Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones

Marine and Petroleum Geology xxx (2015) 1e11

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Research paper

Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones Tongcheng Han*, Michael Ben Clennell, Marina Pervukhina CSIRO Energy Flagship, 26 Dick Perry Avenue, Kensington, Western Australia, 6151, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 December 2014 Received in revised form 23 June 2015 Accepted 31 August 2015 Available online xxx

Marine controlled source electromagnetic sounding has developed rapidly in recent years to complement conventional seismic method for better discrimination of pore fluid. To obtain quantitative and reliable interpretation of the CSEM data, a robust rock physics model is vital to link the bulk rock electrical conductivity to the electrical properties and microstructure of the rock constituents, especially when some of the constituents exhibit extreme electrical behaviours (e.g., pyrite, a common mineral associated with reservoir rocks). Based on the multi-phase incremental model validated on published experimentally measured electrical conductivity of pyrite-bearing sandstones, the effects of key parameters, i.e., pyrite content, porosity, pyrite conductivity, grain aspect ratio and water saturation on the electrical conductivity of pyrite-bearing sandstones and their corresponding CSEM responses were comprehensively studied. The results are expected to assist in the CSEM data interpretation when a pyrite-bearing sandstone reservoir is encountered in the future. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Low-frequency Electrical conductivity Pyrite Sandstone CSEM

1. Introduction Pyrite (FeS2) is the most common heavy mineral associated with sedimentary rocks and has been reported to be present in the sandstones of some important hydrocarbon producing formations throughout the world (Clavier et al., 1976). Among the physical properties of reservoir sandstones that are affected by the presence of pyrite, the electrical behaviours are the most noticeable due to the high conductivity of pyrite which exceeds the conductivity of even highly saline formation water (Klimentos, 1995; Kennedy, 2004). The presence of pyrite can therefore disturb the resistivity measurements that are used in petrophysical evaluation of oil and gas fields and this leads to overestimation of water saturation (and hence underestimation of hydrocarbon saturation). A good understanding of the electrical properties of pyrite-bearing sandstones is therefore of great importance for the interpretation of electrical resistivity logs (Kennedy, 2004). The suppression of rock resistivity by pyrite will also affect electrical survey data, including terrestrial and marine electromagnetic sounding, and pyrite effects must be corrected if those data are to be used for the estimation of hydrocarbon saturation.

* Corresponding author. E-mail address: [email protected] (T. Han).

So far, the study of the electrical properties of pyrite-rich sedimentary rocks has mainly focused on the frequency dependence (e.g., Clavier et al., 1976; Manning and Athavale, 1986; Clennell et al., 2010), that found the pyrite has a more significant effect in reducing electrical resistivity of the rocks at higher frequency (10 kHze100 kHz) than at lower frequency (10 Hze100 Hz). While the results are helpful in understanding the polarisation mechanism associated with pyrite or “IP effect” (e.g., Wong, 1979; Merriam, 2007), they fail to address directly the problem of how pyrite affects the low frequency electrical properties of reservoir sandstones that can be further employed to study the response of low frequency marine controlled source electromagnetic (CSEM) sounding, a rapidly developing exploration technique that complements the conventional seismic method for pore fluid discrimination between high conductivity formation water and low conductivity hydrocarbon (Constable and Srnka, 2007; Constable, 2010). While careful laboratory measurements can provide accurate and reliable knowledge about the pyrite effects, it is difficult to control some specific parameters while keeping the rest constant (e.g., samples having the same porosity but with varying pyrite content) especially when studying natural rocks. Effective medium models derived on the DC (direct current) limit, on the other hand, could offer a more effective way to study comprehensively the effects of various parameters on the low-frequency electrical

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Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037

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properties of pyrite-bearing sandstones that will potentially affect the signals of CSEM sounding, provided that the applicability of the models to pyritic sandstones is validated by well-controlled laboratory data. Cosenza et al. (2009) presented a comprehensive review of the effective medium models used for modelling the relationships between low-frequency electrical conductivity and hydrological variables in soils and rocks aiming to provide a simple presentation of these theoretical approaches and to present their theoretical and practical limitations. Among these theoretical models, the differential effective medium (DEM) models are the category that has had the most success in modelling electrical properties and other physical properties (e.g., elastic parameters, dielectric permittivity, thermal conductivity and coupling properties) of reservoir rocks (e.g., Berryman, 1995; Revil, 2000; Cosenza et al., 2003; Berg, 2007; Han et al., 2011). Based on earlier works carried out within petrophysics and resistivity-logging, Gelius and Wang (2008) extended the DEM models to study production (temperature, saturation, salinity and stress) caused changes in the electrical conductivity of siliciclastic reservoir. Although these models were not developed for pyrite-bearing rocks, the similarity between clay minerals and pyrite in terms of their spatial distribution (e.g., dispersed in the pore space or forming part of the matrix) and higher conductivity than other rock-forming minerals (i.e., quartz for sandstones) makes the models adaptable to pyrite-bearing sandstones, though their validity needs to be tested. We apply the 4-phase incremental model developed by Han et al. (2015) based on the Asami equation (Asami, 2002) to study comprehensively the effects on various parameters (pyrite content, porosity, pyrite conductivity, grain aspect ratio and water saturation) on the electrical conductivity of pyrite-bearing reservoir sandstones. The results are then used to forward model the CSEM responses associated with the conductivity caused by varying the pyrite content parameters. Before application of the incremental model, its validity to the conductivity of pyrite-bearing sandstones is tested on published experimental data. The aim of the study is to provide a sensitivity analysis of the effect of pyrite content and distribution on CSEM responses, which can potentially aid in the interpretation of CSEM survey data for better reservoir characterisation.

