Abstract
Unambiguously determining irreducible water saturation \(\left({S}_{\rm{wirr}}\right)\) poses a formidable challenge, given the availability of multiple independent methods. Traditional approaches often depend on semi-experimental relationships derived from simplified assumptions. These methods, originally designed for oil sandstone reservoirs, result in varying \({S}_{{\text{wirr}}}\) values when employed in carbonate gas reservoirs. Nuclear magnetic resonance (NMR) is the most advanced technique for determining \({S}_{{\text{wirr}}}\). While highly accurate, the NMR-based method necessitates the laboratory measurement of the transverse relaxation time \(\left({T}_{2}\right)\) cutoff. Laboratory-based \({T}_{2}\) cutoff determination is resource-intensive and time-consuming. This research aims to develop a robust model for determining \({S}_{{\text{wirr}}}\) in carbonate gas reservoirs by utilizing NMR well logging measurements and special core analysis (SCAL) tests. Various \({T}_{2}\) cutoff values were initially employed to compute bound water saturation \(\left({S}_{{\text{bw}}}\right)\) at different depths to achieve this. Subsequently, the data points \(\left({T}_{2}, {S}_{{\text{bw}}}\right)\) were graphed on a scatter plot to unveil the relationship between \({S}_{{\text{bw}}}\) and \({T}_{2}\). The scatter plot illustrates an exponential decrease in \({S}_{bw}\) with increasing \({T}_{2}\), forming the basis for the \({S}_{{\text{wirr}}}\) model derived from this relationship. Finally, the parameters of the \({S}_{{\text{wirr}}}\) model were fine-tuned using SCAL tests. Notably, this \({S}_{{\text{wirr}}}\) model not only accurately yields \({S}_{{\text{wirr}}}\) at each depth but also offers a dependable determination of the optimal \({T}_{2}\) cutoff for the reservoir interval.
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Introduction
Accurate determination of water saturation \(\left({S}_{{\text{wirr}}}\right)\) is crucial for conducting a realistic evaluation of hydrocarbon reserves and is critical for reducing the economic risks associated with investments in the petroleum industry. Numerous models have been proposed in the industry to calculate \({S}_{{\text{wirr}}}\). The widely used saturation models, such as the Waxman-Smits-Thomas (WST) and dual-water (DW) models, which are primarily tailored to oil sandstone reservoirs, tend to lose their efficiency in more complex environments, such as carbonate gas reservoirs. Nuclear magnetic resonance (NMR) well logs provide a more precise representation of void space and the fluids residing within than traditional logs. Therefore, this research aims to present a well-defined equation for determining \({S}_{wirr}\) in carbonate gas reservoirs using NMR log data.
The NMR technique has proven to be a relatively straightforward and powerful tool for characterizing reservoir properties over the past few decades. NMR spectroscopy has been widely employed as a diagnostic tool for distinguishing pore fluids (Falong et al. 2016; Liu et al. 2018; Guo et al. 2020; Liao et al. 2021; Jin et al. 2023; Li et al. 2023). There is a wealth of research dedicated to estimating permeability through NMR relaxation measurements (Liu et al. 2017; Aghda et al. 2018; Mason et al. 2019; Masroor et al. 2022; Wu et al. 2022; Chen et al. 2023b). Numerous researchers have highlighted the advantage of the NMR technique in constructing imbibition and drainage curves (Liang and Wei 2008; Onuh and Ogbe 2019; Hosseinzadeh et al. 2020; Wu et al. 2021; Jin and Xie 2022; Heidary 2023). Recent efforts have primarily been focused on determining the wettability index through NMR measurements (Korb et al. 2018; Pires et al. 2019; Wang et al. 2019; Heidary 2021a; Alomair et al. 2023). The NMR technique has shown promise in a wide range of reservoir studies, including the analysis of pore structure and tortuosity (Wang et al. 2016; Liang et al. 2020; Deng et al. 2021; Elsayed et al. 2022; Xin et al. 2022; Zhang et al. 2023), characterization of unconventional shale reservoirs (Song and Kausik 2019; Lawal et al. 2020; Yang et al. 2020; Silletta et al. 2022; Chen et al. 2023a), evaluation of formation damage (Kamal et al. 2019; Adebayo and Bageri 2020; Alomair et al. 2022), determination of fluid movability (Li et al. 2020; Zhu et al. 2021), and detection of gas hydrate-bearing sediments (Bauer et al. 2015; Yang et al. 2017; Zhang et al. 2020, 2021, 2022; Shao et al. 2023).
