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

Iraqi Journal of Chemical and Petroleum 

 Engineering  
Vol. 24 No.1 (March 2023) 125 – 136 

EISSN: 2618-0707, PISSN: 1997-4884 
 

*Corresponding Author:  Name: Zahraa A. Mahdi, Email: arashikeyoto21@gmail.com   

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

 

A Review on Models for Evaluating Rock Petrophysical 

Properties 

 
Zahraa A. Mahdi * and Ghanim M. Farman 

 
Petroleum Engineering Department, College of Engineering, University of Baghdad, Iraq 

 

Abstract 
 

   The evaluation of subsurface formations as applied to oil well drilling started around 50 years ago. Generally, the curent review 

articule includes all methods for coring, logging, testing, and sampling. Also the methods for deciphering logs and laboratory tests 

that are relevant to assessing formations beneath the surface, including a look at the fluids they contain are discussed. Casing is 

occasionally set in order to more precisely evaluate the formations; as a result, this procedure is also taken into account while 

evaluating the formations. The petrophysics of reservoir rocks is the branch of science interested in studying chemical and physical 

properties of permeable media and the components of reservoir rocks which are associated with the pore and fluid distribution. 

Throughout recent years, several studies have been conducted on rock properties, such as porosity, permeability, capillary pressure, 

hydrocarbon saturation, fluid properties, electrical resistivity, self-or natural-potential, and radioactivity of different types of rocks. 

These properties and their relationships are used to evaluate the presence or absence of commercial quantities of hydrocarbons in 

formations penetrated by, or lying near, the wellbore. A principal purpose of this paper is to review the history of development the 

most common techniques used to calculate petrophysics properties in the laboratory and field based primarily on the researchers and 

scientists own experience in this field. 
 

Keywords: Petrophysical Properties, Hydrocarbon, Reservoir, Shale Volume, Porosity, Water Saturation, Permeability, Petroleum Technology, 
Interpretation. 
 

Received on 12/06/2022, Received in Revised Form on 07/08/2022, Accepted on 08/08/2022, Published on 30/03/2023 

 
https://doi.org/10.31699/IJCPE.2023.1.14    

 

1- Introduction 
 

   Interpretation of well log results is one of the 

important processes for engineers and geologists to 

classify the petrophysical properties. The log data is 

important in reservoir engineering calculations, 

especially in the estimation of the reserve. The best 

interpretation for any structure of interest is influenced 

by the quality and quantity of log data available to 

analysts and the type of problem [1]. Generally, there 

are two types of data when analyzing these properties; 

instrumental methods that measure the properties vs. 

depth, which are called logs; and real samples that 

exactly represent the formation that we are dealing with, 

such as cores and cuttings [2] . The Cross plot methods 

are common means to display the effect of combinations 

of logs on lithology and porosity, and they give a visual 

idea of the type of lithology mixtures [3].  

   The quantitative estimation of a hydrocarbon unit in any 

formation requires a correct estimate of shale volume, 

which causes a blockage to the pore space and decreases 

the amount of permeability, which, as a result, decreases 

the reservoir quality [4]. There are several methods for 

calculating porosity, including laboratory testing and/or 

log data. The precision of porosity found from drill 

cuttings can be incredibly affected by the size of the 

cuttings and desaturation time [5]. Likewise, log analysis 

has been utilized for porosity determination. One of the 

significant parts in formation evaluation is the water 

saturation (Sw) that is still difficult regarding well logging 

analysis. A water saturation estimation considering 

resistivity and porosity was first proposed for clean sand 

development and was named the Archie formula. After 

that, a quantity of significant water saturation models 

emerged on traditional logging data for shale-bearing 

sands, such as the Simandoux model , modified 

Simandoux model [6], Indonesian model, total shale 

model, modified total shale model , and dispersed clay 

model , and dual water model. That leads to good results 

for clean sandstone reservoirs. For petroleum engineers, 

permeability is a main input and an important key in 

reservoir management as well as in development. For 

example, when selecting the optimum production rate for 

the field and water injection patterns [7]. Almost all 

analyses of petroleum reservoirs include a calculation of 

net pay. The total reservoir material that will flow an 

economically feasible amount of hydrocarbon under a 

specific production process is known as net pay [8]. If 

unquestioned, the significance of net pay thickness is with 

regard to hydrocarbon in situ and reserve estimation [8]. 

To differentiate between net pay intervals and non-net pay 

intervals, there isn't a standard procedure or approach, 

though. 

 

 

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Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

126 

 

2- Petrophysical Properties Determination 
Techniques 

 

   A variety of parameter techniques were applied to the 

petrophysical parameters. A brief review of these 

methods is discussed in the following subdivisions (see 

Fig. 1). 

 

 
Fig. 1. Petophysical Analysis and Flow Units 

Characterization 

 

2.1. Shale volume determination  

 

   One of the most public problems in formation 

evaluation is the impact of shale in reservoir rocks. A 

precise determination of formation porosity and fluid 

saturation in shaly sand is exposed to several uncertain 

parameters, all of which are prompted by the presence of 

shale in the pay formation. 

