivity and maximum oil recovery [6].  

   In heterogeneous, fractured, and/or anisotropic rocks, 

whole core analysis is required to characterize porosity 

and directional permeability. For heterogeneous 

reservoirs, full core measurements are necessary because 

small-scale variability may not be effectively reflected by 

plug measurements. In heterogeneous rocks, whole core 

analysis (special core analysis) is also required for 

determining multi-phase flow parameters [1]. 

   The findings of relative permeability testing on a large 

number of reservoir rock core samples are typically 

inconclusive. As a result, relative permeability data 

collected from different rock samples must be averaged. 

The relative permeability curves should be standardized 

before being utilized for oil recovery prediction to 

eliminate the effect of variable initial water and critical oil 

saturations. Based on the required fluid saturation for 

each reservoir site, the relative permeability can then be 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

73 

 

de-normalized and assigned to different regions of the 

reservoir [7].  

   According to L.P. Dake (1979) [8], effective 

permeability plots can be adjusted by dividing the scales 

by the absolute permeability k value to obtain relative 

permeability plots. 

 

Kro(Sw)=Ko(Sw)/K                                                              (3) 

 

Krw(Sw)=(Kw(Sw))/K                                                          (4)  

 

   The experimental calculations of relative permeability 

data and compare it with another correlation makes this 

work very important to reduce the cost of doing many 

experiments in the lab. 

   The important of relative permeability data in the 

simulation models makes the normalizing and de-

normalizing methods very important where it can be used 

normalizing process to reduce the number of curves for 

relative permeability data that used in the models and to 

know the wettability of the field from the intersection 

between oil and water relative permeabilities. 

   The goal of this research is to normalize the relative 

permeability that was determined through water flooding. 

 

2- Permeability 
 

   Permeability is assessed by flowing a viscous fluid 

through a core plug with defined dimensions (A and L) 

and measuring the flow rate q and ∆p, as shown in 

Equation 5 [9]: 

 

𝐾 =
𝑞𝜇𝐿

𝐴∆𝑝
                                                                              (5) 

 

   Where: k = proportionality constant, or permeability, 

(Darcy’s), 𝜇 = viscosity (cp), q = flow rate through the 
porous medium, (𝑐𝑚3/sec), l = length of core, (𝑐𝑚), A = 
cross-sectional area, (𝑐𝑚2). 
 

   When measuring permeability, the following conditions 

must be met: 

 Laminar (viscous) flow. 

 There is no response between the fluid and the rock. 

 At 100% pore space saturation, only a single phase is 
present. 

Permeability can be classified into: 

 

2.1. Absolute permeability 

 

   The permeability measurement is sometimes referred to 

as specific or absolute permeability when the medium is 

totally saturated with one fluid. The steady-state flow 

Equation 5 is frequently used to compute absolute 

permeability [9]. 

 

2.2. Effective Permeability 

 

   The effective permeability is the permeability to a 

specific fluid when there are multiple fluids present in the 

rock pore spaces [9]. 

   When a porous media is saturated with more than one 

fluid, effective permeability is a measure of the fluid 

conductance capacity to that particular fluid. 
 

Oil 

𝐾𝑒𝑜 =
𝑞𝑜𝜇𝑜𝐿

𝐴 ∆𝑝𝑜
                                                                                          (6) 

 

Water                         

𝐾𝑒𝑤 =
𝑞𝑤𝜇𝑤𝐿

𝐴 ∆𝑝𝑤
                                                                       (7) 

 

Gas                            

𝐾𝑒𝑔 =
𝑞𝑔𝜇𝑔𝐿

𝐴 ∆𝑝𝑔
                                                                        (8) 

 

2.3. Relative permeability 
 

   When two or more immiscible fluids are present in a 

formation, each fluid tends to obstruct the flow of the 

others. The relative permeability impact is the reduction 

in a fluid's ability to flow through a permeable medium. 

In other terms, it is the ratio of a phase's effective 

permeability. For the oil phase the effective permeability 

Ko and oil relative permeability Kro given by Equation 9 

[9]: 
 

𝐾𝑟𝑜 =
𝐾𝑜

𝐾
                                                                             (9) 

 

𝐾𝑟𝑤 =
𝐾𝑤

𝐾
                                                                          (10) 

 

𝐾𝑟𝑔 =
𝐾𝑔

𝐾
                                                                           (11) 

 

   Where: K=the absolute permeability, 𝑘𝑟𝑜, 𝑘𝑟𝑤, 𝑘𝑟𝑔 is 
the relative permeability for oil, water, gas respectively, 

𝑘𝑜, kw, Kg Is the effective permeability for oil, water, gas 
respectively. 

