The effect of carbonate reservoir heterogeneity on Archie's exponents (a and m), an example from Kangan and Dalan gas formations in the central Persian Gulf

Accepted Manuscript The Effect of Carbonate Reservoir Heterogeneity on Archie’s Exponents (a and m), an Example from Kangan and Dalan Gas Formations in the Central Persian Gulf Maziyar Nazemi, Vahid Tavakoli, Hossain Rahimpour-Bonab, Mehdi Hosseini, Masoud Sharifi-Yazdi PII:

S1875-5100(18)30436-0

DOI:

10.1016/j.jngse.2018.09.007

Reference:

JNGSE 2709

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 4 April 2018 Revised Date:

8 August 2018

Accepted Date: 12 September 2018

Please cite this article as: Nazemi, M., Tavakoli, V., Rahimpour-Bonab, H., Hosseini, M., Sharifi-Yazdi, M., The Effect of Carbonate Reservoir Heterogeneity on Archie’s Exponents (a and m), an Example from Kangan and Dalan Gas Formations in the Central Persian Gulf, Journal of Natural Gas Science & Engineering (2018), doi: https://doi.org/10.1016/j.jngse.2018.09.007. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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The Effect of Carbonate Reservoir Heterogeneity on Archie’s Exponents (a

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and m), an Example from Kangan and Dalan Gas Formations in the Central

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Persian Gulf

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Maziyar Nazemi, Vahid Tavakoli*, Hossain Rahimpour-Bonab, Mehdi Hosseini, Masoud

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Sharifi-Yazdi

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School of Geology, College of Science, University of Tehran, Tehran, Iran

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* Corresponding author, [email protected]

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Abstract

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Calculating hydrocarbon in place is one of the most important aspects to be considered in

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reservoir evaluation. Carbonate rocks with high heterogeneity, exhibit significant changes

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in petrophysical and lithological properties. Archie’s exponents (m and a) are basic

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parameters for saturation calculations. Uncertainties in obtaining these exponents lead to

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considerable errors in the saturation assessment. In this study, various pore and rock

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typing methods were carried out on a Permian–Triassic carbonate reservoir in the central

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Persian Gulf, Iran. The used methods include pore typing, pore facies classification,

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velocity deviation log, reservoir quality index, Winland R35, Pittman R35 and ranges of

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core permeability. Archie’s exponents were obtained for different classes based on

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extracted data from petrographical studies, conventional core analysis and wire line log

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data. Results showed that determination of rock types based on pore typing has the

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greatest effect on the precise determination of Archie’s exponents. On the other hand, the

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most unreliable results were related to the velocity deviation log. Pore types directly

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control the connectivity of the fluid pathways and so have the most important effect.

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Combining pore types in various groups such as velocity deviation or pore facies

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classification, reduce the measurement accuracy of Archie’s exponents and resulted water

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saturation. Finally, it can be concluded that, in addition to the high impact of pore type on

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the accuracy of the obtained exponents, the permeability and pore throat radius are less

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effective in determining the Archie’s exponents.

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Keywords: Archie’s Exponents, Water Saturation, Pore Type, Pore Facies, Rock Type

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1. Introduction Reservoir evaluation is one of the vital tasks in reservoir exploration and field

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development. In this regard, determination of some petrophysical properties such as

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water saturation has great importance. Reservoir characterization in carbonate rocks with

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enormous complexity is a great challenge. Facies changes, diagenetic processes and

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resulted porosity distributions are very complicated compared to siliciclastic reservoirs

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(Lucia, 2007; Bust et al., 2009). Considering numerous studies in the field of carbonates,

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there are still major challenges in identifying many parameters of carbonate reservoirs.

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The key point is to identify the critical link between geological heterogeneity and

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reservoir quality and performance (Chilingarian et al., 1992; Jodry, 1992; Wardlaw,

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1996; Serag et al., 2010; Hamada et al., 2013). Heterogeneity in these reservoirs

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complicates the task of description and interpretation. Carbonate rocks are specified by

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complexity in pore type and pore size distribution, which results in wide permeability

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variations for the same porosity, making it difficult to predict their production ability.

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Calculating water saturation (Sw) is one of the most important tasks in formation

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evaluation. The accurate estimation of Sw and thus hydrocarbon in place is critical to

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diminish the uncertainty of financial forecasting and in developing an oil or gas field. The

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Sw is calculated using Archie’s equation (Archie, 1942) in most cases. This equation

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determines the Sw based on the porosity (Ø), resistivity of the formation (Rt), formation

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water resistivity (Rw), cementation (m) and saturation (n) exponents. It is expressed as:

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Sw =


 ∅ 

(1)

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Cementation exponent represents insulating minerals that reduce the conductivity of the

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formation fluid. Saturation exponent expresses the effect of desaturating the sample or

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replacing of formation water with non-conductive hydrocarbons. The accuracy of the

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water saturation calculation depends on the accuracy of the Archie’s parameters (Rezaee

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et al., 2007). These parameters have been the subject of many studies. It has shown that 2

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the use of inaccurate values for the Archie’s parameters has significant effects on

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Formation Resistivity Factor (FRF) as well as Sw calculations (Hosseini-nia and Rezaee,

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2002; Rezaee et al., 2007). In a routine formation evaluation, m and a are assumed

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constant for a given reservoir rock. It is a common practice to obtain m by assuming a