One of the most frequently applied uses of NMR logs is the determination of fluid saturation. Numerous studies have explored the determination of fluid saturation based on NMR relaxation measurements (Dong et al. 2015; Mitchell et al. 2015; Newgord et al. 2020; Wang and Zeng 2020; Heidary 2021b; Gu et al. 2023). The process of using NMR relaxation data to determine \({S}_{wirr}\) involves deriving the transverse relaxation time \(\left({T}_{2}\right)\) cutoff from NMR measurements conducted on core samples. The measurement of the \({T}_{2}\) cutoff value, routinely performed in the laboratory, becomes impractical when considering the entire reservoir interval due to cost and time constraints. Considering the inherent drawbacks of traditional methods and the challenge posed by determining the \({T}_{2}\) cutoff value in the NMR-based approach, this research endeavor aims to present a rigorous method for determining \({S}_{{\text{wirr}}}\) in carbonate gas reservoirs by leveraging NMR log data and special core analysis (SCAL) tests. This study involves the development of a comprehensive model that relates \({S}_{{\text{wirr}}}\) to \({T}_{2}\) with the model parameter values being derived from SCAL tests. The methodology consists of the following steps:
-
1.
Extraction of transverse relaxation time \(\left({T}_{2}\right)\) data from NMR well logging measurements.
-
2.
Examination of the relationship between \({S}_{{\text{bw}}}\) and \({T}_{2}\) on a scatter plot.
-
3.
Determination of the \({S}_{{\text{wirr}}}\) model.
-
4.
Extraction of \({S}_{{\text{wirr}}}\) model parameter values from SCAL tests.
Materials and methods
This research focuses on developing a mathematical model for the determination of \({S}_{wirr}\) in carbonate gas reservoirs utilizing NMR log data and SCAL tests. The studied reservoirs (A, B, C) are natural-gas condensate reservoirs in the Persian Gulf. The apparent porosity has been adjusted for incomplete polarization and the low gas hydrogen index. SCAL tests have been carried out in all of these reservoirs. Figures 1, 2 and 3 depict the respective target reservoirs' drainage capillary pressure and relative permeability curves.
The method presented in this study aims to develop a robust mathematical model for determining \({S}_{{\text{wirr}}}\) from NMR well logs and SCAL tests. The procedure is as follows:
-
1.
Extraction of the \({T}_{2}\) value from the Carr–Purcell–Meiboom–Gill (CPMG) echo train at each depth.
-
2.
Computation of bound water saturation \(\left({S}_{{\text{bw}}}\right)\) by applying various \({T}_{2}\) cutoff values to the \({T}_{2}\) distribution.
-
3.
Investigation of the relationship between \({S}_{{\text{bw}}}\) and \({T}_{2}\) through scatter plots for different \({T}_{2}\) cutoff values, leading to the establishment of the \({S}_{{\text{wirr}}}\) model.
-
4.
Calibration of the \({S}_{{\text{wirr}}}\) model parameters using SCAL tests.
The terms \({S}_{{\text{bw}}}\) and \({S}_{{\text{wirr}}}\) are, at times, used interchangeably. However, in this study, \({S}_{{\text{bw}}}\) pertains to the conventional method, whereas \({S}_{{\text{wirr}}}\) is used for the new NMR-based approach. Figure 4 provides an illustration of the workflow for this procedure. The \({S}_{{\text{wirr}}}\) model for the target reservoirs was established using this workflow.
Measurement of transverse relaxation time
NMR logging involves rapidly manipulating the hydrogen nuclei within rock formation pores (Luthi 2001). A quintessential multi-pulse sequence for moderately inhomogeneous magnetic fields, extensively employed in conventional NMR applications, is the Carr–Purcell–Meiboom–Gill (CPMG) sequence. The CPMG pulse sequence commences with a 90° pulse, succeeded by a series of 180° pulses. The initial pair of pulses are spaced apart by a time interval denoted as \(\tau\), while the subsequent pulses are separated by \(2\tau\). Echoes manifest themselves precisely midway between the 180° pulses at intervals of \(2\tau\), \(4\tau\), and so forth, up to \(2{\uptau } \times {\text{n}}\), where \(n\) signifies the echo order (refer to Fig. 5). These echoes materialize at the midpoint of successive refocusing pulses (Johns et al. 2015). In multiple-echo sequences, the envelope characterizing consecutive echoes diminishes exponentially over time, with a time constant denominated as \({T}_{2}\). This time constant \({T}_{2}\), governing the decay, is termed the transverse relaxation time. Consequently, \({T}_{2}\) can be determined from the magnitude of the consecutive echoes (Dunn et al. 2002):
In Eq. (1), \(M\left(t\right)\) and \({M}_{0}\) correspond to the magnetization at time t and time 0, respectively. \({M}_{0}\) can be calibrated to yield porosity information.