   To handle this issue in the shale sand reservoir. An 

integrated calculation is given to determine the exact 

value of shale volume from various shale indicator tools, 

and after that, the effective porosity is determined. can 

summarize the methods that are used to determine the 

shale volume:  

   De Witte, presented his model for dispersed shale 

considering very shaly formations. This model can be 

simplified to characterize low shale formations having 

low values of water resistivity, In light of laboratory 

research and field knowledge [9].  

   Winsaur et al., studied the ionic conductivity in double 

layers in reservoir rocks and presented a model for charge 

scattering in shaly sands. He defined the increment in the 

obvious conductivity of shale because of the way that 

clays add to the total conductivity of the rock while the 

rock structure is nonconductive [10].  

   Waxman and Smits, established the conductivity model 

of clay-bearing sandstone to explain the effects of clay 

additional conductivity. It assumes the same formation 

factor clay has a parallel conductive path to the pore 

water. The relationship can be described by the following 

equations [11]: 

 

𝐶𝑜 =
1

𝐹
(𝐶𝑊 + 𝐶𝑒𝑥 )                                                                (1) 

 

𝐶𝑒𝑥 = 𝐵𝑄𝑣                                                                          (2) 

 

𝐵 = 3.83(1 − 0.83𝑒
−

𝐶𝑤

2 )                                                            (3) 

 

𝑄𝑣 =
𝐶𝐸𝐶(1−∅𝑡)𝜌𝐺

∅𝑡
                                                                  (4) 

 

   Where Eq. 1 is an empirical equation derived from Na+ 

at 25°C, The Waxman-Smits model has the ability to 

capture the nonlinear behaviors of the saturated rock 

conductivity vs. the pore-water conductivity at low 

salinity. 

   Poupon and Leveaux, developed a Indonesia model to 

calculate high amount of shale and fresh water saturation 

the equation used the computer -  made cross plot to 

between  the water saturation (SW) and true resistivity of 

formation ,the range of shale recorded (30-70%) [12]. 

 
1

√𝑅𝑡
= [

𝑉𝑐𝑙𝑑

√𝑅𝑐𝑙𝑎𝑦
+

∅𝑚/2

√𝑎𝑅𝑤
]𝑆𝑤 𝑛/2                                                    (5) 

 

   Where; Vclay is volume of shale; Rt, formation true 

resistivity; Rw, formation water resistivity; a, tortuosity, 

ϕ, porosity; Sw, water saturation. 

   Clavier et al., developed equation was used to estimate 

shale volume from gamma ray, density and neutron-

density methods [13,14] were utilized to compute total 

and effective porosities for older rocks. Clavier neutron-

density equation [15]: 

 

𝑉𝑠ℎ𝑎𝑙𝑒 =
 𝑁𝑃𝐻𝐼𝑙𝑜𝑔−𝑁𝑃𝐻𝐼𝑚𝑎+𝑀1(𝜌𝑚𝑎−𝜌𝑙𝑜𝑔)

𝑁𝑃𝐻𝐼𝑠ℎ𝑎𝑙𝑒 −𝑁𝑃𝐻𝐼𝑚𝑎+𝑀1(𝜌𝑚𝑎−𝜌𝑠ℎ𝑎𝑙𝑒)
                                   (6) 

 

   Where: 

 

 𝑀 =
𝑁𝑃𝐻𝐼𝑓−𝑁𝑃𝐻𝐼𝑚𝑎

𝜌𝑓−𝜌𝑚𝑎
                                                         (7) 

 

   Thomas and Stieber, this strategy is used to determine 

shale distributions, sand fractions, and sand porosity. It 

was chosen to account for thin-bed properties on log 

measurements in thin sand, Fig. 2 is a geometrical 

solution of the Thomas–Stieber method for laminated 

sands and shales with sands containing dispersed and/or 

Structural shale which is a base case in this interpretation. 

The bottom vertex of the lower triangle is the dispersed 

shale endpoint where the clean sand pore is filled with 

dispersed shale and top vertex of the upper triangle is the 

structural shale endpoint where the grain of the original 

sand is completely replaced with shale [15, 16]. 

 

 
Fig. 2. Thomas and Stieber (1975) Geometrical Solution 

[7] 
 

   Fertl and Chilingarian, presented the standard Shaly 

clastic reservoir rocks commonly hold variable amounts 



Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

127 

 

of clay minerals. The basic properties of the most 

common public clay minerals vary significantly, 

including chemical composition, matrix density, 

photoelectric cross-sections, hydrogen index (HI), cation 

exchange capacity (CEC), potassium, thorium, and 

uranium (in present unit) [17]. 
  