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constant value for a and calculating m for each sample. Rocks, mainly carbonates, display

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complex pore structures, which significantly affect their electrical resistivity. Since

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physical properties of these rocks may vary significantly from one sample to another, m

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and a values cannot be considered constant (Rezaee et al., 2007). Generally, the fixed

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value of m can be estimated by using cross-plot of porosity versus FRF that can be

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obtained by rock core resistivity measurement (Borai, 1987; Deborah, 2002; Liu et al.,

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2011). Accordingly, the value of m is considered to represent the characteristics of the

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cementation exponent of the reservoirs and is used for reliable estimation of water

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saturation (Qin et al., 2016). In heterogeneous reservoirs, the fixed m cannot be used to

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describe the cementation exponent characteristics; because it will overestimate or

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underestimate the water saturation (Mao et al., 1995; Rezaee et al., 2007; Shi et al.,

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2008). Thus, the variable m is more appropriate to describe the cementation exponent

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characteristics and to calculate water saturation in most of reservoirs, especially

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carbonates (Rasmus, 1983; Tabibi and Emadi, 2003; Xiao et al., 2013). Archie’s

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exponents and their effect on water saturation calculations have been studied by

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numerous researchers (e.g. Rasmus, 1983; Focke and Munn, 1987; Tabibi and Emadi,

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2003; Rezaee et al., 2007, Salazar et al., 2008, Mahmood et al., 2008, Xiao et al., 2013;

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Wang et al., 2014; Qin et al., 2016, Glover., 2017). Rock typing approach is the most

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appropriate method to reduce reservoir heterogeneities (Tiab and Donaldson, 2012).

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Determining the rock types is a method for the classification of reservoir rocks according

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to their ability to conduct and store fluids (Ahr, 2008, Rahimpour-Bonab et al., 2012,

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Aliakbardoust and Rahimpour-Bonab, 2013, Skalinski and Kenter, 2014). Focke and

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Munn (1987) showed that different rock types have different m values. Therefore, it is

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necessary to classify the rocks according to their petrophysical properties and consider

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distinct Archie’s exponents for each rock type.

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In this research, seven different rock and pore typing approaches have been used for this

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purpose including Velocity Deviation Log (VDL), core permeability ranges, Reservoir

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Quality Index (RQI), pore typing, Winland and Pittman equations and pore facies

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classification. Afterward, Archie’s exponents (a and m) were calculated for each rock

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type and the results were compared with each other.

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2. Geological Setting and Stratigraphy

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In the central part of Persian Gulf (Fig. 1), Permian–Triassic sedimentary rocks include

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Faraghan (Early Permian), Dalan (Late Permian) and Kangan (Early Triassic) formations

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(equivalent to Khuff Formation in Arabian nomenclature). The Faraghan Formation with

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a thickness of 200 to 420 meters and siliciclastic lithology is located on the Devonian

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sandstone (Zakin Formation) and is covered by the Dalan Formation (Aali et al, 2006)

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(Fig. 2). The Kangan and Dalan formations were deposited in a seaward region on a ramp

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with gentle slope and very low siliciclastic sediments supply along the passive margin of

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the Arabian plate. Limestone, dolomite and evaporite are the main constituents of these

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carbonate units, which represent their deposition in a shallow marine environment

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(Kashfi, 1992; Alsharhan and Narin, 1997; Ehrenberg et al., 2007; Esrafili-Dizaji and

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Rahimpour-Bonab, 2009; Rahimpour-Bonab et al., 2010). In the studied field,

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hydrocarbon is hosted by the upper Dalan and Kangan formations. Dalan Formation with

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a thickness of more than 680 m is located on the Faraghan Formation with an erosional

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discontinuity and is divided into four reservoir units including K5, middle anhydrite (Nar

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member), K4 and K3 from bottom to top, respectively. The K5 is separated by a 30-meter

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evaporite from the K4 unit. K4 with lithology of dolomite, lime and a little bit of

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anhydrite is the main gas reservoir. This unit is separated from the upper member (K3) by

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two anhydrite layers. The K3 member is composed mainly of dolomite and dolomitic

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limestone. Kangan is divided into K2 and K1 reservoir units, from bottom to top (Fig. 2).

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A regional discontinuity separates the Triassic K2 sediments from the Permian K3 in

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southern Iran (Kashfi, 1992; Rahimpour-Bonab et al., 2009; Tavakoli, 2015;

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Abdolmaleki et al., 2016; Tavakoli and Jamalian, 2018). The Kangan Formation is about

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193 meters thick and consists of lime and dolomite with anhydrite interlayers. Dashtak

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Formation is the cap rock for this reservoir (Aali et al., 2006; Rahimpour-Bonab, 2007).

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One of the important features of the Dalan and Kangan formations is the centimeter-scale

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lithology variations, which is the result of facies and diagenetic changes (Rahimpour-

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Bonab, 2007). Changes in the facies and different diagenetic processes such as

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cementation, dolomitization, dissolution and compaction have had great effects on these

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reservoirs.

