The aim of this study is to assess the accuracy of nuclear magnetic resonance (NMR) method in estimating the porosity and permeability in a carbonate reservoir located in south of Iran. In this study, 26 carbonate samples were selected and common core and NMR experiments were performed. Comparison of core and NMR porosity showed that NMR method is very accurate for estimation of porosity. However, after comparison of core and NMR permeability, it was found that NMR permeability estimation cannot be used with the common coefficients since they are calibrated in the clastic reservoirs. Therefore, it is necessary to modify coefficients in the permeability models of the considered reservoirs. For this purpose, 16 samples were selected to develop the model, and 10 samples for evaluating the accuracy of the model. In this study, free- fluid and mean T models were two main models for permeability estimation using NMR method. Coefficients of the two above-mentioned models were modified in terms of maximizing the coefficient of determination of core permeability and calculated permeability using NMR permeability models. The proposed models were used to estimate permeability in 10 other samples for verifying the reliability of models. Keywords Nuclear magnetic resonance · Permeability model · Porosity · Timur-Coates model · Schlumberger Doll Research model Introduction permeability using indirect methods. Various models and relations have provided to measure the permeability based Porosity indicates the amount of pore spaces in the rocks; on other parameters of reservoir rocks such as porosity (Neu- and permeability represents the capacity of rocks to transmit zil 1994) specific surface area (Kozeny 1927), grain geom- u fl ids. Determination of the two aforementioned petrophysi - etry (Schwartz and Banavar 1989), shape of pores (Yang cal parameters have an undeniable role in evaluation of res- and Aplin 1998) and grain size (Yang and Aplin 2010). The ervoir rocks, consequently, planning for the development advantage of proposed relations is the high precision of and production of the oil field. It is not difficult to determine measurement; and their main drawback is the necessity of the porosity of rocks directly in the laboratory, and it can be having the samples and doing stringent laboratory testing. done in different ways. But determination of the permeabil- Unfortunately, in many cases, the use of these relations is ity of rocks is difficult for various reasons such as high cost, associated with serious problems for various reasons, such time consuming and lack of enough samples. Due to the as the lack of access to samples (especially in horizontal limitations of direct measurement of permeability, research- wells), high cost of doing experiments, as well as its lengthy ers around the world have made many attempts to estimate procedure. NMR technology (in laboratory and well logging) has had many applications in the oil industry from 1990 onwards, * S. M. Fatemi Aghda particularly for determining various parameters of rock and Fatemi@khu.ac.ir fluid such as porosity, fluid type, pore size distribution, and Department of Applied Geology, Faculty of Geological permeability (Kenyon 1992; Kleinberg et al. 1993; Kenyon Science, Kharazmi University, Tehran 15815-3587, Iran et al. 1995a, b; Kleinberg 1996; Straley et al. 1997; Coates Department of Geotechnic, Faculty of Civil et al. 1999; Al-Mahrooqi et al. 2003; Alvarado et al. 2003; and Environmental Engineering, Amirkabir University Westphal et al. 2005). NMR technology is able to directly of Technology, Tehran, Iran Vol.:(0123456789) 1 3 Journal of Petroleum Exploration and Production Technology measure porosity; but it cannot measure permeability accordingly. However, the T values for carbonates should directly. Therefore, a few models have been presented to be determined using NMR experiments in two modes of estimate permeability (Coates et al. 1999). NMR technol- 100% saturation and residual saturation in order the value ogy has been studied well in the sandstones; therefore, it is of producible fluid (BVM) and non-producible fluid (BVI) possible to determine different parameters such as porosity, to be determined precisely. Bulk Volume Movable (BVM), Bulk Volume Irreducible Westphal et al. (2005) classified carbonate samples based (BVI) and permeability in sandstones (Ehrlich et al. 1991; on the pore types (primary and secondary) and used TC and Chang et al. 1994; Kenyon et al. 1995a, b). However, the SDR models as unchanged, with no correction in their coef- situation is different in carbonates; and it