   Mohammadhossein Mohammadlou et al., in this study, 

reservoir clay volume is calculated using fine-grained 

clastic sedimentary rocks composed of clay and pieces of 

other minerals, such as carbonates and siliciclastic. The 

NMR log is used as an easy tool to assess the veracity of 

the shale volume estimate from gamma-ray and spectral 

gamma-ray logs (most clay minerals contain variable 

amounts of water trapped in the mineral structure). In the 

lowermost reservoir region, the inconsistency between the 

shale quantities calculated by different approaches is 

substantial. SEM analysis was used to detect the 

mineralogy and mineral volume fractions in order to solve 

the problem. The SEM data was used as a reference point 

for calibrating the spectral gamma-ray log in order to 

determine the shale volume [18]. 

 

2.2. Porosity Determination methods 

 

   Porosity is the ratio of the pore or void volume to the 

macroscopic or bulk volume, and there are many types of 

porosity. The average flux in pores is associated with the 

bulk Darcy flux. It varies between 0.1 and 50%. The 

porosity is directly measured in the laboratory by 

(collecting cuttings) or from drilling data.  

 

2.2.1. Porosity measured in the laboratory by (collecting 

cutting) 

 

   Onyia, the shown relationship between UCS and 

porosity utilizes Warren's roller cone penetration rate 

model. For this situation, the UCS is determined straight 

from log and drilling data. The Onyia strategy is used on a 

variety of lithologies, including both shale and sandstone 

[19]. 

   Vojko Matko, the Stochastics Method was utilized to 

assess porosity; this method employs a very sensitive 

sensor with less uncertainty in measuring results and less 

effect from disruptive noise signals. It is much simpler 

than the helium pycnometer approach. Furthermore, no 

water is placed on the material. The soil or rock sample is 

instead immersed in water. Due to stability and long-term 

repetition, the porosity sensor employs sensitive 

capacitive-dependent crystals (40 MHz with stability of 1 

ppm in the temperature range of 5 to +55 °C). The direct 

digital method (DDM) reduces the influence of 

disturbances, which reduces the uncertainty of the 

outcome [20]. 

   Erfourth et al., this technique uses UCS data that has 

been collected from laboratory analysis on core, cast, and 

tuff samples to compute the porosity. The Onyia method 

yields much higher porosity values for low UCS sectors 

than the Erfourth method, but the Erfourth method 

becomes inexact for high UCS sectors. The Onyia 

correlation also becomes relatively constant at a UCS 

value of 100 MPa [21]. 

   D El Abassi, A Ibhi, et al., the scientists used an 

ultrasonic reflectivity technique to measure the porosity, 

tortuosity, and longitudinal ultrasound velocity of 

meteorites in this study. They measured the ultrasound 

reflection coefficient of the surface of polished meteorite 

thin plates at two oblique angles of incidence and normal 

incidence. In comparison to other existing laboratory 

procedures, determining porosity with this method is 

simple, quick, inexpensive, and non-destructive. In the 

analyzed meteorite specimens, they discovered a good 

linear association between density and porosity, as well as 

a good linear correlation between the logarithm of 

porosity and the longitudinal velocity of ultrasound. This 

suggests that the porosity of these meteorites can be 

estimated using a simple linear mathematical relationship 

based on the longitudinal velocity of ultrasonic vibrations 

[22]. 

 

2.2.2. Porosity measured in the laboratory from Drilling 

Data 

 

   Westbrook and Redmond, this study applied a single-

unit arrangement of capillary diaphragm. This technique 

provided a means to measure the bulk volume of a great 

number of particles, such as drill cuttings. This method is 

quite accurate and reduces errors present in former 

solutions to measure the porosity of drill cuttings [23]. 

   Horsund Chang et., the researchers in this study used 

the Gamma Ray method to collect data from both core 

and cuttings analyses. To create precise correlations for 

sandstone and shale porosity versus UCS and make 

correlations between the UCS and porosity in sandstone 

and shale lithologies [24]. 

   Siddiqui et al., in this study, applied (histogram-based 

analysis) techniques using laboratory tools to crush the 

plug into cuttings with various mesh sizes to show the full 

description of a carbonate core plug, and afterward, the 

cutting samples were scanned with a CT-scanner to 

determine (bulk densities and porosities)  [25]. 

   Lenormand and Fonta, in this study, the (a medical-

based CT-scan method) was re-examined and showed that 

the accuracy decreased for the cuttings with a diameter of 

less than 2.5 mm. In order to obtain consistent porosity 

from cutting with the sizes down to 0.5 mm, [26]. 

 

2.3.  Water saturation Determination methods 

 

   Water saturation dispersion is the main factor in 

formation evaluation. The right estimation of water 

saturation is required for a correct volumetric calculation, 

which is of commercial interest. Recognizing the 

difference between hydrocarbons and water involving the 

reservoir is critical. This can be done by determining the 

water saturation in the area of interest since the whole 

saturation in the reservoir is 100%. The techniques that 

are used to determine the water saturation are: 

   Archie, the associations of the electrical resistance of 

fluids in porous media and porosity were discovered. He 

converted the analysis of well logs from qualitative 



Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

128 

 

analysis to quantitative analysis by proposing the in-situ 

equations to estimate the fluid saturations. Table 1 Values 

of Archies’ parameters [15]. 