In NMR logging, \({M}_{0}\) and \({T}_{2}\) hold paramount significance, as they harbor valuable petrophysical and geological insights. A considerable level of noise often plagues NMR logging measurements. The initial step in extracting \({M}_{0}\) and \({T}_{2}\) entails noise elimination from the CPMG sequence. Heidary et al. (2019) introduced a proficient approach to managing the noisy spin-echo train at each depth using the wavelet analysis technique. This method was applied to the target reservoirs to derive \({M}_{0}\) and \({T}_{2}\) from the spin-echo train.
Generally, the \({T}_{2}\) value is affected by pore fluid type, fluid saturation, pore size, and wettability. Physical properties such as surface-to-volume ratio influence the \({T}_{2}\) value. The amount of \({T}_{2}\) signal below 33 ms is small for poorly consolidated sandstones and can be hard to resolve from the noise.
Bound water saturation
Reservoir rocks exhibit pores of varying sizes and contain multiple types of fluids. Consequently, the spin-echoes recorded during the CPMG measurement do not solely exhibit decay with a single \({T}_{2}\) value; instead, they display a distribution of \({T}_{2}\) value (Coates et al. 1999). The inversion of NMR log data yields the necessary information for computing bound water saturation \(\left({S}_{{\text{bw}}}\right)\). The \({T}_{2}\) distribution within rocks is a continuous function; however, to facilitate fitting the CPMG sequence, the inversion process employs a multi-exponential model. The primary focus of the inversion process is to identify relaxation times, \({T}_{2j}\), along with their corresponding porosity components, \({f}_{j}\), from the spin-echo decay data, \({g}_{i}\), while minimizing the error \({\varepsilon }_{i}\) (Dunn et al. 2002):
Figure 6 serves as a typical illustration of the outcome of the inversion process. The vertical cutoff in the \({T}_{2}\) distribution distinguishes between different pore sizes and quantifies the volume of bound water. Consequently, bound water saturation \(\left({S}_{{\text{bw}}}\right)\) is derived from the \({T}_{2}\) distribution function, \(f\left({T}_{2}\right)\), using the following Equation (Johns et al. 2015):
where \({T}_{2{\text{max}}}\) and \({T}_{2{\text{min}}}\) represent the maximum and minimum values of \({T}_{2}\), respectively. Determining the appropriate \({T}_{2}\) cutoff value is of utmost importance in calculating \({S}_{{\text{bw}}}\). This value is determined through NMR measurements on water-saturated core samples. The suitable \({T}_{2}\) cutoff value can vary from one reservoir to another. For carbonates, for instance, the \({T}_{2}\) cutoff value may range from 90 to 150 ms, with the default value set at 90 ms (Coates et al. 1999).
\({S}_{{\text{bw}}}\) is contingent upon the chosen \({T}_{2}\) cutoff value. Sometimes, the \({T}_{2}\) cutoff value is variable. Using a single \({T}_{2}\) cutoff value to calculate \({S}_{bw}\) is not reasonable in a formation. Accurate determination of the \({T}_{2}\) cutoff values requires NMR laboratory measurements on many core samples. However, it is essential to note that NMR experiments can only be conducted on a limited number of core samples. In other words, \({T}_{2}\) cutoff values obtained from core NMR measurements cannot be extrapolated to the entire reservoir interval. Therefore, it is essential to develop a mathematical model independent of the \({T}_{2}\) cutoff value for precise determination of \({S}_{{\text{wirr}}}\). The \({S}_{{\text{wirr}}}\) model can be obtained by establishing the relationship between \({S}_{{\text{bw}}}\) and \({T}_{2}\). To achieve this, a scatter plot of \({S}_{{\text{bw}}}\) versus \({T}_{2}\) is employed to unveil this connection. By calibrating the parameters of the \({S}_{{\text{wirr}}}\) model with special core analysis (SCAL) tests, it becomes solely a function of the \({T}_{2}\) value. This calibration eliminates the necessity of measuring the \({T}_{2}\) cutoff value at each depth.
Results and discussion
The \({S}_{{\text{wirr}}}\) model has been developed for the target reservoirs using the proposed method, and the results obtained from each step are presented in this section.
CPMG sequence parameters
The CPMG sequence parameters, denoted as \(\left({M}_{0},{T}_{2}\right)\), were determined at various depths. The NMR porosity \(\left({\phi }_{{\text{NMR}}}\right)\) and \({T}_{2}\) logs for reservoirs A, B, and C are illustrated in Figs. 7, Fig. 8 to Fig. 9, respectively.
