A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones

Journal of Earth Science, Vol. 28, No. 3, p. 56 522, June 7 ISSN 674-487X Printed in China DOI:.7/s2583-6-93-6 A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones Cheng Feng, Yujiang Shi 2, Jiahong Li 3, Liang Chang 4, Gaoren Li 2, Zhiqiang Mao * 5. Faculty of Petroleum, China University of Petroleum-Beijing at Karamay, Karamay 83, China 2. PetroChina Changqing Oilfield Company, Xi an 78, China 3. Research Institute of Petroleum Exploration and Development, PetroChina, Beijing 83, China 4. Research Institute of Exploration and Development, Xinjiang Oilfield Company, PetroChina, Karamay 83, China 5. Key Laboratory of Earth Prospecting and Information Technology, China University of Petroleum, Beijing 2249, China Cheng Feng: http://orcid.org/--977-687; Zhiqiang Mao: http://orcid.org/-2-943-353 ABSTRACT: Pore structure reflected from capillary pressure curves plays an important role in low-permeability formation evaluation. It is a common way to construct capillary pressure curves by Nuclear Magnetic Resonance (NMR) log. However, the method s efficiency will be severely affected if there is no NMR log data or it cannot reflect pore structure well. Therefore, on the basis of and diagenetic facies classification, a new empirical model for constructing capillary pressure curves from conventional logs is proposed here as a solution to the problem. This model includes porosity and the relative value of natural gamma rays as independent variables and the saturation of mercury injection as a dependent variable. According to the 5 core experimental data sets of three diagenetic facies from the bottom of the Upper Triassic in the western Ordos Basin, China, the model s parameters in each diagenetic facies are calibrated. Both self-checking and extrapolation tests show a positive effect, which demonstrates the high reliability of the proposed capillary pressure curve construction model. Based on the constructed capillary pressure curves, NMR T 2 spectra under fully brine-saturated conditions are mapped by a piecewise power function. A field study is then presented. Agreement can be seen between the mapped NMR T 2 spectra and the MRIL-P log data in the location of the major peak, right boundary, distribution characteristics and T 2 logarithmic mean value. In addition, the capillary pressure curve construction model proposed in this paper is not affected by special log data or formation condition. It is of great importance in evaluating pore structure, predicting oil production and identifying oil layers through NMR log data in low-permeability sandstones. KEY WORDS: low-permeability, conventional logs, capillary pressure curve,, NMR T 2 spectrum. INTRODUCTION Pore structure is the geometrical shape, size, distribution and connectivity of pores and throats in rock, which comprehensively shows the oil/gas storage capability and permeability of reservoirs (Luo and Wang, 986). It is of great significance to find out pore structure of reservoirs, especially those of low-permeability sandstones because such reservoirs have gone through complex sedimentation and diagenesis which ultimately leads to a variety of pore structures. Capillary pressure curves are widely used to describe pore structure (Zhang et al., 6). However, despite the high accuracy of the rock s *Corresponding author: maozq@cup.edu.cn China University of Geosciences and Springer-Verlag Berlin Heidelberg 7 Manuscript received August 7, 6. Manuscript accepted December 8, 6. experimental data, reservoirs cannot be evaluated in a continuous way. Thus, researchers have tried to establish ties between well logs and capillary pressure curves in order to construct continuous capillary pressure curves via log data. For the sake of continuously evaluating pore structure, research into the relationship between capillary pressure curves and well logs has been conducted over the past two decades. Achievements have mainly been made by transforming NMR log data into capillary pressure curves. During the previous decade, researchers made the transformation primarily through the adoption of the linear formula. They thought a linear relationship obtained between NMR T 2 spectra and pore radius distribution transformed by capillary pressure curves. Marschall et al. (995) carried out their study from the perspective of core analysis. The relationship was then applied to formation evaluation (Altunbay et al., ; Hodgkins and Howard, 999; Lowden et al., 998; Hassoun et al., 997). However, these researches Feng, C., Shi, Y. J., Li, J. H., et al., 7. A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones. Journal of Earth Science, 28(3): 56 522. doi:.7/s2583-6-93-6. http://en.earth-science.net