To account for this problem, Asami (2002) increased the initial low volume fraction gradually by infinitesimal addition of the grains so that Equation (1) derived for dilute suspensions is valid in each addition of the grains. Therefore the increment in effective conductivity of the new mixture ds due to an infinitesimal addition of the grains is related to the increment in volume fraction dF0 by submitting s þ ds, s and dF0 =ð1  F0 Þ for s, sa and F in Equation (1), respectively,

2. Multi-phase incremental model based on Asami equation for electrical properties of pyrite-bearing sandstones

The Asami model (Equation (4)) reduces to the well-known Hanai-Bruggeman (HB) equation for electrical conductivity (Bruggeman, 1935; Hanai, 1960a, b; Bussian, 1983) in the case of spherical grains (a ¼ 1 and Lz ¼ 1/3) and further simplifies to Archie's equation (Archie, 1942) when the conductivity of the grains (sg) is negligible. However the model was developed for a 2phase medium and cannot be applied to the multi-phase case. I.e., pyrite-rich hydrocarbon-bearing reservoir sandstones that contain four phases formation water (brine, of variable conductivity), hydrocarbon (oil or gas, insulating), quartz (plus all other nonconductive mineral grains) and pyrite (a strongly conductive mineral). Motivated by the incremental method employed by Asami (2002) and Berg (2007), Han et al. (2015) presented a multi-phase incremental model to extent the Asami equation to be able to model the conductivity of real reservoir rocks that contain more than 2 phases. As shown schematically in Fig. 1, the inclusions in the incremental model are introduced in an infinitesimal manner (C/n, where C is the initial concentration of each phase and n is the incremental number that is set to be 1000) into the background medium forming a new effective medium for the next step where the next phase is included. After all the 3 inclusion phases (i.e., hydrocarbon, pyrite and quartz) are added in the first increment where water is the staring background medium, the next

2.1. Asami equation Based on MaxwelleWagner theory (Maxwell, 1891; Wagner, 1914) Asami (2002) derived an equation for the electrical conductivity (s) of a 2-phase mixture where dilute ellipsoid inclusions (with conductivity of sg) are oriented randomly as a suspension within a background medium with conductivity of sa, given as

2

3 X s  s 1 g a   5; s ¼ sa 41 þ F 3 s þ sg  sa Lk k¼x;y;z a

(1)

where F is the volume fraction of the inclusions, and Lk is the depolarisation factor of the inclusions along the k-axis satisfying Lx þ Ly þ Lz ¼ 1. Equation (1) is derived for the case of a low volume fraction of inclusions or dilute suspension (F << 1), implying that there are no interactions between the inclusions. This is obviously not the case for reservoir rocks where the inclusions (i.e., quartz for sandstones) not only interact with the suspending medium (i.e., formation water) they also contact each other.

2 31 X dF0 3 1 4   5 ds:   ¼  1  F0 s s  sg s þ sg  s Lk k¼x;y;z

(2)

By successive infinitesimal additions of grains, the mixture reaches the final grain volume fraction F and conductivity s, an integral equation is obtained as

ZF 0

dF0  ¼ 1  F0

Zs sa

2 31 X 3 1    5 ds: 4 s s  sg s þ sg  s Lk k¼x;y;z

(3)

Solving this equation and approximating the quartz in sandstones to be spheroids (Lx ¼ Ly s Lz), the final form of the Asami equation is obtained:

 f¼

sa ð1 þ 3LÞ þ sg ð2  3LÞ sð1 þ 3LÞ þ sg ð2  3LÞ

C 

 s  sg sa 3T ; sa  sg s

(4)

where f ¼ 1 e F is the volume fraction of suspension (i.e., porosity for reservoir sandstones), L ¼ Lx ¼ Ly ¼ (1 e Lz)/2, and T ¼ Lð12LÞ 23L , 2

2ð13LÞ C ¼ ð23LÞð1þ3LÞ .

The z-axis depolarisation factor Lz for oblate spheroids with aspect ratio a < 1 is given by

Lz ¼

1 a 1  3=2 cos a: 1  a2 1  a2

(5)

2.2. Multi-phase incremental model

Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037

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Fig. 2. Comparison of model prediction to the conductivity of 2 pyrite-bearing sandstones as a function of water conductivity measured by Clavier et al. (1976) at the frequency of 19 Hz. Input parameters for the incremental model and the correlation coefficients between the modelled and measured results are also given in the figure.