is not possible ficients. The results showed that well-related pores (inter - to estimate parameters, in particular permeability, in these particle and intercrystalline pores) had more proper results kind of rocks. There are two main reasons for this issue. compared with unrelated or isolated pores (moldic, vugs and One is the complexities inherent in the type and structure of intraparticle pores). To achieve better results, they found the pore spaces, and the other, is the lack of sufficient study it necessary to correct the models with experimental data. on carbonates for developing permeability models through Daigle and Dugan (2009, 2011) conducted studies on laboratory experiments (Kaufman 1994; Lucia 1995; Ama- determining the correction coefficient of SDR model using beoku et al. 2001; Westphal et al. 2005). other parameters such as gamma log and physical properties Kenyon et al. (1995a, b) conducted a laboratory study of of rocks (Grain size, specific surface, porosity, magnetic sus- NMR and its relation to depositional texture and petrophysi- ceptibility, grain density, and surface relaxivity) and showed cal properties in the Thamama carbonate group of Mubarraz that the value of correction coefficient in the SDR model can field. Various models were used to estimate permeability, be determined using above methods, and thereby perme- indicating that coefficients m and n in Eqs. 3 and 4 must be ability can be estimated by SDR model, with routine coef- changed, in the first step. Second, constant coefficients of ficients. In this study, only SDR model was discussed; and these models are smaller in carbonates than in the sand- the model coefficients were announced without correction. stones. Third, NMR permeability model with parameter Samples used in the present study were mainly moldic, transverse relaxation time (T ), gives better results alone vuggy and intraparticle porosity type. It tried to do neces- compared to the Schlumberger Doll Research (SDR) model sary examinations on the accuracy of routine models used 4 2 with routine coefficients ( ⋅ T ) in samples with high to predict permeability; and if necessary, to make needed 2gm corrections and adjustments to provide an appropriate model permeability. Fourth, in the models where T parameter is for carbonate rocks with low permeability. present in a way, give better results compared to the models where only porosity contributes. Geological description Allen et al. (2001) divided carbonate samples into 4 groups based on the ratio of pore throat sorting to T and Asmari Formation tested SDR model for the estimation of permeability. The results showed that permeability was associated with the The Oligo-Miocene Asmari Formation was firstly defined square of porosity; and power of T cannot be changed as by Thomas (1950) and then by James and Wynd (1965). well. The value of correction coefficients can be consid- In its type section (Kuh-e-Asmari), the formation consists ered constant in all samples. The important point is that the of fossiliferous limestone with sandstone tongues in the reduction of value of coefficient of porosity from 4, which is lower part. Toward SW from type locality, these carbonates used in sandstones (Straley et al. 1997), to 2 in the carbon- change laterally to mixed clastic-carbonate and sandstone ates indicates that with reduced porosity, pore networks unu- facies (Ahwaz Member). In addition, a thick anhydrite unit sually have a good relation with each other. In this research, (Kalhur Member) is recognized in the south of Lurestan the free-fluid model has not been examined well, and its province within the Asmari carbonates. Depositional his- capacity to estimate permeability in carbonates has not been tory and regional stratigraphic architecture of this formation investigated. Moreover, the assumption of the impossibility are reviewed by Ehrenberg et al. (2006) and Van Buchem of changes in T can also be discussed. et al. (2010). Amabeoku et al. (2001) have conducted a research on applying Timur-Coates (TC) and SDR models in carbonate Burgan Formation rocks and setting parameters of permeability models through laboratory studies. They provided 3 relations with differ - The Burgan Formation, Lower Cretaceous (Albian) sands ent coefficients for 3 different wells; but in the model cor - and shales, is lateral equivalent of the Kazhdumi Formation rected for TC, the value of routine cutoff T (T ) (100 ms) 2 2c in the northwestern side of the Persian Gulf. The formation was used, and the values of BVI and BVM were determined and its equivalents (such as Nahr Umar Formation; Safaniya 