 

𝑆𝑤 = (
𝑎𝑅𝑤

∅𝑡
𝑚𝑅𝑡

)
1

𝑛                                                                      (8) 

 

Table 1. Values of Archies’ Parameter for Different 

Lithologies [27] 
Description of rocks a m 

Weakly cemented detrital rocks, such as sand 

,sandstone ,and some limestones with a porosity range 

from 25 to 45 % usually Tertiary in age. 

0.88 1.37 

Moderately well cemented sedimentary rocks 

including Sandstones and limestones, with a porosity 

range from 18 to 35% usually Mesozoic in age. 

0.62 1.72 

Well–cemented sedimentary rocks such with porosity 

in the range 5 to 25 %. 
0.62 1.95 

Highly porous volcanic rocks, such as tuff , aa ,and 

pahoehoe , with porosity in the range 20 to 80 %. 
3.5 1.44 

Rocks with less than 4% porosity , including dense 

igneous rocks and metamorphosed sedimentary rocks. 
1.4 1.58 

 

   Dunlap, in this method found the water saturation factor 

"n" can vary (from 1.18 to 2.90) based on core rock sort 

and different saturation methods [28]. 

   Dewitte, established a means to determine water 

saturation in dispersed shaly formations. The method 

known as the clay slurry model involves the clay 

dispersed in the pore space with a clean sand pore 

structure. In other words, the clay minerals in the 

formations are expected to exist in a slurry with the 

formation fluid. This model is given by the following 

equation [29]: 

 

𝑆𝑤 =
1

1−𝑞
(√

𝑎𝑅𝑤

∅𝑡𝑚
2 +

𝑞2

4
−

𝑞

2
 )                                                     (9) 

 

   Wyllie and Rose (1950), in the numerical sense, 

assumed factor (M) can range between one and infinity; 

however, it lies between (1.3 and 3.0) depending on the 

first experimental by Archie 1942 [28]. 

   Hingle, suggested the graphical solution. It is the first 

commonly used solution to solve Archie’s equation. To 

interpret this method, use a specially designed graph 

paper and look for the cementation exponent value, m, 

where the y-axis varies with that value. the hingle plot 

(Fig. 3) assume the saturation exponent and cementation 

exponent both equal to 2.0  and rewrite the Archi formula 

in form [30]: 

 
1

√𝑅𝑡
= 𝑆𝑤

1

√𝑅𝑤
∅                                                                  (10) 

 

   Keller, showed that electrical resistivity experiments 

treated sandstones. The research introduced the exponent 

"n" range in (1.5 to 11.7) depending on how the cores 

were dealt with [31]. 
 

   Dobrynin, presented with a factor (m) value, it can be 

determined as a function of lithology and pressure. 

Furthermore, the greatest variety in (m) relies upon the 

quantity of small conductivity channels in the rock [32]. 

 

 
Fig. 3. Hingle Plot [30] 

 

   Simandoux, developed a model to predict water 

saturation during the production of shaly sand. The model 

was created as a consequence of laboratory tests done on 

a physical A reservoir model made of synthetic sand and 

clay was created in the Institute of English Petroleum 

(IFP). the Simandoux still One of the most common 

models used for water saturation models and a very 

important basis for subsequent research in this field. The 

Simandoux equation [29]: 

 

𝑆𝑤 =
𝑎𝑅𝑤

2 ∅𝑚
[(

−𝑉𝑠ℎ

𝑅𝑠ℎ
) + √(

𝑉𝑠ℎ

𝑅𝑠ℎ
)

2

− (
4∅𝑚

𝑎𝑅𝑤𝑅𝑡
)]                                 (11) 

 

   Buckles, after Buckles produced this technique to 

calculate average water saturation, he concluded that the 

invention of water saturation and porosity in intervals at 

irreducible water saturation would be a constant related to 

pore surface area [6]. 

   Pickett's, this strategy is based on the Archie equation, 

which effectively used to predict main parameters (a and 

m) in clean formation and relies on a graphical plot to 

include resistivity at the water zone vs. porosity to 

approximation factor (m) from data of well logs (Fig. 4) 

[33, 30]. 

 

log 𝑅𝑡 = −𝑚𝑙𝑜𝑔∅ + log(
𝑅𝑤

𝑆𝑤𝑛
)                                               (12) 

 

 
Fig. 4. Pickett Plot [30] 
 

   Waxman and Smith, established a dual water model 

depending on the CEC of shale. The (CEC) is measured 

as the main shale properties. which is expressed in milli 

equivalent unit pore volume of pore fluids, Qv (meq/cc). 



Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

129 

 

In a general laboratory study, a saturation resistivity 

relationship for shaly formation was found that linked the 

resistivity impact of the shale to the (CEC) of the shale. 