Correlation of CPMG sequence parameters
A robust correlation exists between \({\phi }_{{\text{NMR}}}\) and \({T}_{2}\) in water-wet rock that is fully saturated with water. In oil reservoirs, \({T}_{2}\) demonstrates a strong correlation with \({\phi }_{{\text{NMR}}}\). Consequently, the \({T}_{2}\) distribution proves to be a reliable indicator for determining \({S}_{{\text{bw}}}\) in oil reservoirs. However, in the target reservoirs, the correlation between \({\phi }_{{\text{NMR}}}\) and \({T}_{2}\) is insignificant due to the low hydrogen index of gas. The correlation coefficient \(\left({r}_{{\text{corr}}}\right)\) between \({\phi }_{{\text{NMR}}}\) and \({T}_{2}\) is calculated as follows (Shevlyakov and Oja 2016):
Here, \(\overline{{\phi }_{{\text{NMR}}}}\) and \(\overline{{T }_{2}}\) represent the mean values of \({\phi }_{{\text{NMR}}}\) and \({T}_{2}\) logs, respectively. The calculated values of \({r}_{{\text{corr}}}\) for reservoirs A, B, and C are − 0.03, − 0.14, and − 0.06, respectively. Figures 10a–c depict scatter plots of \({T}_{2}\) versus \({\phi }_{{\text{NMR}}}\) for reservoirs A, B, and C, respectively. Consequently, developing a comprehensive \({S}_{{\text{wirr}}}\) model, independent of \({T}_{2}\) cutoff, is crucial for the target reservoirs. Calibration of the derived model with experimental tests obviates the need for laboratory measurement of \({T}_{2}\) cutoff.
Irreducible water saturation model
The calculation of \({S}_{{\text{bw}}}\) was carried out within the target reservoirs, considering various values of the \({T}_{2}\) cutoff. A scatter plot of \({S}_{{\text{bw}}}\) against \({T}_{2}\) reveals an exponential relationship, as depicted in Figs. 11a–c, for reservoirs A, B, and C, respectively. The regression coefficient \(\left({R}^{2}\right)\) is influenced by the chosen \({T}_{2}\) cutoff value. Consequently, the \({S}_{{\text{wirr}}}\) model is expressed as follows:
The parameter values \(\left(a,b\right)\) are unique to each reservoir. \({S}_{{\text{bw}}}\) is contingent upon the selected \({T}_{2}\) cutoff value at each depth. There is a specific \({T}_{2}\) cutoff value from which the resulting \({S}_{{\text{bw}}}\) log closely matches the \({S}_{{\text{wirr}}}\) log. This particular \({T}_{2}\) cutoff, referred to as the optimal one, yields the highest correlation coefficient between \({S}_{{\text{bw}}}\) and \({S}_{{\text{wirr}}}\). The determination of parameter values for the target reservoirs is crucial for the precise determination of \({S}_{{\text{wirr}}}\) at various depths. These parameter values are obtained through the calibration of Eq. (5) with SCAL tests, and the procedure for acquiring \(a\) and \(b\) is explained in the following section.
Model parameters
Determining the model parameter values requires establishing a relationship between \({T}_{2}\) and SCAL tests. The function of \({T}_{2}\) in porous media is analogous to resistivity. \({S}_{{\text{bw}}}\) decreases with increasing \({T}_{2}\) (or resistivity). Taking the natural logarithm of Eq. (5) yields:
The \({S}_{{\text{wirr}}}\) model parameters are obtained by determining \({S}_{{\text{wirr}}}\) from SCAL tests at two different depths. Substituting the minimum and maximum values of \({S}_{{\text{wirr}}}\) \(\left({S}_{{\text{wirr}}}^{{\text{min}}},{S}_{{\text{wirr}}}^{{\text{max}}}\right)\) in Eq. (6) and solving for the \({S}_{{\text{wirr}}}\) model parameters yield:
where \({T}_{2}^{{\text{max}}}\) and \({T}_{2}^{{\text{min}}}\) are the maximum and minimum values of\({T}_{2}\), respectively. \({S}_{{\text{wirr}}}^{{\text{min}}}\) and \({S}_{{\text{wirr}}}^{{\text{max}}}\) correspond to \({T}_{2}^{{\text{max}}}\) and\({T}_{2}^{{\text{min}}}\), respectively. \({S}_{{\text{wirr}}}^{{\text{min}}}\) is determined from the capillary pressure curve measured on the core sample taken from a depth corresponding to \({T}_{2}^{{\text{max}}}\) (Figs. 1, 2 and 3). \({S}_{w}^{max}\) is associated with the residual gas saturation\(\left({S}_{{\text{gr}}}\right)\);\({S}_{{\text{wirr}}}^{{\text{max}}}=1-{S}_{{\text{gr}}}\). There is no SCAL test regarding the determination of \({S}_{{\text{gr}}}\) in the target reservoirs. Hence, this research resorted to the correlation relating \({S}_{{\text{gr}}}\) to petrophysical parameters. There are several correlations in the literature to estimate \({S}_{{\text{gr}}}\) in gas reservoirs. Agarwal developed a correlation for limestones in terms of porosity\(\left(\phi \right)\), absolute permeability\(\left(k\right)\), and initial gas saturation \(\left({S}_{{\text{gi}}}\right)\) as follows (Lee and Wattenbarger 1996):
\({S}_{{\text{gi}}}\) can be obtained from the gas–water relative permeability curve (Figs. 1, 2 and 3). The values of \(a\) and \(b\) were calculated using Eq. (8) and SCAL test results for the target reservoirs. Table 1 shows the values of \(a\) and \(b\) for each reservoir.
