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Introducing a method for calculating water saturation in a carbonate gas reservoir
Journal of Natural Gas Science and Engineering 70 (2019) 102942
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Introducing a method for calculating water saturation in a carbonate gas reservoir
T
Ata Movahheda, Majid Nabi Bidhendib,*, Mohsen Masihic, Abolghasem Emamzadehd a
Department of Natural Resources and Environment, Science and Research Branch, Islamic Azad University, Tehran, Iran Institute of Geophysics, University of Tehran, Tehran, Iran c Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran d Department of Chemical and Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran b
ARTICLE INFO
ABSTRACT
Keywords: Vp/Vs ratio Water saturation Carbonate gas reservoir NMR NDS
Cementation factor greatly affects water saturation estimation. Factors such as depositional environment, diagenesis and depositional architecture make the estimation of water saturation a big challenge in carbonate reservoirs. The current study is introduced a method for calculating cementation factor in Archie formula. First, (MRGC) technique was applied on the (NMR) logging parameters along with (NDS) data to obtain the optimum number of clustering. After that, fuzzy logic method was applied on conventional log parameters obtained from the wells without any NMR log data. In the third part of the study, a novel crossplot introduced including compressional to shear-wave velocity ratio (Vp/Vs ratio) and NDS parameters. Finally, available core data was used to obtain a relationship between cementation factor and effective porosity for each region. Proposed method had advantage of obtaining a variable cementation factor instead of a constant one.
1. Introduction Cementation factor (m) is an important parameter for water saturation calculation thus affecting the calculation of the amount of hydrocarbon in place. This parameter is usually considered constant for the whole reservoir interval. This assumption leads to large uncertainties in the estimation of water saturation content especially in carbonate reservoirs. Given the microbial and diagenetic processes, carbonate reservoirs have heterogeneous rock properties strongly related to m value and the m value is strongly affected by pore connectivity. Grain and pore shapes and the connectivity between pores determine the cementation factor (Salem and Chilingarian, 1999). Average value of m in literature is 2, representative of interparticle porosity (Archie, 1942). Some special cases make m value to be deviated from 2. For instance, fractured rocks have smaller m value because of better electrical connectivity (Aguilera, 1976; Rasmus, 1983; Towle, 1962). In contrast, rocks having non-touching vugs have large values for m (Focke and Munn, 1987; Lucia, 1983). Carbonate reservoirs contain both fractures and vugs; hence, porosity varies when depth changes. For these kinds of formations, due to heterogeneous behavior, a physical model with triple porosity system was used for the estimation of the m value. This model assumed that the non-connected
(separate or non-touching) vugs, fractures and matrix contributed to the total porosity of the system. Kadhim et al. (2013) conducted a comprehensive investigation on the properties of carbonate reservoirs with a focus on determining the cementation factor. They suggested the Gomes and Pickett correlation for determining m value, usually between 1.3 and 3. They stated the existence of very limited correlations for defining variable cementation factor. Arifianto et al. (2018) Investigated the Leverett J-function for characterizing carbonate reservoir and calculating precise water saturation. They concluded that water saturation, calculated from Leverett J-Function method, provided a more precise result when compared to Archie's water saturation method. Rafiee et al. (2014) used the results of electrical resistivity experiments to develop a new cementation factor correlation for a carbonate reservoir. Using this new correlation, they proposed a new method for calculating water saturation. Rahuma and Ghawar (2017) performed a sensitivity analysis for investigating the effect of variation of cementation factor and saturation exponent parameters on water saturation in carbonate reservoirs. They observed a maximum spread difference of 15% resulting from the variation of these parameters. Nabawy (2015) showed that the great variation of cementation factor (or porosity exponent) was due to their dependence on several factors, e.g. porosity, permeability and
*
Corresponding author. E-mail addresses: [email protected] (A. Movahhed), [email protected] (M.N. Bidhendi), [email protected] (M. Masihi), [email protected] (A. Emamzadeh). https://doi.org/10.1016/j.jngse.2019.102942 Received 18 March 2019; Received in revised form 25 June 2019; Accepted 13 July 2019 Available online 24 July 2019 1875-5100/ © 2019 Elsevier B.V. All rights reserved.
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Table 1 Data obtained from each well. Well
Full set data
NMR data
Core data
A B C
✓ ✓ ✓
✓
✓ ✓ ✓
formation factor. Riazi (2018) conducted a case study on rock typing and flow unit classification for a carbonate reservoir. She implemented four different petrophysical methods including Rock Fabric Number (RFN), Winland porosity-permeability plot (R35), Reservoir Quality Index/Flow Zone Indicator (RQI/FZI), and Bulk Volume Water (BVW) on four exploration wells. Shahi et al., 2018 established a new correlation between petrophysical parameters and porosity and compared it with Borai et al. correlations. Their results showed that the proposed method worked slightly better than the above-mentioned well-established methods. Petrophysical parameters such as porosity, water and oil saturations, formation resistivity factor, etc. describe the storage capability of the porous media or the capacity of rocks to hold fluids. The Archie's equation, also called the saturation equation, is used to determine the water saturation. Archie's parameters, namely “m”, “n” and “a” are sometimes assumed constant to simplify petrophysical measurements, But these parameters are not constant, particularly in heterogeneous reservoirs. Inaccurate estimates of these parameters can cause significant errors in the calculation of water saturation when using Archie's equation and lead to discrepancies between log interpretation and production test results. There are many factors affecting cementation factor (m) such as porosity, pore throat size, type of rock grains, type and distribution of clay content, degree of cementation, and overburden pressure (Rastegarnia et al., 2018). The current study used Vp/Vs ratio and NDS parameters along a novel crossplot for identifying the cementation factor and other controlling factors in gas reservoirs with different types of porosities (fracture, vuggy, vuggy channels and intercrystalline).
Fig. 1. The flow chart that shows the steps to perform the analysis.
NMR responses and Fullset data were used to find the electrofacies based on the relaxation groups. Concept of relaxation group was equal to the hydraulic unit concept. In order to do this, the equation of logT2 = log(ϕz)+log[1(ρSgv)] is used where T2 is the observed transverse relaxation time and ϕz is the porosity group which is obtained from (1−ϕ)/ϕ equation. The parameter l/ρSgv is often recognized as the relaxation factor representing the relaxation power and textural attributes of the formation (Rastegarnia and Khadkhodaie, 2013a, 2013b; Rastegarnia et al., 2017). As Table 1 shows, well A had NMR and fullset data whereas wells B and C had only conventional data. So, relaxation groups modeling was first applied on well A for the analysis. Then the relaxation group was propagated to wells B and C using Fuzzy logic method. The results were compared to those of petrophysical evaluation and core data for the verification of the propagated relaxation groups. The comparison showed great agreement. Fig. 1 shows the steps to perform the analysis which are summarized in the flowchart.
2. Geological setting The studied region was located on the Iran-Qatar border in the Persian Gulf shared by these two countries. The study examined the Kangan formation. This formation was subdivided into two principal reservoir units: Lower part of the Kangan Formation (K2 unit) Upper part of the Kangan Formation (K1 unit) Main lithology of K2 unit is composed of dolomite (in the upper part) and limestone (in the lower part). K2 reservoir unit is dominated by a stack of lime oomoldic and biomoldic grainstones having good porosity. Within the limestones, the dominant porosity types are moldic; within the dolomites, the dominant porosity types are vuggy, interparticle and intercrystalline. K1 reservoir units are mainly characterized by the development of limestone and dolomitic beds with moderate reservoir characteristics. The reservoir units start with dolomitized oolitic facies with moderate poroperm characteristics (intergranular, moldic and vuggy porosities). Within the central part of K1, there is a limited reservoir development, which is developed in limestone tidal oolitic grainstone.
3.1. NMR relaxation based rock typing Hydraulic properties of reservoir rocks are critical in controlling the fluid flow in porous media (De Marsily, 1986). Permeability estimation is more important and permeability measuring on core data, while reliable, is expensive, time consuming, and restricted only to the cored intervals. Moreover, depending on the sampling strategy and recovery, preservation and preparation of some severe discrepancies from reservoir conditions may occur (Gharachelou et al., 2018). Because of their continuous nature, the well logs data are proper substitutes for permeability determination (Song, 2013). In this regard, NMR logging technique is recommended for continuous estimation of porosity, permeability, capillary pressure (Pc), water saturation (Sw) and pore size distribution in carbonate hydrocarbon reservoirs (Gharachelou et al., 2018). On the other hand, NMR data analysis provides valuable
3. Materials and methodology The study used three wells petrophysical and core data. These wells were A, B and C located in Kangan formation in one of the Iranian southwestern gas fields. Table 1 summarizes the wells' data. 2
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Fig. 2. a) Cross plot of MRGC clustering results in the identification of relaxation groups. Fig. 2 b) Cross-plot of neutron porosity and density well logs classified by electrofacies, well A. Fig. 2c) Cross-plot of neutron porosity and sonic well logs classified by electrofacies, well A.
