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394 Pet.Sci.(2011)8:394-405 DOI 10.1007/s12182-011-0157-6 The inÀ uence of pore structure on P- & S-wave velocities in complex carbonate reservoirs with secondary storage space 1 1 2 2 Wang Haiyang , Sam Zandong Sun , Yang Haijun , Gao Hongliang , 2 1 Xiao Youjun and Hu Hongru Laboratory for Integration of Geology & Geophysics, China University of Petroleum, Beijing 102249, China Research Institute of Exploration & Development, PetroChina Tarim Oil¿ eld Company, Korla, Xinjiang 841000, China © China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg 2011 Abstract: Secondary storage spaces with very complex geometries are well developed in Ordovician carbonate reservoirs in the Tarim Basin, which is taken as a study case in this paper. It is still not clear how the secondary storage space shape influences the P- & S-wave velocities (or elastic properties) in complex carbonate reservoirs. In this paper, three classical rock physics models (Wyllie time- average equation, Gassmann equation and the Kuster-Toksöz model) are comparably analyzed for their construction principles and actual velocity prediction results, aiming at determining the most favourable rock physics model to consider the influence of secondary storage space shape. Then relationships between the P- & S-wave velocities in carbonate reservoirs and geometric shapes of secondary storage spaces are discussed from different aspects based on actual well data by employing the favourable rock physics model. To explain the inÀ uence of secondary storage space shape on V -V relationship, it is ana- P S lyzed for the differences of S-wave velocities between derived from common empirical relationships (in- cluding Castagna’s mud rock line and Greenberg-Castagna V -V relationship) and predicted by the rock P S physics model. We advocate that V -V relationship for complex carbonate reservoirs should be built for P S different storage space types. For the carbonate reservoirs in the Tarim Basin, the V -V relationships for P S f ractured, fractured-cavernous, and fractured-hole-vuggy reservoirs are respectively built on the basis of velocity prediction and secondary storage space type determination. Through the discussion above, it is expected that the velocity prediction and the V -V relationships for complex carbonate reservoirs should P S fully consider the inÀ uence of secondary storage space shape, thus providing more reasonable constraints for prestack inversion, further building a foundation for realizing carbonate reservoir prediction and À uid prediction. Key words: Complex carbonate reservoir, secondary storage space, velocity prediction, V -V P S relationships proposed by Gassmann in 1951 and re-expounded by Biot in 1 Introduction 1956), and the Kuster-Toksöz model (considering the effect In the rock physics study, P- & S-wave velocity prediction of pore shape through adjusting pore aspect ratio proposed is the primary issue because it directly reÀ ects the “bridge” by Kuster and Toksöz in 1974). Other rock physics models role of rock physics linking reservoir physical properties with for velocity prediction are mostly the extended models on the elastic properties. And the predicted velocities also provide basis of the three basic models, such as the Xu-White model key constraint data for the following pre-stack inversion. (Xu and White, 1995) for clay-sand mixtures (integrating Currently, many rock physics models regarding velocity the Gassmann equation and the Kuster-Toksöz model), prediction have been established. The most basic and classic differential effective medium model (incrementally adding models are the Wyllie time-average equation (proposed inclusions to the matrix on the basis of the Kuster-Toksöz based on effective average theory by Wyllie et al in 1956), model). Therefore, this paper focuses on the analysis of these the Gassmann equation (considering the effect of pore À uids basic classical rock physics models, and discusses how the secondary storage space shape influences the P- & S-wave velocities in carbonate reservoirs. * Corresponding author. email: szd@cup.edu.cn, samzdsun@yahoo.com The reason why we focus on discussing the inÀ uence of Received March 18, 2011 secondary storage space shape is derived from the specific 396 Pet.Sci.