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3. Materials and Methods

Our dataset includes 58 core plug samples for FRF tests in about 300 m cores, a total of

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1300 porosity and permeability data, 1306 thin sections and wire line log data in about

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326 m, which were studied from the pay zones of a single well in one gas field in the

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central Persian Gulf. Samples were selected from 1990 m to 2317 m in a well with K1

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and K2 (Kangan Formation), K3 and K4 (Dalan Formation) units. For recognizing calcite

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from dolomite, thin sections were stained by alizarin red-S and half of the samples were

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impregnated by blue-dyed epoxy to exhibit pore types, textures and grain size. Choquette

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and Pray (1970) classification scheme was used for pore typing in thin sections

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petrography. Comparison charts were used to determine the total porosity and the

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percentage of each pore type in thin sections. Core plug samples were cleaned with

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Soxhlet extraction method, dried and used to measure the porosity and permeability by

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means of Boyle’s and Darcy’s laws, respectively. VDL was calculated by neutron-density

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data from wire line logs using Anselmetti and Eberli formula (Anselmetti and Eberli,

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1993) for better perception of entire distribution of pore type in studied units. Pore facies

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were determined based on ternary plot for pore types and pore facies classification of

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Kopaska-Merkel and Mann (1993) (modified by Tavakoli et al., 2011).

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The electrical resistivity of the brine saturated core plugs was measured at ambient

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conditions. The FRF at ambient conditions was calculated using the following

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relationship:

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= 

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(2)

Where:

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Ro = resistivity of the 100% saturated core plug, Ω.m

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Rw = resistivity of the formation brine, Ω.m

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A composite graph of log FRF versus log porosity was made for the suite of samples. The

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line of best fit through the data points was determined with the least squares regression

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method. The gradient of the resulting line is considered as porosity exponent “m” in

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accordance with Archie’s formula:

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FRF= Ø

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(3)

Where:

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a = intercept with the Y-axis, (a=1 when the line is fitted through (1, 1))

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m = porosity exponent (or cementation exponent)

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Ø = porosity (fraction)

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FRF = Formation Resistivity Factor

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The correlation of determination (R2) and coefficient of variation (CV) were used for

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evaluating data heterogeneity within each sub-class of samples. The R2 shows the degree

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of variation in dependent variable which is explained by all the independent variables

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together. CV is the ratio of standard deviation to mean of the samples and show the data

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scattering around the mean.

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4. Results

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In the following sections, different observations for various pore and rock typing

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approaches are explained to find the most accurate relationship between porosity and

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FRF.

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4.1 FRF and Porosity of All Samples

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The relationship between FRF and porosity for all core plug samples demonstrates a low

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R2 and data shows significant scatter (Fig. 3). In order to decrease heterogeneity, different

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rock typing methods were investigated.

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4.2 Pore Types

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Unlike single homogeneous porosity system of a sandstone reservoir (mostly

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intergranular), carbonates usually have a multi-porous systems, which typically cause

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petrophysical heterogeneity in these reservoirs (Mazzullo and Chilingarian, 1992). The

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various pore types in studied intervals of the Kangan and Dalan formations include 1-

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interparticle 2- intraparticle 3- moldic 4- intercrystalline 5- vuggy 6- fenestral and 7–

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fracture (Fig. 4). Among all specified pore types, moldic, interparticle and intercrystalline

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pores are the main pore systems and fracture, vuggy and fenestral are less frequent (Fig.

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5). Five classes were determined for classifying pore types, including 1-interparticle 2-

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moldic 3-intercrystalline 4-vug and 5-fracture. Accordingly, the values of FRF plotted

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versus porosity for each pore type. Every single pore system represents particular

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Archie’s exponents with specific Archie equation (Table. 1) (Fig. 6, for example)

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4.3 Pore Facies

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Pore facies (PF) designation is a new method for classifying reservoir rocks, which is

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based on pore system characteristics (Ahr, 2008). Pore facies encompass particular

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characteristics such as fluid-flow, pore-throat size distributions and reservoir properties

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for various reservoir rocks. Generally, pore facies are defined by considering several pore

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types but they also may comprise only single pore type (Bahrami et al., 2017). In studied

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units, the identified pore facies were categorized in three main groups according to

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Tavakoli and his co-workers (Tavakoli et al., 2011) (Fig. 7). These groups include 1-

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primary or sedimentary pores (interparticle, intraparticle and fenestral); 2- fabric selective

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pores (moldic and intercrystalline formed by fabric retentive dolomitization); and 3- non-

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fabric selective pores (vuggy, cavernous, fracture, channel, and intercrystalline formed by

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fabric destructive dolomitization). Generally, 6 pore facies were determined, whereas 3 of

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them are more abundant (pore facies4> pore facies2 > pore facies 1) in studied units. PF

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1 forms volumetrically up to 70 % by the depositional processes, which is called

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depositional pore facies. In this group, observed pores include interparticle, intraparticle

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and fenestral, which are less affected by diagenetic processes. Pore spaces in pore facies

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2 are consist of 30 to 70 % of the depositional and fabric selective diagenetic pores.

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Indeed, this pore facies includes petrophysical attributes of both pore facies 1 and 4. Pore

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facies 3 is composed of PF1 and PF6, which is a mixture of pore facies analogous to pore

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facies 2. In this group, between 30 to 70 % of pores are non-fabric selective or

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depositional pore types. PF 4 volumetrically is composed of more than 70 % of

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diagenetic fabric-selective pores (moldic and fabric-retentive intercrystalline), which is

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called fabric selective pore facies. In PF 5 about 70 % of pores have diagenetic origin and

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fabric-selective and non-fabric-selective pores form about 30 to 70 % of this PF. This PF

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is determined as mixture of PF4 and PF6 properties. PF 6 is called non-fabric-selective

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pore, which over 70 % of its pores are non-fabric-selective. This pore facies includes

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vuggy, cavernous, fracture, stylolitic, and fabric-destructive intercrystalline pore type.