The \({S}_{{\text{wirr}}}\) model was established for the target reservoirs after calculating \(a\) and \(b\). Figures 1213 and 14 demonstrate the plot of \({S}_{{\text{wirr}}}\) and \({S}_{{\text{bw}}}\) versus depth for reservoirs A, B, and C, respectively. The \({S}_{{\text{bw}}}\) logs were obtained with the optimal \({T}_{2}\) cutoff value. The optimal \({T}_{2}\) cutoff value is less than the \({T}_{2}\) cutoff value at the depths where \({S}_{{\text{wirr}}}\) is greater than \({S}_{{\text{bw}}}\) \(\left({S}_{{\text{wirr}}}>{S}_{{\text{bw}}}\right)\). Similarly, the optimal \({T}_{2}\) cutoff value is greater than the \({T}_{2}\) cutoff value at the depths where \({S}_{{\text{wirr}}}\) is less than \({S}_{{\text{bw}}}\) \(\left({S}_{{\text{wirr}}}{<S}_{{\text{bw}}}\right)\).
Conclusions
In this study, a precise model has been successfully developed using transverse relaxation time \(\left({T}_{2}\right)\) and special core analysis (SCAL) tests to ascertain irreducible water saturation \(\left({S}_{{\text{wirr}}}\right)\) in carbonate gas reservoirs. The key findings of this study are as follows:
-
1.
An exponential relationship exists between the \({S}_{{\text{wirr}}}\) and \({T}_{2}\) values derived from the recorded CPMG sequences in carbonate gas reservoirs.
-
2.
The calibration of the \({S}_{{\text{wirr}}}\) model with SCAL tests obviates the necessity for determining \({T}_{2}\) cutoff in the novel methodology.
-
3.
The \({S}_{{\text{wirr}}}\) model can be effectively utilized to determine the optimal \({T}_{2}\) cutoff value in gas reservoirs.
-
4.
The recommended optimal \({T}_{2}\) cutoff values for reservoirs A, B, and C are 130 ms, 100 ms, and 110 ms, respectively.
Abbreviations
- CPMG:
-
Carr–Purcell–Meiboom–Gill echo train
- NMR:
-
Nuclear magnetic resonance
- SCAL:
-
Special core analysis
- \(a\) :
-
A constant in Eq. (5), dimensionless
- \(b\) :
-
A constant in Eq. (5), dimensionless
- \(f\) :
-
Partial porosity, dimensionless
- \({g}_{i}\) :
-
Echo amplitude, dimensionless
- \(k\) :
-
Permeability, mD
- \({M}_{0}\) :
-
Initial magnetization, A/m
- \(M\left(t\right)\) :
-
Magnetization at time \(t\), A/m
- \({r}_{{\text{corr}}}\) :
-
Correlation coefficient, dimensionless
- \({S}_{{\text{bw}}}\) :
-
Bound water saturation, dimensionless
- \({S}_{{\text{gi}}}\) :
-
Initial gas saturation, dimensionless
- \({S}_{{\text{gr}}}\) :
-
Residual gas saturation, dimensionless
- \({S}_{{\text{wirr}}}\) :
-
Irreducible water saturation, dimensionless
- \({S}_{{\text{wirr}}}^{{\text{max}}}\) :
-
Maximum irreducible water saturation, dimensionless
- \({S}_{{\text{wirr}}}^{{\text{min}}}\) :
-
Minimum irreducible water saturation, dimensionless
- \(t\) :
-
Time, ms
- \({T}_{2}\) :
-
Transverse relaxation time, ms
- \(\overline{{T }_{2}}\) :
-
Average transverse relaxation time, ms
- \({T}_{2{\text{max}}}\) :
-
Maximum transverse relaxation time, ms
- \({T}_{2{\text{min}}}\) :
-
Minimum transverse relaxation time, ms
- \({\varepsilon }_{i}\) :
-
Noise, dimensionless
- \(\tau\) :
-
A half-time of echo pulse, ms
- \(\phi\) :
-
Porosity, dimensionless
References
AR Adebayo BS Bageri 2020 A simple NMR methodology for evaluating filter cake properties and drilling fluid-induced formation damage J Pet Explor Prod Technol 10 4 1643 1655
SMF Aghda M Taslimi A Fahimifar 2018 Adjusting porosity and permeability estimation by nuclear magnetic resonance: a case study from a carbonate reservoir of south of Iran J Pet Explor Prod Technol 8 4 1113 1127 https://doi.org/10.1007/s13202-018-0474-z
O Alomair A Elsharkawy W Al-Bazzaz S Ok 2022 Low-field NMR investigation on interaction of ZnO nanoparticles with reservoir fluids and sandstone rocks for enhanced oil recovery J Pet Explor and Prod Technol https://doi.org/10.1007/s13202-022-01547-5