1 3 Journal of Petroleum Exploration and Production Technology and Khafji Members) form important reservoir rock in sev - Upper and lower contacts of this formation are conformable eral supergiant and many giant oil fields (Alsharhan 1991, in many locations. It can be correlated with Minagish For- 1994; Al-Eidan et al. 2001; Strohmenger et al. 2006; Van mation in Kuwait, Habashan Formation in UAE, and Salil Buchem et al. 2010). The Great Burgan Field in the Kuwait Formation in Oman. This formation is equivalent of the has been ranked as the world’s second largest oil field (after Fahliyan Formation (Khami group) in the onshore Zagros Ghawar field) and mainly produces from the Burgan clastics. (James and Wynd 1965). The Yamama Formation and its As well as, many oil fields have been discovered from these equivalents produce oil (or represent oil show) in the South intervals in the Arabian countries (Iraq, Kuwait, Saudi Ara- Iraq, Kuwait, Saudi Arabia, Bahrain, Qatar and UAE (Nairn bia, Qatar, UAE and Oman) and also Iran (Alsharhan 1994). and Alsharhan 1997). The Burgan Formation was introduced and described first by Owen and Nasr (1958) and it consists of several tens to Sulaiy Formation a few hundred of meters of sands, shale, ooid ironstone and some limestone (Alsharhan 1994; Van Buchem et al. 2010). There are few published descriptions of the Tithonian–Val- anginian Sulaiy Formation in the literature. The formation Dariyan Formation and its lithostratigraphic equivalents are among the best source rocks in southern Iraq, Kuwait, Saudi Arabia and The Aptian-aged Dariyan Formation, known as Orbitolina southwest Iran (Beydoun 1991; Nairn and Alsharhan 1997; Limestone, is one of the most important petroleum reservoirs Saad and Goff 2006; Al-Ameri et al. 2009). Owing to geo- in the Dezful Embayment and Persian Gulf areas (Motiei logical location and formation similarity, the nomenclature 1995; Ghazban 2007). Firstly, James and Wynd (1965) used here is borrowed from the Saudi stratigraphic naming. defined this formation in the Kuh-e-Gadvan. The forma- The Makhul and Garau Formations are lithostratigraphic tion belongs to the Khami Group and composed mainly of equivalents of this formation in the Arabian and Iranian ter- Orbitolina-rich carbonates. This formation has been divided ritories, respectively. Based on the existing information, the into two informal units: Lower and Upper Dariyan. Unlike Sulaiy Formation was first defined by Steineke and Bram - its equivalent in Arabian countries (Shuaiba Formation), kamp (1952). Powers et al. (1966) re-described the forma- the Dariyan Formation is not well studied and documented tion in terms of occurrence, thickness, lithological character, in the Zagros area of south and southwest Iran (Alsharhan nature of contacts, paleontology and age, and also economic 1985; Alsharhan et al. 2000). aspects. They indicated that this formation is lithologically uniform and is composed mainly of tan, chalky, massive Ghadvan Formation bedded, aphanitic limestone. The Gadvan Formation (type section in Kuh-e-Gadvan), is dominantly composed of alternating marls and shallow- Fundamentals water limestones, including a limestone marker bed in the upper part that so called Khalij (Dictyoconnus arabicus or Nuclear magnetic resonance (NMR) Montseciella arabicus) member (James and Wynd 1965; Schroeder et al. 2010; Van Buchem et al. 2010). It is respec- The phenomenon of nuclear magnetic resonance occurs in tively overlaid and underlined by the Dariyan (Shuaiba) and the atoms with an odd number of protons or neutrons. Pro- Fahliyan (Yamama) Formations, with gradual boundaries. tons and neutrons rotate around their axis. When the num- Previously, the age of formation was thought to range from ber of neutrons and protons are equal, rotations are neutral- the Barremian to Aptian. Van Buchem et al. (2010) revised ized with each other, and there will be no longer a spinning age of this formation to the Barremian, based on benthic nucleus. But the nucleus of atoms with disparities in the foraminifera, ammonites, planktonic foraminifera and car- number of protons and neutrons, rotates around its axis bon isotope curves (Vincent et al. 2010). and therefore, according to Faraday’s law, they will be con- verted into a magnetic dipole. Normally, orientation of these Yamama Formation dipoles is random, but in the presence of an external constant magnetic field (B ), bipolar is polarized and is placed in The Yamama Formation, from Thamama group in Arabian line with the B field. The vector sum of bipolar is the mass countries (Saudi Arabia, Bahrain