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Cementation and tortuosity factors (a and m) were obtained by drawing FRF versus

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porosity for each pore facies (Table. 2) (Fig. 8, for example).

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4.4 Reservoir Quality Index (RQI)

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Pore geometrical properties are the main factors controlling fluid flow parameters of

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reservoir rocks. The Reservoir Quality Index (RQI) (Amaefule et al., 1993) defines these

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parameters. Practical parameters such as RQI assist to estimate and assess the reservoir

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quality by using the incorporation of porosity and permeability data. Reservoir rocks can

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be classified into homogenous classes using RQI in reservoir studies (Amaefule et al.,

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1993). The concept of Amaefule et al., (1993) method is based on the calculation of RQI,

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defined as follows:

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RQI = 0.0314/Ø

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(4)

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Where RQI is reservoir quality index (µm), K is permeability (mD), Ø is porosity

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(volume fraction) and 0.0314 is the conversion factor. Log-log cross plot of RQI versus

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PHIZ values is shown in Fig. 9. Minimum, mean and maximum values of calculated RQI

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for studied well were calculated (Table. 3). Based on all collected core plug samples in

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studied intervals, 3 rock types with different RQI range values (0.2 to 0.5, 0.5 to 1 and 1

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to 2) were classified. By drawing FRF versus Ø for each rock type, m, a, R2 and

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equations were obtained (Table. 4) (Fig. 10, for example).

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4.5 Velocity Deviation Log (VDL)

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Anselmetti and Eberli (1999) introduced Velocity Deviation Log (VDL), which is known

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as a procedure for recognizing the main pore systems in carbonate reservoirs. The VDL is

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calculated from incorporating sonic log with neutron porosity or density log. The

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discrepancy between the velocity calculated from the actual sonic log and that from a

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synthetic velocity log is defined and plotted as VDL, which is calculated by converting

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porosity log data to a synthetic velocity log in the time average equation (Wyllie and

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Gardner, 1956):

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  ∅

∅

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VP = Vpreal – Vpsyn

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(5)

(6)



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Where VPreal is real compressional velocity and VPsyn is synthetic compressional velocity.

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Various rock physical properties of the different pore types cause different deviations,

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hence deviations are the consequence of the diverse velocity at certain porosity (Tavakoli

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et al., 2011). In general, positive deviation zones are characterized by pores within a 9

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dense, cemented matrix, where the pores are not commonly connected (Anselmetti and

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Eberli, 1999). Zones, with low permeability values are illustrated with positive deviation.

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Unlike the zones with positive deviation, zones with small deviation are commonly well

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connected and yield moderate to high permeability (Anselmetti and Eberli, 1999).

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Usually zones with small deviations illustrate the abundant of interparticle or high

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microporosity. In zones with constant negative deviation, factors other than lithology,

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control these velocity deviations. Three feasible reasons including caving or irregularities

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of the borehole wall, fracture porosity and high content of free gas explain negative

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deviation. The VDL was generated by combination of porosity from density and neutron-

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porosity logs in the studied intervals. Logs were corrected for the effect of gas as well as

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bad-hole intervals before analysis. As can be seen, the zero and positive deviations in the

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studied well are much higher, while zones with negative deviations are rarely observed

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(Fig. 11).

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Based on the classification of the deviation ranges of VDL, five rock types were defined

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including 0-500, 500-1000, 1000-2600, -500-0 and -500-(-1000). Values of FRF and Ø

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were depicted against each other for obtaining cementation factor (m), tortuosity factor

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(a) and R2 for each type of rock (Table. 5) (Fig. 12, for example).

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4.6 Winland R35

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Winland used mercury injection capillary pressure (MICP) curves to develop an

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empirical relationship between porosity, permeability, and pore throat radius for reservoir

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rocks. Winland’s experiments revealed that the effective pore system that dominates flow

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through rocks in his set of samples corresponded to a mercury saturation of 35%. No

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satisfactory explanation has been presented to explain why this relationship is 35%, but it

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corresponds to a mean pore throat size of 0.5 µm in the Winland samples. Winland

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developed the following empirical relationship between porosity, air permeability, and

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pore throat size corresponding to a mercury saturation of 35% using sandstone and

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carbonate samples:

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Log R35 = 0.732 + 0.588 (Log Kair) – 0.864 (Log Ø)

(7)

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Where K is the uncorrected air permeability (in millidarcies), Ø is the porosity (volume

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fraction), and R35 (expressed in microns) is the pore throat radius at 35% mercury

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saturation from a mercury injection capillary pressure test. Porosity and permeability

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values were depicted against each other on log-log cross plot and rock typing was carried

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out based on Winland R35 method (Fig. 13).

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Considering the location of each core plug sample in different ranges of pore throats, five

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rock types were determined based on Winland R35 method. FRF and porosity values

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were drawn against each other to acquire m and a exponents for each rock type. To check

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the accuracy of the obtained exponents for each rock type, R2, CV and equations were

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also considered (Table. 6) (Fig. 14 for example).