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proposed multi-dimensional dot-pattern recognition (MRGC) as a new clustering method for electro-facies analyses. MRGC is based on nonparametric K-nearest neighbor and graph data representation. This method uses Kernel Representative Index (KRI) and Neighborhood Index (NI) parameters which discern it from conventional methods. NI parameter replaces the distance parameter. When two points are close to each other, they can be simply separated if they have high NI. Unlike other hierarchical methods, depending on the facies behavior, the user can specify the number of facies (Pabakhsh et al., 2012; Bisht et al.). KRI is a combination of NI, distance and weighted distance function M (x, y) which determine boundaries and distinguish different group by the allocation of the degree of membership for M. (Pabakhsh et al., 2012). If it is low, it is affected by M; otherwise, it has a high membership degree and is not affected by M (Pabakhsh et al., 2012; Bisht et al.).
Table 2 Results of MRGC clustering in well A. Facies No
Color
Phie (v/v)
Perm (md)
T2lm(ms)
Dominant Lithology
1 2 3 4 5 6 7 8 9
Blue Green Yellow Orange Black Cyan Red Magenta Brown
0.003 0.05 0.085 0.117 0.225 0.01 0.071 0.13 0.17
0 0.16 0.73 5 42 0.1 0.76 1.5 1.5
5.79 42.25 111.27 153.53 319.12 19.22 132.63 231.28 338.35
Anhydrite Anhydrite + Dolomite Dolomite Dolomite Dolomite Lime Lime Lime Lime
information on about parameters controlling the fluid flow, pore-filling fluids and petrophysical characteristics associated with relaxation processes. In NMR analysis, fluids interactions in porous medium control the relaxation process by three independent mechanisms. These mechanisms include bulk fluid processes, surface relaxation and diffusion. Surface relaxation depends on the specific internal surface area based on pore size, permeability and capillary pressure. It must be noted that the pore geometric properties derived from NMR measurements are controlled by pore throat size and the connectivity of the pores besides permeability and capillary pressure (Saidian and Prasad, 2015; Meiboom and Gill, 1958; Meiboom and Gill, 1958, 1958 Kleinberg et al., 1994). A fundamental problem normally observed in the derived relationships was correlating pore body size to pore throat size. To solve this problem, Ohen et al. (1996) proposed a relation between the surface area to volume ratio of the pore space, porosity, and the specific surface per grain volume ratio (Sgv). The relaxation groups are defined as follows (Ohen et al., 1996):
n 1
NI (X ) =
KRI = NI (x ) M (x , y ) D (x , y )
*10
1.95)/(2.95
[(0.45
1.95)]
NPHI )/(( 0.15)
0.45)]*10
(4)
In which M, is the weighting distance, D is the distance between x and y (Bisht et al.). In this method, the disadvantages of other clustering methods such as prior-knowledge about the number of clusters, initial parameters, and the reliability of results were eliminated. MRGC is a tool which analyzes the structure of the complex data and partition natural data groups into different shapes, sizes, and densities. MRGC is a recognition method for determining the optimal number of clusters which allows geologist to define flow units (Eberli et al., 2003). In this study, MRGC technique was coupled with the relaxation group analysis to cluster similar permeability, porosity and volume T2 distributions according to 1/ρSgv and NDS parameters on well A. Fig. 2a shows the crossplot of 1/ρSgv versus NDS for Kangan formation obtained from MRGC clustering technique. Variation of relaxation time for each extracted flow units is depicted in Fig. 2a as well. Reservoir properties for each relaxation group are presented in Table 2. Fig. 2b and c shows crossplots for different logs. Crossplots are normally used for investigating the correctness of the model. Fig. 2b depicts the crossplot between neutron and density logs. This figure clarified that the value of density was different for various relaxation groups. Relaxation group 1 (Blue), for instance, had high densities, hence having lower porosity. It is generally accepted that the porosity value increases as the density decreases. Relaxation group 4 (Orange), on the other hand, was more scattered. Rock texture, diagenesis and dolomitization must be the reason behind this scattering behavior. Fig. 2c depicts DT log versus NPHI. It can be inferred from this figure that the dolomitized relaxation group had higher porosities than the others did. This fact confirmed the validity of the model. Relaxation groups obtained from MRGC clustering technique on well A are depicted in Fig. 3. Agreements between core permeability, gas content, water saturation and T2 indicated the reliability of the technique used for clustering. In this figure, Track 1 depicted understudied depths, Track 2 was related to gamma ray and caliper logs and bit size. Track 3 showed NPHI and density logs, Track 4 was the resistivity log, Track 5 was DT compressional with neutron density separation, Track 6 was lithology, Track 7 was the volume of gas-water. Moreover, Track 8 was relaxation results from MRGC method, Track 9 was T2 distribution achieved from NMR log, T2LM was logarithmic mean of T2, Track 10 was the effective porosity distribution, whose red points was related to core porosity and finally, and Track 11 depicted core permeability.
Here, T2 is the observed transverse relaxation time, Sgv is the specific surface per grain volume ratio, φz is the porosity group and the ρ is the relaxation surface. T2 parameter can be easily converted to porosity. Relaxation time is also related to porosity and forms the base of relaxation group concept. The concept of relaxation group is very much alike the hydraulic unit concept. The factor 1/ρSgv is often recognized as relaxation product, representing the relaxation power and textural attributes of the formation. Equation (1) states that the logarithmic plot of T2 versus ϕz would be a straight line where 1/ρSgv would be a constant one. It is important to mention that the porosity measurement by NMR log is not affected by matrix materials. NMR porosity is independent of lithology; hence, it does not need to be calibrated for different lithologies and different intervals of a well. This is one of the significant advantages of NMR compared with conventional logs like sonic, neutron and bulk density logs. Another concept to be introduced is the neutron-density separation (NDS) concept where density and neutron porosity logs are combined to enhance the accuracy of facies identification. NDS can be obtained from the following equation (Ohen et al., 1996):
NDS = [(RHOZ
(3)
Where ‘m’ the neighbor ranking, ‘a’ is the resolution parameter.
(1)
log [T2] = log ( z ) + log (1/ Sgv )
exp ( mn. a ) N =1
(2)
In this study, the relaxation groups were defined based on 1/ρSgv parameter that obtained NMR data and combining it with NDS log. This process allowed the capture of both primary and secondary porosity types. 3.2. Determining of optimum number of relaxation group Recently, the multi-resolution graph-based clustering (MRGC) has been widely used for the reservoir studies. Ye S and Rabiller (2000) 4
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Fig. 3. Relaxation groups (facies) that were obtained after applying MRGC clustering on well A.
4. Fuzzy logic for relaxation groups prediction in wells without NMR data
corresponding to “true” and “false” (Von Altrock, 1995). Fuzzy logic helps guarantee precision and quality and avoid inconsistency and uncertainty (Bilgen, 2010). Fuzzy logic systems have been applied successfully in different research areas such as reservoir characterization, rock typing and lithofacies in uncored but logged wells (Bilgen, 2010; Cuddy, 2000; Saggaf and Nebrija, 2003; Abdulraheem et al., 2007; Hamidi et al., 2010; Shokir, 2006; Taghavi, 2005). Modestus and Angella (2018) reviewed the applications of fuzzy logic in petroleum exploration, production and
Fuzzy Logic is a suite of modules that uses fuzzy mathematics for prediction of relaxation groups from wireline logs. Fuzzy logic works by assigning a probability to the quality of the prediction from each parameter, and then combines the probabilities and predicts the most likely outcome. The basic idea of fuzzy logic is to deal with the whole interval [0,1] as degrees of truth in addition to the values 1 and 0 5
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Fig. 4. The comparison between the relaxation groups obtained from MRGC and Fuzzy logic techniques in well A.
Table 3 The accuracy and recall values of each relaxation group predicted by Fuzzy logic method.
Recall Value Accuracy
Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7
Class 8
Class 9
0.944 0.97
0.93 0.96
0.82 0.81
0.73 0.96
0.91 0.82
0.84 0.76
0.79 0.71
0.82 1
0.96 0.85
6
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Fig. 5. Relaxation group predicted by Fuzzy logic method in well B.
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Fig. 6. Relaxation group predicted by Fuzzy logic method in well C.