(Waxman–Smits relationship) [34, 35]. 

   Morris and Biggs, the researchers in this research 

reached the conclusion that the porosity-water saturation 

produced was a fraction of bulk volume water, BVW. 

used as a constant (often denoted as "Buckles number"). 

This constant is used not only to classify transition zones 

from zones at irreducible saturation, but also to 

approximation permeability. A Buckles plot is a plot of 

water saturation (Sw) vs. porosity (Fig. 5). Contours of 

equal bulk volume water (BVW) are drawn on the plot. 

 Points plot on a hyperbolic BVW line where the 
formation is near immobile water if the points come 

from a reservoir with consistent pore type and pore 

geometry. 

 Points scatter on a Buckles plot where the formation 
falls below the top of the transition zone [36]. 

 

 
Fig. 5. Buckles Constant  Relates to Capillary Pressure, Fluid Distribution, Fluid Recovery and Porosity in a Reservoir 

[36] 

 

   Poupon and Leveaux, the Formulated Indonesia model 

[37];was established to remove the limitations of other 

techniques in reservoir studies when  determine water 

saturation in laminated and shaly formations The 

Indonesia model was developed by field observation in 

Indonesia, rather than by laboratory experimental 

measurement support, also does not particularly assume 

any specific shale distribution. The Indonesian model also 

has an extra feature as the only model considered the 

saturation exponent (n). This model is given by the 

following equation [29]:  

 

1

Rt
= Sw

n

2 (
Vsh

1−
Vsh

2

√Rsh
+ (

∅
m
2

√aRw
))                                                (13) 

 

   Miyairi and Itoh, depended on the Poupon et al. model 

(1971) for shaly sands to produce a method to obtain three 

shaly sand factors: a, n, and m. This strategy can be 

defined by using several crossplots, like true resistivity 

formation versus porosity (R, vs p) and true resistivity 

formation versus porosity of the shaly formation (R, vs 

cpst) [38]. 

   Ellis & Singer, found The value of (n) is measured from 

core sample data laboratory and (n) is estimated from 

slope line for resistivity index (Rt/Ro, where Ro is the 

water filled resistivity and Rt is the true resistivity) on a 

log-log scale with water saturation measurements [39]. 

   Yang Kebing, Xie Li, et al., based on Archie's formula 

and the formation invasion model, the scientists in this 

study developed a formula for calculating reservoir water 

saturation by radial resistivity ratio under the most 

extensive conditions. The use of radial resistivity ratios 

can reduce the effect of reservoir lithology and physical 

property variations on water saturation calculation. A 

power function describes the relationship between the 

radial resistivity ratio and reservoir water saturation. The 

bigger the radial resistivity ratio, the better the reservoir's 

oil bearing; the lower the radial resistivity ratio, the worse 

the reservoir's oil bearing; there is a one-to-one 

relationship between them. This approach is useful for 

evaluating low resistivity oil and high water layers [40]. 

   Dahai Wang, Jinbu Li, et al., the triple-porosity model 

was established for determining the cementation exponent 

of triple-porosity media reservoirs by merging the 

Maxwell-Garnett theory and the series-parallel theory, 

which corresponded with genuine physical-experiment 

data of rocks.They developed a new model based on the 

link between total porosity and cementation exponent m 

of a triple-porosity medium composite system with 

various combinations of fractures and nonconnected vug 

porosity. The results showed that the fractures decreased 

the reservoir's cementation exponent while the vugs rose. 

Because of the mixture of matrix pores, fractures, and 

vugs, the cementation exponent of the triple-porosity 

media reservoir varied around 2.0. The cementation 

exponent proposed in the work could reasonably predict 



Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

130 

 

the cementation exponent of the strongly inhomogeneous 

triple-porosity media reservoir [41]. 

 

2.4. Permeability Determination methods 

 

   Typically, permeability data are obtained through 

routine analysis in the field or laboratory Core analysis is 

one of the most reliable techniques to determine 

permeability, with the disadvantages of high cost and 

time-consuming. An average value of permeability could 

be obtained by well testing, which gives information on 

the extension and connectivity of the reservoir. By 

applying the (MDT) technique, more accurate 

permeability data can also be achieved. The NMR log is 

now widely used to provide a fast estimation of the 

permeability profile along the wells. The most important 

methods developed to measure the permeability are: 

   Carman-Kozeny, developed an equation to evaluate 

permeability (k). The result of this calculation was a 

mixing between Darcy’s and Poiseuille’s laws. Where 

Darcy’s law macroscopically quantifies fluid flow, 

Poiseuille’s law explains the parabolic displacement of a 

viscous fluid in a straight-circular tube. The semi-

analytical Carman-Kozeny (CK) equation does not 

correctly capture the permeability’s dependence on 

porosity because  (a) this equation has been derived for a 

solid medium with pipe conduits, rather than for a 

granular medium and (b) even if a grain size is used in 

this equation, it is not obvious that it does not vary with 

varying porosity [42, 43]. 