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4.7 Pittman R35

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Pittman (1992) tested the Winland method on samples corrected for gas slippage from

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clastic reservoirs (sandstone). These sandstone formations vary in composition, texture,

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and structure. Pittman improved the Winland method by developing a technique to more

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accurately define modal pore aperture. The Pittman equation for pore throat size at 35 %

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non-wetting phase saturation (R35) is as follows:

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Log R35 = 0.255 + 0.565 (Log Kair) – 0.523 (Log Ø)

(8)

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In the Pittman R35 equation, uncorrected air permeability (Kair) is given in millidarcies,

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porosity (Ø) is in volume fraction, and R35 is expressed in microns. Porosity versus

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permeability values were plotted on log-log cross plot and rock typing was carried out

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according to Pittman R35 method (Fig. 15).

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According to the classification of reservoir rocks by Pittman method, five rock types

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were determined. FRF and porosity, which were previously obtained for each core plug

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sample in ambient conditions, were plotted against each other for acquiring cementation 11

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and tortuosity factor for each rock type. The results are plotted in Table. 7 and Fig. 16,

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for example.

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4.8 Ranges of Permeability

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Classification of core plug samples was carried out according to their permeability

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categories to assess the effect of permeability on the FRF-porosity plot. The permeability

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classes were defined as: 0.01
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porosity versus FRF was drawn for 4 rock types. The m, a, R2, CV, and the equation for

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each rock type are exhibited in the Table. 8 and Fig 17, for example.

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Plot of R2 vs CV for all sub-classes (Fig. 18) shows a negative correlation. Such

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correlation demonstrates that the pore typing methods (pore type and pore facies) have

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the lowest CV. All CVs also show a general negative correlation with R2 which also

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confirms the validity of both.

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5. Discussion

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Archie’s parameters are often controlled by the pore and rock texture characteristics such

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as lithology and physical and chemical attributes of the rock, which alter gradually in

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both vertical and horizontal directions (Nabawy, 2015). Relatively high values of

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cementation exponents are usually found in carbonate rocks, where pore spaces are not

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well-connected (Glover et al., 1997; Tiab and Donaldson, 2012). The observed

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relationship between FRF and porosity for all samples indicates a relatively low R2 (0.57)

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(Fig. 3). Among the five classes specified, the fracture porosity with higher correlation of

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determination (R2=1), vuggy (R2=0.99) and intercrystalline porosity with R2 of 0.91,

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provide the most accurate answers. In the process of sample selection for special tests in a

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core analysis project, fractured samples are removed because the fluid pass through the

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fracture and not the matrix. So, the very high R2 for the fractured class is due to the low

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number of samples. The lowest R2 is related to the samples with interparticle porosity.

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The average of R2 obtained for these 5 classes is 0.81. The determined rock types based

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on considered pore facies in the formation, show a lower R2 than the pore types. The

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highest R2 belong to the pore facies 6 (0.98), then the pore facies 4 (0.74), the pore facies

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1 (0.54) and the lowest R2 belongs to the pore facies 2. The reason for the diminution in

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the R2 of pore facies in comparison with the pore types is that each pore facies has at least

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a subset of two pore types, which makes it possible to differentiate effective parameter in

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obtaining Archie’s exponents. The average of R2 obtained for all determined classes with

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respect to pore facies is 0.67, which is lower, compared to the rock types marked with

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pore types. The CV also shows the lowest values for these two methods. Three classes

348

were identified in determining the rock types by RQI method. The best correlation of

349

determination belonged to classes 1 (RQI 0.2-0.5), class 3 (1 to 2) and class 2 (RQI 0.5-

350

1), respectively. It can be considered that decreasing RQI, increases the accuracy of the

351

obtained exponents. The mean value of R2 for the three rock types indicated the 0.63 by

352

RQI method, which is lower than that obtained from the pore types and the pore facies.

353

One of the reasons that can be considered for the low R2 obtained from RQI is that, to

354

calculate RQI permeability was involved. This indicates that the effect of pore type can

355

be greater than the impact of permeability and pore throat radius. The results of VDL

356

classification show that with increasing positive deviations in each class, tortuosity

357

exponent increases and the cementation exponent decreases. The best R2 in the

358

determined rock types is related to class 3 (VDL 1000-2600) with a R2 of 0.68. Classes 2

359

and 5 have the lowest R2. This is because of velocity deviation can vary from positive to

360

negative in intraparticle, moldic, interparticle, intercrystalline and high microporosity

361

pore types (Anselmetti and Eberli, 1999). The R2 average of the determined rock types by

362

the velocity deviation assortment is very low compared to the classification based on the

363

pore types, pore facies and RQI. This is related to the high heterogeneities in each class,

364

which are categorized from positive to negative deviations. Due to the low average of R2

365

in the classes determined on the basis of velocity deviation, acquiring Archie’s exponents

366

is unreliable by this method. The CV is 0.16 that is higher than other methods, except

367

permeability ranges. Determination of rock types using Winland R35 showed that the

368

Archie’s exponents obtained from this method can be more reliable than the two previous

369

ones (rock types specified by RQI and velocity deviation). One of the reasons for

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improving the R2 through Winland R35 method is that, in addition to using porosity and

371

permeability data, pore throat radius was involved in the calculations. By comparing the

372

correlation of determination for five rock types obtained from the Winland R35 method,

373

it can be observed that class 1 and class 5 have the highest values and the exponents (a,

374

m) are more reliable than the other determined classes (RQI, VDL and pore facies). The