Fig. 1. Schematic diagram showing the steps used in the first increment in the incremental model, where water is the starting medium. The effective medium formed in the last step of each increment becomes the starting background for the next increment. CHC, Cpy and Cqz are the initial concentration of hydrocarbon, pyrite and quartz, respectively and n is the incremental number. Adapted from Han et al. (2015).

increment starts until the incremental number n is reached. The Asami equation (Equation (4)) is employed in each step to obtain the electrical conductivity of the effective medium and the volume fraction of each component in the final medium can be calculated from the initial concentration C and incremental number n based on the equations given in the Appendix. The incremental method used in both the Asami equation and the incremental model makes them essentially differential medium models. However, previous multi-phase differential effective medium models depend on the inclusion mixing order (Gelius and Wang, 2008; Han et al., 2011), the infinitesimal addition of inclusions used by the incremental model makes it independent of the ordering effects (Berg, 2007), and this differs the current model from conventional DEM models. It is also because of the trajectory independency, the order of adding the different inclusions shown in Fig. 1 is only schematic and will not affect the final results. In addition to minimizing the ordering effects, the incremental method keeps the inclusions in the final mixture interconnected which resembles the contacting relationships between various rock-forming materials in real reservoir rocks (Berg, 2007).

and quartz grains (apy and aqz, respectively) and the pyrite conductivity (spy) of the 2 rock samples, we set them as fitting parameters, and it is found by using reasonable parameters given in Fig. 2, the incremental model gives satisfactory fit to the laboratory data, with squared correlation coefficient (R2) better than 0.99. The successful prediction of the conductivity of the fully saturated pyrite-bearing sandstones confirms the validity of the threephase (i.e., brine, quartz and pyrite, respectively) incremental model, and we then consider a multiple-salinity partially saturated artificial sand-pyrite pack with pyrite content (PC, volume fraction) of 16.5% (from Clavier et al., 1984) to test the full capacity of the four-phase incremental model. Again, By using aspect ratios of 0.2, 0.9, and 0.1 for quartz, pyrite and gas, respectively, and a pyrite conductivity of 6 S/m, the 4-phase incremental model gave a reasonable fit to the experimental data with a squared correlation coefficient R2 ¼ 0.9966, as shown in Fig. 3. The satisfactory fit of the model to various laboratory data not only confirms the validity of the incremental model in predicting

2.3. Model validity To test the applicability of the multi-phase incremental model to pyrite-bearing sandstones, we compare the modelled electrical conductivity to the laboratory measured conductivity of 2 fully saturated pyrite-bearing sandstones as a function of water conductivity from Clavier et al. (1976), as shown in Fig. 2. The sandstone samples, named Core No. 5 and Core No.6 have porosity of 0.122 and 0.225, respectively, and pyrite content (PC, volume fraction) of 3.7% and 5.1%, respectively. The conductivity was measured using a 4-electrode technique at the frequency of 19 Hz. Since there was no information about the geometry of the pyrite

Fig. 3. Comparison of model prediction to the conductivity of 3 sand-pyrite packs as a function of water saturation and conductivity measured by Clavier et al. (1976) at the frequency of 19 Hz. Input parameters for the incremental model and the correlation coefficients between the modelled and measured results are also given in the figure.

Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037

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We first investigate the effect of pyrite content (PC, volume fraction) on the electrical conductivity of reservoir sandstones showing porosity (f) varying from 0.05 to 0.3 to cover the typical porosity range of sandstones. The pyrite content is confined to be less than 10% to represent typical pyrite concentration in sandstones although higher content of pyrite can be possible in

reservoir rocks (e.g., Clavier et al., 1976). The samples are partially saturated with insulating hydrocarbon and conductive seawater (with conductivity of 4.69 S/m) at a water saturation of 50%, and the geometric information of pyrite and quartz and the conductivity of pyrite are taken from the modelling of the experimental data presented above, i.e., aspect ratio of 0.3 and 0.22 for pyrite and quartz, respectively and electrical conductivity of 15 S/m for pyrite. The modelling results are demonstrated in Fig. 5. The rock conductivity shows an approximate linear increase with pyrite conductivity on a semi-logarithmic scale, and the increase for samples with a lower porosity is more pronounced than sandstones with a higher porosity. The increasing rock conductivity with pyrite content is not surprising because pyrite is the most conductive in the rock-forming materials and the more profound impact of pyrite content on the conductivity of lower porosity samples can be explained as follows: a higher porosity sandstone sample contains more conductive formation water in the pore space and therefore shows higher conductivity at zero pyrite content, as pyrite content increases the rock conductivity also increases but the increase is suppressed by the high base conductivity at zero pyrite content. On the other hand, for samples with a lower porosity there is less pore space to keep conductive formation water resulting in lower conductivity, which in turn makes the conductivity more sensitive as the pyrite content is increased. Based on the conductivity of the pyrite-bearing sandstones calculated from the incremental model, the CSEM responses of the low porosity (f ¼ 0.05) and high porosity (f ¼ 0.3) reservoir with varying pyrite content are shown in Fig. 6a and b, respectively. The CSEM signals show the highest relative magnitude when the sandstone is pyrite-free (the grey curves corresponding to zero pyrite content), and the relative magnitude reduces as the pyrite content increases, indicating the increasing rock conductivity caused by the pyrite has the effects of reconciling the CSEM anomaly of a hydrocarbon-bearing reservoir. In addition, although the CSEM responses of the low porosity reservoir is much more sensitive to pyrite content than the case of high porosity reservoir, the relative magnitude of the low porosity signals remains as high as about 20 when the sandstone contains 10% pyrite, while the relative magnitude is less than about 2 for the high porosity reservoir at the same pyrite content (i.e., 10%), suggesting the hydrocarbon is detectable by CSEM for the low porosity reservoir that contains 10% pyrite but is not detectable for the high porosity reservoir.

Fig. 4. Earth structure model used for the CSEM modelling.