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Table 4 Vp/Vs ratio recall values in different lithology. lithology
Vp/Vs Value
Sandstone Dolostone (Dolomite) Limestone Anhydrite and Shale
1.55–1.70, 1.65–1.80, 1.80–1.90, 1.90–2.00,
normally normally normally normally
near near near near
1.60 1.70 1.80 1.95
was the effective porosity distribution. Redpoints were related to core porosity. In Fig. 6, Track 1 depicted the studied depths, Track 2 was standard gamma ray log, Track 3 was DT compressional and NPHI logs, Track 4 showed lithology, Track 5 was effective porosity, Track 6 was the obtained facies, Track 7 was the effective porosity distribution, red points were related to core porosity. Finally, Track 8 depicted core permeability. In Fig. 7, Track 1 depicted understudied depths, Track 2 was gamma ray log, Track 3 was DT compressional and NPHI logs, Track 4 showed lithology, Track 5 was effective porosity, Track 6 showed facies, Track 7 was the effective porosity distribution, red points were related to core porosity and finally, Track 8 indicated core permeability Data points were colored according to the obtained relaxation group from fuzzy logic. 4.1. Introducing a Vp/Vs versus NDS crossplot for calculation of the cementation factor Heterogeneity, particularly texture and porosity type, greatly affect the acoustic velocities of carbonate rocks (Modestus and Angella, 2018; Weger et al., 2009; King, 1966). Therefore, Vp/Vs ratio and its relation with porosity may be affected by these parameters. Vp/Vs ratio can be used to identify different lithologies as shown in Table 4. This ratio is very sensitive to pore fluids. When compared to brine saturated samples, it is usually lower about 10 and 20 percent in dry samples (King, 1966; Tatham, 1982; Tatham and Stoffa, 1976). Based on these facts, Vp/Vs was a good parameters used for identifying rock and fluid types (Tatham, 1982; Tatham and Stoffa, 1976). It is generally accepted that a significant indication to detect gas bearing formations is the separation between neutron and density logs. Sonic log is only sensitive to the primary intergranular porosity. By contrast, the density and neutron logs record the total porosity. The neutron and density logs are, therefore, responses to pores of all sizes. Furthermore, sonic logs are a measure of intergranular or intercrystalline porosity, largely insensitive to fractures or vugs, which is a wellknown fact. Finally, the points on this crossplot, related to the relaxation groups obtained from previous steps were colored. These points were divided into regions based on fluid saturation, porosity type and lithology (Fig. 8-a, 8-b). Relaxation groups were classified according to the reservoir properties. The results of neutron log was commonly expressed in apparent water-filled porosity units. A constant lithology was assumed; therefore, this log was not always representative of actual pore fluid. On the other hand, the measurements by NMR and/or core data were closer to reality; hence, providing reliable estimations of reservoir capacity. Vuggy carbonate reservoir characterization was difficult though. NMR data could be used to see the difference between vuggy and matrix porosity, as a result of which, pore size could be characterized correctly. Vuggy systems can be divided into two different categories; i.e., separate and touching vugs. T2 curves are different for these two classes. In case of separate vugs, T2 curve is broad; spanning at least three peaks across T2 time axis with each one showing tri-modal curve peaks. These curves are not repeatable, i.e. each curve has a unique shape. In contrast, T2 curves for touching vugs showed poly modal amplitude peaks with the same span. A relationship between cementation factor and effective porosity is shown in Table 5. This relationship was obtained based on the core data provided for each
Fig. 7. Cross plot of porosity and core permeability.
distribution operations. In this study, Fuzzy mathematical method is applied to predict relaxation groups in wells with no NMR data (i.e., wells B and C) for the relaxation groups previously obtained by MRGC clustering technique and the available wireline data. The number of logs used for the prediction is not limited. However, a sensitivity study showed that four logs had competitive importance in rock typing. These logs included effective porosity (PHIE), neutron porosity (NPHI), neutron density separation (NDS) and sonic (DT). Relaxation group for the well A (having NMR data) obtained by MRGC technique was compared with the result obtained by fuzzy logic technique applied on this well. This was done to test the uncertainty of rock typing method. The comparison showed a very good agreement (see Fig. 4). The accuracy and recall value of each relaxation group were also calculated and presented in Table 3. The results obtained from fuzzy logic prediction in wells B and C calibrated with core and petrophysical data are depicted in Figs. 5 and 6. The comparison between the results of fuzzy logic predictions and petrophysical evaluations showed an acceptable agreement. Crossplot of core permeability versus core porosity was plotted for well B (Fig. 7) to validate the fuzzy model. The color of points were derived from the related relaxation group. As can be seen in this figure, the clustering method was performed correctly. In class 2, some data with high permeability had low porosity. This feature was the sign of fractures. In Fig. 5, Track 1 depicted understudied depths, Track 2 was standard gamma ray log, track 3 was DT compressional and NPHI logs. Moreover, Track 4 showed lithology, Track 5 was effective porosity, Track 6 included facies obtained from MRGC method, Track 7 was the volume of gas and water obtained from fuzzy logic method and finally Track 8 9
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Fig. 8. a) Crossplot of NDS and Vp/Vs ratio. Different colors were related to different relaxation groups, Fig. 8b) Lithology related to Crossplot of NDS and Vp/Vs ratio.
Table 5 The relationship between cementation factor and effective porosity for each relaxation group. Class No.
Cementation factor equation
Class Class Class Class Class Class Class Class
m = −17.523 phie2 + 7.671 phie +1.3088 m = 0.5272 phie+ 2.049 2 to 2.2
1 2 3 4 5 6 7 8
m m m m
= = = =
Table 6 Comparison of the new water saturation method with the old method (m = 2).
7.2105 phie +1.6156 9.8118 phie +1.5384 1.452 phie +1.7527 1.4948 phie +1.8726
Well
Mean of calculated Sw by new M
Mean of calculated Sw by M=2
Difference (%)
A B C
0.4968 0.4351 0.5654
0.4092 0.2757 0.4503
9% 16% 11%
following table, the new water saturation is compared with the old method (m = 2). The advantage of the new crossplot is its easiness to be applied because it introduces a variable cement exponent in calculation of water saturation. The Archie's equation is used to determine the water saturation that cement exponent (m) is the most importance entrance in Archie's equation. In fact, cement exponent is strongly dependent on the pore pattern distribution, wettability, pore throat size, type of rock grains and mineralogical properties. This parameter is sometimes assumed constant to simplify the petrophysical measurements in the wells without core data whereas this is variable particularly in the heterogeneous carbonate reservoirs. Inaccurate estimates of this parameter lead to significant error in the water saturation. In the present study, NMR log was used to determine the cement factor using new crossplot and provides information about pore size distribution, formation permeability, hydrocarbon porosity, vugs, fractures and grain size that have a direct relation with cement factor. Actually, the new crossplot introduces a variable cement exponent in calculation of the water saturation. This crossplot can be used in the wells without core data and
relaxation group. It must be mentioned that the cementation factor values were provided for the specified reservoir condition as higher values related to the vuggy porosity and lower values related to fracture porosity. The above-mentioned method had the advantage of being quick and robust for predicting the cementation factor in complex carbonate gas reservoirs. This cross plot reduced the uncertainty in the water saturation calculations (see Table 6). 5. Comparing the calculated new saturation water with the old saturation In this study, the calculated new saturation water was compared with the old method (m = 2). In the new saturation, water was used as a variable cement exponent that was obtained from the novel crossplot. This saturation was more consistent with the production report. In the
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Fig. 9. Comparison of the calculation of water saturation with the new method and the old method (m = 2) in WELL A.