and Qatar), is Neocomian magnetization (M ) which is the first step in creating nuclear limestones between the dense Sulaiy limestone below and magnetic resonance. In addition to causing polarization, the Buwaib or Ratawi Formations above (Steineke and application of B field causes the nuclei to have a preces - Bramkamp 1952; Sadooni 1993; Shebl and Alshahran sion around B with a specific frequency (Larmor). Larmor 1994; Nairn and Alsharhan 1997; Alsharhan et al. 2000). frequency varies for different nuclei and it is the basis for 1 3 Journal of Petroleum Exploration and Production Technology creating a resonance effect. Because by applying oscillating The remarkable point is that the dimensions of correction magnetic field (B ) with specified Larmor frequency, which coefficients C and A are dependent on coefficients m and n is the larmor frequency of hydrogen nucleus in NMR stud- (in Eqs. 3 and 4). ies, nuclei are deflected from B and do in-phase precession in the transverse plane. The phenomenon causes resonance signal and its recording in the coils, which are located in Materials and methods the transverse plane. By cutting off the oscillating field, the nuclei begin to return to the original relaxation state. This The present study was conducted on a field located in the phenomenon is characterized by longitudinal relaxation northwest of the Persian Gulf. The studied samples were time (T ) and transversal relaxation time (T ); which are the selected from different formations, and a total of 26 samples 1 2 output of nuclear magnetic resonance test. In NMR experi- (16 samples for modeling and 10 samples to test the accu- ments, due to the rapid decay of the signal, resonance pulse racy of models) were studied (Table 1). sequence is applied, so that the desired parameters can be Macroscopic and microscopic tests were conducted on recorded (Coates et al. 1999). samples; then lithology, facies, and type of pores were In general, there are three types of relaxation: bulk relaxa- determined, and in general, characterization of samples tion, diffusion-induced relaxation, and surface relaxation. was performed. The studied formations included Asmari, Due to the relationship between the surface relaxation and Burgan, Dariyan, Gadvan, Yamama, and Solaiy. Porosity the pore size, conditions in the laboratory is designed and ranged from 2.47 to 33.76% and permeability ranged from provided in such a way that the surface relaxation is the 0.00013 to 18.37 md. Pores were also of vuggy, fine pores, dominant mechanism; so that the obtained time T represents intraparticle and moldic type, detailed information of which the pores size. Therefore, having distribution T as the output is given in Table 2. of resonance experiment, the pores size distribution can be obtained (Kleinberg et al. 1994; Coates et al. 1999). Routine core analysis NMR permeability models The spectral gamma logging was first performed on the cores and the results were compared with gamma logging NMR permeability estimation models have been developed data to depth matching. After preparation of cores, sam- mainly through the study of sandstones (Coates et al. 1999). ples were prepared and cleaned in the Soxhlet using toluene TC model (Timur 1968; Coates and Denoo 1981; Coates and methanol. The cleaned samples were dried under the et al. 1991) (Eq. 1) and SDR model (Kenyon et al. 1988) temperature of 90 °C; and their grain density, porosity and (Eq. 2) are among two main models of NMR permeability permeability were measured. estimation models. NMR experiment BVM k = × , (1) Nuclear magnetic resonance device used in this study works C BVI under the following conditions: 4 2 k = A × × T , Ambient temperature of 5–35 °C (2) 2gm Humidity less than 80% where k is permeability (millidarcy-md), φ is porosity (m / Atmospheric pressure of 84–107 kPa 3 3 3 m ), BVM is producible part of porosity (m /m ), BVI is 220 V power supply and (1 ± 50) Hz 3 3 non-producible part of porosity (m /m ), C is the formation- The time needed to prepare to work less than 2 h −0.25 dependent correction coec ffi ient (md ), T is geometric 2gm mean of the T distribution (ms), A is the formation-depend- 2 After NMR experiment, the device output which is a reso- −2 ent correction coefficient (md ms ). These models can be nance signal decreasing curve is obtained. Then the values rewritten in parametric form (Eqs. 3 and 4) (Amabeoku et al. of porosity and pore size distribution are measured using the 2001). software embedded in the device. After above-mentioned common core tests, the steps neces- BVM sary for the preparation