(2011)8:394-405 parts including gas, oil, water, and matrix in a layered reservoirs with various secondary storage spaces (e.g., cracks, structure. This equivalence is only appropriate for pure rock holes, and caves). The Kuster-Toksöz model is derived on and there is no concept of pore geometry. The Gassmann the basis of long-wavelength ¿ rst-order scattering theory and equation is a classical À uid substitution model and considers describes various pore geometries using different pore aspect well the connectivity among pores. This model also can be ratios, thus well characterizing the actual storage spaces in used for velocity prediction when the elastic moduli of dry reservoirs. Therefore, the Kuster-Toksöz model may be very rocks are known (Sun et al, 2004). However, because it is suitable for considering the influence of secondary storage free of assumption of the pore geometry change (generally spaces on elastic wave velocities in carbonate reservoirs. The spherical pores are assumed), it may be very difficult to equivalent schemes for the above three rock physic models use this model to predict the wave velocities in carbonate are shown in Fig. 2. Gas Oil Gassmann Time-average Kuster-Toksöz Water equation equation model Matrix Fig. 2 Equivalent schemes for the Wyllie time-average equation, the Gassmann equation, and the Kuster-Toksöz model The formulas of the Wyllie time-average equation and the physics models and measured by sonic logging is shown Gassmann equation can be easily understood (see Wyllie et in Fig. 3. The moduli and densities of minerals and fluids al, 1956; Gassmann, 1951; Biot, 1956; Sun et al, 2004; Wang used for the velocity prediction are listed in Table 1, and et al, 2009). The key formulas of the Kuster-Toksöz model they are also the basic parameters used for other studies in are expressed as follows: this paper. From Fig. 3 we can see that all of the three rock physics models above can predict the velocities (the inverse of slowness) of carbonate reservoirs in different accuracies. 34 K u *m mm i (1) However, there are apparent deviations between the data K K K KP m i m 34 Ku i 1 measured and that predicted by the Wyllie time-average equation and the Gassmann equation, especially for the former. Significantly, the results predicted by the Kuster- P] m m *mi P P x PP Q (2) Toksöz model agree well with those measured. The reason mm ¦ ii P] i 1 m why the Kuster-Toksöz model has the best predicted results is that through adjusting pore aspect ratio or the proportion * * where K and ȝ are the unknown bulk and shear moduli of of various 3D pores it can effectively model the geometries the saturated rock; K and ȝ are the bulk and shear moduli of various storage spaces, which is the dominant factor m m of the rock matrix; K and ȝ are the bulk and shear moduli influencing the velocities of the elastic-wave propagating i i of the ith inclusion; P and Q are the coef¿ cients describing in this type of complex carbonate reservoirs. Next, we will elastic properties of the pore phase. There are two kinds of employ the best model (the Kuster-Toksöz model) to discuss calculation algorithms for the coefficients P and Q. One is the influence of secondary storage space shape on P- & Wu’s arbitrary pore aspect ratio (Wu, 1966), and the other is S-wave velocities in complex carbonate reservoirs in the Berryman’s 3D special pores ( sphere, needle, penny-shaped Tarim Basin. crack, and disk ) (Berryman, 1995). In this paper, the Kuster- Table 1 The moduli and densities of minerals and À uids used in this paper Toksöz model with arbitrary pore aspect ratio is called the 2D KT model, and the one with 3D special pores is called the 3D Minerals Density Bulk modulus Shear modulus KT model. References and À uids g/cm GPa GPa Then the availability of the three rock physics models above will be comparatively analyzed for two actual wells Calcite 2.71 76.80 32.000 Simmons (1965) (Well A in the Tazhong area and Well B in the Lungu area, the Nur and Tarim Basin). Dolomite 2.87 94.90 45.000 Simmons (1969) A comparison of the results predicted by the three rock Clays 2.55 25.00 9 Han et al (1986) Brine (3%) 1.03 2.50 — Adams (1931) When discussing with James G. Berryman in 2009, he definitely Oil 0.87 1.58 — Standing (1952) indicated that the disk-shaped pores are actually artificial. Hence, the Gas 0.14 0.029 — Thomas et al (1970) disk-shaped pores are not used in this study. 61900308 1:200 6200 6210 1:200 6380 6390 6400 Pet.Sci.(2011)8:394-405 397 Depth Fluid analysis Rock analysis Pre.-AC Pre.-AC error Depth Porosity Rock analysis Pre.-AC Pre.