 

Dh =
4εV

Sv
=

4ε

(1−ε)av
=

εd

(1−ε)
                                                    (14) 

 

   Where: 

 

 𝑎𝑣 =
𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒

𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑣𝑜𝑙𝑢𝑚𝑒
                                                            (15) 

 

   Wyllie and Rose, they proposed a modification of the 

Carman-Kozeny equation to calculate permeability from 

irreducible water saturation and formation resistivity 

factor (Fig. 6). Many assumptions about their equation are 

made. Firstly, there is no variance between minimum 

water saturation and irreducible water saturation. 

Secondly, this value of water saturation is a linear 

function of the grain surface. Finally, the same tortuosity 

of the porous media exerts an influence on the electrical 

conductivity as well as on the flow of the wetting phase 

fluid [44]. 

 

K =
P∅Q

SwiR
                                                                           (16) 

 

   Where, Wyllie-Rose relationship is a generalized 

equation that requires the determination of values for the 

constants P, Q, and R to be calibrated from core 

measurements. 

   Tixier, the Tixier equation generated the experimental 

permeability equation by utilizing the Wyllie Rose 

equation. The outcomes of the Tixier equation were 

approximately similar to the permeability calculations 

from the Morris-Biggs gas equation [46]. 

   Gary and Fatt, investigated the influence of stress on 

sandstone permeability, finding that not only rock 

permeability, but also permeability anisotropy in many 

sandstones, is a function of overburden pressure, and 

permeability reduction owing to stress effect is also a 

function of the radial to axial stress ratio [47]. 

 

 
Fig. 6. Permeability Contours Drawn on Pickett Plot of 

Sandstone Data, Using a Wyllie-Rose Relationship with 

both Porosity and Irreducible Water Saturation [45] 
 

   Morris Biggs, using the Wyllie Rose equation, we 

provided permeability equations for both oil and gas 

reservoirs. The permeability obtained by Morris-Biggs in 

a completely gas saturated area (at irreducible water 

saturation) differs slightly from the permeability 

calculated by Timur. unlike the Timur model, presents the 

permeability equation for gas fields and does not require 

correlation utilizing irreducible water saturation and 

effective porosity of gas reservoirs [48]. 

 
 

𝐾1/2 = 𝐶
∅3

𝑆𝑤𝑖
                                                                      (17) 

 

   Where, C = constant, oil =250, gas =80. 

   Timur, suggested equation to estimate permeability by 

using in-situ measurements of residual water saturation 

and formation porosity. He tested several options in the 

laboratory by taking different measurements of 

permeability, porosity, as well as residual water saturation 

depending on 155 samples of sandstone that belonged to 

three oil fields. The main constraint of this equation is the 

fixed value of the cementation exponent (m), which is 

equal to 1.5 while this parameter may have other values in 

specific conditions [49]. 

   Winland, the Winland hydraulic flow unit method was 

applied on core data and produced five groups to 

predicate permeability depending on pore throat size at 

mercury saturation of 35%. used the r35 parameter, along 

with other petrophysical, geological, and engineering 

data, to identify flow units in five carbonate reservoirs, 

r35 can be computed from permeability and porosity 

measurements on core samples [50]. 

 
 

log 𝑟35 = 0.732 + 0.588 log 𝑘 − 0.8641𝑙𝑜𝑔∅                         (18) 

 

In Fig. 7, note that at a given porosity, permeability 

increases roughly as the square of the pore throat radius. 

And for a given throat size, the dependence of 



Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

131 

 

permeability on porosity is slightly less than Φ2. 

Hartmann and Coalson also They state that r35 is a 

function of both entry size and pore throat sorting and is a 

good measure of the largest connected pore throats in a 

rock with intergranular porosity [24]. 

 

 
Fig. 7. Empirical Model Based on Regression Attributed 

to Winland [51] 

 

   Coates and Dumanoir, from irreducible water saturation 

and various types of effective porosity, an experimental 

relationship for the permeability estimates of average 

gravity oil reservoirs was presented[48, 52]. 

 

𝐾1/2 =
𝐶

𝑊4

∅2𝑊

𝑅𝑤

𝑅𝑡𝑖

                                                                   (19) 

 

   Where: 

 

 C=23+465𝜌h-188𝜌ℎ2  and 𝑊 2 = (3.75 − ∅) +
1

2
(log10 (

𝑅𝑤

𝑅𝑡𝑖
) + 2.2)2 

 

   Bo Shen, et al., they devised a method for assessing 

permeability in glutenite reservoirs using well logs. This 

technique is based on the K-C model, the geometry 

equivalent parameter, and the flow porosity. Furthermore, 

the authors present a method for determining flowing 

porosity that can be employed by researchers interested in 

electrical current flow in pores. Although this method is 

more difficult than the usual permeability estimation 

method, it produces a consistent and accurate result for 

glutenite reservoirs with high variability [53]. 