   Effective and a number of factors influences Relative 

Permeability: 

 Saturations of fluids. 

 Rock pore space geometry and grain size distribution. 

 Wettability of rocks as shown in Fig. 2. 

 History of fluid saturation (i.e., imbibition or 
drainage). 

 

-Effect of wettability on relative permeability 
 

   The importance of relative permeability curves in 

reservoir evaluations stems from their capacity to predict 

fluid output during reservoir investigation. They found a 

connection between phase saturation and the rock's 

capacity to produce for a particular phase. These curves 

are determined through a sequence of standard 

measurements and calculations carried out in specialized 

core laboratories, typically utilizing specific forms of 

frontal advance theory. 

   The single most crucial stage in generating an accurate 

history match and properly projecting future performance 

is the production of realistic relative permeability curves. 

The engineer is frequently forced to seek analog data 

from offset rocks in the absence of relative permeability 

data, which will hopefully represent the fluid flow 

characteristics inside the reservoir of interest [9]. 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

74 

 

 
Fig. 2. Effect of Wettability on Relative Permeability 

 

3- Permeability from the Core 
 

   For a fluid of known viscosity, all laboratory methods 

for estimating permeability rely on the measurement or 

interpretation of a flow rate through and a pressure drop 

across a sample of known length and cross sectional area. 

Darcy law is then used to examine the data. In principle, 

the type of the fluid should not matter; but, when the rock 

and fluid interact, the nature of the fluid is critical. 

   The permeability measuring method can be classified 

depending on the sample type (plug or complete Demeter 

core), the fluid employed (gas or liquid), and the 

procedure used (Steady or unsteady state conditions). 

Standard laboratory analysis processes will generally 

offer reliable data on permeability of core samples, but 

the sample type affects the amount and quality of 

information that may be obtained. If the rock is not 

homogeneous, whole core analysis, will most likely 

produce more accurate results than core plug analysis 

(small pieces cut from the core) [10]. 

   Cutting the core with an oil-base mud is one procedure 

that has been utilized to improve the accuracy of the 

permeability determination. Using a pressure-core barrel 

and reservoir oil to conduct the permeability tests. 

   Overburden pressure affects permeability because it is 

an evaluation of the permeability of the reservoir rock in 

the system, which is an isotropic property of porous rock 

in some defined sections of the system, meaning it is 

directional. This factor should be taken into account in 

deep wells. Plug samples drilled parallel to bedding 

planes called Horizontal permeability (Kh) and 

perpendicular to the bedding plane called vertical 

permeability (Kv) [10]. 

   When calculating reservoir permeability, various factors 

must be addressed as possible sources of inaccuracy. 

These are the factors: 

 Because of reservoir variability, a core sample may 
not be typical of the reservoir rock. 

 It's possible that core recuperation isn't complete. 

 When the core is cut or dried in preparation for 
analysis, the permeability of the core may be altered. 

When the rock contains reactive clays, this problem 

is more likely to arise. 

 The sampling procedure could be skewed. There is a 
strong tendency to analyze only the best portions of 

the core. 
 

4- Experimental Materials and Setup 
 

4.1. Materials 
 

   All investigations used reservoir crude oil from the 

Mishrif formation in the WQ1 field. To eliminate any 

possible solid particles, the oil was filtered using a 5.0-lm 

filter paper (using a vacuum pump). At room temperature 

of 25 oC, the oil density and viscosity are 0.9 g/cc and 10 

cp, respectively. The high viscosity of crude oil making 

the experiments are difficult. The dead oil diluted by gas 

oil with percentage 80 % to decrease the viscosity where 

the viscosity and density of the new oil prepared are 4.5 

cp and 0.82 g/cc. 

   Formation water taken from the field that used to 

saturate core plugs and to make water-flooding 

experiments. The salinity of formation water is 180 

Kppm. The composition of formation water as shown in 

Table 1. 

   For the experiments, five core samples were used. XRD 

(X-Ray Diffraction) examination revealed that samples 

were primarily composed of calcite, which accounted for 

more than 97 percent of the rock's mineralogy. The 

permeability of the cores ranged from (6.02-143 mD), 

with porosities ranging from 15 to 25%. Table 2 shows 

the petrophysical parameters of the core. Each core is 1.5 

inch (3.81 cm) in diameter and varies in length between 

(7.09-7.3 cm). 