-AC error WTKT (a=0.05) TKT (a=0.05) TKT (Cracks) WTKT (Cracks) 80 40 -0.1 0.1 s/ft 60 s/ft 40 -0.1 0.1 TWL WTWL TWL WTWL DOLO (0-100) 80 40 s/ft -0.1 0.1 DOLO (0-100) 60 s/ft -0.1 0.1 PORW TGM WTGW PORW WTGW TGM LIME (0-100) 10 0 80 40 % s/ft -0.1 0.1 LIME (0-100) 10 % 0 s/ft 40 -0.1 0.1 ZERO AC ZERO Hydrocarbon (10-0) SH (0-100) AC 80 s/ft 40 -0.1 0.1 Hydrocarbon(10-0) SH (0-100) -0.1 0.1 60 s/ft 40 (b) (a) Fig. 3 Comparisons of P-wave slowness between predicted by the Wyllie time-average equation (WL), the Gassmann equation (GM), and the Kuster- Toksöz model (KT) respectively and measured by sonic logging (AC). For each part of the ¿ gure, the ¿ rst three columns denote the results of logging interpretation; in the fourth column (Pre.-AC), symbols ‘TKT’ (green curve), TGM (pink curve), and TWL (blue curve) denote the slowness predicted by the Kuster-Toksöz model, the Gassmann equation, and the Wyllie time-average equation respectively; in the ¿ fth column (Pre.-AC error), symbols ‘WTKT’, ‘WTGM’, and ‘WTWL’ denote the corresponding relative errors of the predicted results compared with the measured results is sharper when the pore aspect ratio increases from 0.05 to 3 The analysis of secondary storage space 0.3. However the increase trend is reduced when the pore shape inÀ uencing P- & S-wave velocities aspect ratio increases from 0.3, and it tends to stop when the pore aspect ratio increases approximately to 0.5. Now, the This part will employ the Kuster-Toksöz model with predicted P- & S-wave slowness is more consistent with the arbitrary pore aspect ratio (i.e., the 2D KT model) and that measured slowness although there still is some deviation. All with 3D special pores (i.e., the 3D KT model) respectively above illustrate that the dominant secondary storage spaces to analyze the inÀ uence of secondary storage space shape on are dissolution holes or caves with high pore aspect ratio. velocity prediction. Additionally, this paper de¿ nes 0.3 as the critical value of the 3.1 Arbitrary pore aspect ratio pore aspect ratio, which is the turning point of the increase trend of predicted velocities for this type of carbonate rocks. For the 2D KT model, the storage space shape is The value is determined by the inherent elastic properties of described by the pore aspect ratio, the value of which is rock and should be varied for different lithologies. However, ranging from 0 to 1. In this part, Well C with very complex for carbonate rocks, the critical aspect ratio (0.3) may be secondary storage spaces is selected as an example. When constant because Sun et al (2004) also obtained a similar using the 2D KT model to predict velocities in the reservoir, value for western Canada carbonate rocks. the pore aspect ratio alters from 0.05 to 0.9. Fig. 4 shows To account for the relationship between the pore aspect the corresponding calculated P- & S-wave slowness of the ratio and the P- & S-wave velocities more clearly, three well for each pore aspect ratio. The figure shows that both relatively ideal depth points in Fig. 4 are chosen. They are P- & S-wave slowness decrease with an increase in the pore respectively the depth of 6,186 m (Depth I) with a high aspect ratio, illustrating that the spherical pores with high porosity and a low clay content, the depth of 6,190 m aspect ratio tends to be stiffer than the oblate pores with low (Depth II) with a low porosity and a high clay content, and aspect ratio. That is to say, P- & S-wave velocities in the the depth of 6,200 m (Depth III) with a low porosity and a reservoir with spherical pores tend to be higher than that with low clay content. The predicted P- & S-wave slowness for oblate pores. It can be easily understood because stiffer pores the three depth points with different pore aspect ratios are contribute to the stiffness of the whole rock while oblate extracted and converted into the corresponding P- & S-wave pores contribute to the compliance of the whole rock. The velocities (Velocity (m/s)=304,800/Slowness (ȝ s/ft)]. The ¿ gure also shows that the increase in P- & S-wave velocities 398 Pet.Sci.(2011)8:394-405 ¿ nal velocities for the three depth points under different pore ratio while for the reservoirs with high pore aspect ratio the aspect ratios are plotted in Fig. 5. increasing trend is lower. This phenomenon illustrates that The ¿ gure supports the following results: the major factor inÀ uencing the large-scale velocity change is 1) As the whole, both P- & S-wave velocities increase oblate pores (or cracks). For deep-buried carbonate reservoirs, with the pore aspect ratio, but obviously the influence of the brittleness of rock is very strong, so cracks always occur pore geometry on the P-wave velocity is greater than that more or less. It further illustrates the signi¿ cance of the study on the S-wave velocity. The varying range of the P-wave of how