375

lowest R2 and highest CV belong to the third class (0.19 and 0.20 respectively). With

376

increasing Winland value, the pore throat radiuses also increase, while for more accurate

377

evaluation, the permeability, porosity, and pore throat radius should be considered. The

378

mean R2 obtained for this method is 0.74, which is more reliable than RQI, VDL and

379

pore facies, but still less than pore types. In Pittman R35 method, class 5 has the highest

380

correlation coefficient (R2 = 0.99), and among other classes determined by the Pittman

381

R35 method, it has the maximum permeability and pore throat radius. The lowest

382

coefficient of determination (0.59) belongs to class 2 (Pittman 0.2-0.5). The average R2

383

obtained from this method is 0.74, which is higher than the mean coefficient

384

determinations obtained by Winland R35, pore facies, VDL, RQI, but still lower than the

385

average R2 (0.81) obtained from pore type. Finally, determination of rock types were

386

carried out based on the core permeability and four classes were specified. The best and

387

weakest correlation determinations are respectively for class 1 (permeability of 0.01-0.1)

388

and class 3 (permeability of 1-10). The mean R2 was acquired from the total classes was

389

0.71, which is more reliable than classified rock types based on Winland R35, VDL, pore

390

facies and less reliable than pore type and Pittman R35. In previous studies Rezaee et al

391

(2007) showed that for heterogeneous carbonates with complicated pore network, the

392

relationship between FRF and porosity is not straightforward. The other results of their

393

research were that the classification of rocks based on petrofacies, permeability and flow

394

zone indicator (FZI) is insufficient to acquire precise values for m and a. Xu and White

395

(1995) performed one of the basic studies that compared petrophysical characteristics

396

(porosity versus velocity) to extract an acceptable model (Xu-White model). One of the

397

results was that, the pore geometry (pore aspect ratio) can explain most of the scatter in

398

the porosity-velocity relationship. Kazemzadeh et al (2007) concluded in their study that

of

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cementation exponent in the Archie equation is strongly dependent on pore type. They

400

stated that by classification of carbonate rocks into the texture-porosity types, the

401

obtained R2 from FRF versus porosity is considerably increased. Other issue that

402

Kazemzadeh and his co-worker (2007) found in their study was that, by increasing the

403

value of velocity deviation, a decreases and the m increases, which is entirely the

404

opposite of the result obtained in this study. Nabway (2015) concluded in his study that

405

the major variation of both a and m were due to their dependence on several factors,

406

including porosity, permeability and formation factor. He stated that the m is often

407

dependent on the pore volume and elongation pore fabric, while the a is dependent on the

408

porosity, lithology and permeability. The overall comparison of the mean R2 were

409

obtained from the seven sorts of diverse rock typing approaches, indicate that the

410

classification based on the pore types has the most effective and more reliable results.

411

Although other approaches have somewhat values near pore types, it can finally be

412

concluded that the effect of pore types in obtaining of Archie’s exponents are more

413

accurate than other approaches. The lowest average R2 was related to velocity deviation,

414

which we can conclude that the Archie exponents obtained from this approach can’t be

415

reliable. In each designated rock type based on the difference in velocity deviation, the

416

heterogeneity of petrophysical properties, including differences in pore types,

417

permeability, pore throat radius and other related characteristics, can lead to large errors

418

in obtaining Archie’ exponents.

419

A carbonate reservoir with relatively high porosity and permeability with different pore

420

types has been considered in this study. The average porosity in the studied samples is

421

more than 10 % and they have been deposited in a carbonate ramp environment. Most of

422

the reservoir samples are grain-dominated with meteoric diagenesis. So, the method

423

should be tested in formations with different petrophysical, petrographical, environmental

424

and diagenetic conditions. Regarding the heterogeneous nature of the Permian–Triassic

425

carbonates in the central part of Persian Gulf, more studies with more FRF samples and

426

petrographical studies are required to achieve a scientific theory about a perfect method

427

of rock typing for classifying the samples according to their Archie’s exponents.

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428 429

6. Conclusions This study was performed to investigate the effect of heterogeneity on Archie’s

431

exponents. Many equations have been introduced that relate FRF to porosity with

432

constant exponents (m and a), but the classification of reservoir rocks based on various

433

parameters demonstrated that the Archie parameters are different for each rock type.

434

Archie’s exponents and the R2 obtained from the classification of reservoir rocks based

435

on velocity deviation indicated a very low and inauthentic values. So, the classification of

436

reservoir rocks based on velocity deviation can’t be a good basis for obtaining Archie’s

437

exponents in heterogeneous carbonate formations. Archie’s exponents in the Archie

438

equation are highly dependent on the pore type. The classification based on the pore

439

types resulted the highest R2 and lowest CV between porosity and the FRF in comparison

440

with the rock types specified by other parameters. Other things to consider is that, the

441

pore type has a greater impact than the permeability on acquiring the Archie’s exponents.

442

Although pore throat radius and permeability play an important role in calculating the

443

Archie’s exponents, they are not as effective as pore type on determination of Archie’s

444

exponents. After classifying according to the pore types, determining the rock types

445

based on Pittman R35 has a high R2 in obtaining Archie’s exponents. Finally, it should be

446

noted that the existence of similar pore types in each rock type has a great influence on

447

obtaining Archie’s exponents in comparison with other parameters in heterogeneous

448

carbonate reservoirs.