A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones 57 were based on the fact that water saturation equals to %. In order to eliminate the influence of hydrocarbons on NMR T 2 spectra, Volokitin et al. (999) succeeded in constructing continuous capillary pressure curves by reconstructing the T 2 spectra under S w =% conditions in the presence of hydrocarbons. The models have been improved in the last decade. He et al. (5) found that the T 2 spectra did not match well with the pore radius distribution when the linear relationship was applied to complex formation conditions. They proposed a piecewise power function model as a solution to substitute for the linear model. In recent years, Gao et al. deduced a nonlinear function by radial interpolation and used NMR data to construct capillary pressure curves in carbonate reservoirs. On the basis of the and SDR model, Xiao et al. (2) constructed continuous capillary pressure curves in tight sandstones by building the relation between the mercury saturation, porosity and logarithmic mean of the T 2 spectrum. Eslami et al. (3) first estimated combinable magnetic resonance bin porosities from well logs, then used them to predict P c values through an inversion process; however, the estimated P c values and the experimental data didn t show a positive effect when mercury injection saturation was higher than 35%. Hence, Xiao et al. (5) pointed out that the uncertainty of Eslami s method was caused by the dimension difference of mercury injection pressure and 8 T 2 porosity bins, and improved it with a better effect. Although a strong correlation exists between NMR T 2 spectra and capillary pressure curves under certain conditions, its shortcomings are also obvious. First of all, only key wells are measured by NMR logging, so the relevant data is few. Especially in our study area, there are tens of thousands of development wells with only conventional logs. Besides, if reservoirs contain hydrocarbons or present oil-wet conditions, NMR T 2 spectra cannot reflect their pore structures or be used to construct the capillary pressure curves directly. These shortcomings limit its application in formation evaluation. In order to solve these problems, this paper proposes a new empirical model for constructing capillary pressure curves by means of conventional logs. The study area is located in the bottom of the Upper Triassic in the western Ordos Basin, China. It is a braided river delta sedimentation and its reservoirs are typical low-permeability with a depth generally greater than 2 m, which experience complex sedimentation and diagenesis (Du et al., 6; Ren et al., 6; Hu et al., 5; Wu et al., 5). METHOD OF CONSTRUCTING CAPILLARY PRESSURE CURVES. J Function Based on dimensional analysis, was first proposed by Leverett (94). It is now a function used to average the capillary pressure curves. The formula is presented in the following equation. ( ) J S w ( ) Pc Sw K = σ cosθ φ where S w is the wetting phase saturation under its corresponding pressure of mercury injection, %; P c (S w ) is the capillary pressure under its corresponding wetting phase saturation, dyn/cm 2 ; σ is the interfacial tension between the two fluids, dyn/cm; θ is the contact angle between the interface separating the two fluids and the surface of the rock, ; K is permeability, md; ϕ is porosity, %..2 Permeability Model Yong and Zhang (7) proposed a linear relationship between permeability and median size in log-log plots after analyzing 4 373 core experimental data sets from 8 oilfields in China. Hence, the permeability model is expressed as Eq. (2), which consists of the two parameters of porosity and median size. For the sake of obtaining the median size continuously, it is calculated by the relative value of natural gamma rays in Eq. (3) (Yong and Zhang, 7; Tan and Zhang, 995). ( ) ( φ ) ( ) log K = c log + d log Md + e (2) log( Md) = f Δ GR+ g (3) GR GR Δ GR = GR GR max min min where Md is median size, mm; ΔGR is the relative value of natural gamma rays, decimals; GR max, GR min and GR are the maximum, minimum and actual values of natural gamma rays, API; c, d, e, f and g are model parameters..3 Capillary Pressure Curve Construction Model A great amount of core experimental data show that a power function relation exists between wetting phase saturation and the J function under a given capillary pressure (Xiao et al., 2; Wang et al., 6). The relation can be expressed as Eq. (5). w bi ( ) ( w ) (4) S i = a i J S i (5) where a and b are model parameters, i =, 2,, N represents the number of the injection pressure increments. In sequence, substitute Eqs., (2) and (3) into Eq. (5) to derive Eq. (6). w S i = a i P i σ cosθ φ ( c log( φ ) + d f Δ GR+ d g+ e) c bi Take the logarithm base of both ends of Eq. (6) to yield Eq. (7). log ( Sw i ) = ( ) (6) bi c bi d f log( φ ) + Δ GR+ 2 2 log( ai ) + bi ( log( Pc i) log( σ cosθ) ) + bi ( d g + e) 2 (7)