 

Table 1. The Analysis Composition of Formation Water 
Example Column(A) 

Water injected Formation water 

component ppm 
Cl 96205 

So4 650 

Na 50089 
Ca 12390 

Mg 3736 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

75 

 

Table 2. Core Dimensions and Petrophysical Properties  

sample Length(cm) 
Pore 

volume,cm3 
Porosity,% 

Permeability 

,mD 

1 7.3 12.91 16.06 7.597 
2 7.25 13.28 16.62 143.7 

3 7.3 17.71 22.01 8.583 

4 7.09 18.22 23.39 6.02 
5 7.25 17.83 22.42 6.375 

 

   XRD was test before injection for limestone core 

sample as shown in Fig. 3 for the plug 4. From XRD test 

we notice that the mineral composition for limestone plug 

4 is CaCO3 (calcite) with percentage 97% and SiO2 

(Quartz) with percentage 3%. 

 

 
Fig. 3. XRD for the Plug 4 

 

4.2. Core Saturation Procedure  

 

   The following procedure applied to saturate the core 

plugs and calculate the absolute permeability: 

1. Cleaning the core plugs by using toluene or methanol 

in the soxhlet extraction device [11]. 

2. After placing the cores in the desiccator, a vacuum was 

applied for one hour to eliminate any remaining air. 

3. In the desiccator, drops of formation brine were 

administered until the formation brine filled the cores 

inside the beaker. 

4. Set the vacuum pump to remove all potential air from 

the core for 6 to 8 hours. 

5. The cores were vacuum-sealed and kept in the 

desiccator for two days. 

6. The pore volume was calculated using the weight 

difference (wet weight -dry weight) and brine density. At 

this point, the porosity may be computed. The computed 

pore volume and porosity are presented in Table 2. 

 

5- The Methodology 
 

 Relative Permeability Calculations  
 

   Following the completion of the flooding sequence and 

operations, the following approach was used to collect all 

of the necessary data for relative permeability estimates 

[12]. 

 

 Johnson, Bossler and Naumann (JBN) Correlation 
 

   A three-step process may be summarized as follows: 

Equation 12 provides the injection of pore volume 

 

𝑃𝑉𝑖𝑛𝑗 =
𝑊𝑖

𝑃𝑉
                                                                       (12) 

 

   Where: 𝑃𝑉𝑖𝑛𝑗 = Pore volume injection, Wi = Water 
injected in total, cc. 

   Equation 13 of the Welge technique calculates average 

water saturation at the outlet face of rock samples. 

 

𝑆𝑊𝑎𝑣𝑔 = 𝑆𝑊𝑖 +
𝑁𝑃

𝑃𝑉
                                                                          (13) 

 

   Where: Np = Oil production through time, Swi= Initial 

saturation with water, fraction, Sw avg= the average 

water saturation of the rock samples' outflow face, 

fraction. 

   Welge demonstrated that displacing phase saturation 

downstream at the core's end (Sw2) is related to average 

displacing phase saturation (SWavg), fractional flow of 

the displaced phase (oil), and injected pore volume as in 

Equation 14. 

 

𝑆𝑤2 = 𝑆𝑊𝑎𝑣𝑔 − (𝑓𝑜 ∗ 𝑊𝑖)                                                             (14) 

 

   Where: Sw₂ = End-of-core saturation, fraction, fo = the 
displaced phase's fractional flow (oil), fraction. 

   For any given injection, the fractional flow of oil may 

be determined by determining the average and intercept 

saturations: 

 

𝑓𝑜 =
∆𝑆𝑤

∆𝑃𝑣𝑖𝑛𝑗
                                                                                         (15) 

 

Also, 

 

𝑓𝑤 = 1 − 𝑓𝑜                                                                      (16) 

 

   Where: fw= the displacing phase's fractional flow of 

water, fraction. 

   Darcy's Law was used to calculate the average oil 

viscosity for each pressure drop: 

 

𝜇𝑜 =
𝐾𝑜∗𝐴∗Δ𝑃𝑖𝑛𝑗

𝑞∗𝐿∗14700
                                                                                   (17) 

 

   Where: μ₀= obtained average oil viscosity, cp, Ko = 
Permeability of oil, mD, Q = Flow rate, cc/sec. 