Fig. 5. Modelled variation of rock conductivity as a function of pyrite content for sandstone samples with a range of porosity.

the electrical conductivity of pyrite-bearing sandstones but also provides practical knowledge to constrain the input parameters (i.e., apy, aqz and spy) that are employed for the study of the electrical properties of pyrite-bearing reservoir sandstone presented in the following section. 3. Modelling the electrical conductivity of pyrite-bearing sandstones and their CSEM responses Having validated the applicability of the incremental model and obtained geometric and electrical information of the pyrite minerals, the effects of key parameters (i.e., pyrite content, porosity, pyrite conductivity, grain aspect ratio and water saturation) in affecting the electrical conductivity of hydrocarbon (a hydrocarbon saturation of 50% is assumed unless otherwise stated in the ‘Water saturation’ section) and pyrite bearing reservoir sandstones are presented in this section, the CSEM responses of the sandstone reservoir with the conductivity computed from the incremental model are also demonstrated. In the calculation of the CSEM responses, the program CSEM1D based on the theory of Chave and Cox (1982) was employed. The CSEM experiments used a horizontal electric dipole (HED) source placed 20 m above the seafloor to transmit 0.25 Hz frequency electromagnetic signals to an array of receivers sitting on the seafloor. The depth of the sea water of 1000 m with a conductivity of 4.69 S/m was chosen to minimize the effect of airwaves, and the sandstone reservoir with thickness of 200 m was set to be 800 m below the homogeneous overburden with conductivity of 1 S/m, as schematically shown in Fig. 4. The inline horizontal electrical filed component was simulated for an inline polarised HED source and the relative electrical field magnitude (i.e., the ratio between the electrical field magnitude with and without the reservoir) was presented. 3.1. Pyrite content

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Fig. 7. Modelled variation of rock conductivity as a function of porosity for sandstone samples with a range of pyrite content.

Fig. 6. Modelled CSEM responses as a function of pyrite content based on the conductivity of reservoir sandstones predicted by the incremental model, for the case of (a) low porosity and (b) high porosity, respectively.

3.2. Porosity Porosity is the first order parameter that affects the electrical properties of both clean and clay-rich reservoir sandstones (e.g., Archie, 1942; Glover et al., 2000; Rabaute et al., 2003; Leroy et al., 2008; Revil and Skold, 2011). The modelled effect of porosity on the electrical conductivity of pyrite-rich sandstones is shown in Fig. 7 for samples with a range of pyrite content. Hydrocarbon saturation, geometry of the quartz and pyrite grains and the electrical conductivity of pyrite are the same as in the previous section. The rock conductivity increases dramatically with porosity when the porosity is low and the increasing rate reduces as the porosity gets higher. A slightly bigger amount of the increase in conductivity is seen in the samples with lower pyrite content than those with higher pyrite contents. This indicates that although pyrite is more conductive than the formation water and any other constituent of the rock, porosity is still the most important parameter in controlling the electric properties of pyrite-rich sandstones for pyrite content considered in this study (i.e., up to 10% volume fraction). The modelled effects of rock porosity on the CSEM responses are shown in Fig. 8a and b for the case of low pyrite content (PC ¼ 1%) and high pyrite content (PC ¼ 10%) reservoirs, respectively. The CSEM responses are very sensitive to the variation of porosity for both cases. At low porosity the relative magnitude of the low pyrite

Fig. 8. Modelled CSEM responses as a function of porosity based on the conductivity of reservoir sandstones predicted by the incremental model, for the case of (a) low pyrite content and (b) high pyrite content, respectively.

content (1%) reservoir is more than 3 times of the reservoir with 10% pyrite content. The relative magnitude reduces as the porosity increases and for the case of the highest porosity considered the

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high porosity and is only noticeable when the porosity is low. 3.3. Pyrite conductivity

Fig. 9. Modelled variation of rock conductivity as a function of pyrite conductivity for sandstone samples with varying porosity and pyrite content.

relative magnitude becomes comparable between the 1% and 10% pyrite content. The variation of the CSEM responses with porosity and pyrite content as demonstrated in Figs. 6 and 8 suggests that while pyrite content has a significant effect in increasing the electrical conductivity of reservoir sandstones, porosity remains the primary parameter that controls the CSEM responses, and the pyrite effect can be suppressed by the conductive formation water at

The conductivity of the pyrite minerals employed for the simulation of the electrical properties of pyrite-bearing sandstones and their corresponding CSEM responses presented in the previous sections is based on the value obtained to describe the experimental data (i.e., 15 S/m, a conductivity between 6 S/m, 10.7 S/m and 17.5 S/m that are found to best predict the conductivity of the sand-pyrite pack and the core samples No. 5 and No. 6, respectively). However, the pyrite conductivity reported in the literature varies widely from less than 1 S/m to around 1000 S/m (e.g., Clavier et al., 1976; Abraitis et al., 2004; Clennell et al., 2010). The influence of such broad pyrite conductivity on the electrical properties of rocks is therefore of great importance. Fig. 9 shows the modelled variation of sandstone conductivity as a function of pyrite conductivity from 1 S/m to 1000 S/m for a low porosity (f ¼ 0.05) and a high porosity (f ¼ 0.3) sample containing 1% and 10% pyrite, respectively. The porosity and pyrite content are chosen to bracket the conductivity of the rocks with intermediate porosity and pyrite content. As expected the conductivity of sandstones with low pyrite content is less affected by the pyrite conductivity than that of the samples with higher pyrite content. In fact the increase of the rock conductivity with pyrite conductivity from 1 S/m to 1000 S/m for samples with 1% pyrite content (thin curves in Fig. 9) can be negligible especially for sandstones with high porosity (red (in the web version) thin curve in Fig. 9). The conductivity of rocks with high pyrite content (thick curves in Fig. 9)

Fig. 10. Modelled CSEM responses as a function of pyrite conductivity based on the conductivity of reservoir sandstones predicted by the incremental model, for the case of (a) low porosity and low pyrite content, (b) low porosity and high pyrite content, (c) high porosity and low pyrite content and (d) high porosity and high pyrite content, respectively.