58 Cheng Feng, Yujiang Shi, Jiahong Li, Liang Chang, Gaoren Li and Zhiqiang Mao If the value of capillary pressure P c is fixed, the third item on the right of Eq. (7) can be regarded as a constant. To further simplify the model, three set-up parameters A * (i), B * (i) and C * (i) are used to substitute for the model parameters in Eq. (7), as shown in Eqs. (8), (9) and. A B i ( c ) * bi * i = (8) 2 bi d f = (9) 2 log( ai ) + = ( log( c ) log( σ cosθ) ) + bi ( d g + e) 2 * C i b i P i where A * (i), B * (i) and C * (i) are model parameters. Meanwhile, during mercury injection experiments, if the general pore space is assumed to be, the sum of the wetting phase fluid and the non-wetting one is. Thus, Eq. can be written as S i + S i = Hg wetting_phase where S Hg is the corresponding mercury injection saturation under a mercury injection pressure, %; S wetting_phase is the wetting phase saturation under its corresponding mercury injection pressure, %. In the study area, cores exhibit water-wet after washing oil. Thus, S w (i) can be use to replace S wetting_phase (i) in Eq.. After Eqs. (8), (9), and are substituted into Eq. (7), Eq. (2), a new formula, is deduced ( SHg i ) log( φ ) log = + Δ + * * * A i B i GR C i (2) On the condition that capillary pressure is fixed, the porosity and relative value of natural gamma rays in Eq. (2) are independent variables, while the mercury injection saturation is a dependent variable. The other model parameters A * (i), B * (i) and C * (i) can be estimated via the calibration of core experiment data. 2 EXPERIMENTAL DATA On the premise of the same, Eq. (5) and the derived Eq. (2) can be used to construct capillary pressure curves accurately. If not, they don t work well. In the study area, 5 core samples from 37 wells were collected and their capillary pressure curve experimental data were measured by the mercury injection method (Fig. a). The distribution of the porosity and permeability of the cores ranged from 3.4% to 5.6% and from.3 to 7.49 md respectively. For most of them, the permeability was lower than. md. The corresponding s of these capillary pressure curves are calculated and presented in Fig. b. They show a large variation, indicating that the same cannot be obtained directly. Brown (95) investigated a large amount of core experimental data including limestone and dolomite from the Edwards Formation in Jourdanton field. Through this data, under the condition of the same lithology type, the good consistency of the was verified. Therefore, the reservoirs to be studied should be classified first in order to use the same type of. They are divided into three categories according to the previous study on diagenetic facies (Shi et al., ). Among them, Class I is mainly made up of weak dissolution diagenetic facies with chlorite film, Class II of dissolution diagenetic facies and Class III of carbonate cementation and tight diagenetic facies. Based on this classification, 5 core capillary pressure curves and their corresponding s are exhibited in Fig. 2. Though the distributions of the core capillary pressure curves are different in each category of diagenetic facies (Figs. 2a, 2c and 2e), their corresponding s are almost the same (Figs. 2b, 2d and 2f). After classifying the diagenetic facies, the same acquired in each category can be substituted into Eqs. (5) and (2) to construct capillary pressure curves. Since the capillary pressure curve construction model proposed here needs to be given capillary pressure P c values in advance, the values should be unified. According to the distribution characteristics of the core capillary pressure curves in Figs. 2a, 2c and 2e, Their maximal pressure values are largely about 5. MPa. The threshold pressure values of cores in classes I, II and III diagenetic facies are mostly higher than.5,.3 and. MPa, respectively. Therefore, the P c values are set as.,., and 5. MPa to cover a wide range. However, some of the selected core experimental data has different P c value distributions. On the condition that the shapes of the curves are not changed, the P c values of all the core experimental data sets are unified to the above set point via cubic spline interpolation. (a) (b).. Por: 3.%-5.% Perm:.3-7.49 md... Figure. (a) Fifty-one core capillary pressure curve experimental data sets and the s of 5 core capillary pressure curves (b).