 

2.5. Net pay evaluation method 

 

   Well net pay is an effective thickness that is important 

for determining flow units and objective intervals for well 

completions and stimulation programs. Thus, a section of 

the reservoir with high storability (driven by porosity), 

high transmissivity (driven by fluid mobility, which is 

defined as a ratio of permeability to fluid viscosity), and 

large hydrocarbon saturation is defined (driven by water 

saturation, Sw), The most important methods developed 

to measure net pay are: 

   McKenzie, the effective pore throat size was connected 

to show "producible and non-producible rock types." by 

the  
 𝐾

∅ 
  ratio (Fig. 8) [54]. 

   Kolodzie, to associate the permeability and porosity 

with a pore throat radius (r) equal to varied mercury 

saturations, the Winland method was developed. He 

discovered that the 35th percent, or 35 percent of the pore 

volume ("R35," where he saw the inflexion on the 

mercury injection capillary curve vs. mercury saturation), 

had the best correlation with the Spindle Field data (it 

corresponds to a 0.5 m pore throat threshold value)  [55]. 

 

 
Fig. 8. Porosity Cut off [26] 
 

   Worthington and Cosentino, summarized that the cut-

off values should be "dynamically conditioned" with a 

hydraulic parameter like pore throat radius, absolute 

permeability, or fluid mobility  [56]. 

   Jensen and Menke, the accuracy and mistakes in 

approximating multiple porosity cut-off values were 

investigated using a probabilistic approach. To calculate 

porosity cut-off values, they used a semilog porosity vs. 

permeability plot and the Y-on-X regression line. The 

regression line delivers the best results for estimating the 

net pay, while the RMA line gives the best results for 

NGR. [57]. 

   Proposed Method, this method (Based on Diffusivity 

Equation) Diffusivity equation is designed to determine 

the pressure as a function of time and distance from the 

well for a radial flow regime of slightly compressible 

fluids. 

 
∂2p

∂r2
+

1

r

∂p

∂r
=

∅μc

0.000264k

∂p

∂t
                                                                      (20) 

 

   If a net pay zone has a greater flow rate in comparison 

to the other net pay zone, we can rank the first zone in a 

higher grade in comparison to the second one. Pressure is 

an important parameter causing fluid flow in hydrocarbon 

reservoirs as it can be inferred from Darcy’s law. In the 

proposed method, division of flow rate by pressure 

difference is introduced as an index for net pay 

determination, after that, this index is calculated from 

diffusivity equation [8]. 

   Lucia, demonstrated that by plotting interparticle 

porosity against permeability in carbonate reservoirs (Fig. 

9), one could derive the type of rock fabric and detect 

pore-size classes. Additional pore types (vuggy, 

dissolution-enhanced) might modify these relationships. 

The permeability and porosity cut-off values should be 

defined based on these considerations. A unique 

permeability cut-off value based on engineering 

considerations (i.e. mainly depending on the fluid 

mobility) will lead to several porosity cut-off values 

depending on the rock fabric, i.e. the particle size [8, 58]. 

 



Z. A. Mahdi and G. M. Farman / Iraqi Journal of Chemical and Petroleum Engineering 24,1 (2023) 125 - 136 

 

 

132 

 

 
Fig. 9. Lucia Model for Porosity-Permeability 

Relationships Based on Rock Fabric [59] 
 

   Jensen and Menke, used a probabilistic approach to 

analyze the accuracy and errors in prediction of various 

porosity cut-off values. In the case where either 

determination of reservoir NGR and/or NP is obtained by 

cross-plotting surrogate quantities as Sw, Vsh, and/or φ, 

investigating the errors inherent to the regression methods 

giving log (k) vs. φ best fit lines is crucial since the 

misuse of regression methods may lead to additional 

errors. Such statistical issues related to the selection of 

porosity cut-offs based on regression lines [60]. 

 

3- Conclusion 
 

   The main scope of this paper is to provide a general 

review of the development of the field of formation 

evaluation and the available studies and applications to 

solve the problem. After reviewing a fair number of 

studies and papers on the formation evaluation studies the 

following were made: 

1. The most popular and accurate method for 
determining shale volume is the gamma ray (single 

clay indicator method) to calculate shale volume. 

This method can be used for any formation that has 

shaly layers. The factor that effects clay volume 

calculating is The hole size, which refers to a large 

volume of drilling mud, has an impact on the gamma-

ray record, and the reading can be influenced by 

environmental adjustment. 

2. Using drilling data to achieve modified porosity and 
UCS values is beneficial in various formations. The 

modifications are not only applied in sandstone and 

shale formations, but the addition of gamma ray data 

permits such modifications to be possible for 

calculating porosity in formations of varied 

lithologies. They used drilling data in combination 

with the gamma ray (a better indicator) to determine 

porosity. 