   The average oil viscosity and the injected pore volume 

affect the effective viscosity: 

 

𝜆 = 𝜇𝑎𝑣𝑔 − (
Δ𝜇𝑎𝑣𝑔

Δ𝑃𝑣𝑖𝑛𝑗
) ∗ 𝑃𝑣𝑖𝑛𝑗)                                                          (18) 

 

   Where: λ = Effective viscosity, cp. Finally, the 

following equations are used to calculate the relative 

permeabilities: 

 

𝐾𝑟𝑜 = 𝜇𝑜 ∗
𝑓𝑜

𝜆
                                                                                     (19) 

 

𝐾𝑟𝑤 =
𝜇𝑜∗𝑓𝑤

𝜆
                                                                                      (20) 

 

6- Results and Discussion 
 

   Because absolute permeability is a significant aspect in 

the calculations of relative permeability, the absolute 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

76 

 

permeability for the five core plugs discovered after the 

saturation process with varying flow rates for larger pore 

volumes. 

 

6.1. Absolute permeability calculations 

 

   After the core plugs saturated with formation water by 

vacuum pump, the liquid permeability for the core plugs 

are calculated by injection the brine [13]. 

   Pore volume for core plug 1 is 12.91 cm3 as shown in 

Table 2. Therefore, we injected more than 1.5 pore 

volumes from the brine with injection rate 2 cm3/min to 

calculate the absolute permeability where the pressure 

stabilizes at 50 psi as shown in Fig. 4 after applying 

Darcy law the absolute permeability found 7.14 md. 

   The absolute permeability for plug 2, calculated by 

injection various rates and record pressure drop as shown 

in Fig. 5. By applying Darcy law and taking the average 

value for the absolute permeability, we calculate it 143.7 

md. 

   The same procedure for the other plugs where more 

than one pore volume injected to calculate the absolute 

permeability before relative permeability water flooding 

experiments. The absolute permeability for the plug 3, 4 

and 5 as seen in Table 3 and Fig. 6 and Fig. 7. 

 

 
Fig. 4. Absolute Permeability for Plug 1 

 

 
Fig. 5. Time Versus Pressure to Calculate Absolute 

Permeability for Plug 2 

 

6.2. Oil injection experiment 

 

   The oil injected with flowing rate 0.5 cm3/min for all 

core-flooding experiments to calculate the oil relative 

permeability and residual water saturation where the 

results seen in Table 3. The high value of residual water 

saturation for plug 2, which is 44% and low value for the 

plugs 1 and 3, which is 20%. 

 

 
Fig. 6. Time Versus Pressure to Calculate Absolute 

Permeability for Plug 3 

 

 
Fig. 7. Time Versus Pressure to Calculate Absolute 

Permeability for Plug 4 

 

6.3. Coreflood experiments 

 

   After the cores flooded with oil, the final pressure of oil 

injected recorded and stopped the injection process [14]. 

   To measure the oil and water relative permeabilities, the 

formation water injected with rate 0.5 cm3/min after the 

system pressure raised to the last pressure value from the 

oil experiment. For plug 1, the oil and water relative 

permabilities as shown in Fig. 8. Where the intersection 

between Kro and Krw is more than 50%, which mean this 

plug is water wet. 

   The same procedure for the other plugs as shown in Fig. 

9 to Fig. 12 for the plugs 2, 3, 4, and 5. Table 3 

summarize the relative permeability calculations. 
 

Table 3. Summarize of special core analysis data  
parameters Plug 1 Plug 2 Plug 3 Plug 4 Plug 5 

Swi,% 20 44 20 28.1 27.12 

IOIC,cc 10 7.92 13 13.11 13.64 

KL,md 7.514 143.7 8.45 6 6.23 
Ko,md 4.35 36.27 4.56 2.98 5.39 

Kw,md 2.46 34.92 4.16 1.87 3.19 

Krw 0.327 0.642 0.492 0.311 0.512 
Kro 0.579 0.667 0.540 0.497 0.865 

Sor,% 18 24 19.95 37.37 13.87 

NP,cc 8.311 6 10.65 8.1 11.775 
RF,% 83.11 75.76 81.92 61.78 88.71 

RF at bt,% 40 37.87 58.46 38.14 66 

wettability 
Water-
wet 

Water-
wet 

Water-
wet 

Water-
wet 

Water-
wet 

 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

77 

 

 
Fig. 8. Relative Permeability Curve for Plug 1 
 

 
Fig. 9. Relative Permeability Curve for Plug 2 
 

 
Fig. 10. Relative Permeability Curve for Plug 3 
 

 
Fig. 11. Relative Permeability Curve for Plug 4 
 

6.4. Normalization and averaging relative permeability 

data 
 

   The procedure for normalize relative permeability data. 