A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones 59 (a) (b)..... (c) (d)..... (e) (f)..... Figure 2. Core capillary pressure curve (a) and the corresponding s (b) in Class I diagenetic facies. Core capillary pressure curve (c) and the corresponding s (d) in Class II diagenetic facies. Core capillary pressure curve (e) and the corresponding s (f) in Class III diagenetic facies. Core capillary pressure curve and the corresponding s in different diagenetic facies. Class I (a), (b); Class II (c), (d); Class III (e), (f). 3 PROCEDURES FOR CONSTRUCTING CAPILLARY PRESSURE CURVES According to the above theoretical analysis, the procedures for constructing capillary pressure curves can be briefly described as follows. Collect a certain amount of core capillary pressure curves and their corresponding conventional log data in the study area. The core experimental data can be acquired by the mercury injection method, semipermeable baffle plate or centrifuging method. However, considering the oil-wet effect on reservoirs, it is highly recommended to adopt the mercury injection method. (2) A depth correction is carried out on the acquired experimental data. It is clear that the longitudinal resolution of well log data is very large compared with the core capillary pressure curve experimental data. They are difficult to match, especially in low-permeability reservoirs. In order to solve this problem, the depth is first corrected between log data and core porosity and permeability experimental data. For many core porosity and permeability experimental data in the study area, the first depth correction is relatively simple. It indicates that the correction can be accurate. Then, the depth correction of core capillary pressure curve experimental data is achieved via making the core porosity and permeability in it equal to those in the corrected core porosity and permeability experimental data above. The diagenetic facies classes of their corresponding reservoirs are identified and the cores of the same class are classified into a group to build the model. Next, the maximum, minimum and actual values of natural gamma rays are obtained in accordance with the corrected depth. After that, the capillary pressures of all the cores are reset to a fixed value via cubic spline interpolation. (3) Substitute the experimental data and log data in Step 2 for S Hg, ϕ and ΔGR in Eq. (2). Via the multiple statistic regression method, the values of model parameters A * (i), B * (i) and C * (i) for each reservoir class under different capillary pressures are estimated, and the model for calculating the corresponding mercury injection saturation S Hg is constructed. (4) In field data processing, the reservoir s diagenetic facies should first be identified. Next, the porosity and the relative value of natural gamma rays are substituted into the model established in Step (3). Finally, the calculated mercury injection saturation and pre-fixed capillary pressure are mapped into a scatter plot, namely the constructed capillary pressure curves.

5 Cheng Feng, Yujiang Shi, Jiahong Li, Liang Chang, Gaoren Li and Zhiqiang Mao 4 BUILDING THE MODEL IN THE STUDY AREA 4. Calibration of the Model Parameters According to the procedures proposed in the above section, the experimental data of the 5 core samples capillary pressure curves and their log data are substituted into Eq. (2) successively. In this way the parameters A * (i), B * (i) and C * (i) for different diagenetic facies are regressed. As is shown in Table, most of the correlation s are higher than.8, which demonstrates the model s high accuracy. 4.2 Self-Checking of the Model In order to check the reliability of the capillary pressure curve construction model by the parameters in Table, the constructed curves are compared with the core experimental data. Since it is impractical to display all of them, 3 out of the 5 comparison results are selected and displayed in Fig. 3a; the results of the remaining 48 samples are similar to those of these 3 representatives. In the figure, the red, blue and green dots stand for the constructed results of the classes I, II and III diagenetic facies respectively. The rest represent the core experimental data. This figure shows that the two kinds of curves corresponded well, which in turn proves the high reliability of the proposed model. 4.3 Extrapolation Test of the Model For the sake of fully checking the reliability of the proposed model, 3 cores chosen from 5 have been studied. Here, a comparison is made between the results deduced from the model and the experimental data. The results are presented in Fig. 3b, in which the colored dots have the same significance as those in Fig. 3a. In general, the capillary pressure curves constructed by the new model correspond to the experimental data, except for a relatively large divergence when the capillary pressure is equal to 3., 6. and 2. MPa. On the whole, the extrapolation test further proves the reliability of the model proposed here. 5 APPLICATIONS OF THE MODEL The precondition that capillary pressure curves can be constructed continuously makes it possible to evaluate pore structure via successive calculation, and this has great significance in low-permeability formation evaluation. Additionally, NMR T 2 spectra under fully brine-saturated conditions can be constructed from the constructed capillary pressure curves by the piecewise power function T 2 =mʹ(/p c ), which is the deformation of He s model (He et al., 5). In this research, the experimental data of 28 core NMR T 2 spectra were collected to calibrate the model parameters. Based on the calibration of these experimental data, the radius boundaries of large pore and small one are.3 and. μm in classes II and III diagenetic facies, and the models for constructing the T 2 spectra were set up in accordance with the above method, as shown in Table 2. Table Model parameters of constructing the capillary pressure curves in the study area Capillary pressure Class I diagenetic facies Class II diagenetic facies Class III diagenetic facies A * B * C * Correlation A * B * C * Correlation A * B * C * Correlation.2 -.79.2 2.88.97.4 -.2.4 3.2.96 -.7 -.2 2.6.76.8 -.85.75 2.76.85 -.23.5 2.2.74.6 -.8.67 2.64.93 -.24.6 3.2. -.4.2 2.2.74 3.2 -.75.48 2.5.89 -.95.43 2.6.93 -.7.2.95.79 6.4 -.7.5 2.38.87 -.6.29 2.8.86 -.26.36.94.95 2.8 -.76.52 2.37.87 -.55.28 2.5. -.48.8 2.8.83 25.6 -.3.5 2.68.85 -.7.8 2.6. -.68. 2.4.92 5.2 -..3 2..76 -.7.8 2..78 -.69.6 2.6.89 (a) (b).. T (3.%,.3 md) (7.%,.9 md) T3 (3.%, 2.64 md) Measured curves Constructed curves.. T4 (5.%,.5 md) T5 (7.%,.2 md) T6 (2.%,.7 md) Measured curves Constructed curves Figure 3. Results of the model s self-checking (a) and extrapolation test (b).