of samples were performed for testing k = × , (3) C BVI nuclear magnetic resonance. For this purpose, samples were cleaned with xylene and methanol in the Soxhlet device and m n saturated with salt water (brine). Then, the nuclear magnetic k = A × × T , 2gm (4) resonance experiment at 100% saturation and data analysis 1 3 Journal of Petroleum Exploration and Production Technology Table 1 Porosity and Row Porosity (fraction) Permeability (md) Row Porosity (fraction) Permeability (md) permeability of samples Modeling Test 1 0.301 1.638 1 0.3043 3.75 2 0.0569 0.0037 2 0.3376 18.376 3 0.0364 0.0002 3 0.2022 3.2347 4 0.0434 0.0012 4 0.0909 0.1876 5 0.2713 5.5485 5 0.0813 0.0723 6 0.131 0.3241 6 0.0712 0.01354 7 0.0826 0.0051 7 0.1366 0.891 8 0.0391 0.0005 8 0.0353 0.0001 9 0.1206 0.0228 9 0.0247 0.0023 10 0.186 0.4898 10 0.0408 0.0053 11 0.1884 0.9494 12 0.1251 0.2051 13 0.0279 0.0002 14 0.1046 0.1999 15 0.1088 0.0906 16 0.0588 0.0034 were performed and T distribution graph was obtained as in Results and discussion Fig. 1. In the next step, for testing nuclear magnetic resonance in a Presence of very low permeability (between 0 and 1 md) state of residual saturation, the samples were placed in centri- samples in this study causes that comparison between the fuge, thus samples with residual saturation were obtained, and core permeability and permeability of models (in the ordi- nuclear magnetic resonance experiment was performed in the nary scale) will be encountered with error in calculating state of residual saturation. After determining the distribution the coefficient of determination. The influence of very low graph T in residual saturation as in Fig. 2, the necessary steps permeability values is very low in comparison with larger to determine the exact T was performed for each sample to amounts in the coefficient of determination. Therefore, the 2c examine incremental graph T in the two states of 100% satura- logarithm of permeability results was used for comparing tion and residual saturation (see Fig. 3). core and model permeabilities, to display the errors that After determining the value of T for the samples, given occur at low levels whose influence on the coefficient of 2c the importance of the parameters of BVM, BVI and T in determination is not shown well. 2gm permeability estimation models TC and SDR, these values were calculated for each sample as in Fig. 4. It should be noted that normally in sandstones and carbonates, the values of 33 Porosity and 92 ms are used for T , respectively (Straley et al. 1997; 2c Westphal et al. 2005; Yao et al. 2010). However, in this study, Porosity is one of the most important parameters that is to increase the accuracy of the models, values of T for each paramount of importance in the study of reservoirs and 2c sample were determined through comparing the NMR results plays significant role in permeability models. For this rea - in both saturated and unsaturated states; Then by having a T son, it should be specified to what extent is the accuracy 2c value for each sample, the T distribution graph for each sam- of NMR method for determining porosity in the samples. ple was divided into two parts of BVM and BVI, and their In the NMR experiment results, the surface area under T values were calculated for each sample. The results of ana- distribution graph can be considered as the porosity for lyzing the porosity and permeability estimation models are the samples (Coates et al. 1999). Thus, porosity for 26 proposed bellow. 1 3 Journal of Petroleum Exploration and Production Technology Table 2 Samples LITHOLOGY/ LITHOLOGY/ FACIES/ FACIES/ MICROPHOTOGRAPH MICROPHOTOGRAPH PORE TYPE/ PORE TYPE/ CORE DEPTH CORE DEPTH Limestone/ Limestone/ Bioclasc, Coated grain Bioclasc- Sandy 1 7 Wack/Packstone/ mudstone/wackstone/Vuggy/ Vuggy and moldic/ 625.6 m 2339 m Limestone/ Limestone/ Large Bioclast Bioclasc, Coated grain 2 packstone/ﬂaotstone/ 8 Wack/Packstone/ Intergranular,vuggy/ Vuggy and moldic/ 626.2 m 2338 m Limestone/ Limestone/ Large Bioclast Molusca, Green algae 3 packstone/ﬂaotstone/ 9 Wackstone/ Vuggy and moldic/ intraparcle/ 626.5 m 2372 m Limestone/ Limestone/ Mixed Bioclasc, Orbitolina, Orbitolina/bioclasc limestone/ Micropeloid 4 10 moldic/ Wacke/Packstone/ 2132 m Vuggy/ 2405 m Limestone/ Limestone/ Orbitolina-Algal debris- Microbioclast Mud/Wackestone/ bioclasc 5 11 Microporosity/ wackstone/mudstone/ 2276 m Microporosity/ 2490 m Limestone/ Limestone/ Mixed Bioclasc, Orbitolina Bioclasc/Peloid/Foram 6 Wack/Packstone/ 12 packstone/grainstone/ Intraparcle, microporosity/ microporosity/ 2296 m 2490 m Limestone/ Limestone/ Bioclasc/Peloid/Foram Foram- Algal debris-Bioclasc 13 packstone/grainstone/ 20 wackestone/packstone/ Microporosity, vuggy/ Moldic, vuggy/ 2492 m 2759 m 1 3 SAMPLE SAMPLE Journal of Petroleum Exploration and Production Technology Table 2 (continued) Limestone/ Marl/ Bioclasc/Peloid/Foram Fossil-bearing Marls/ 14 packstone/grainstone/ 21 Vuggy/ Interparcle/ 2760 m 2491 m Limestone/ Limestone/ Orbitolina-Algal debris-bioclasc Bioclasc-Sponge Spicule 15 wackstone/mudstone/ 22 wackestone/ Inter/intra parcle/ Intercrystalline/ 2496 m 2843 m Limestone/ Limestone/ Large Foram-Lithocodiom Bioclasc-Sponge Spicule 16 wackestone/ﬂoatstone/ 23 wackestone/ Intraparcle/ Vuggy/ 2746 m 2844 m Limestone/ Limestone/ Intraclast, Bioclasc Microbioclasc 17 Wackestone/Packstone/ 24 Mudstone/Wackestone/ Vuggy and intraparcle/ Microporosity/ 2755 m 2999 m Limestone/ Limestone/ Foram-Algal debris-Bioclasc Micro-peloid/bioclasc 18 wackestone/packstone/ 25 Wackestone/Packstone/ Vuggy, intraparcle/ Microfractures/ 2756 m 3000 m Limestone/ Argillaceous Limestone/ Foram-Algal debris-Bioclasc Pelagic Argillaceous Lime 19 wackestone/packstone/ 26 Mudstone/ Moldic/ Microfractures/ 2757 m 3049 m carbonate samples studied in the laboratory was meas- Studies on clean sandstones represent a good match ured using Helium Porosity method. Then, using nuclear between the NMR porosity and core porosity (helium poros- magnetic resonance device, porosity of 26 samples were ity) which shows the error of about 1% (Coates et al. 1999). measured at 100% saturation mode. Regression analysis The studies conducted on sandstones, total porosity is equal between the results of laboratory-obtained porosity and to effective porosity due to the lack of the fine porosities. NMR-obtained porosity showed that a good relationship Comparison of helium porosity and NMR porosity in coals is between the porosities obtained using NMR method and showed good accuracy of NMR method in measuring the porosities obtained using Helium technique (R = 0.95). porosity (Yao et al. 2010). In this study, based on the results Therefore, the porosity obtained by NMR method can be used in the estimations and calculations (see Fig. 5). 1 3 Journal of Petroleum Exploration and Production Technology Fig. 1 T distribution curve (100% saturation-sample 33) Fig. 2 T distribution curve (residual saturation-sample 33) Fig. 3 Accumulative porosity curves for determination of T 2c (sample 33) obtained in comparison of the core porosity and NMR Permeability porosity, it was shown that NMR technique can be used for accurate estimation of porosity in the carbonate samples (see As mentioned, NMR method gives indirect permeability. Fig. 5). Equations provided in TC and SDR models (Eqs. 3 and 4) (Amabeoku et al. 2001), were used as the two main models for estimating permeability using NMR. Equations 1 and 1 3 Journal of Petroleum Exploration and Production Technology Fig. 4 Determination of BVM and BVI using T in T distri- 2c 2 bution curve (sample 33) Fig. 5 NMR and core porosity comparison 2 were first used to estimate permeability for the aim of TC model The first step in estimating the permeability using examining the accuracy of aforesaid equations with rou- TC model is to determine the correction coefficient of the tine coefficients which are mainly provided for sandstones. Eq. 1 (C factor). To determine the amount of C, it is required Then, Eqs. 3 and 4 were used to estimate permeability, so to rewrite the Eq. 1 as follows (Coates et al. 1999): that from 26 available samples, 16 samples were used to � � 2 BVM develop the model and correction of coefficients, and 10 k ⋅ C = ⋅ , (5) core BVI samples were used to test the accuracy of the proposed models. Finally, the estimated permeability in different As mentioned, correction coefficient C is formation states was compared with core permeability measured in dependent, and its value is considered to be 6.2 for sand- laboratory using Air Permeability method. These proce- stones (Coates et al. 1999). Thus, according to Eq. 5, using dures are described below. the proposed coefficients m = 4 and n = 2 for sandstones, 2 BVM diagram ⋅ against k was drawn (with zero core BVI Routine mode intercept), and the slope of the best linear fit of data repre- sents the value of C. As mentioned, this value has been As mentioned, in this mode, Eqs. 1 and 2 were used as the obtained as equal to 6.2 for sandstones (Coates et al. 1999). models used to estimate permeability. In the following, the For the samples used in this study, the value of C should be procedure and the conducted studies are provided