secondary storage spaces influence the velocities of velocity is 983-2,285 m/s while that of the S-wave velocity the elastic wave propagating in complex carbonate reservoirs. is 261-680 m/s. The result gives us an implication: due to the 3) It can be also found that for different reservoir influence of pore geometry, not only the respective values conditions (e.g., porosity and clay content) the ranges of of P- and S-wave velocities (V and V ) but also the relative P- & S-wave velocities are different. Under the same pore P S value between them will be altered. That is to say, the V - aspect ratio, the P- & S-wave velocities (V , V ) for reservoir P PI SI V relationships of the complex carbonate reservoirs may be condition I (high porosity and low clay content) are the not the same for different secondary storage space types. The lowest and those (V , V ) for reservoir condition III (low PIII SIII detailed relationships will be discussed in Section 4. porosity and low clay content) are the highest. And the 2) Similarly to the results from Fig. 4, for the reservoirs reservoir condition II (low porosity and high clay content) with low pore aspect ratio (smaller than 0.3) the P- & S-wave has intermediate P- & S-wave velocities (V , V ). Those PII SII velocities will significantly increase with the pore aspect above mainly reÀ ect the inÀ uence of lithology and reservoir Fig. 4 The change characteristics of P- & S-wave slowness predicted by the 2D KT model when the pore aspect ratio increases from 0.05 to 0.9. Symbols ‘TKT’ and ‘DSKT’ denote the predicted P- & S-wave slowness using the KT model respectively; Symbols ‘AC’ and ‘DS’ denote the measured P- & S-wave slowness respectively; ‘a’ in each bracket denotes the pore aspect ratio Pet.Sci.(2011)8:394-405 399 part (shown in Fig. 6(a)). In the first model, the proportion of crack, needle, and sphere is 0.8: 0.1: 0.1 (namely, crack PIII as the dominate storage space). In the second model, the proportion is 0.1: 0.8: 0.1 (namely, needle-shaped void as the 5000 PII dominate storage space). In the third model, the proportion is 0.1: 0.1: 0.8 (namely, sphere as the dominate storage space). The P- & S-wave slowness (TKT and DSKT) predicted by PI 3500 the 3D KT model for the combination of different storage SIII 261m spaces are shown in Fig. 6(b) (Well C is still selected as an example). Fig. 6 shows that if the dominant storage V 267.5m SII 680m space type is crack-shaped pore, the predicted P- & S-wave SI slowness (see the curves named “TKT” and “DSKT”) are far from the corresponding measured P- & S-wave slowness (see 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 the curves named “AC” and “DS”). If sphere-shaped pore or Pore aspect ratio needle-shaped pore is assumed as the dominant storage space The characteristics of P- & S-wave velocities varying with the Fig. 5 type, the difference between the predicted and the measured pore aspect ratio. Reservoir condition I-high porosity, low clay content; is reduced. And especially at the assumption of needle- reservoir condition II-low porosity, high clay content; reservoir condition shaped pore, the difference is minimum. Incorporating with III-low porosity, low clay content the results obtained when employing the 2D KT model (the storage space in the interest interval has high pore aspect ratio), it can be concluded that the dominant storage space physical properties on P- & S-wave velocities. However, type for the interest interval should be dissolution holes. the wave velocities under the same reservoir conditions may Therefore, the integrated application of the 2D and 3D KT be also significantly different if the pore aspect ratios are models can help us properly determine the storage space different. Meanwhile, even there are obvious differences types of the complex carbonate reservoir, thus providing in different reservoir conditions (dominating the range of much more information to enable us to have a deeper insight reservoir velocities), the velocities may also be similar to each into the reservoir. other if the difference of pore aspect ratios is big enough. For Additionally, it also should be noticed that the dominant example, the P-wave velocity in a low-porosity and high- secondary pores in different intervals in a well are generally clay-content reservoir (corresponding to reservoir condition different. The difference can significantly influence the II) with a pore aspect ratio of 0.9 is approximately to that in a predicted results of wave velocities. To illustrate this issue, low-porosity and low-clay-content reservoir (corresponding