A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones 52 Table 2 NMR T 2 spectrum models by capillary pressure curves Diagenetic facies Models for large pore Correlation Models for small pore Correlation Class I = 87.72 Pc.77.96 = 87.72 Pc.77.96 Class II = 2.82 Pc.32.95 = 7.95 Pc.36.86 Class III = 354. Pc 2.47.9 = 22.5 Pc.53.87 Figure 4. A field study of formation evaluation from conventional logs. In order to examine the application effects of the above models, a field study is presented in Fig. 4. A well interval ranging from 2 2 to 2 437 m is selected for the diagram. In the figure, the first three tracks are conventional log curves, and the eight tracks from No. 5 to No. 2 represent porosity, diagenetic facies, the constructed capillary pressure curves, the median pressure values, the median radius values, MRIL-P log data, the derived NMR T 2 spectra under fully brine-saturated conditions and the logarithmic mean of T 2 spectra respectively. In the 6th track, the yellow, red and blue intervals correspond with diagenetic facies classes I, II and III respectively. The red lines in tracks five, seven, eight and nine represent the experimental data of mercury capillary pressure curves and the corresponding reservoir parameters; the constructed capillary pressure curves and calculated reservoir parameters conform closely to them. As for tracks ten and eleven, the major peaks, right boundaries and distribution characteristics of the constructed NMR T 2 spectra and MRIL-P log data show a positive effect. Moreover, the error in the logarithmic mean is also minor, which can be indicated by comparing the black curve with the blue one in track 2th. To sum up, its good application effect and high reliability suggest that the model proposed for constructing capillary pressure curves through conventional logs is of great value. 6 CONCLUSIONS On the basis of and diagenetic facies classification, a new empirical model for constructing capillary pressure curves from conventional logs is proposed. This model includes the calculation of non-wetting phase saturation from porosity and the relative value of natural gamma rays. In combination with the 5 core experimental data sets, the model parameters are calibrated in each diagenetic facies. Both the self-checking and the extrapolation test show a positive effect, which demonstrates the new model s high reliability. Based on these constructed capillary pressure curves, the NMR T 2 spectra under fully brine-saturated conditions are mapped by a piecewise power function. According to a field study, the comparison results of capillary pressure curves, reservoir parameters and those of T 2 spectra prove the model s favorable application effects and high reliability. Moreover, the proposed new model is not affected by the limitations of log data or formation conditions. In conclusion, this new model is of great importance in evaluating pore structure, predicting oil production and identifying oil layers through NMR log data in low-permeability sandstones.

522 Cheng Feng, Yujiang Shi, Jiahong Li, Liang Chang, Gaoren Li and Zhiqiang Mao ACKNOWLEDGMENTS The authors are grateful to the editors of Journal of Earth Science and the reviewers for their useful comments. Research for this paper was supported by the Scientific Research Starting Foundation of China University of Petroleum-Beijing at Karamay (No. RCYJ6B--8) and the Major National Oil & Gas Specific Project of China (No. 6ZX558). The final publication is available at Springer via http://dx.doi..7/s2583-6-93-6. REFERENCES CITED Altunbay, M., Martain, R., Robinson, M.,. Capillary Pressure Data from NMR Logs and Its Implications on Field Economics. The SPE Annual Technical Conference and Exhibition, New Orleans Brown, H. W., 95. Capillary Pressure Investigations. Journal of Petroleum Technology, 3(3): 67 74 Du, W., Jiang, Z. X., Li, Q., et al., 6. Sedimentary Characterization of the Upper Paleozoic Coal-Bearing Tight Sand Strata, Daniudi Gas Field, Ordos Basin, China. 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