O Alomair A Elsharkawy W Al-Bazzaz S Ok 2023 Low-field NMR investigation on interaction of ZnO nanoparticles with reservoir fluids and sandstone rocks for enhanced oil recovery J Pet Explor Prod Technol 13 1 219 235 https://doi.org/10.1007/s13202-022-01547-5
K Bauer J Kulenkampff J Henninges E Spangenberg 2015 Lithological control on gas hydrate saturation as revealed by signal classification of NMR logging data J Geophys Res Solid Earth 120 9 6001 6017
JH Chen M Boudjatit SM Althaus 2023a NMR and its applications in tight unconventional reservoir rocks Phys Fluid Flow Transp Unconv Reserv Rocks https://doi.org/10.1002/9781119729914.ch6
X Chen X Zhao P Tahmasebi C Luo J Cai 2023b NMR-data-driven prediction of matrix permeability in sandstone aquifers J Hydrol 618 129147 https://doi.org/10.1016/j.jhydrol.2023.129147
GR Coates L Xiao MG Prammer 1999 NMR logging: principles and applications Gulf Professional Publishing Houston
T Deng C Xu X Lang J Doveton 2021 Diagenetic facies classification in the arbuckle formation using deep neural networks Math Geosci 53 7 1491 1512 https://doi.org/10.1007/s11004-021-09918-0
X Dong J Sun J Li H Gao X Liu J Wang 2015 Experimental research of gas shale electrical properties by NMR and the combination of imbibition and drainage J Geophys Eng 12 4 610 619
KJ Dunn DJ Bergman GA LaTorraca 2002 Nuclear magnetic resonance: petrophysical and logging applications 32 Elsevier Amsterdam
M Elsayed A BinGhanim MS Aljawad A El-Husseiny R Al-Abdrabalnabi M Mahmoud 2022 Quantifying acid diversion efficiency through NMR tortuosity measurements J Pet Explor Prod Technol https://doi.org/10.1007/s13202-022-01587-x
H Falong Z Cancan L Chaoliu X Hongjun Z Fengming S Zhaowei 2016 Water spectrum method of NMR logging for identifying fluids Pet Explor Dev 43 2 268 276
M Gu R Xie J Guo G Jin 2023 Evaluation of fluid saturation in shale using 2D nuclear magnetic resonance Energy Fuels 37 4 2713 2720 https://doi.org/10.1021/acs.energyfuels.2c03383
J Guo R Xie L Xiao 2020 Pore-fluid characterizations and microscopic mechanisms of sedimentary rocks with three-dimensional NMR: tight sandstone as an example J Nat Gas Sci Eng 80 103392 https://doi.org/10.1016/j.jngse.2020.103392
M Heidary 2021a Determination of in situ wettability using wavelet analysis and nuclear magnetic resonance log data Nat Resour Res 30 2777 2788 https://doi.org/10.1007/s11053-021-09847-z
M Heidary 2021b A novel computational method for determination of water saturation in oil reservoirs using discrete wavelet transform and nuclear magnetic resonance (NMR) T2 log J Pet Sci Eng https://doi.org/10.1016/j.petrol.2021.108828
M Heidary 2023 A new insight into in situ capillary pressure curve: upscaling nuclear magnetic resonance measurements using wavelet analysis Transp Porous Media 147 1 1 13 https://doi.org/10.1007/s11242-022-01890-5
M Heidary E Kazemzadeh A Moradzadeh AM Bagheri 2019 Improved identification of pay zones in complex environments through wavelet analysis on nuclear magnetic resonance log data J Petrol Sci Eng 172 465 476 https://doi.org/10.1016/j.petrol.2018.09.092
S Hosseinzadeh A Kadkhodaie S Yarmohammadi 2020 NMR derived capillary pressure and relative permeability curves as an aid in rock typing of carbonate reservoirs J Petrol Sci Eng 184 106593 https://doi.org/10.1016/j.petrol.2019.106593
G Jin R Xie 2022 A new method for capillary pressure curve prediction based on NMR echo data using integral transform, the quantum genetic algorithm, and the artificial neural network in tight sandstone J Petrol Sci Eng 217 110860 https://doi.org/10.1016/j.petrol.2022.110860