Well D (a well with relative complex storage spaces) in the to reservoir condition III) with a pore aspect ratio of 0.1. Both study area is taken as an example. Under the assumptions of the P- & S-wave velocities in a high-porosity and low-clay- crack-shaped pore and sphere-shaped pore as the dominant content reservoir (corresponding to reservoir condition I) with pore respectively, the 3D KT model is employed to predict pore aspect ratios more than 0.9 are approximately the same the P- & S-wave slowness of the well (shown in Fig. 7). as those in a low-porosity and high-clay-content reservoir According to the figure, it can be seen that for the (corresponding to reservoir condition II) with a pore aspect upper and lower intervals marked by the light blue pane, ratio less than 0.2, and even the P-wave velocity of the former the predicted P- & S-wave slowness (green lines: TKT(C), is higher than the latter when the difference of their pore DSKT(C)) under the assumption of crack-shaped pores as aspect ratios is big enough (e.g., 0.9 for the former and 0.1 the dominant storage space are closer to the corresponding for the latter). All of the phenomena above illustrate that the measured slowness (dark lines: AC, DS) than those (purple inÀ uence of secondary storage space shape on P- & S-wave lines: TKT(N-S), DSKT(N-S)) under the assumption of velocities may outweigh that of lithology and reservoir needle- and sphere-shaped pores as the dominant storage physical properties on P- & S-wave velocities, similarly to space. However, for the middle interval marked by light red the conclusions presented by Wang (2001). pane, the predicted slowness under the latter assumption is closer to the measured than those under the former 3.2 Combination of 3D special pores in certain assumption. Hereby we can judge that the dominant storage proportion space in the upper and lower intervals of the well are fractures (or cracks), so the geometric coefficient of Berryman’s In the 3D KT model, storage space shape is described by penny-shaped crack can be used for the modeling. Similarly, Berryman’s 3D special pores (Berryman, 1995). To model it can be judged that the dominant storage space types in the the secondary storage space shape in the complex carbonate middle interval of the well are dissolution holes and vugs, reservoir discussed in this paper, the storage spaces in each so the geometric coefficient of Berryman’s sphere- and set of the reservoirs are assumed to be the combination of needle-shaped pores can be used here. The differences of cracks, needles (representing needle-shaped dissolution the dominant storage space types of different intervals in the holes), and spheres (representing dissolution caverns) in same well indicate that the velocity prediction process needs certain proportion. To model various secondary storage spaces, to be done interval by interval. three storage space combining models are established in this Velocity, m/s 983m 2285m 1124m 51819536 6190 6200 1:200 400 Pet.Sci.(2011)8:394-405 Model 1-Cracks dominated Model 2-Needles dominated ModeL 3-Spheres dominated 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0 0 Pore Pore Pore Cracks Needles Spheres Cracks Needles Spheres Cracks Needles Spheres (a) Rock analysis Pre.-AC Pre.-DC Pre.-AC error Pre.-DS error Depth DSKT(N) WTKT(N) WDSKT(N) TKT(N) POR 100 40 -0.1 // 0.1 0 80 s/ft 80 s/ft 140 -0.1 / 0.1 DSKT(S) TKT(S) WDSKT(S) WTKT(S) DOLO (0-100) 40 140 20 s/ft 80 s/ft -0.1 / 0.1 -0.1 / 0.1 TKT(C) DSKT(C) WDSKT(C) WTKT(C) LIME (0-100) 20 US/ft 80 40 US/ft 140 -0.1 / 0.1 -0.1 / 0.1 AC DS ZERO ZERO SH (0-100) 20 40 s/ft 140 -0.1 / 0.1 -0.1 / 0.1 s/ft 80 (b) Three sets of secondary storage space combination models (a) and the comparison between the predicted P- & S-wave Fig. 6 slowness (‘TKT’ and ‘DSKT’) by employing 3D KT model and the corresponding measured P- & S-wave slowness (‘AC’ and ‘DS’) (b). Symbol ‘N’ denotes needle-shaped pore; Symbol ‘S’ denotes sphere-shaped pore; Symbol ‘C’ denotes crack-shaped pore; other symbols are the same to those above Pet.Sci.(2011)8:394-405 401 Fig. 7 The inÀ uence of the difference of dominant storage space types in different intervals in a well on predicted results of wave velocities These results not only consider more factors but also 4 The V -V relationships relating with P S represent the special elastic characters of the study area well, secondary storage space shape thus providing more reasonable constraint information for the subsequent prestack inversion. 