in two determined with respect to the core data, measured models of TC and SDR. 1 3 Journal of Petroleum Exploration and Production Technology Fig. 6 Determination of C value in TC model (m = 4, n = 2) permeability, and the results of NMR, as well as the values SDR model To estimate the permeability using SDR model of BVM and BVI. in routine mode (Eq. 2), the value of A should be calculated 2 BVM using core permeability data and geometric mean of trans- Finally, diagram ⋅ against k was drawn core BVI verse relaxation time (T ). To calculate the value of A, it is 2gm needed to put the value of permeability in Eq. 2 and draw (with zero intercept) and linear regression analysis was per- diagram k against ⋅ T . Then, the slope of the best formed and the value of C was determined as in Fig. 6. core 2gm As is evident in Fig. 6, the value of coefficient of deter - linear fit of the data with zero intercept represents the value mination (R = 0.93) for the fitted equation is acceptable; of A as in Fig. 8. According to the coefficient of determina- therefore, this value of C (0.281) can be used for all samples. tion 0.96, this value of A, i.e., 0.0939 can be used for the Using the value of C in Eq. 1, the permeability of samples samples. can be estimated using TC model, and the obtained values After determining the value of A, NMR permeability is can be compared with the permeability values measured in calculated in the SDR model using Eq. 2 (see Fig. 9). As the laboratory (see Fig. 7). As is shown in Fig. 7, coefficient is evident in Fig. 9, there is not a good match between the of determination is equal to 0.79 between core and TC model results of core permeability and SDR model (R = 0.11). permeabilities. Fig. 7 Correlation of estimated permeability by TC model and core permeability (m = 4, n = 2) 1 3 Journal of Petroleum Exploration and Production Technology Fig. 8 A determination in SDR model (m = 4, n = 2) (log–log scale) Fig. 9 Correlation of estima- tion SDR permeability and core permeability (m = 4, n = 2) Modified mode the values of n and m (Eq. 3) were corrected to the extent that coefficient of determination of calculated permeability As shown in the previous section, TC and SDR models and core permeability to be maximized. Coefficient of deter - with routine coefficients are not able to estimate permeabil- mination of core permeability and TC permeability reached ity in the studied samples appropriately, and therefore, it its maximum in the amount of 0.919; and the values of m is required to correct the coefficients. For this purpose, 26 and n were obtained equal to 3.9 and 0.51, respectively. The studied samples were divided into two groups of 16 and 10. value of C was determined as equal to 0.222, with determi- The group with 16 samples was used for coefficient cor - nation coefficient of 0.948 (see Figs. 10, 11). The modified rection, and the group with 10 samples was used to test the TC model can be rewritten as follows (Eq. 6). accuracy of the corrected models. It should be noted that, the 3.9 0.51 estimation of permeability is one of the main goals in this BVM k = . (6) TC study, therefore, in modifying the models, non-linear fitting 0.222 BVI with criteria of maximizing the coefficient of determination between core permeability and the permeability obtained by To determine the accuracy of Eq. 6 (modified TC model), the models was applied. the resulting model was used to estimate the permeability of the samples in the group with 10 samples. The coefficient Modified TC model As mentioned, in TC model, the deter- of determination of calculated permeability and core perme- mination of coefficient between calculated permeability and ability was equal to 0.918 which is a reasonable coefficient core permeability was used as an appropriate criterion, and of determination as in Fig. 12. 1 3 Journal of Petroleum Exploration and Production Technology Fig. 10 C determination in modified TC model (design model, m = 3.91, n = 0.51) Fig. 11 Correlation of core permeability and permeability of modified TC model (design model, m = 3.91, n = 0.51) Fig. 12 Correlation of core per- meability and permeability of modified TC model (test model, m = 3.91, n = 0.51) 1 3 Journal of Petroleum Exploration and Production Technology Fig. 13 A determination in modified SDR model (design model, m = 1.64, n = 1.68) Fig. 14 Correlation of Core permeability and permeability of modified SDR model (design model, m = 1.64, n = 1.68) Modified SDR model Similar to the previous section, in appropriate value for the coefficient of determination (see SDR model, the determination