Y Jin L Xiao W Li G Wang W Long 2023 Simulation of nuclear magnetic resonance response based on 3D CT images of sandstone core J Pet Explor Prod Technol 13 2015 2029 https://doi.org/10.1007/s13202-023-01662-x
M Johns E Fridjonsson S Vogt A Haber 2015 Mobile NMR and MRI: developments and applications Royal Society of Chemistry London
MS Kamal M Mahmoud M Hanfi S Elkatatny I Hussein 2019 Clay minerals damage quantification in sandstone rocks using core flooding and NMR J Pet Explor Prod Technol 9 593 603
JP Korb B Nicot I Jolivet 2018 Dynamics and wettability of petroleum fluids in shale oil probed by 2D T1–T2 and fast field cycling NMR relaxation Microporous Mesoporous Mater 269 7 11 https://doi.org/10.1016/j.micromeso.2017.05.055
LO Lawal AR Adebayo M Mahmoud BM Dia AS Sultan 2020 A novel NMR surface relaxivity measurements on rock cuttings for conventional and unconventional reservoirs Int J Coal Geol 231 103605 https://doi.org/10.1016/j.coal.2020.103605
WJ Lee RA Wattenbarger 1996 Gas reservoir engineering Society of Petroleum Engineers Richardson
C Li G Liu Z Cao W Yuan P Wang Y You 2020 Analysis of petrophysical characteristics and water movability of tight sandstone using low-field nuclear magnetic resonance Nat Resour Res 29 4 2547 2573 https://doi.org/10.1007/s11053-019-09582-6
B Li M Tan Z Haitao G Jianying X Yang G Haopeng 2023 Novel fluid typing method of NMR dual-TW logging in mixed-wet reservoirs Geoenergy Sci Eng 229 212097 https://doi.org/10.1016/j.geoen.2023.212097
X Liang Z Wei 2008 A new method to construct reservoir capillary pressure curves using NMR log data and its application Appl Geophys 5 2 92 98 https://doi.org/10.1007/s11770-008-0017-3
Y Liang Y Tan F Wang Y Luo Z Zhao 2020 Improving permeability of coal seams by freeze-fracturing method: the characterization of pore structure changes under low-field NMR Energy Rep 6 550 561 https://doi.org/10.1016/j.egyr.2020.02.033
G-Z Liao W-L Chen F-R Zong F Deng H-B Liu B-S Wu 2021 NMR fluid analyzer applying to petroleum industry Pet Sci 18 54 91 https://doi.org/10.1007/s12182-020-00529-8
M Liu R Xie C Li L Gao 2017 A new method for determining tight sandstone permeability based on the characteristic parameters of the NMR T 2 distribution Appl Magn Reson 48 10 1009 1029 https://doi.org/10.1007/s00723-017-0924-7
Y Liu Y Yao D Liu S Zheng G Sun Y Chang 2018 Shale pore size classification: an NMR fluid typing method Mar Pet Geol 96 591 601
S Luthi 2001 Geological well logs: their use in reservoir modeling Springer Science & Business Media Berlin
HE Mason MM Smith SA Carroll 2019 Calibration of NMR porosity to estimate permeability in carbonate reservoirs Int J Greenhouse Gas Control 87 19 26 https://doi.org/10.1016/j.ijggc.2019.05.008
M Masroor M Emami Niri AH Rajabi-Ghozloo MH Sharifinasab M Sajjadi 2022 Application of machine and deep learning techniques to estimate NMR-derived permeability from conventional well logs and artificial 2D feature maps J Pet Explor Prod Technol 12 2937 2953
J Mitchell A Howe A Clarke 2015 Real-time oil-saturation monitoring in rock cores with low-field NMR J Magn Reson 256 34 42
C Newgord S Tandon Z Heidari 2020 Simultaneous assessment of wettability and water saturation using 2D NMR measurements Fuel 270 117431 https://doi.org/10.1016/j.fuel.2020.117431
HM Onuh DO Ogbe 2019 Genetic units averages of kappa for capillary pressure estimation from NMR transversal T2 distributions (Niger Delta as field case study) J Pet Explor Prod Technol 9 1161 1174
LO Pires A Winter OV Trevisan 2019 Dolomite cores evaluated by NMR J Petrol Sci Eng 176 1187 1197
Z Shao J Wang K Lv Z Wang Y Bai R Wang 2023 NMR based experiment of fluid invasion to natural gas hydrate reservoir and hydrate dissociation inhibition mechanism Fuel 354 129372 https://doi.org/10.1016/j.fuel.2023.129372