4.1 Analysis of S-wave velocity estimation using However, at present, an improper method is commonly common V -V relationships P S used to obtain the two constraint conditions, especially on- site in oil¿ elds. Due to lack of the measured S-wave data and In the following simultaneous inversion based on prestack the limitations of carrying on complex rock physics analysis P-wave data (discussed in the next paper of the special edition for velocity prediction, some known empirical relationships, (Zhang et al, 2011), the P- & S-wave velocities (V and V ) P S such as Castagna’s mud-rock line (Castagna et al, 1985) and of each well are not only taken as the constraint for well- Greenberg-Castagna’s V -V relationship (Greenberg and seismic-calibration and wavelet extraction but also the startup P S Castagna, 1992) (see Eqs. (3) and (4)), are directly treated as term to build the relationship between P-impedance (PI) the startup term to build the relationship between PI and SI, and S-impedance (SI). For accurate P- & S-wave velocity and are also employed to derive the S-wave velocity based on prediction, we resort to employ or establish a proper rock the measured P-wave velocity. physics model that can consider various factors including porosity, pore shape, À uid types, etc. After the standardization VV 0.862 1.172 (3) of the predicted velocities, the V -V relationship fitting for SP P S the study area can be built through mathematical regression. 402 Pet.Sci.(2011)8:394-405 (4) inversion. V 1.03 1.017 VV 0.055 S PP To illustrate the above problem more intuitively, based on where both P- & S-wave velocities are in km/s. actual logging data of a well (Well E), the results of S-wave Though Castagna’s mud-rock line and Greenberg- slowness (reverse of velocities) derived from the above two Castagna’s V -V relationship are well-known, they are conventional V -V relationships that have nothing to do P S P S built for only one or several areas, so they cannot represent with secondary storage space shape are compared with the the elastic properties of reservoirs in other areas due to the measured data. The P- & S-wave slowness predicted by the differences of burial depth, compaction, lithology, pore Kuster-Toksöz model (taking into consideration the effect of shapes, etc. Especially for the carbonate reservoirs with secondary storage space geometry) are also plotted in Fig. very complex storage spaces in the Tarim Basin, the V -V 8. The ¿ gure shows that the DSC (S-wave slowness derived P S relationship is seriously dependent on the secondary storage from Castagna’s mud-rock line) is consistently furthest space shape (corresponding to the explanation for Fig. 5). from the DS (the measured S-slowness) because Castagna’s For complex carbonate reservoirs, it would be absurd if mud-rock line was developed for clastic rocks; the DSGC those empirical relationships having nothing to do with pore (S-wave slowness derived from the Greenberg-Castagna V - geometry and the derived S-wave data from them were taken V relationships) is relatively closer to the DS because the as the two important constraint conditions for pre-stack Greenberg-Castagna V -V relationship was developed on P S A comparison of S-wave slowness derived from conventional V -V relationships and that measured. The P- & S-wave slowness Fig. 8 P S ‘TKT’ and ‘DTKT’ predicted by the KT model are also plotted together. Symbols ‘DSC’ and ‘DSGC’ denote the S-wave slowness derived from Castagna’s mud-rock line and the Greenberg-Castagna V -V relationship respectively; Symbols ‘WDSC’ and ‘WDSGC’ denote the P S relative errors of the estimated S-wave slowness compared with that measured; other symbols are the same to those above Pet.Sci.(2011)8:394-405 403 water-saturated limestones (the main lithology of carbonate rocks); the DSKT (S-wave slowness predicted by the KT model) is consistent best with to the DS because lithology and reservoir physical properties are not only considered in the KT model but also more importantly secondary storage space geometries are taken into account. It should be pointed out that we do not advocate using empirical relationships to derive S-wave information. However, it should not absolutely negate the practical value of empirical relationships because they indeed can provide a ready way to estimate S-wave information when high accuracy is not required in oilfield practice. We just Fig. 9 The built V -V relationships respectively for fractured, fractured- emphasize that empirical relationships should not directly P S cavernous, and fractured-hole-vuggy carbonate reservoirs in the Tarim Basin copy the results from other areas but should be built based on