Fig. 10. Comparison of the calculation of water saturation with the new method and the old method (m = 2) in WELL B.
reduces error in calculation of the water saturation. In Figs. 9–11, the new water saturation is compared with the old method (m = 2) in wells A, B and C, respectively. In these figures, the old water saturation is displayed by the red curve in the last track from the right.
distribution, pore geometry, and wettability of the reservoir rock affected the amount of cementation factor (m) and saturation exponent (n) in Archie formula (Wardlaw, 1980; Elias and Steagall, 1996). Choquette and Pray (1970) identified fifteen basic pore types. Indeed, the effect of vugs, connected (touching) or not connected pores, and the extent to which vuggy porosity contributed to total porosity were considered in the classification of carbonate porosity (Lucia, 1983). Ahr (2008) proposed the genetic classification of porosity for carbonate reservoirs. He classified pores by their geological origin, related pore geometry, vug type and geologic processes and brought about a simple and applicable conceptual model. This classification was
6. Discussion Cementation factor was greatly affected by secondary porosity, surface area per unit volume, cement properties, pore throat size and water conductivity (Tatham and Stoffa, 1976; Ransom, 1984; Rasmus, 1986). Moreover, it depended on the shape and surface of composite particles and tortuosity factor. Other researchers showed that factors like reservoir pressure and temperature, mineralogy, pore throat size 11
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Different parameters like pore size, the strength of the surface relaxation, wettability of rock surface and type of fluid contained in rock pores determined which of the abovementioned mechanisms was dominant. In general, these mechanisms acted in parallel. Pore origin was related to different pore geometries as well. Depositional, diagenetic and hybrid origin were, in turn, used for identifying the NMR signature characteristics. T2 time was a measure of surface-to-volume ratio, so that rapid relaxation in T2 time corresponded to small pores and long T2 relaxation time was related to large pores. Therefore, each T2 value corresponded to different pore sizes. Based on Fig. 12, porosity type could affect T2 curve distribution obtained from NMR. Carbonates, for instance, exhibited T2 curves with low amplitude. Pores in carbonates were diagenetically reduced by cementation. T2 relaxation time was therefore very short in these rocks. On the other hand, rocks containing vugmolds, intercrystalline and interparticle pores had high T2 amplitudes. Generally, higher amplitude values were associated with larger and more frequent pores. It is generally accepted that in carbonate rocks, hybrid and intercrystalline pores show near symmetric, narrow wavelengths in T2 time. Moreover, it is believed that moldic pores and rocks with both separate and touching vugs display fast-skewed with curve widths spanning 3 peaks in T2 time. 6.1. Cementation factor (m) and Vp/Vs ratio Two classes of parameters affected the velocity of waves in carbonate rocks. One class was related to rock structure. Parameters like lithology, porosity and grain size were involved in this class. The second class contained parameters describing the depositional environment, which was not related to rock structure. Parameters like confining stress, age of deposition and burial depth were involved in this class. Fluid velocity was higher in rocks with vuggy porosity because increasing fluid pressure in pore space would reduce the porosity and the grain contacts becoming closer to each other and would increase fluid velocity as a result. Therefore, pressure controls fluid velocity in vuggy rocks saturated with brine or hydrocarbon. 7. Conclusions Accurate determination of cementation factor (m) provided reliable saturation results and consequently provided hydrocarbon reserve calculations. A novel crossplot was introduced in this study, where each class of rocks had a relationship between cementation factor and effective porosity. This crossplot provided a quick method of estimating the cementation factor in carbonate gas reservoirs with complex structures. The presented methodology was advantageous as the water saturation could be calculated with the least uncertainty because a continuous log of m value was provided for different rock types. The new crossplot was created from various types of logs such as NMR, density, neutron, compressional and shear sonic and core data as well. The crossplot included important parameters like mineralogy, secondary porosity, pore geometry, pore throat size distribution, water and mineral conductivity, cementation characteristics and surface area per unit volume. Thus, the crossplot helped us achieve a new classification confirming that of Ahr. Genetic pore types best distinguished pore throat size distribution. Therefore, genetic pores were directly related to permeability value. Carbonates had different porosity types and different T2 relaxation curves for their permeability. The present work provides a strategy for separating reservoir into different layers. This provided the idea of reservoir quality at different depths and the idea on how heterogeneity might affect reservoir quality.
Fig. 11. Comparison of the calculation of water saturation with the new method and the old method (m = 2) in WELL C.
probably the best choice to identify flow units in stratigraphic contexts (Fig. 13). The study used different logs including NMR, neutron, density and compressional and sonic shear to obtain a classification like that of Ahr. NMR data, valuable and reliable data, could be used to determine rock type in carbonate formations. In addition, three independent relaxation mechanisms were used to determine fluids contained in rock pores. Theses mechanisms were as follows: 1 Surface relaxation at solid 2 Bulk relaxation 3 Diffusion-induced relaxation 12
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Fig. 12. Classification of fifteen carbonate pore types. The five most common types of pores in this study have been outlined in black (Choquette and Pray, 1970).
Fig. 13. Genetic classification of porosity after Ahr (2008).
Acknowledgements
References
The authors would like to gratitude Mahdi Rastegarnia and Morteza Amiri, the head of Petrophysic department in Asmary Company and POGC, respectively for providing cooperation, guidance and sharing knowledge and valuable experience.
Abdulraheem, A., Sabakhy, E., Ahmed, M., Vantala, A., Raharja, P.D., Korvin, G., 2007, January. Estimation of permeability from wireline logs in a middle eastern carbonate reservoir using fuzzy logic. In: SPE Middle East Oil and Gas Show and Conference. Society of Petroleum Engineers. Aguilera, R., 1976. Analysis of naturally fractured reservoirs from conventional well logs (includes associated papers 6420 and 6421). J. Pet. Technol. 28 (07), 764–772. Ahr, W.M., 2008. A new genetic classification of carbonate porosity and its application to reservoir characterization. In: American Association of Petroleum Geology Annual Convention (Abstract), San Antonio. Archie, G.E., 1942. Electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME 146 (01), 54–62. Arifianto, I., et al., 2018. Application of flow zone indicator and Leverett J-function to characterise carbonate reservoir and calculate precise water saturation in the Kujung formation, North East Java Basin. 15 (4), 1753.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jngse.2019.102942. 13
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A. Movahhed, et al. Bilgen, B., 2010. Application of fuzzy mathematical programming approach to the production allocation and distribution supply chain network problem. Expert Syst. Appl. 37 (6), 4488–4495. Bisht, B. S., Konka, S., & Dobhal, J. P. Prediction of Missing Log Data Using Artificial Neural Networks (ANN), Multi-Resolution Graph-Based Clustering (MRGC) and Multiple Regression Techniques. Choquette, P.W., Pray, L.C., 1970. Geologic nomenclature and classification of porosity in sedimentary carbonates. AAPG Bull. 54 (2), 207–250. Cuddy, S.J., 2000. Litho-facies and permeability prediction from electrical logs using fuzzy logic. SPE Reserv. Eval. Eng. 3 (04), 319–324. De Marsily, M., 1986. Quantitative Hydrogeology; Groundwater Hydrology for Engineers. Academic Press, San Diego. Eberli, G.P., et al., 2003. Factors controlling elastic properties in carbonate sediments and rocks. Lead. Edge 22 (7), 654–660. Elias, V.L.G., Steagall, D.E., 1996. The impact of the values of cementation factor and saturation exponent in the calculation of water saturation for Macae formation, Campos basin. In: SCA Conference. Focke, J., Munn, D., 1987. Cementation exponents in Middle Eastern carbonate reservoirs. SPE Form. Eval. 2 (02), 155–167. Gharachelou, S., Amini, A., Kadkhodaei, A., Hosseini, Z., Honarmand, J., 2018. Rock typing and reservoir zonation based on the NMR logging and geological attributes in the mixed carbonate-siliciclastic Asmari Reservoir. Geopersia 8 (1), 77–98. Hamidi, J.K., Shahriar, K., Rezai, B., Bejari, H., 2010. Application of fuzzy set theory to rock engineering classification systems: an illustration of the rock mass excavability index. Rock Mech. Rock Eng. 43 (3), 335–350. Kadhim, F.S., Samsuri, A., Kamal, A., 2013. A review in correlation between cementation factor and carbonate rock properties. Life Sci. J. 10 (4), 2451–2458. King, T.J., 1966. Nuclear transplantation in amphibia. In: Methods in Cell Biology. Elsevier, pp. 1–36. Kleinberg, R.L., Kenyon, W.E., Mitra, P.P., 1994. Mechanism of NMR relaxation of fluids in rock. J. Magn. Reson. Ser. A 108, 206–214. Lucia, F., 1983. Petrophysical parameters estimated from visual descriptions of carbonate rocks: a field classification of carbonate pore space. J. Pet. Technol. 