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increases gently with increasing pyrite conductivity when the pyrite conductivity is low and the increasing rate decreases as the pyrite conductivity further increases. It is also explicitly demonstrated in Fig. 9 that pyrite content shows a more significant effect in raising the conductivity of rocks with a lower porosity at any pyrite conductivity studied. Fig. 10 shows the modelled CSEM responses of the sandstone reservoir as a function of pyrite conductivity for samples with varying porosity and pyrite content. For samples with low pyrite content (Fig. 10a and c), the CSEM responses are not sensitive to the pyrite conductivity although the relative magnitude of the low porosity reservoir is much higher than that of the high porosity reservoir which is caused by the lower conductivity associated with the low porosity sandstones. The insensitivity of the CSEM signals to the pyrite conductivity for low pyrite content reservoirs indicates that for such cases the CSEM responses can be interpreted as pyritefree reservoirs no matter how conductive the pyrite is. This, however is not the case for sandstones that contain a significant amount of pyrite content (i.e., 10%) as shown in Fig. 10b and d, where the relative magnitude reduces dramatically from zero pyrite conductivity (corresponding to pyrite-free reservoirs) to 15 S/m pyrite conductivity and then becomes less sensitive to the further increase of pyrite conductivity, indicating that the high pyrite content can be easily identified from the CSEM signals but it would be difficult to distinguish between the pyrite conductivity. 3.4. Grain aspect ratio Grain geometry determines the microstructure of how the

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various rock constituents are arranged to each other that affects the rock conductivity significantly, and without such information the effective medium models give only the upper and lower bounds of the effective electrical properties (Hashin and Shtrikman, 1962; Berryman, 1995; Mavko et al., 2009). The grain geometry employed for the simulation of the electrical conductivity of reservoir rocks include cementation coefficient and grain aspect (e.g., Sen et al., 1981; Berryman, 1995; de Lima et al., 2005; Ellis et al., 2010; Berryman and Hoversten, 2013; Revil, 2013; Sævik et al., 2014). While cementation coefficient gives implicit information about the microstructure of the rock (Glover, 2009), grain aspect ratio provides explicit physical meaning of the grain shape and the alignments of the grains in the rock. The incremental model assumes that all the inclusions, each with a specific aspect ratio, are arranged randomly in the water background to give homogeneous and isotropic electrical conductivity. The previous analyses employ grain aspect ratio of 0.3 and 0.22 for pyrite and quartz, respectively that is determined for the incremental model be best simulate the experimental data. The aspect ratio of pyrite and quartz however may vary in different reservoirs, and it is therefore necessary to study the effects of varying grain aspect ratio on the electrical behaviours of sandstones, which are shown in Fig. 11 with aspect ratio of pyrite and quartz changing from 0.1 to 1. The rock conductivity increases generally with increasing quartz aspect ratio and decreasing pyrite aspect ratio, which can be explained in terms of the contact of the grains and their conductivity: since all the grains in the incremental model are inter-connected, the connected insulating quartz may block the connectivity of the conductive formation water (the

Fig. 11. Modelled variation of rock conductivity as a function of pyrite and quartz aspect ratio for sandstone samples with (a) low porosity and low pyrite content, (b) low porosity and high pyrite content, (c) high porosity and low pyrite content and (d) high porosity and high pyrite content, respectively.

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Fig. 12. Modelled CSEM responses as a function of pyrite aspect ratio based on the conductivity of reservoir sandstones predicted by the incremental model, for the case of (a) low porosity and low quartz aspect ratio, (b) low porosity and high quartz aspect ratio, (c) high porosity and low quartz aspect ratio and (d) high porosity and high quartz aspect ratio, respectively.

blocking effect), and this blocking effect will reduce as the quartz aspect ratio increases, leading to an increasing rock conductivity with increasing quartz aspect ratio; on the other hand for conductive pyrite (with conductivity of 15 S/m), in addition to blocking the connectivity of the pore water, the bridging pyrite provides an addition path for conduction between the pores (the conductive effect), which will result in decreasing rock conductivity as the pyrite aspect ratio increases. The increasing rock conductivity with reducing pyrite aspect ratio indicates that the pyrite conductive effect overwhelms its blocking effect. The conductivity of rocks with higher pyrite content (Fig. 11b and d) increases more than those with lower pyrite content (Fig. 11a and c) with decreasing pyrite aspect ratio and the same is true for samples with lower porosity (Fig. 11a and b) than those with higher porosity (Fig. 11c and d), implying that the pyrite conductive effect is stronger in low porosity sandstones with high pyrite content. Noticing the stronger effects of pyrite aspect ratio on the conductivity of sandstones with higher pyrite content, the samples with 10% pyrite content are selected to study the CSEM responses as shown in Fig. 12. The reservoir with low porosity and low quartz aspect ratio (Fig. 12a) shows the most significant relative magnitude, however the CSEM responses are not sensitive to the variation of pyrite aspect ratio especially when the pyrite aspect ratio is greater than 0.3, which results in so low conductivity of the sandstones that leads to extremely high relative magnitude of the CSEM signals. For reservoirs with the same porosity (f ¼ 0.05) but high quartz aspect ratio (aqz ¼ 1), the relative magnitude becomes dramatically lower, and reduces with decreasing pyrite aspect ratio,