coefficient between calcu- Fig. 15). lated permeability and core permeability was used as an appropriate criterion, and the values of n and m in Eq. (4) were changed to the extent that the selected criterion was Summary and conclusions maximized. The maximum coefficient of determination was equal to 0.965 and the values of 1.64 and 1.68 were obtained In this study it was shown that using NMR method, the for m and n, respectively. Also value of 0.0216 for A (md porosity in the carbonate samples (with low permeability) 1.68 ms ) was determined with a coefficient of determination can be estimated well. However, parameters of NMR perme- of 0.955 as in Figs. 13 and 14. The following equation (the ability model have to be adjusted to the carbonate reservoir. modified SDR model) was used to examine the accuracy of TC and SDR models, as the main models of NMR per- the model and to estimate the permeability of 10 samples meability, were examined as an example; and it was shown specified for the tests. that these models (Eqs. 1 and 2) must be modified. The necessary corrections were made based on maximizing the 1.64 1.68 k = 0.0216 ⋅ ⋅ T coefficient of determination of core permeability and model (7) SDR 2gm permeability; and the modified models verified by samples The coefficient of determination for calculated perme- specified for the test. The results of matching the core per - ability and core permeability is equal to 0.966 that is an meability and model permeability shows that the coefficient 1 3 Journal of Petroleum Exploration and Production Technology Fig. 15 Correlation of core permeability and permeability of modified SDR model (test model, m = 1.64, n = 1.68) Alsharhan A (1985) Depositional environment, reservoir units evo- of determination in TC model increase from 0.79 to 0.918 lution, and hydrocarbon habitat of Shuaiba formation, Lower and in SDR model increase from 0.11 to 0.966 which is Cretaceous, Abu Dhabi, United Arab Emirates. AAPG Bull proper ability of the models to estimate the permeability. In 69(6):899–912 TC and SDR proposed model (in most samples) estimated Alsharhan A (1991) Sedimentological interpretation of the Albian Nahr Umr Formation in the United Arab Emirates. Sediment Geol permeability is higher than core permeability that shows, 73(3–4):317–327 proposed models a little over-estimated permeability. This Alsharhan A (1994) ALBIAN CLASTICS IN THE WESTERN study showed that the permeability estimation models for the ARABIAN GULF REGION: A SEDIMENTOLOGICAL AND study area must be corrected to make sure that the results PETROLEUM-GEOLOGICAL INTERPRETATION. J Pet Geol 17(3):279–300 are reliable (see Eqs. 6 and 7). In this research, porosity Alsharhan AS et al (2000) Stratigraphy, stable isotopes, and hydro- of the carbonate samples with low permeability, was well carbon potential of the Aptian Shuaiba Formation, UAE estimated and shows the proper ability of NMR method for Alvarado RJ et al (2003) Nuclear magnetic resonance logging while determining porosity in such samples (Fig. 5). drilling. Oilfield Rev 15(2):40–51 Amabeoku MO et al (2001) Calibration of permeability derived from NMR Logs in carbonate reservoirs. SPE Middle East Oil Show, Acknowledgements We would like to thank National Iranian Oil Com- Society of Petroleum Engineers pany (NIOC) for supplying data for this study. Beydoun ZR (1991) Arabian plate hydrocarbon geology and potential Chang D et al (1994) Effective porosity producible fluid and perme- Open Access This article is distributed under the terms of the Crea- ability in carbonates from Nmr logging. In: SPWLA 35th annual tive Commons Attribution 4.0 International License (http://creat iveco logging symposium, Society of Petrophysicists and Well-Log mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- Analysts tion, and reproduction in any medium, provided you give appropriate Coates G, Denoo S (1981) The producibility answer product. Tech credit to the original author(s) and the source, provide a link to the Rev 29(2):54–63 Creative Commons license, and indicate if changes were made. Coates GR et al (1991) The MRIL In Conoco 33-1 an investigation of a new magnetic resonance imaging log. In SPWLA 32nd annual logging symposium, Society of Petrophysicists and well- log analysts References Coates GR et al (1999) NMR logging: principles and applications. Houston: Haliburton Energy Services Daigle H, Dugan B (2009) Extending NMR data for perme- Al-Ameri TK et al (2009) Petroleum system analysis of the Mishrif res- ability estimation in fine-grained sediments. 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