35 (03), 629–637. Meiboom, S., Gill, D., 1958. Modified spin echo method for measuring nuclear relaxation times. Rev. Sci. Instrum. 29 (8), 668–691. Modestus, Okechukwu Okwu, Angella, N., 2018. A review of fuzzy logic applications in petroleum exploration, production and distribution operations. J. Pet. Explor. Prod. Technol. 5. https://doi.org/10.1007/s13202-018-0560-2. Nabawy, B.S., 2015. Impacts of the pore-and petro-fabrics on porosity exponent and lithology factor of Archie's equation for carbonate rocks. J. Afr. Earth Sci. 108, 101–114. Ohen, A.H., Ajufo, A., Enwere, M.P., 1996. Laboratory NMR relaxation measurements for the acquisition of calibration data for NMR logging tools. In: Paper SPE 35683 Presented at the SPE Western Regional Meeting Held in Anchorage, Alaska, pp. 22–24. Pabakhsh, M., Ahmadi, K., Riahi, M.A., Shahri, A.A., Branch, T., 2012. Prediction of PEF and LITH logs using MRGC approach. Life Sci. J. 9 (4), 974–982. Rafiee, S., Hashemi, A., Shahi, M., 2014. A new cementation factor correlation in carbonate parts of oil fields in south-west Iran. Iran. J. Oil Gas Sci. Technol. 3 (2), 1–17. Rahuma, K.M., B.M.B., Ghawar, 2017. Effect of saturation exponent and cementation factor on water saturation in carbonate reservoir. Pet. Coal 59 (1). Ransom, R.C., 1984. A Contribution to a Better Understanding of the Modified Archie
Formation-Resistivity-Factor Relationship. The Log Analyst. SPWLA. Rasmus, J., 1983. A variable cementation exponent, m, for fractured carbonates. Log. Anal. 24 (06). Rasmus, J.C., 1986. A summary of the effects of various pore geometries and their wettabilities on measured and in-situ values of cementation and saturation exponents. In: SPWLA 27th Annual Logging Symposium. Society of Petrophysicists and Well-Log Analysts. Rastegarnia, A., Khadkhodaie, A., 2013a. Estimation of flow zone indicator distribution by using seismic data: a case study from a central Iranian oilfield. Iran. J. Oil Gas Sci. Technol. 2 (4), 12–25. Rastegarnia, A., Khadkhodaie, A., 2013b. Permeability estimation from the joint use of stoneley wave velocity and support vector machine neural networks: a case study of the Cheshmeh Khosh field, South Iran. Geopersia 3 (2), 87–97. Rastegarnia, M., Talebpour, M., Sanati, A., 2017. Prediction of electrofacies based on flow units using NMR data and SVM method: a case study in Cheshmeh Khush field, southern Iran. J. Pet. Sci. Technol. 7 (3), 84–99. Rastegarnia, M., Sanati, A., Javani, D., 2018. Application of TDA technique to estimate the hydrocarbon saturation using MRIL Data: a Case study for a Southern Iranian Oilfield. J. Geopersia 8 (1), 99–110. Riazi, Z., 2018. Application of integrated rock typing and flow units identification methods for an Iranian carbonate reservoir. J. Pet. Sci. Eng. 160, 483–497. Saggaf, M.M., Nebrija, E.L., 2003. A fuzzy logic approach for the estimation of facies from wire-line logs. AAPG Bull. 87 (7), 1223–1240. Saidian, M., Prasad, M., 2015. Effect of mineralogy on porosit, pore size distribution and surface relaxivity on nuclear magnetic resonance characterizations: a case study of middle Bakken and three forks formations. J. Fuel (submitted for publication). Salem, H.S., Chilingarian, G.V., 1999. Cementation factor of Archie's equation for shaly sandstone reservoirs. J. Pet. Sci. Eng. 23 (2), 83–93. Shahi, M., Salehi, M.M., Kamari, M., December 2018. New correlation for estimation of cementation factor in Asmari carbonate rock reservoirs. Egypt. J. Pet. 27 (4), 663–669. Shokir, E.M., 2006. A novel model for permeability prediction in uncored wells. SPE Reserv. Eval. Eng. 9 (03), 266–273. Song, Y.Q., 2013. Magnetic resonance of porous media (MRPM): a perspective. J. Magn. Reson. 229, 12–24. Taghavi, A.A., 2005. Improved permeability estimation through use of fuzzy logic in carbonate reservoir from Southwest Iran. In: SPE 93269 Presented at the 14th SPE Middle East Oil and Gas Show and Conference Held in Bahrain International Exhibition Centre, 12–15 March. Tatham, R.H., 1982. V p/V s and lithology. Geophysics 47 (3), 336–344. Tatham, R.H., Stoffa, P.L., 1976. V p/V s—a potential hydrocarbon indicator. Geophysics 41 (5), 837–849. Towle, G., 1962. An analysis of the formation resistivity factor-porosity relationship of some assumed pore geometries. In: SPWLA 3rd Annual Logging Symposium. Society of Petrophysicists and Well-Log Analysts. Von Altrock, C., 1995. Fuzzy Logic and Neurofuzzy Applications Explained. Prentice-Hall, Inc. Wardlaw, N., 1980. The Influence of Pore Structure in Rocks on the Entrapment of Oil. Weger, R.J., et al., 2009. Quantification of pore structure and its effect on sonic velocity and permeability in carbonates. AAPG Bull. 93 (10), 1297–1317. Ye S, J., Rabiller, P., 2000. A new tool for electro-facies analysis: multi-resolution graphbased clustering. In: SPWLA 41th Annual Logging Symposium.
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Introducing a method for calculating water saturation in a carbonate gas reservoir
T
Ata Movahheda, Majid Nabi Bidhendib,*, Mohsen Masihic, Abolghasem Emamzadehd a
Department of Natural Resources and Environment, Science and Research Branch, Islamic Azad University, Tehran, Iran Institute of Geophysics, University of Tehran, Tehran, Iran c Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran d Department of Chemical and Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran b
ARTICLE INFO
ABSTRACT
Keywords: Vp/Vs ratio Water saturation Carbonate gas reservoir NMR NDS
Cementation factor greatly affects water saturation estimation. Factors such as depositional environment, diagenesis and depositional architecture make the estimation of water saturation a big challenge in carbonate reservoirs. The current study is introduced a method for calculating cementation factor in Archie formula. First, (MRGC) technique was applied on the (NMR) logging parameters along with (NDS) data to obtain the optimum number of clustering. After that, fuzzy logic method was applied on conventional log parameters obtained from the wells without any NMR log data. In the third part of the study, a novel crossplot introduced including compressional to shear-wave velocity ratio (Vp/Vs ratio) and NDS parameters. Finally, available core data was used to obtain a relationship between cementation factor and effective porosity for each region. Proposed method had advantage of obtaining a variable cementation factor instead of a constant one.
1. Introduction Cementation factor (m) is an important parameter for water saturation calculation thus affecting the calculation of the amount of hydrocarbon in place. This parameter is usually considered constant for the whole reservoir interval. This assumption leads to large uncertainties in the estimation of water saturation content especially in carbonate reservoirs. Given the microbial and diagenetic processes, carbonate reservoirs have heterogeneous rock properties strongly related to m value and the m value is strongly affected by pore connectivity. Grain and pore shapes and the connectivity between pores determine the cementation factor (Salem and Chilingarian, 1999). Average value of m in literature is 2, representative of interparticle porosity (Archie, 1942). Some special cases make m value to be deviated from 2. For instance, fractured rocks have smaller m value because of better electrical connectivity (Aguilera, 1976; Rasmus, 1983; Towle, 1962). In contrast, rocks having non-touching vugs have large values for m (Focke and Munn, 1987; Lucia, 1983). Carbonate reservoirs contain both fractures and vugs; hence, porosity varies when depth changes. For these kinds of formations, due to heterogeneous behavior, a physical model with triple porosity system was used for the estimation of the m value. This model assumed that the non-connected
(separate or non-touching) vugs, fractures and matrix contributed to the total porosity of the system. Kadhim et al. (2013) conducted a comprehensive investigation on the properties of carbonate reservoirs with a focus on determining the cementation factor. They suggested the Gomes and Pickett correlation for determining m value, usually between 1.3 and 3. They stated the existence of very limited correlations for defining variable cementation factor. Arifianto et al. (2018) Investigated the Leverett J-function for characterizing carbonate reservoir and calculating precise water saturation. They concluded that water saturation, calculated from Leverett J-Function method, provided a more precise result when compared to Archie's water saturation method. Rafiee et al. (2014) used the results of electrical resistivity experiments to develop a new cementation factor correlation for a carbonate reservoir. Using this new correlation, they proposed a new method for calculating water saturation. Rahuma and Ghawar (2017) performed a sensitivity analysis for investigating the effect of variation of cementation factor and saturation exponent parameters on water saturation in carbonate reservoirs. They observed a maximum spread difference of 15% resulting from the variation of these parameters. Nabawy (2015) showed that the great variation of cementation factor (or porosity exponent) was due to their dependence on several factors, e.g. porosity, permeability and
*
Corresponding author. E-mail addresses: [email protected] (A. Movahhed), [email protected] (M.N. Bidhendi), [email protected] (M. Masihi), [email protected] (A. Emamzadeh). https://doi.org/10.1016/j.jngse.2019.102942 Received 18 March 2019; Received in revised form 25 June 2019; Accepted 13 July 2019 Available online 24 July 2019 1875-5100/ © 2019 Elsevier B.V. All rights reserved.