Step 1. Calculate the normalized water saturation Sw* for 

each core sample by using Equation: 

 𝑆𝑤 ∗=
𝑆𝑤−𝑆𝑤𝑐

1−𝑆𝑤𝑐−𝑆𝑜𝑐
                                                                               (21) 

 

Step 2. Determine the relative permeability of oil 

[(Kro)swc] and relative permeability to water [(Krw)sor] 

from the experiments as shown in Table 4 

 

 
Fig. 12. Relative Permeability Curve for Plug 5 

 

Table 4. The Relative Permeability Values at Critical 

Saturation [12] 
Plug no Plug 1 Plug 2 Plug 3 Plug 4 Plug 5 

Kro(Swc) 0.831 0.254 0.926 0.497 0.647 
Krw(Sor) 0.327 0.217 0.564 0.324 0.319 

 

Step 3. Calculate the normalized Kro* and Krw* for all 
core samples as shown in Table 4 from the following 

equations: 

 

𝐾𝑟𝑜 ∗=
𝐾𝑟𝑜

(𝐾𝑟𝑜)𝑆𝑤𝑐
                                                                  (22) 

 

𝐾𝑟𝑤 ∗=
𝐾𝑟𝑤

(𝐾𝑟𝑤)𝑆𝑜𝑐
                                                                 (23) 

 

   Where: kro =relative permeability of oil at different Sw, 

Kro(Swc)= relative permeability of oil at connate water 

saturation, Kro* = normalized relative permeability of oil, 

(krw)Soc is the relative permeability of water at the 

critical oil saturation. 

   The normalized water saturation and relative 

permeability shown in Table 5. 

 

Table 5. Normalized Water Saturation and Relative 

Permeability [12] 
Plug no 5  Plug no 6  

Sw* Kro* Krw* Sw* Kro* Krw* 

0 1 0 0 1 0 

0.433321 0.54837 0.291199 0.392409 0.222224 0.288452 

0.643981 0.264407 0.42 0.59791 0.458341 0.458341 

0.831976 0.0937 0.699048 0.658771 0.535723 0.535723 

0.930373 0.04815 0.634664 0.826436 0.021732 0.737022 

0.94 0.036113 0.7 0.928106 0.000233 0.920774 

0.96 0.001204 0.909685 1 0 1 

0.98 0.00000012 0.999308    

1 0 1    

 

Step 4: Calculate the average normalized relative 

permeability for the oil and water from the following 

equations: 

 

(𝐾𝑟𝑤 ∗)𝑎𝑣𝑔 =
∑ (ℎ𝑘 𝐾𝑟𝑤∗)𝑖𝑛𝑖=1

∑ (ℎ𝑘)𝑖𝑛𝑖=1
                                                             (24) 

 

(𝐾𝑟𝑜 ∗)𝑎𝑣𝑔 =
∑ (ℎ𝑘 𝐾𝑟𝑜∗)𝑖𝑛𝑖=1

∑ (ℎ𝑘)𝑖𝑛𝑖=1
                                                               (25) 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

78 

 

   Where: n=total number of core samples, hi= thickness 

of sample I, Ki=absolute permeability of sample i. 

Step 5. Plot the normalized values of kro* and krw* 

versus Sw* for each core on a regular graph paper as 

shown in Fig. 13. 

 

 
Fig. 13. The Normalized Values of Kro* and Krw* vs 

Sw* 

 

Step 6. Select arbitrary values of Sw* and calculate the 

average kro* and krw* by applying Equations 24 and 25 

as shown in Table 6 and Fig. 14. 

 

Table 6. The Average Relative Permeability Versus sw* 
Sw* Kroavg Krwavg 

0 1 0 

0.2 0.603367 0.134923 
0.4 0.4215 0.314 

0.6 0.312 0.4125 

0.8 0.156 0.699048 
1 0 1 

 

 
Fig. 14. Average Relative Permeability Versus Average 

sw 

 

6.5. De-normalizing the relative permeability data 

 

   Taking the average connate water saturation and 

residual oil saturation for the five core plugs where 

(Swc)avg=0.226 and (Sor)avg=0.278, de-normalize the 

data to generate the required relative permeability data as 

shown in Table 7 and Fig. 15. 