GL Shevlyakov H Oja 2016 Robust correlation: theory and applications 3 Wiley Hoboken
EV Silletta GS Vila EA Domené MI Velasco PC Bedini Y Garro-Linck 2022 Organic matter detection in shale reservoirs using a novel pulse sequence for T1–T2 relaxation maps at 2 MHz Fuel 312 122863 https://doi.org/10.1016/j.fuel.2021.122863
Y-Q Song R Kausik 2019 NMR application in unconventional shale reservoirs—a new porous media research frontier Prog Nucl Magn Reson Spectrosc 112 17 33 https://doi.org/10.1016/j.pnmrs.2019.03.002
F Wang F Zeng 2020 Novel Insights into the movable fluid distribution in tight sandstones using nuclear magnetic resonance and rate-controlled porosimetry Nat Resour Res 29 5 3351 3361 https://doi.org/10.1007/s11053-020-09635-1
F-F Wang T-Z Tang T-Y Liu H-N Zhang 2016 Evaluation of the pore structure of reservoirs based on nmr t 2 spectrum decomposition Appl Magn Reson 47 4 361 373
J Wang L Xiao G Liao Y Zhang Y Cui Z Sun 2019 NMR characterizing mixed wettability under intermediate-wet condition Magn Reson Imaging 56 156 160 https://doi.org/10.1016/j.mri.2018.09.023
B Wu R Xie M Liu G Jin C Xu J Liu 2021 Novel method for predicting mercury injection capillary pressure curves of tight sandstone reservoirs using NMR T 2 distributions Energy Fuels 35 19 15607 15617 https://doi.org/10.1021/acs.energyfuels.1c02146
F Wu Y Li B Burnham Z Zhang C Yao L Yuan 2022 Fractal-based NMR permeability estimation in tight sandstone: a case study of the Jurassic rocks in the Sichuan Basin, China J Petrol Sci Eng 218 110940 https://doi.org/10.1016/j.petrol.2022.110940
Y Xin G Wang B Liu Y Ai D Cai S Yang 2022 Pore structure evaluation in ultra-deep tight sandstones using NMR measurements and fractal analysis J Petrol Sci Eng 211 110180 https://doi.org/10.1016/j.petrol.2022.110180
M Yang ZR Chong J Zheng Y Song P Linga 2017 Advances in nuclear magnetic resonance (NMR) techniques for the investigation of clathrate hydrates Renew Sustain Energy Rev 74 1346 1360
K Yang PRJ Connolly M Li SJ Seltzer DK McCarty M Mahmoud 2020 Shale rock core analysis using NMR: Effect of bitumen and water content J Petrol Sci Eng 195 107847 https://doi.org/10.1016/j.petrol.2020.107847
Y Zhang Y Zhao X Lei M Yang Y Zhang Y Song 2020 Quantitatively study on methane hydrate formation/decomposition process in hydrate-bearing sediments using low-field MRI Fuel 262 116555
Z Zhang L Liu C Li C Liu F Ning Z Liu 2021 A testing assembly for combination measurements on gas hydrate-bearing sediments using x-ray computed tomography and low-field nuclear magnetic resonance Rev Sci Instrum https://doi.org/10.1063/5.0040858
Z Zhang F Ning W Lu J Zhou L Liu Y Ji 2022 Analysis of the effect of hydrate on water retention curves in gas hydrate-bearing sediments using gas drainage combined with NMR J Nat Gas Sci Eng 108 104833 https://doi.org/10.1016/j.jngse.2022.104833
N Zhang S Wang X Xun H Wang X Sun M He 2023 Pore structure and fractal characteristics of coal-measure sedimentary rocks using nuclear magnetic resonance (NMR) and mercury intrusion porosimetry (MIP) Energies 16 9 3812 https://doi.org/10.3390/en16093812
C Zhu W Guo Y Li H Gong J Sheng M Dong 2021 Effect of occurrence states of fluid and pore structures on shale oil movability Fuel 288 119847 https://doi.org/10.1016/j.fuel.2020.119847
Funding
This research has no funding by any organization or individual.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical approval
I confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Heidary, M. An NMR-based model for determining irreducible water saturation in carbonate gas reservoirs. J Petrol Explor Prod Technol 14, 927–939 (2024). https://doi.org/10.1007/s13202-024-01758-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13202-024-01758-y