3. Water saturation factor can be computed using an 
intermediate parameter such as shale volume in 

sandstone reservoirs or directly anticipated from core 

data, well logs, or seismic characteristics. Well log 

data has been used to assess water saturation since 

1942, when the Archie formula was introduced. To 

address the issue of needed water saturation 

approximation from core analysis in previous works, 

interpretation has recently used seismic data to 

directly calculate water saturation values or estimate 

proper rock physical properties such as shale volume, 

both of which are useful in the water saturation 

estimation process. These strategies make use of 

artificial intelligence computational agents to 

discover previously unknown non-linear correlations 

between seismic properties and the reservoir property 

of interest, which in this case is the water level. 
4. There are two types of permeability approaches (non-

experimental and experimental). Some theoretic 

methods are used in non-experimental methods to 

approximate the permeability, taking into account a 

fully saturated domain (Kozeny Carman), whereas 

laboratory methods combine three types of 

classifications: capillary effects (saturated and 

unsaturated), flow regime (constant pressure and 

constant flow), and flow direction (unidirectional and 

radial); then, the mathematical model of the method 

is established, taking into account such a 

combination. 

5. The systematic use of ordinary least-squares 
regression for determining porosity cut-off values 

from permeability cut-off values may result in 

erroneous results and does not ensure good NP and 

NGR estimation. The regression line, as defined by 

Jensen and Menke, mathematically guesses the ideal 

porosity cut-off values by the use of another line, the 

Major Reduced Axis. 

 

Nomenclature 

 

(CEC)    Cation Exchange Capacity 

(Φt )      Total Porosity 

(𝜌g)       Average Particle Density of Rock 
(𝜌f)      Effective Fluid Density in Flushed (Invaded) Zone 
(𝜌mf)     A Density of Mud Filtrate 
(𝜌ma)     A Density of Matrix  
(SEM)    Scanning Electron Microscopes 

(HI)        Hydrogen Index  

(UCS)     Unconfined Compressive Strength 

(ROP)      Rate Of Penetration  

(BVW)     Bulk Volume Water  

(MDT)     Modular Dynamics Tester  

(RQI)       Reservoir Quality Index  

(HFU)      Hydraulic Flow Unit  

(NP)         Net Pay 

(NGR)      Net to Gross Ratio  

(N)           Water saturation exponent 

(M)           Cementation factor 

(r35)  The Pore Throat Radius at 35% Mercury Saturation 

(K)            Air Permeability 

(Φ)            Porosity In Percent Unit 

 

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136 

 

 
 تطور الطرق المستخدمة لتقيم الخواص البتروفيزيائيةمراجعة لمراحل 

 
 غانم مديح فرمانو  * زهراء أياد مهدي 

 
 قسم هندسة النفط، كلية الهندسة، جامعة بغداد، العراق

 
 الخالصة

 
ع طرق ، ويشمل جمياالبار النفطية المحفورة سنة في 50تحليل التكوينات الجوفية بدأ تطبيقه قبل اكثر من    

ذات  والنتائج المختبرية ساسات الجسوالتسجيل واالختبار وأخذ العينات بشكل عام. حيث يتم مناقش قيالحفر 
ه  ، بما في ذلك إلقاء نظرة على عينات السوائل التي تم اخذها من هذلصلة بتقييم التكوينات تحت السطحا

لى إاء" مصطلح يستخدم لإلشارة لتعريف مصطلح "البتروفيزي .رمن أجل تقييم التكوينات بدقة أكب التكوينات
ا كون منهاألكبر التي تت أنظمة الصخور ، بينما تتعلق الجيوفيزياء بفيزيائيةأنواع معينة من الصخور فيزيائية
ة فيزيائيعلم البتروفيزيائية للصخور المكمنية هو العلم الذي يركز على دراسة الخصائص الكيميائية وال األرض.

ت . خالل السنواالمسؤولة عن توزيع المسام والسوائل المكمنية المكونة للصخورللوسط المسامي والعناصر 
، يد من الدراسات حول خصائص الصخور، مثل المسامية، والنفاذية، والضغط الشعري ، تم إجراء العداألخيرة

عاعي اإلش لنشاط، واوالتشبع الهيدروكربوني، وخصائص السوائل، والمقاومة الكهربائية، والجهد الذاتي أو الطبيعي
ن ألنواع مختلفة من الصخور. ُتستخدم هذه الخصائص وعالقاتها لتقييم وجود أو عدم وجود كميات تجارية م
و هالهيدروكربونات في التكوينات التي تم اختراقها أو تقع  بالقرب منها. الغرض الرئيسي من هذا البحث 

 ل بناءً لحساب خصائص البتروفيزياء في المختبر والحقو  مراجعة تاريخ تطور التقنيات األكثر شيوًعا المستخدمة
  .العلماء و الباحثين في هذا المجالعلى خبرة 

 
  .، تفسيرتقنيات نفطية ،نفاذية ،مسامية، تشبع مائي، مكمن ،حجم السجيل ،هايدروكاربون  ،الخواص البتروفيزيائية :دالةالكلمات ال