 

 

 

Table 7. Average Relative Permeability and Water 

Saturation 
Sw Kro Krw 

0.2782 0.630796 0 

0.377294 0.380602 0.047298 
0.476388 0.265881 0.110075 

0.575481 0.196808 0.144605 

0.674575 0.098404 0.245057 
0.773669 0 0.350558 

 

 
Fig. 15. Average Relative Permeability Versus Average 

sw 

 

   After normalize all relative permeability data we 

noticed that the intersection between oil and water relative 

permeabilities at water saturation 0.6 which means that 

the Mishrif formation in West Qurna-1 is water wet. 

 

7- Conclusions 

 We apply normalize technique to remove the effect 
of variable irreducible water saturation in the relative 

permeability calculations. 

 The absolute permeability is important factor in the 
calculations of relative permeability, therefore it must 

be known for different flow rates and record different 

pressure drop. 

 After applying de-normalize technique for carbonate 
core plugs of Mishrif formation, we found that 

Mishrif formation is water-wet where the intersection 

of relative permeability for the oil and water versus 

water saturation more than 50%. 

  The relative permeability curves should be adjusted 
before being used for oil recovery prediction to 

eliminate the effect of variable initial water and 

critical oil saturations. Based on the essential fluid 

saturation for each reservoir location, the relative 

permeability can then be de-normalized and given to 

distinct regions of the reservoir. 

   From relative permeability data, we noticed that the 

higher values of oil and water relative permabilities are 

0.865 and 0.642 respectively. 

 

Acknowledgment 

 

   The authors are grateful to Basra Oil Company, ministry 

of oil for providing core samples, oil and brine solutions. 

Grateful to the petroleum department use the lab and 

facilities. 

 

 



A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

79 

 

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A. R. Wattan and M. S. Aljwad / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 71 - 80 

 

 

80 

 

 
 ةنالمشرف في حقل غرب القر  ةلتكوين طبق ةالنسبي ةلبيانات النفاذي ةتعديل وتسوي

 :عمل تجريبي1
 

 محمد صالح الجوادو احمد راضي وطن 
 

 قسم هندسة النفط/ كلية الهندسة/ جامعة بغداد
 

  الخالصة
 

تشار التي تؤثر على ان مهم في الجريان هي عامل ةالنسبي ة, النفاذيفي الكثير من انظمه استخالص النفط   
لحصول ل ةمن المكمن واجراء دراسات مختبري ةتم اخذ نماذج صخري تقليديا   .ةالنفطيالمائع وتنتج من المصادر 
كل فانه توزيع ش المائعلتشبع  ةهي دال ةالنسبي ةان النفاذي ةبالرغم من حقيق .ةعلى خواص المكمن المهم

 ههذ .ةلنسبيا ةفاذي, الشد البيني, وتاريخ التشبع جميعها تؤثر على قيم النة, التبلليةالمطلق ةمسامات, النفاذيال
 الى اخرى وهذا يجعل من غير الممكن قياس جميع قيم ةبصورة كبيرة من منطق خصائص الصخرة/المائع تتغير

ماذج ن ةلخمس ةالنسبي ةالمستقرة استخدمت لحساب النفاذي غير ةالحال ةطريق .المناطق هلهذ ةالنسبي ةنفاذيال
 ةمعادل ةبواسط ةالمحسوب ةالنسبي ةالنفاذي .1-ةالمشرف لحقل غرب القرن ةكاربونيت من طبق ةصخري

Johnson, Bossler and Naumann (JBN) المستقرة وجدت ان غير  ةاحد طرق النفاذي التي تعتبر
ت لتشبعاوا ةاثير تشبع الماء غير قابل لالزاحت ةمبدا تعديل استخدم الزال بالماء. ةهي مبلل ةالنماذج الصخري

يتم  ةنسبيال ةفان النفاذي ةعلى تشبع الماء غير قابل لألزاح اعتمادا   .التي تتغير من صخرة الى اخرى  ةالمتبقي
 ةسبيالن ةاذيفالهدف من هذا البحث تعديل الن .)نوع الصخرة( من المكمن ةتسويتها وتعيينها للمقاطع الواضح

 .التي تم ايجادها خالل تجارب حقن الماء
 

 .ةالتسوي , التعديل,ةالمطلق ةالنفاذي, ةالنسبي ةالكلمات الدالة: النفاذي