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Table 1 Data obtained from each well. Well
Full set data
NMR data
Core data
A B C
✓ ✓ ✓
✓
✓ ✓ ✓
formation factor. Riazi (2018) conducted a case study on rock typing and flow unit classification for a carbonate reservoir. She implemented four different petrophysical methods including Rock Fabric Number (RFN), Winland porosity-permeability plot (R35), Reservoir Quality Index/Flow Zone Indicator (RQI/FZI), and Bulk Volume Water (BVW) on four exploration wells. Shahi et al., 2018 established a new correlation between petrophysical parameters and porosity and compared it with Borai et al. correlations. Their results showed that the proposed method worked slightly better than the above-mentioned well-established methods. Petrophysical parameters such as porosity, water and oil saturations, formation resistivity factor, etc. describe the storage capability of the porous media or the capacity of rocks to hold fluids. The Archie's equation, also called the saturation equation, is used to determine the water saturation. Archie's parameters, namely “m”, “n” and “a” are sometimes assumed constant to simplify petrophysical measurements, But these parameters are not constant, particularly in heterogeneous reservoirs. Inaccurate estimates of these parameters can cause significant errors in the calculation of water saturation when using Archie's equation and lead to discrepancies between log interpretation and production test results. There are many factors affecting cementation factor (m) such as porosity, pore throat size, type of rock grains, type and distribution of clay content, degree of cementation, and overburden pressure (Rastegarnia et al., 2018). The current study used Vp/Vs ratio and NDS parameters along a novel crossplot for identifying the cementation factor and other controlling factors in gas reservoirs with different types of porosities (fracture, vuggy, vuggy channels and intercrystalline).
Fig. 1. The flow chart that shows the steps to perform the analysis.
NMR responses and Fullset data were used to find the electrofacies based on the relaxation groups. Concept of relaxation group was equal to the hydraulic unit concept. In order to do this, the equation of logT2 = log(ϕz)+log[1(ρSgv)] is used where T2 is the observed transverse relaxation time and ϕz is the porosity group which is obtained from (1−ϕ)/ϕ equation. The parameter l/ρSgv is often recognized as the relaxation factor representing the relaxation power and textural attributes of the formation (Rastegarnia and Khadkhodaie, 2013a, 2013b; Rastegarnia et al., 2017). As Table 1 shows, well A had NMR and fullset data whereas wells B and C had only conventional data. So, relaxation groups modeling was first applied on well A for the analysis. Then the relaxation group was propagated to wells B and C using Fuzzy logic method. The results were compared to those of petrophysical evaluation and core data for the verification of the propagated relaxation groups. The comparison showed great agreement. Fig. 1 shows the steps to perform the analysis which are summarized in the flowchart.
2. Geological setting The studied region was located on the Iran-Qatar border in the Persian Gulf shared by these two countries. The study examined the Kangan formation. This formation was subdivided into two principal reservoir units: Lower part of the Kangan Formation (K2 unit) Upper part of the Kangan Formation (K1 unit) Main lithology of K2 unit is composed of dolomite (in the upper part) and limestone (in the lower part). K2 reservoir unit is dominated by a stack of lime oomoldic and biomoldic grainstones having good porosity. Within the limestones, the dominant porosity types are moldic; within the dolomites, the dominant porosity types are vuggy, interparticle and intercrystalline. K1 reservoir units are mainly characterized by the development of limestone and dolomitic beds with moderate reservoir characteristics. The reservoir units start with dolomitized oolitic facies with moderate poroperm characteristics (intergranular, moldic and vuggy porosities). Within the central part of K1, there is a limited reservoir development, which is developed in limestone tidal oolitic grainstone.
3.1. NMR relaxation based rock typing Hydraulic properties of reservoir rocks are critical in controlling the fluid flow in porous media (De Marsily, 1986). Permeability estimation is more important and permeability measuring on core data, while reliable, is expensive, time consuming, and restricted only to the cored intervals. Moreover, depending on the sampling strategy and recovery, preservation and preparation of some severe discrepancies from reservoir conditions may occur (Gharachelou et al., 2018). Because of their continuous nature, the well logs data are proper substitutes for permeability determination (Song, 2013). In this regard, NMR logging technique is recommended for continuous estimation of porosity, permeability, capillary pressure (Pc), water saturation (Sw) and pore size distribution in carbonate hydrocarbon reservoirs (Gharachelou et al., 2018). On the other hand, NMR data analysis provides valuable
3. Materials and methodology The study used three wells petrophysical and core data. These wells were A, B and C located in Kangan formation in one of the Iranian southwestern gas fields. Table 1 summarizes the wells' data. 2
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Fig. 2. a) Cross plot of MRGC clustering results in the identification of relaxation groups. Fig. 2 b) Cross-plot of neutron porosity and density well logs classified by electrofacies, well A. Fig. 2c) Cross-plot of neutron porosity and sonic well logs classified by electrofacies, well A.
3
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proposed multi-dimensional dot-pattern recognition (MRGC) as a new clustering method for electro-facies analyses. MRGC is based on nonparametric K-nearest neighbor and graph data representation. This method uses Kernel Representative Index (KRI) and Neighborhood Index (NI) parameters which discern it from conventional methods. NI parameter replaces the distance parameter. When two points are close to each other, they can be simply separated if they have high NI. Unlike other hierarchical methods, depending on the facies behavior, the user can specify the number of facies (Pabakhsh et al., 2012; Bisht et al.). KRI is a combination of NI, distance and weighted distance function M (x, y) which determine boundaries and distinguish different group by the allocation of the degree of membership for M. (Pabakhsh et al., 2012). If it is low, it is affected by M; otherwise, it has a high membership degree and is not affected by M (Pabakhsh et al., 2012; Bisht et al.).
Table 2 Results of MRGC clustering in well A. Facies No
Color
Phie (v/v)
Perm (md)
T2lm(ms)
Dominant Lithology
1 2 3 4 5 6 7 8 9
Blue Green Yellow Orange Black Cyan Red Magenta Brown
0.003 0.05 0.085 0.117 0.225 0.01 0.071 0.13 0.17
0 0.16 0.73 5 42 0.1 0.76 1.5 1.5
5.79 42.25 111.27 153.53 319.12 19.22 132.63 231.28 338.35
Anhydrite Anhydrite + Dolomite Dolomite Dolomite Dolomite Lime Lime Lime Lime
information on about parameters controlling the fluid flow, pore-filling fluids and petrophysical characteristics associated with relaxation processes. In NMR analysis, fluids interactions in porous medium control the relaxation process by three independent mechanisms. These mechanisms include bulk fluid processes, surface relaxation and diffusion. Surface relaxation depends on the specific internal surface area based on pore size, permeability and capillary pressure. It must be noted that the pore geometric properties derived from NMR measurements are controlled by pore throat size and the connectivity of the pores besides permeability and capillary pressure (Saidian and Prasad, 2015; Meiboom and Gill, 1958; Meiboom and Gill, 1958, 1958 Kleinberg et al., 1994). A fundamental problem normally observed in the derived relationships was correlating pore body size to pore throat size. To solve this problem, Ohen et al. (1996) proposed a relation between the surface area to volume ratio of the pore space, porosity, and the specific surface per grain volume ratio (Sgv). The relaxation groups are defined as follows (Ohen et al., 1996):
n 1
NI (X ) =
KRI = NI (x ) M (x , y ) D (x , y )
*10
1.95)/(2.95
[(0.45
1.95)]
NPHI )/(( 0.15)
0.45)]*10
(4)
In which M, is the weighting distance, D is the distance between x and y (Bisht et al.). In this method, the disadvantages of other clustering methods such as prior-knowledge about the number of clusters, initial parameters, and the reliability of results were eliminated. MRGC is a tool which analyzes the structure of the complex data and partition natural data groups into different shapes, sizes, and densities. MRGC is a recognition method for determining the optimal number of clusters which allows geologist to define flow units (Eberli et al., 2003). In this study, MRGC technique was coupled with the relaxation group analysis to cluster similar permeability, porosity and volume T2 distributions according to 1/ρSgv and NDS parameters on well A. Fig. 2a shows the crossplot of 1/ρSgv versus NDS for Kangan formation obtained from MRGC clustering technique. Variation of relaxation time for each extracted flow units is depicted in Fig. 2a as well. Reservoir properties for each relaxation group are presented in Table 2. Fig. 2b and c shows crossplots for different logs. Crossplots are normally used for investigating the correctness of the model. Fig. 2b depicts the crossplot between neutron and density logs. This figure clarified that the value of density was different for various relaxation groups. Relaxation group 1 (Blue), for instance, had high densities, hence having lower porosity. It is generally accepted that the porosity value increases as the density decreases. Relaxation group 4 (Orange), on the other hand, was more scattered. Rock texture, diagenesis and dolomitization must be the reason behind this scattering behavior. Fig. 2c depicts DT log versus NPHI. It can be inferred from this figure that the dolomitized relaxation group had higher porosities than the others did. This fact confirmed the validity of the model. Relaxation groups obtained from MRGC clustering technique on well A are depicted in Fig. 3. Agreements between core permeability, gas content, water saturation and T2 indicated the reliability of the technique used for clustering. In this figure, Track 1 depicted understudied depths, Track 2 was related to gamma ray and caliper logs and bit size. Track 3 showed NPHI and density logs, Track 4 was the resistivity log, Track 5 was DT compressional with neutron density separation, Track 6 was lithology, Track 7 was the volume of gas-water. Moreover, Track 8 was relaxation results from MRGC method, Track 9 was T2 distribution achieved from NMR log, T2LM was logarithmic mean of T2, Track 10 was the effective porosity distribution, whose red points was related to core porosity and finally, and Track 11 depicted core permeability.