450

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451

Acknowledgements

452

The first author would like to thanks his fiancé (Sh. Lund. Shahedi), who gave him so

453

much morale to write this article and she has always supported him. The authors thank

454

the editor and referees for their help in improving the paper.

455

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596 597

Figure Captions

598

Fig. 1. Geographical location of the Persian Gulf and studied area. The main hydrocarbon fields and main

599

Zagros trust belt is obvious

601

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600 Fig. 2. Stratigraphy of Dalan and Kangan formations in the central Persian Gulf Basin

602

Fig. 3. Relationship between FRF and porosity for all samples. R2, a and m are obvious for all samples

605 606 607 608

Fig. 4. Photomicrographs show pore types in the Kangan and Dalan formations of the studied well. (a) fenestral porosity; (b) fracture porosity; (c) intercrystalline porosity; (d) interparticle porosity; (e) moldic porosity; (f) vuggy porosity; (g) intraparticle porosity

609

Fig. 5. Frequency of all pore types in studied well. The percentage of each pore type was determined

610

based on visual estimation in petrographical studies using comparison charts.

M AN U

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603 604

611

Fig. 6. An example of log–log cross plot of porosity versus FRF for specified pore types (moldic porosity in this example). R2, a and m are obvious

615 616 617 618 619 620 621 622 623

Fig. 7. Ternary plot for classification of pore facies and pore types by Kopaska-Merkel and Mann (1993) (extended by Tavakoli and his co-workers (Tavakoli et al., 2011)). Studied samples in considered intervals are displayed with star symbols. Determined pore facies types are shown with “PF”. The percentage of each pore type was determined based on visual estimation in petrographical studies using comparison charts.

624 625 626 627 628 629 630 631 632 633 634 635 636

Fig. 9. Log –log cross plot of PHIZ versus RQI for classifying rock type based on permeability and porosity of samples. Cut offs demonstrate the classification of samples according to the range of samples placement (Amaefule et al., 1993; Abbaszadeh et al., 1996)

TE D

612 613 614

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Fig. 8. An example of log–log cross plot of porosity versus FRF for specified rock types (PF 4 for example). R2, m and a are obvious

Fig. 10. Log–log cross plot of porosity versus formation resistivity factor for specified rock type based on RQI (0.2-0.5). R2, m and a are obvious Fig. 11. Velocity deviation obtained from a neutron–porosity log Fig. 12. Log–log cross plot of porosity versus formation resistivity factor for specified rock type based on VDL (0-(-500)). R2, m and a are obvious

22

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Fig. 13. Log–log cross plot of porosity versus permeability with Winland R35 method for classifying rock type based on permeability and porosity of samples. Cut offs demonstrate the classification of samples according to the range of samples placement (Amaefule et al., 1993; Abbaszadeh et al., 1996) Fig. 14. Log–log cross plot of porosity versus FRF for specified rock type based on Winland R35 (2-5 µm for example). R2, m and a are obvious

643 644 645 646

Fig. 15. Log–log cross plot of porosity versus permeability with Pittman R35 method for classifying rock type based on permeability and porosity of samples. Cut offs demonstrate the classification of samples according to the range of samples placement (Amaefule et al., 1993; Abbaszadeh et al., 1996)

647 648

Fig. 16. Log–log cross plot of porosity versus formation resistivity factor for specified rock type based on Pittman R35 (0.5-1 µm for example). R2, m and a are obvious

649 650 651 652 653

Fig. 17. Log–log cross plot of porosity versus formation resistivity factor for specified rock type based on core permeability (0.1-1 µm for example). R2, m and a are obvious

SC

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637 638 639 640 641 642

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Fig. 18. Cross-plot of R2 versus CV for all rock typing methods. A general negative correlation is obvious.

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Table 1. The results of Archie’s exponents calculation based on classifying pore types. R2, a, m and equations for 5 rock types are obvious. The high R2 value for fracture class is due to the low number of samples. SD: standard deviation, CV: coefficient of variation

a

m

R2

m (mean)

m (SD)

Fracture

3.95

1.14

1

1.84

Intercrystalline

14.94

0.76

0.91

Interparticle

2.18

1.74

Moldic

17.67

Vuggy Average

Equations

0.07

0.04

F= 3.95Ø-1.14

1.75

0.32

0.18

F= 14.94Ø-0.76

0.56

2.11

0.22

0.10

F= 2.18Ø-1.74

0.76

0.57

2.15

0.39

0.18

F= 17.67Ø-0.76

0.99

1.74

0.99

F= 0.99Ø-1.71

1.23

0.81

0.04 0.21

0.02

7.97

1.74 1.92

RI PT

m (CV)

0.1

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Table. 2. The results of Archie’s parameters for determined rock types based on classifying pore facies. R2, a, m and equations for 4 rock types are obvious

a

m

R

2

2.48

1.65

0.54

PF2

5.60

1.35

0.43

PF4

19.27

0.72

0.74

PF6

1.81

1.53

0.98

Average

7.29

1.31

0.67

m (SD)

m (CV)

2.10

0.23

0.11

2.19

0.27

0.12

2.07

0.44

0.21

1.79

0.08

0.04

2.04

0.25

0.12

Equation

M AN U TE D EP AC C

F= 2.48Ø

-1.65

F= 5.60Ø

-1.35 -0.72

F= 19.27Ø

SC

PF1

m (mean)

RI PT

Pore Facies

F = 1.81Ø

-1.53

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Table. 3. Minimum, mean and maximum values of calculated RQI for studied well in Kangan and Dalan formations

Min.