as shown in Fig. 12b. A similar effect of pyrite aspect ratio on the CSEM behaviours is seen between reservoirs with low porosity and high quartz aspect ratio (Fig. 12b) and those with high porosity and low quartz aspect ratio (Fig. 12c), indicating although decreasing quartz aspect ratio can reduce the reservoir conductivity which in turn leads to a significant increase in the CSEM relative magnitude, the decreasing reservoir conductivity and the elevated relative magnitude caused by the decreasing quartz aspect ratio can be reconciled by an increase in the rock porosity, the first order parameter in determining the electrical properties of reservoir sandstones. The conductivity of reservoirs with high porosity and high quartz aspect ratio gets so high that leads to weak but noisy CSEM relative magnitude as shown in Fig. 12d, implying that hydrocarbon can be ‘completely’ undetectable by CSEM due to the raising reservoir conductivity as a combined result of high porosity, high pyrite content and high grain aspect ratio. 3.5. Water saturation Discriminating between pore fluids with contrasting electrical conductivity and quantifying the fluid saturation is the main advantage of CSEM over conventional seismic method. As demonstrated above pyrite has the effects of raising the rock conductivity, whereas the decreasing water saturation (increasing hydrocarbon saturation) shows opposite effects of reducing the rock conductivity (e.g., Clavier et al., 1984; Knight and Nur, 1987; Seleznev et al., 2004), the electrical properties of pyrite-bearing sandstones with varying water saturation need further investigation.

Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037

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Fig. 13. Modelled variation of rock conductivity as a function of water saturation for sandstone samples with varying porosity and pyrite content.

Fig. 13 shows the incremental model prediction of the rock conductivity as a function of water saturation from 0.2 to 1 for sandstones with varying porosity and pyrite content, using pyrite and quartz parameters obtained to fit the experimental data. The modelled rock conductivity increases with water saturation and the amount of the increase reduces with increasing pyrite content. This can be explained in terms of the conductivity of pyrite: in pyrite-

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free sandstones, the conductivity of rocks comes only from the conductive formation water, and a small increase in the water saturation will lead to a significant increase in the rock conductivity; on the other limit for sandstones making of pure pyrite grains, the higher conductivity of pyrite than formation water will dominate the rock conductivity, and the increase in the saturation of the less conductive water will have a less noticeable effect in increasing the rock conductivity. It is also interesting to note the approximately parallel rock conductivity with varying water saturation between samples with the same pyrite content but different porosity (i.e., the thin curves representing pyrite content of 1% and the think curves sanding for 10% pyrite content, respectively), which suggests a similar effect of pyrite content on the electrical conductivity of rocks with varying porosity and water saturation. The modelled CSEM responses of the pyrite-bearing sandstone reservoir as a function of water saturation are shown in Fig. 14 based on the conductivity of sandstones calculated using the incremental model. The CSEM relative magnitude decreases generally with increasing water saturation due to the increasing rock conductivity caused by water saturation. The relative magnitude is very sensitive to the variation of water saturation for reservoirs with low porosity (Fig. 14a and b) and pyrite content from 1% to 10%. The increase in reservoir porosity significant reduces the relative magnitude as shown in Fig. 14b and d, respectively, again suggesting the dominance of porosity on the electrical properties of sandstones. The CSEM relative magnitude of reservoir with high porosity and high pyrite content (Fig. 14d) is low and is not sensitive to the variation in water saturation especially when water saturation is above 0.4, this is due to the high conductivity of the rock

Fig. 14. Modelled CSEM responses as a function of water saturation based on the conductivity of reservoir sandstones predicted by the incremental model, for the case of (a) low porosity and low pyrite content, (b) low porosity and high pyrite content, (c) high porosity and low pyrite content and (d) high porosity and high pyrite content, respectively.

Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037

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T. Han et al. / Marine and Petroleum Geology xxx (2015) 1e11

resulting from high pyrite content and high porosity saturating with greater amount of conductive formation water. 4. Concluding remarks The rapidly developing marine controlled source electromagnetic sounding that complements conventional surface seismic surveys for better discrimination of pore fluid requires a robust rock physics model to link the bulk rock electrical conductivity to the electrical properties and microstructure of the rock constituents to get reliable interpretation. The common existence of highly conductive pyrite in reservoir rocks will dramatically affect the electrical properties and the CSEM responses, and therefore needs comprehensive study. We have confirmed the validity of the multiphase incremental model in describing the electrical conductivity of pyrite-bearing sandstones, and the effects of key parameters, i.e., pyrite content, porosity, pyrite conductivity, grain aspect ratio and water saturation on the electrical conductivity of hydrocarbon and pyrite bearing sandstones and their corresponding CSEM responses were theoretically studied for the first time. It was found that porosity is the dominant parameter in affecting the electrical properties of sandstones with pyrite content up to 10%, on top of which pyrite content and conductivity, grain aspect ratio and water saturation can all significantly influence the CSEM behaviours and therefore should be taken into account in CSEM data analyses. The results are expected to assist in the CSEM data interpretation when a pyrite-bearing sandstone reservoir is encountered in the future. Acknowledgement The authors would like to thank Matthew Josh, Lionel Esteban and David Annetts for helpful discussion of the results and CSIRO Energy Flagship for financial support of this work. Appendix A. Calculation of volume fraction of each phase in the incremental model In the first increment (indicated by the column number), the volume fraction of each component after the hydrocarbon phase is included (step 1, denoted by the row number) is given by