Here, T2 is the observed transverse relaxation time, Sgv is the specific surface per grain volume ratio, φz is the porosity group and the ρ is the relaxation surface. T2 parameter can be easily converted to porosity. Relaxation time is also related to porosity and forms the base of relaxation group concept. The concept of relaxation group is very much alike the hydraulic unit concept. The factor 1/ρSgv is often recognized as relaxation product, representing the relaxation power and textural attributes of the formation. Equation (1) states that the logarithmic plot of T2 versus ϕz would be a straight line where 1/ρSgv would be a constant one. It is important to mention that the porosity measurement by NMR log is not affected by matrix materials. NMR porosity is independent of lithology; hence, it does not need to be calibrated for different lithologies and different intervals of a well. This is one of the significant advantages of NMR compared with conventional logs like sonic, neutron and bulk density logs. Another concept to be introduced is the neutron-density separation (NDS) concept where density and neutron porosity logs are combined to enhance the accuracy of facies identification. NDS can be obtained from the following equation (Ohen et al., 1996):
NDS = [(RHOZ
(3)
Where ‘m’ the neighbor ranking, ‘a’ is the resolution parameter.
(1)
log [T2] = log ( z ) + log (1/ Sgv )
exp ( mn. a ) N =1
(2)
In this study, the relaxation groups were defined based on 1/ρSgv parameter that obtained NMR data and combining it with NDS log. This process allowed the capture of both primary and secondary porosity types. 3.2. Determining of optimum number of relaxation group Recently, the multi-resolution graph-based clustering (MRGC) has been widely used for the reservoir studies. Ye S and Rabiller (2000) 4
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Fig. 3. Relaxation groups (facies) that were obtained after applying MRGC clustering on well A.
4. Fuzzy logic for relaxation groups prediction in wells without NMR data
corresponding to “true” and “false” (Von Altrock, 1995). Fuzzy logic helps guarantee precision and quality and avoid inconsistency and uncertainty (Bilgen, 2010). Fuzzy logic systems have been applied successfully in different research areas such as reservoir characterization, rock typing and lithofacies in uncored but logged wells (Bilgen, 2010; Cuddy, 2000; Saggaf and Nebrija, 2003; Abdulraheem et al., 2007; Hamidi et al., 2010; Shokir, 2006; Taghavi, 2005). Modestus and Angella (2018) reviewed the applications of fuzzy logic in petroleum exploration, production and
Fuzzy Logic is a suite of modules that uses fuzzy mathematics for prediction of relaxation groups from wireline logs. Fuzzy logic works by assigning a probability to the quality of the prediction from each parameter, and then combines the probabilities and predicts the most likely outcome. The basic idea of fuzzy logic is to deal with the whole interval [0,1] as degrees of truth in addition to the values 1 and 0 5
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Fig. 4. The comparison between the relaxation groups obtained from MRGC and Fuzzy logic techniques in well A.
Table 3 The accuracy and recall values of each relaxation group predicted by Fuzzy logic method.
Recall Value Accuracy
Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7
Class 8
Class 9
0.944 0.97
0.93 0.96
0.82 0.81
0.73 0.96
0.91 0.82
0.84 0.76
0.79 0.71
0.82 1
0.96 0.85
6
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Fig. 5. Relaxation group predicted by Fuzzy logic method in well B.
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Fig. 6. Relaxation group predicted by Fuzzy logic method in well C.
8
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Table 4 Vp/Vs ratio recall values in different lithology. lithology
Vp/Vs Value
Sandstone Dolostone (Dolomite) Limestone Anhydrite and Shale
1.55–1.70, 1.65–1.80, 1.80–1.90, 1.90–2.00,
normally normally normally normally
near near near near
1.60 1.70 1.80 1.95
was the effective porosity distribution. Redpoints were related to core porosity. In Fig. 6, Track 1 depicted the studied depths, Track 2 was standard gamma ray log, Track 3 was DT compressional and NPHI logs, Track 4 showed lithology, Track 5 was effective porosity, Track 6 was the obtained facies, Track 7 was the effective porosity distribution, red points were related to core porosity. Finally, Track 8 depicted core permeability. In Fig. 7, Track 1 depicted understudied depths, Track 2 was gamma ray log, Track 3 was DT compressional and NPHI logs, Track 4 showed lithology, Track 5 was effective porosity, Track 6 showed facies, Track 7 was the effective porosity distribution, red points were related to core porosity and finally, Track 8 indicated core permeability Data points were colored according to the obtained relaxation group from fuzzy logic. 4.1. Introducing a Vp/Vs versus NDS crossplot for calculation of the cementation factor Heterogeneity, particularly texture and porosity type, greatly affect the acoustic velocities of carbonate rocks (Modestus and Angella, 2018; Weger et al., 2009; King, 1966). Therefore, Vp/Vs ratio and its relation with porosity may be affected by these parameters. Vp/Vs ratio can be used to identify different lithologies as shown in Table 4. This ratio is very sensitive to pore fluids. When compared to brine saturated samples, it is usually lower about 10 and 20 percent in dry samples (King, 1966; Tatham, 1982; Tatham and Stoffa, 1976). Based on these facts, Vp/Vs was a good parameters used for identifying rock and fluid types (Tatham, 1982; Tatham and Stoffa, 1976). It is generally accepted that a significant indication to detect gas bearing formations is the separation between neutron and density logs. Sonic log is only sensitive to the primary intergranular porosity. By contrast, the density and neutron logs record the total porosity. The neutron and density logs are, therefore, responses to pores of all sizes. Furthermore, sonic logs are a measure of intergranular or intercrystalline porosity, largely insensitive to fractures or vugs, which is a wellknown fact. Finally, the points on this crossplot, related to the relaxation groups obtained from previous steps were colored. These points were divided into regions based on fluid saturation, porosity type and lithology (Fig. 8-a, 8-b). Relaxation groups were classified according to the reservoir properties. The results of neutron log was commonly expressed in apparent water-filled porosity units. A constant lithology was assumed; therefore, this log was not always representative of actual pore fluid. On the other hand, the measurements by NMR and/or core data were closer to reality; hence, providing reliable estimations of reservoir capacity. Vuggy carbonate reservoir characterization was difficult though. NMR data could be used to see the difference between vuggy and matrix porosity, as a result of which, pore size could be characterized correctly. Vuggy systems can be divided into two different categories; i.e., separate and touching vugs. T2 curves are different for these two classes. In case of separate vugs, T2 curve is broad; spanning at least three peaks across T2 time axis with each one showing tri-modal curve peaks. These curves are not repeatable, i.e. each curve has a unique shape. In contrast, T2 curves for touching vugs showed poly modal amplitude peaks with the same span. A relationship between cementation factor and effective porosity is shown in Table 5. This relationship was obtained based on the core data provided for each
Fig. 7. Cross plot of porosity and core permeability.
distribution operations. In this study, Fuzzy mathematical method is applied to predict relaxation groups in wells with no NMR data (i.e., wells B and C) for the relaxation groups previously obtained by MRGC clustering technique and the available wireline data. The number of logs used for the prediction is not limited. However, a sensitivity study showed that four logs had competitive importance in rock typing. These logs included effective porosity (PHIE), neutron porosity (NPHI), neutron density separation (NDS) and sonic (DT). Relaxation group for the well A (having NMR data) obtained by MRGC technique was compared with the result obtained by fuzzy logic technique applied on this well. This was done to test the uncertainty of rock typing method. The comparison showed a very good agreement (see Fig. 4). The accuracy and recall value of each relaxation group were also calculated and presented in Table 3. The results obtained from fuzzy logic prediction in wells B and C calibrated with core and petrophysical data are depicted in Figs. 5 and 6. The comparison between the results of fuzzy logic predictions and petrophysical evaluations showed an acceptable agreement. Crossplot of core permeability versus core porosity was plotted for well B (Fig. 7) to validate the fuzzy model. The color of points were derived from the related relaxation group. As can be seen in this figure, the clustering method was performed correctly. In class 2, some data with high permeability had low porosity. This feature was the sign of fractures. In Fig. 5, Track 1 depicted understudied depths, Track 2 was standard gamma ray log, track 3 was DT compressional and NPHI logs. Moreover, Track 4 showed lithology, Track 5 was effective porosity, Track 6 included facies obtained from MRGC method, Track 7 was the volume of gas and water obtained from fuzzy logic method and finally Track 8 9
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A. Movahhed, et al.