Avg.

Max.

0.01

0.24

8.93

AC C

EP

TE D

M AN U

SC

RI PT

Reservoir quality index RQI values

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RQI RQI (0.2-0.5)

a 0.84

m 2.26

R2 0.82

m (mean) 2.05

m (SD) 0.33

m (CV) 0.16

Equations F = 0.84Ø-2.26

RQI (0.5-1)

14.93

0.69

0.45

2.14

0.48

0.22

F= 14.93Ø-0.69

RQI (1-2)

19.91

0.53

0.64

2.17

0.22

0.1

F = 19.91Ø-0.53

Average

11.89

1.16

0.63

2.12

0.34

RI PT

Table. 4. The results of experiments for determined rock types based on classifying RQI. R2, a, m and equations for 3 rock types are obvious

AC C

EP

TE D

M AN U

SC

0.16

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Table. 5. The results of experiments for determined rock types based on classifying VDL. R2, a, m and equations for 5 rock types are obvious

a 9.28

m 1.04

R2 0.41

2.14

0.27

m (CV) 0.13

Equations F= 9.28Ø-1.04

VDL 500-1000

34.55

0.45

0.09

1.87

0.14

0.07

F= 34.55Ø-0.45

VDL 1000-2600

14.60

0.83

0.68

1.87

0.32

0.17

F= 14.60Ø-0.83

VDL 0-(-500)

14.20

0.86

0.56

2.21

0.45

0.20

F= 14.20Ø-0.86

VDL (-500)(1000) Average

38.15

0.38

0.04

2.16

0.26

0.12

F= 38.15Ø-0.38

22.15

0.71

0.36

2.05

0.29

0.14

m (SD)

AC C

EP

TE D

M AN U

SC

m (mean)

RI PT

VDL VDL 0-500

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Table. 6. The results of experiments for determined rock types based on classifying Winland R35. R2, a, m and equations for 5 rock types are presented

Winland R35 (µm) Winland R35 (less than 0.2) Winland R35 (0.20.5) Winland R35 (0.5-1)

a 19.80

m 0.77

R2 0.92

m (mean) 2.07

m (SD) 0.27

m (CV) 0.13

19.72

0.7

0.65

2.05

0.34

0.17

F= 19.72Ø

23.19

0.62

0.19

2.16

0.44

0.20

F= 23.19Ø

-0.62

Winland R35 (1-2)

12.54

0.86

0.82

2.06

0.40

0.19

F= 12.54Ø

-0.86

Winland R35 (2-5)

0.50

2.45

0.91

2.11

0.16

0.07

F= 0.50Ø

Average

15.15

1.08

0.70

2.09

0.33

-0.70

RI PT 0.16

SC M AN U TE D EP AC C

Equations F= 19.80Ø-0.77

-2.45

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Table. 7. The results of experiments for determined rock types based on classifying Pittman R35. R2, a, m and equations for 5 rock types are obvious

Pittman R35 Pittman R35 (less than 0.2) Pittman R35 (0.2-0.5)

a 19.22

m 0.79

R2 0.75

m (mean) 2.12

m (SD) 0.29

m (CV) 0.14

21.51

0.67

0.59

2.06

0.33

0.16

F= 21.51Ø

-0.67

Pittman R35 (0.5-1)

12.19

0.83

0.63

2.00

0.51

0.25

F= 12.19Ø

-0.83

Pittman R35 (1-2)

2.99

1.73

0.70

2.31

0.24

0.1

F= 2.99Ø

-1.73

Pittman R35 (2-5)

0.82

2.13

0.99

2.02

0.05

0.02

F= 0.82Ø

-2.13

Average

11.35

1.23

0.74

2.10

0.28

RI PT 0.13

SC M AN U TE D EP AC C

Equations F= 19.22Ø-0.79

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Table. 8. The results of experiments for determined rock types based on classifying core permeability. R2, a, m and equations for 4 rock types are obvious

a 53.74

m 0.30

R2 0.98

m (mean) 1.92

m (SD) 0.4

m (CV) 0.21

Equations F= 53.74Ø-0.30

Perm 0.1-1

19.11

0.73

0.62

2.03

0.31

0.15

F= 19.11Ø-0.73

Perm 1-10

12.64

0.92

0.31

2.23

0.40

0.18

F= 12.64Ø-0.92

Perm 10-100

4.94

1.12

0.89

1.91

0.31

0.16

Average

22.61

0.77

0.70

2.02

0.35

0.17

AC C

EP

TE D

M AN U

SC

RI PT

Permeability Perm 0.01-0.1

F= 4.94Ø-1.12

AC C

EP

TE D

M AN U

SC

RI PT

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Archie’s exponents in Kangan and Dalan formations in Iran considered for the first time. Various rock and pore typing methods used for considering the effect of heterogeneity. Pore typing is the best method for classifying the reservoir rocks according to their m and a exponents.

RI PT

Increasing heterogeneity decrease the accuracy of water saturation calculation in carbonate reservoirs.

AC C

EP

TE D

M AN U

SC

Reducing accuracy from pore type to pore facies and velocity-deviation log demonstrate the effect of heterogeneity.