Vw ð1; 1Þ ¼ 1  CHC =n; VHC ð1; 1Þ ¼ CHC =n; Vpy ð1; 1Þ ¼ 0; Vqz ð1; 1Þ ¼ 0;

(A.1)

where Vw is the volume fraction of water and VHC, Vpy and Vqz are the volume fraction of phase hydrocarbon, pyrite and quartz, respectively. The volume fraction of the constituents when phase pyrite is added (step 2) is calculated as

   Vw ð1; 2Þ ¼ Vw ð1; 1Þ$ 1 Cpy n ;  VHC ð1; 2Þ ¼ VHCð1; 1Þ$ 1  Cpy n ; Vpy ð1; 2Þ ¼ Cpy n; Vqz ð1; 2Þ ¼ 0;

(A.2)

and after the final step (step 3) when quartz is finally included in the first iteration, the volume fraction of each element can be found by

   Vw ð1; 3Þ ¼ Vw ð1; 2Þ$ 1 Cqz n ;  VHC ð1; 3Þ ¼ VHC ð1; 2Þ$ 1  Cqz n ; Vpy ð1; 3Þ ¼ Vpyð1; 2Þ$ 1  Cqz n ; Vqz ð1; 3Þ ¼ Cqz n:

(A.3)

The effective medium formed in the last step of each increment

performs as the starting background for the next increment, therefore the volume fraction of each component in the i-th increment (2  i  n), after phase hydrocarbon, pyrite and quartz are added is given respectively by

Vw ði; 1Þ ¼ Vw ði  1; 3Þ$ð1  CHC =nÞ; VHC ði; 1Þ ¼ VHC ði  1; 3Þ$ð1  CHC =nÞ þ CHC =n; Vpy ði; 1Þ ¼ Vpy ði  1; 3Þ$ð1  CHC =nÞ; Vqz ði; 1Þ ¼ Vqz ði  1; 3Þ$ð1  CHC =nÞ;

(A.4)

   Vw ði; 2Þ ¼ Vw ði; 1Þ$ 1 Cpy n ;  VHC ði; 2Þ ¼ VHC ði; 1Þ$ 1  Cpy n ;  Vpy ði; 2Þ ¼ Vpy ði; 1Þ$ 1  Cpy n þ Cpy n; Vqz ði; 2Þ ¼ Vqz ði; 1Þ$ 1  Cpy n ;

(A.5)

and

   Vw ði; 3Þ ¼ Vw ði; 2Þ$ 1  Cqz n ; VHC ði; 3Þ ¼ VHC ði; 2Þ$ 1  Cqz n ; Vpy ði; 3Þ ¼ Vpy ði; 2Þ$ 1 Cqz  n ; Vqz ði; 3Þ ¼ Vqz ði; 2Þ$ 1  Cqz n þ Cqz n:

(A.6)

The sum of the volume fraction of each component in each step of any increment satisfies Vw ði; jÞ þ VHC ði; jÞ þ Vpy ði; jÞ þ Vqz ði; jÞ ¼ 1, where i ¼ 1 : n, and j ¼ 1 : 3. References Abraitis, P.K., Pattrick, R.A.D., Vaughan, D.J., 2004. Variations in the compositional, textural and electrical properties of natural pyrite: a review. Int. J. Miner. Process. 74, 41e59. Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Am. Inst. Min. Metall. Eng. 146, 54e62. Asami, K., 2002. Characterization of heterogeneous systems by dielectric spectroscopy. Prog. Polym. Sci. 27, 1617e1659. Berg, C., 2007. An effective medium algorithm for calculating water saturations at any salinity or frequency. Geophysics 72, E59eE67. Berryman, J.G., 1995. Mixture theories for rock properties. In: Ahrens, T.J. (Ed.), Rock Physics and Phase Relations. American Geophysical Union, pp. 205e208. Berryman, J.G., Hoversten, G.M., 2013. Modelling electrical conductivity for earth media with macroscopic fluid-filled fractures. Geophys. Prospect. 61, 471e493. Bruggeman, D.A.G., 1935. Berechnung verschiedener physikalischer konstanten von heterogenen Substantzen. Ann. Phys. 24, 636e664. Bussian, A.E., 1983. Electrical conductance in a porous medium. Geophysics 48, 1258e1268. Chave, A.D., Cox, C.S., 1982. Controlled electromagnetic sources for measuring electrical conductivity beneath the oceans, part 1: forward problem and model study. J. Geophys. Res. 87, 5327e5338. Clavier, C., Coates, G., Dumanoir, J., 1984. Theoretical and experimental bases for the dual-water model for interpretation of shaly sands. Soc. Petrol. Eng. J. 24, 153e168. Clavier, C., Heim, A., Scala, C., 1976. Effect of pyrite on resistivity and other logging measurements. In: 17th SPWLA Annual Logging Symposium, Paper HH. Clennell, M.B., Josh, M., Esteban, L., Hill, D., Woods, C., McMullan, B., Delle Piane, C., Schmid, S., Verrall, M., 2010. The influence of pyrite on rock electric properties: a case study from NW Australian gas reservoirs. In: 51st SPWLA Annual Logging Symposium, Paper UUU. Constable, S., 2010. Ten years of marine CSEM for hydrocarbon exploration. Geophysics 75, A67e75A81. Constable, S., Srnka, L.J., 2007. An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration. Geophysics 72, WA3eWA12. Cosenza, P., Camerlynck, C., Tabbagh, A., 2003. Differential effective medium schemes for investigating the relationship between high-frequency relative dielectric permittivity and water content of soils. Water Resour. Res. 39, 1230e1242. rin, R., Tabbagh, A., 2009. Cosenza, P., Ghorbani, A., Camerlynck, C., Rejiba, F., Gue Effective medium theories for modelling the relationships between electromagnetic properties and hydrological variables in geomaterials: a review. Near Surf. Geophys. 7, 563e578. de Lima, O.A.L., Clennell, M.B., Nery, G.G., Niwas, S., 2005. A volumetric approach for the resistivity response of freshwater shaly sandstones. Geophysics 70, F1eF10. Ellis, M.H., Sinha, M.C., Minshull, T.A., Sothcott, J., Best, A.I., 2010. An anisotropic model for the electrical resistivity of two-phase geologic materials. Geophysics 75, E161eE170. Gelius, L.J., Wang, Z., 2008. Modelling production caused changes in conductivity for a siliciclastic reservoir: a differential effective medium approach. Geophys. Prospect. 56, 677e691. Glover, P.W.J., 2009. What is the cementation exponent? A new interpretation. Lead.

Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037

T. Han et al. / Marine and Petroleum Geology xxx (2015) 1e11 Edge 28, 82e85. Glover, P.W.J., Gomez, J.B., Meredith, P.G., 2000. Fractures in saturated rocks undergoing triaxial deformation using complex electrical measurements. Earth Planet. Sci. Lett. 183, 201e213. Han, T., Best, A.I., MacGregor, L.M., Sothcott, J., Minshull, T.A., 2011. Joint elasticelectrical effective medium models of reservoir sandstones. Geophys. Prospect. 59, 777e786. Han, T., Clennell, M.B., Josh, M., Pervukhina, M., 2015. Determination of effective grain geometry for electrical modeling of sedimentary rocks. Geophysics 80, D319eD327. Hanai, T., 1960a. Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions. Kolloid Zeitschrift 171, 23e31. Hanai, T., 1960b. A remark on “Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions”. Kolloid Zeitschrift 175, 61e62. Hashin, Z., Shtrikman, S., 1962. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33, 3125e3131. Kennedy, M., 2004. Gold fool's: detecting, quantifying and accounting for the effects of pyrite in modern logs. In: 45th SPWLA Annual Logging Symposium, Paper WWW. Klimentos, T., 1995. Pyrite volume estimation by well log analysis and petrophysical studies. Log Anal. 36, 11e17. Knight, R.J., Nur, A., 1987. Geometrical effects in the dielectric response of partially saturated sandstones. Log Anal. 28, 513e519. Leroy, P., Revil, A., Kemna, A., Cosenza, P., Gorbani, A., 2008. Complex conductivity of water-saturated packs of glass beads. J. Colloid Interface Sci. 321, 103e117. Manning, M.J., Athavale, K.A., 1986. Dielectric properties of pyrite samples at 1100 Mhz. Geophysics 51, 172e182.

11

Mavko, G., Mukerji, T., Dvorkin, J., 2009. The Rock Physics Handbook, second ed. Cambridge University Press, Cambridge. Maxwell, J.C., 1891. Treatise on Electricity and Magnetism. Clarendon Press, Oxford. Merriam, J.B., 2007. Induced polarization and surface electrochemistry. Geophysics 72, 157e166. Rabaute, A., Revil, A., Brosse, E., 2003. In situ mineralogy and permeability logs from downhole measurements: application to a case study in chlorite-coated sandstones. J. Geophys. Res. 108, 2414. Revil, A., 2000. Thermal conductivity of unconsolidated sediments with geophysical application. J. Geophys. Res. 105, 16749e16768. Revil, A., 2013. On charge accumulation in heterogeneous porous rocks under the influence of an external electric field. Geophysics 78, D271eD291. Revil, A., Skold, M., 2011. Salinity dependence of spectral induced polarization in sands and sandstones. Geophys. J. Int. 187, 813e824. Sævik, P.N., Jakobsen, M., Lien, M., Berre, I., 2014. Anisotropic effective conductivity in fractured rocks by explicit effective medium methods. Geophys. Prospect. 62, 1297e1314. Seleznev, N., Boyd, A., Habashy, T., 2004. Dielectric mixing laws for fully and partially saturated carbonate rocks. In: 45th SPWLA Annual Logging Symposium, Paper CCC. Sen, P.N., Scala, C., Cohen, M.H., 1981. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics 46, 781e795. €nge auf Grund Wagner, K.W., 1914. Erkl€ arung der dielektrishen Nachwirkungsvorga Maxerllsher Vorstellungen. Arch. Electrotech. Berl. 2, 371e387. Wong, J., 1979. An electrochemical model of the induced polarization phenomenon in disseminated sulfide ores. Geophysics 44, 1245e1265.

Please cite this article in press as: Han, T., et al., Modelling the low-frequency electrical properties of pyrite-bearing reservoir sandstones, Marine and Petroleum Geology (2015), http://dx.doi.org/10.1016/j.marpetgeo.2015.08.037