the data of the corresponding study area. Meanwhile, the inÀ uence of pore geometry should be also taken into account Table 2 The coef¿ cients of quadratic empirical relationships (Eq. (5)) for for reservoirs that have complex pore spaces. Thus, with different carbonate reservoir types in the Tarim Basin respect to complex carbonate reservoirs in the Tarim Basin, which way is reasonable to build the V -V relationship? Our P S Carbonate reservoir types Į ȕȖ answer is that respective V -V relationship must be built for P S Fractured reservoir í 0.1397 2.2638 5.4223 different secondary storage spaces. Fractured-cavernous reservoir í 0.1048 1.669 í 3.1092 4.2 The building of V -V relationships related with P S Fractured-hole-vuggy reservoir í 0.0375 0.7966 í 0.2907 secondary storage space shape The Ordovician carbonate reservoirs in the Tarim Basin 5 Conclusions are representative of complex carbonate reservoirs dominated by secondary storage spaces, and are also very important for The topics discussed in this paper include: 1) Illustration China’s future oil and gas supplies. Hence, it is important to of the conceptual differences between the three classical build proper V -V relationships for this basin. P S basic rock physics models (the Wyllie time-average equation, On the basis of accurate P- & S-wave velocity prediction Gassmann equation, and the Kuster-Toksöz model) and and secondary storage space modeling for more than 50 wells the comparison of their velocity prediction results. 2) The in the Tazhong area and the Lungu area (the major production influence of secondary storage space shape on velocity areas in the Tarim Basin), incorporating with some available prediction results; 3) The establishment of V -V relationships P S measured P- & S-wave velocities and referring to reservoir related to secondary storage space shape. type classi¿ cation data provided by the Tarim Oil¿ eld Co., we As for the above topics, a number of assumptions or built three sets of quadratic V -V relationships respectively P S approximations are performed. We assume the medium of for fractured, fractured-cavernous, and fractured-hole-vuggy carbonate rocks in this case study is isotropic, which is also carbonate reservoirs in the Tarim Basin (shown in Fig. 9). the postulation permitting us to employ these rock physics To simplify these relationships, we can write them in a models for our discussion. The À uids are assumed to be zero standard form, namely, shear modulus (i.e., to be in¿ nitely compressible) so that pore compressions do not induce changes in pore pressure. VV D EJ V (5) SP P With the above discussed results and limitations in mind, the following conclusions can be derived from the discussion where both V and V are in km/s; coefficients Į , ȕ and Ȗ P S regarding the inÀ uence of secondary storage space shape on determine the V -V relationship that corresponds to the type P S P- & S-wave velocities for complex carbonate reservoirs in of carbonate reservoir, and their values are listed in Table 2. this paper: 1) Wyllie time-average equation, Gassmann equation, and Kuster-Toksöz model are three basic classical rock physics The naming rule is that dominant pore type as the headword is placed models. Through the comparison for the model-constructing in the latter part and subsidiary pore type as the modi¿ er is placed in the principles and velocity prediction results, the Kuster-Toksöz former part. In our opinion, due to the strong brittleness of rocks in deep- model is proven to be the best one to discuss the influence buried carbonate reservoir, fractures always exist to a greater or lesser of secondary storage space shape on P- & S-wave velocities. extent in the reservoir, so each secondary storage space combining type And the dominant storage space type can be derived by the includes fracture. Furthermore, because fractured-holed reservoir with integration of the 2D KT model and the 3D KT model. fracture and pure-needle-shaped pores is few in this study and it is often 2) Secondary storage space shape signi¿ cantly inÀ uences classi¿ ed into fractured-hole-vuggy reservoir in oil¿ eld site, so there is the P- & S-wave velocities in carbonate reservoirs. Both no special V -V relationship built for fractured-holed reservoir here. P S P- & S-wave velocities increase with pore aspect ratio, but 404 Pet.Sci.(2011)8:394-405 Car lson R L. How crack porosity and shape control seismic velocities obviously the influence of pore geometry on the P-wave in the upper oceanic crust: Modeling downhole logs from Holes velocity is greater than that on the S-wave velocity. 