Fig. 8. a) Crossplot of NDS and Vp/Vs ratio. Different colors were related to different relaxation groups, Fig. 8b) Lithology related to Crossplot of NDS and Vp/Vs ratio.
Table 5 The relationship between cementation factor and effective porosity for each relaxation group. Class No.
Cementation factor equation
Class Class Class Class Class Class Class Class
m = −17.523 phie2 + 7.671 phie +1.3088 m = 0.5272 phie+ 2.049 2 to 2.2
1 2 3 4 5 6 7 8
m m m m
= = = =
Table 6 Comparison of the new water saturation method with the old method (m = 2).
7.2105 phie +1.6156 9.8118 phie +1.5384 1.452 phie +1.7527 1.4948 phie +1.8726
Well
Mean of calculated Sw by new M
Mean of calculated Sw by M=2
Difference (%)
A B C
0.4968 0.4351 0.5654
0.4092 0.2757 0.4503
9% 16% 11%
following table, the new water saturation is compared with the old method (m = 2). The advantage of the new crossplot is its easiness to be applied because it introduces a variable cement exponent in calculation of water saturation. The Archie's equation is used to determine the water saturation that cement exponent (m) is the most importance entrance in Archie's equation. In fact, cement exponent is strongly dependent on the pore pattern distribution, wettability, pore throat size, type of rock grains and mineralogical properties. This parameter is sometimes assumed constant to simplify the petrophysical measurements in the wells without core data whereas this is variable particularly in the heterogeneous carbonate reservoirs. Inaccurate estimates of this parameter lead to significant error in the water saturation. In the present study, NMR log was used to determine the cement factor using new crossplot and provides information about pore size distribution, formation permeability, hydrocarbon porosity, vugs, fractures and grain size that have a direct relation with cement factor. Actually, the new crossplot introduces a variable cement exponent in calculation of the water saturation. This crossplot can be used in the wells without core data and
relaxation group. It must be mentioned that the cementation factor values were provided for the specified reservoir condition as higher values related to the vuggy porosity and lower values related to fracture porosity. The above-mentioned method had the advantage of being quick and robust for predicting the cementation factor in complex carbonate gas reservoirs. This cross plot reduced the uncertainty in the water saturation calculations (see Table 6). 5. Comparing the calculated new saturation water with the old saturation In this study, the calculated new saturation water was compared with the old method (m = 2). In the new saturation, water was used as a variable cement exponent that was obtained from the novel crossplot. This saturation was more consistent with the production report. In the
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A. Movahhed, et al.
Fig. 9. Comparison of the calculation of water saturation with the new method and the old method (m = 2) in WELL A.
Fig. 10. Comparison of the calculation of water saturation with the new method and the old method (m = 2) in WELL B.
reduces error in calculation of the water saturation. In Figs. 9–11, the new water saturation is compared with the old method (m = 2) in wells A, B and C, respectively. In these figures, the old water saturation is displayed by the red curve in the last track from the right.
distribution, pore geometry, and wettability of the reservoir rock affected the amount of cementation factor (m) and saturation exponent (n) in Archie formula (Wardlaw, 1980; Elias and Steagall, 1996). Choquette and Pray (1970) identified fifteen basic pore types. Indeed, the effect of vugs, connected (touching) or not connected pores, and the extent to which vuggy porosity contributed to total porosity were considered in the classification of carbonate porosity (Lucia, 1983). Ahr (2008) proposed the genetic classification of porosity for carbonate reservoirs. He classified pores by their geological origin, related pore geometry, vug type and geologic processes and brought about a simple and applicable conceptual model. This classification was
6. Discussion Cementation factor was greatly affected by secondary porosity, surface area per unit volume, cement properties, pore throat size and water conductivity (Tatham and Stoffa, 1976; Ransom, 1984; Rasmus, 1986). Moreover, it depended on the shape and surface of composite particles and tortuosity factor. Other researchers showed that factors like reservoir pressure and temperature, mineralogy, pore throat size 11
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Different parameters like pore size, the strength of the surface relaxation, wettability of rock surface and type of fluid contained in rock pores determined which of the abovementioned mechanisms was dominant. In general, these mechanisms acted in parallel. Pore origin was related to different pore geometries as well. Depositional, diagenetic and hybrid origin were, in turn, used for identifying the NMR signature characteristics. T2 time was a measure of surface-to-volume ratio, so that rapid relaxation in T2 time corresponded to small pores and long T2 relaxation time was related to large pores. Therefore, each T2 value corresponded to different pore sizes. Based on Fig. 12, porosity type could affect T2 curve distribution obtained from NMR. Carbonates, for instance, exhibited T2 curves with low amplitude. Pores in carbonates were diagenetically reduced by cementation. T2 relaxation time was therefore very short in these rocks. On the other hand, rocks containing vugmolds, intercrystalline and interparticle pores had high T2 amplitudes. Generally, higher amplitude values were associated with larger and more frequent pores. It is generally accepted that in carbonate rocks, hybrid and intercrystalline pores show near symmetric, narrow wavelengths in T2 time. Moreover, it is believed that moldic pores and rocks with both separate and touching vugs display fast-skewed with curve widths spanning 3 peaks in T2 time. 6.1. Cementation factor (m) and Vp/Vs ratio Two classes of parameters affected the velocity of waves in carbonate rocks. One class was related to rock structure. Parameters like lithology, porosity and grain size were involved in this class. The second class contained parameters describing the depositional environment, which was not related to rock structure. Parameters like confining stress, age of deposition and burial depth were involved in this class. Fluid velocity was higher in rocks with vuggy porosity because increasing fluid pressure in pore space would reduce the porosity and the grain contacts becoming closer to each other and would increase fluid velocity as a result. Therefore, pressure controls fluid velocity in vuggy rocks saturated with brine or hydrocarbon. 7. Conclusions Accurate determination of cementation factor (m) provided reliable saturation results and consequently provided hydrocarbon reserve calculations. A novel crossplot was introduced in this study, where each class of rocks had a relationship between cementation factor and effective porosity. This crossplot provided a quick method of estimating the cementation factor in carbonate gas reservoirs with complex structures. The presented methodology was advantageous as the water saturation could be calculated with the least uncertainty because a continuous log of m value was provided for different rock types. The new crossplot was created from various types of logs such as NMR, density, neutron, compressional and shear sonic and core data as well. The crossplot included important parameters like mineralogy, secondary porosity, pore geometry, pore throat size distribution, water and mineral conductivity, cementation characteristics and surface area per unit volume. Thus, the crossplot helped us achieve a new classification confirming that of Ahr. Genetic pore types best distinguished pore throat size distribution. Therefore, genetic pores were directly related to permeability value. Carbonates had different porosity types and different T2 relaxation curves for their permeability. The present work provides a strategy for separating reservoir into different layers. This provided the idea of reservoir quality at different depths and the idea on how heterogeneity might affect reservoir quality.
Fig. 11. Comparison of the calculation of water saturation with the new method and the old method (m = 2) in WELL C.
probably the best choice to identify flow units in stratigraphic contexts (Fig. 13). The study used different logs including NMR, neutron, density and compressional and sonic shear to obtain a classification like that of Ahr. NMR data, valuable and reliable data, could be used to determine rock type in carbonate formations. In addition, three independent relaxation mechanisms were used to determine fluids contained in rock pores. Theses mechanisms were as follows: 1 Surface relaxation at solid 2 Bulk relaxation 3 Diffusion-induced relaxation 12
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Fig. 12. Classification of fifteen carbonate pore types. The five most common types of pores in this study have been outlined in black (Choquette and Pray, 1970).
Fig. 13. Genetic classification of porosity after Ahr (2008).
Acknowledgements
References
The authors would like to gratitude Mahdi Rastegarnia and Morteza Amiri, the head of Petrophysic department in Asmary Company and POGC, respectively for providing cooperation, guidance and sharing knowledge and valuable experience.
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