504B and 1256D. Geochemistry Geophysics Geosystems. 2010. 11: Additionally, the increase in amplitude for lower pore aspect Q04007 ratios is greater than that for higher pore aspect ratios. That Cas tagna J P, Batzle M L and Eastwood R L. Relationships between is to say, oblate pores or cracks influence the P- & S-wave compressional-wave and shear-wave velocities in clastic silicate velocities in reservoirs more signi¿ cantly. rocks. Geophysics. 1985. 50: 571-581 3) Secondary storage space shape also influences the Che ng C H and Toksöz M N. Inversion of seismic velocities for the pore relationship between the P-wave velocity (V ) and S-wave aspect ratio spectrum of a rock. Journal of Geophysical Research. velocity (V ) in carbonate reservoirs. On the basis of velocity 1979. 84(B13): 7533-7543 prediction and secondary storage space type modeling, the Ebe rli G P, Baechle G T, Anselmetti F S, et al. Factors controlling elastic corresponding V -V relationships are built respectively P S properties in carbonate sediments and rocks. The Leading Edge. for fractured, fracture-cavernous, and fracture-hole-vuggy 2003. 22: 654-660 carbonate reservoirs, thus making common simple V -V P S Gas smann F. Über die Elastizität poröser Medien. Viertel. der Natur. relationship to relate with secondary storage space shape. This Gessellschaft in Zürich. 1951. 96: 1-23 work has important practical significance for simultaneous Gre enberg M L and Castagna J P. Shear-wave velocity estimation in inversion using PP data, to help improve complex carbonate porous rocks: Theoretical formulation, preliminary veri¿ cation and reservoir prediction results. applications. Geophysical Prospecting. 1992. 40: 195-209 But we have to point out that there are some limitations Han D H, Nur A and Morgan D. Effects of porosity and clay content on in the Kuster-Toksöz model. Firstly, this model is appropriate wave velocities in sandstones. Geophysics. 1986. 51: 2093-2107 to ultrasonic laboratory condition, so the velocities predicted Kum ar M and Han D H. Pore shape effect on elastic properties of by this model generally exhibit differences with seismic carbonate rocks. 75th SEG Annual Meeting, Expanded Abstracts. wave velocities in low-frequency bands (this is the velocity 2005. 1477-1481 dispersion issue that will be discussed in the future). Kus ter G T and Toksöz M N. Velocity and attenuation of seismic waves Secondly, this model is limited to dilute concentrations of in two-phase media. Geophysics. 1974. 39: 587-618 pores. That is to say, the porosity could not be too high. To Lü X, Jiao W, Zhou X, et al. Paleozoic carbonate hydrocarbon solve the problem, differential effective medium theory can accumulation zones in Tazhong Uplift, Tarim Basin, western China. be used to modify this model for better velocity prediction Energy, Exploration & Exploitation. 2009. 27(2): 69-90 results. But the two problems will not obviously inÀ uence the Nur A and Simmons G. The effect of viscosity of a fluid phase on results discussed in this paper because the secondary storage velocity in low-porosity rocks. Earth and Planetary Science Letters. space shape plays a dominant role in influencing the P- & 1969. 7: 99-108. S-wave velocities of the reservoir for carbonate reservoirs Pan g X, Zhou X and Lin C, et al. Classi¿ cation of complex reservoirs with complex storage space types in the Tarim Basin. in superimposed basins of western China. Acta Geological Sinica. Acknowledgments 2010. 84(5): 1011-1034 Sim mons G. Single crystal elastic constants and calculated aggregate The work is co-supported by the National Basic Research properties. Journal of the Graduate Research Center, Southern Program of China (Grant No. 2011CB201103) and the Methodist University Press. 1965. 34: 1-269 National Science and Technology Major Project (Grant No. Sta nding M B. Volumetric and Phase Behavior of Oil Field Hydrocarbon 2011ZX05004003). The authors would like to thank the Systems. New York: Reinhold Publishing Corporation. 1952. 122 Laboratory for Integration of Geology and Geophysics (LIGG) Sun S Z, Stretch S R and Brown R J. Comparison of borehole velocity- at China University of Petroleum for the permission to prediction models and estimation of fluid saturation effects: From publish this work and Tarim Oil¿ eld Co., PetroChina for their rock physics to exploration problem. Journal of Canadian Petroleum help in providing ¿ eld data. 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Petroleum Science – Springer Journals
Published: Dec 8, 2011
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